characterization of optical fibers in the mid-infrared
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DIPLOMARBEIT
Characterization of Optical Fibers
in the Mid-Infrared
ausgefuhrt am Institut furNachrichtentechnik und Hochfrequenztechnik der
Technischen Universitat Wienvon
Martin Dirnwober
Satzenweg 22211 Pillichsdorf
Matrikelnummer 9325512
Wien, im Mai 2005
Betreuer:
Dr. Martin PfennigbauerProf. Dr. Walter R. Leeb
Zusammenfassung
Diese Diplomarbeit befasst sich mit Fasern, die zur Ubertragung von elektromagnetischenWellen mit Wellenlangen im Bereich von 2 − 20 µm konzipiert sind. Der Einsatz von Fasernan Stelle von Freistrahloptik in optischen Instrumenten ist, neben geringerem Gewicht undPlatzbedarf, vor allem aufgrund der Moglichkeit der flexiblen Strahlfuhrung von Vorteil.
Teile dieser Arbeit sind in das Projekt Phase Cap “Phasing Cababilities for Fiber-OpticDevices” eingeflossen, das vom Institut fur Nachrichtentechnik und Hochfrequenztechnik derTechnischen Universitat Wien fur die Europaische Weltraumorganisation ESA durchgefuhrtwird. Das Ziel dieses Projektes ist es, Einsatzmoglichkeiten von Fasern in Weltrauminstru-menten zu untersuchen.
Wellenfuhrung innerhalb des erwahnten Wellenlangenbereiches lasst sich durch verschiedeneWellenleiterstrukturen (Fasern mit solider Kern-Mantel Struktur, hohle Wellenleiter sowiemikrostrukturierte Fasern) und mit verschiedenen Materialien (Fluorid, Chalcogenid, Ger-manat, Saphir, Silberhalid) realisieren. Der erste Teil der Arbeit beinhaltet eine Beschreibungder verschiedenen Faserstrukturen, Materialien und Wellenleitungsmechanismen.
Im zweiten Teil werden Parameter beschrieben, die eine Charakterisierung jener Fasereigen-schaften ermoglichen, die fur den Einsatz in Weltrauminstrumenten bedeutend sind. DieFasern werden hierbei hinsichtlich ihrer mechanischen, thermischen und optischen Eigen-schaften beschrieben.
Es wurde eine Suche nach den fur den Wellenlangenbereich 2− 20 µm erhaltlichen Faserndurchgefuhrt. Der dritte Teil meiner Diplomarbeit enthalt Informationen uber den Preis derFasern, die Hersteller, sowie einen Uerblick uber die von den Herstellern angegebenen Param-eter.
Im vierten Teil werden Messmethoden fur die wichtigsten der zuvor behandelten Parame-ter beschrieben, da viele hinsichtlich der gewnschten Einsatzbereiche wichtige Parameter vonden Herstellern nicht oder nur teilweise angegeben werden, und weiters fur Fasern fur dieseWellenlangenbereiche keine standardisierten Messmethoden existieren. Besonderes Augen-merk wurde dabei auf die Durchfuhrbarkeit dieser Messungen mit der im optischen Labor desInstitutes fur Nachrichtentechnik und Hochfrequenztechnik vorhandenen Ausstattung gelegt.
Summary
The topic of this thesis is fibers transmitting light of wavelenghts within 2 − 20 µm. Usingfibers instead of bulk optics in optical instruments enables flexible beam guiding as well asmechanical advantages of reduced weight and space consumption arise.
Parts of this work have been used for the project PhaseCap “Assessment of Phasing Ca-pabilities for Fiber-Optic Devices”, performed by the Insitute of Communications and Radio-Frequency Engineering of Vienna University of Technology for the European Space AgencyESA. The aim of this project is to investigate possible fields of application for fibers in spaceinstruments.
Waveguiding within the wavelength range of 2− 20 µm can be realized with various struc-tures (fibers with solid core-cladding structure, hollow waveguides, and microstructured fibers)and materials (Fluoride, Chalcogenide, Germanate, Sapphire, Silver Halide). The first part ofthis thesis contains a description of fiber structures, materials, and waveguiding mechanisms.
Parameters allowing to characterize fibers, especially concerning employment in spaceborne applications, are specified in part two. The fibers are characterized by their mechanical,thermal, and waveguiding properties.
In part three of this thesis the results of a comprehensive market survey are presented.Information of all infrared fibers (that can transmit light above 2 µm) presently offered, aswell as information about the vendors, and a comparison of parameters of these fibers is given.
Part four comprises descriptions of measurement methods for parameters important fordeployment of fibers in space instruments. A lot of parameters are not given by the vendorsand there are a no standardized measurement methods for fibers transmitting light above2 µm. Technical feasibility of this methods with labaratory equipment, presently available inthe optical labaratory of the Institute of Communications and Radio-Frequency Engineering,was especially taken into account.
Danksagung
Ich mochte mich bei allen bedanken, die zum Gelingen dieser Diplomarbeit beigetragen haben.
Ich bedanke mich bei meinen Eltern, Rosa und Martin Dirnwober, die mir das Studium derElektrotechnik ermoglicht haben, fur ihre Unterstutzung.
Herzlichen Dank an Herrn Prof. Dr. Walter Leeb, Vorstand des Institutes fur Nachrichten-und Hochfrequenztechnik, fur die zahlreichen Anregungen und Hilfestellungen in Bezug aufdiese Diplomarbeit.
Mein ganz besonderer Dank gilt Herrn Dr. Martin Pfennigbauer, fur die ausgezeichnete Betreu-ung, die vielen Ratschlage und aufschlussreichen Diskussionen, sowie seine kollegiale Unter-stutzung bei der Durchfuhrung meiner Diplomarbeit.
Ich danke Herrn Dr. Oswald Wallner und Herrn DI Franz Fidler fur ihre Hilfe, sowie meinenStudienkollegen fur aufschlussreiche Diskussionen und ihre Hilfe bei technischen Problemen.
Martin Dirnwober
Contents
1 Introduction 11.1 Infrared fibers − advantages and applications . . . . . . . . . . . . . . . . . . . 11.2 Fiber types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Solid-Core Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Crystalline Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.3 Hollow Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.4 Photonic Crystal Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Identification of fiber parameters 62.1 Physical parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.2 Mechanical parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.3 Thermal parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Waveguiding parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 Transmission parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Wavelength parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.3 Fiber coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.4 Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Market survey 123.1 Fibers offered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 Fiber vendors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.3 Comparison of fibers offered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3.1 Chalcogenide Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3.2 Flouride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.3.3 Polycrystalline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.4 Other IR fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3.5 Standard single mode telecommunication fibers and photonic crystal
fibers for 1.5 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4 Measurement methods 274.1 Attenuation vs. wavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1.1 Cut-back technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.1.2 Taper-based technique . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Attenuation vs. bending radius . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.3 Minimum bending radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
i
4.4 Cut-off wavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.4.1 Transmitted power technique . . . . . . . . . . . . . . . . . . . . . . . . 32
4.5 Mode field diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.5.1 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.5.2 Far-field scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.5.3 Near-field scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.5.4 Variable aperture technique . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.6 Effective numerical aperture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.7 Output divergence angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.8 Coupling efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.9 Chromatic dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.9.1 Non-Fourier-transform methods . . . . . . . . . . . . . . . . . . . . . . . 404.9.2 Fourier-transform methods . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.10 Temperature coefficient of optical length . . . . . . . . . . . . . . . . . . . . . . 474.11 Coeffiecient of elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5 Outlook 52
A Data sheets 53A.1 IR Photonics: MID-infrared single mode fiber . . . . . . . . . . . . . . . . . . . 53A.2 IR Photonics: MID-infrared multi mode fiber . . . . . . . . . . . . . . . . . . . 54A.3 ARTPhotonics: CIR fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55A.4 ARTPhotonics: PIR fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56A.5 CeramOptec: Optran MIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58A.6 Beijing S-Fiber Technology: Infrared Fiber . . . . . . . . . . . . . . . . . . . . 60A.7 Amorphous Materials: C1, C2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62A.8 Polymicro: HWCA, HWEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64A.9 Hitachi: hollow fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66A.10 CoreActive: IRT-SU, IRT-SE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67A.11 Photran LLC: Sapphire optical fiber . . . . . . . . . . . . . . . . . . . . . . . . 69A.12 Infrared Fiber Sensors: Spectral grade Silverhalide fibers . . . . . . . . . . . . . 70A.13 Infrared Fiber Systems: HP fiber . . . . . . . . . . . . . . . . . . . . . . . . . . 71A.14 Infrared Fiber Systems: SG fiber . . . . . . . . . . . . . . . . . . . . . . . . . . 73A.15 FiberLabs Inc.: SMFF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75A.16 FiberLas Inc.: MMFF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Bibliography 77
ii
Chapter 1
Introduction
The research done in this thesis is part of the project PhaseCap “Assessment of Phasing Ca-pabilities for Fiber-Optic Devices” for the European Space Agency on using fibers designedto guide light within the wavelength range of 2 − 20 µm in space borne applications. In thischapter, I will point out which advantages could arise by using fibers, especially in space-applications, as well as other fields of applications for infrared fibers. There are fibers ofdifferent structures and materials to cover this large wavelength-range. I will provide a classi-fication and description of these different fiber types.
1.1 Infrared fibers − advantages and applications
For components taken to space it is important to have low weight and space consumption.Concerning these facts, fiber-optic components are potentially superior to bulk optics forspecial applications. Besides from mechanical properties, advantages also arise due to thefiber’s waveguiding mechanism that allows for flexible beam guidance. Furthermore, fiberscould also be deployed advantageously as modal wavefront filters, optical path delay lengthcontrol, or for multiaxial beam combining [1].
There are various fields of application for infrared fibers, each one requiring special fiberproperties:
• In nulling interferometry, an extrasolar planet orbiting a star (with a light intensityhigher than that of the planet by several orders of magnitude) can be detected by in-terferometrically combining light received from spatially separated antennas. A certaindifference in optical path length between the two interferometer-arms (depending on thewavelength of the incoming light) is used for “nulling” the light emitted by the star bymeans of destructive interference.
• High precision, flexible and low mass imaging instruments based on phasing can be real-ized with fibers [2].
• In spectroscopy, the spectrum of light is determined. The use of a fiber-bundle allowsfor scanning large areas of the sky (“integral field spectroscopy”) or obtaining spectralinformation of many objects simultaneously by connecting each fiber of the bundle toa separate detector. To enable high packing density of the fibers the cladding diametershould be chosen not too large [2].
1
CHAPTER 1. INTRODUCTION 2
• Another field of application for infrared fibers is radiometry, where temperature radiationis measured. At room temperature thermal radiation has its maximum at a wavelengthof about 10 µm. Therefore fibers guiding light in the mid-infrared have used.
1.2 Fiber types
Fibers can be categorized by structure, guiding-type, and material. Figure 1.1 shows a classi-fication of fiber types by structure: solid-core fibers, hollow waveguides, and micro-structuredfibers (so-called photonic crystal fibers). Figure 1.2 gives a rough overview of attenuation andrange of transmission for different types of fibers. In the following, I will provide a descriptionof the different types.
Infrared Fiber
Glass
Heavy MetalFluoride
Chalcogenide
GermanateSapphire
Ag/AgI
Silver Halide
Poly−crystalline
LeakyGuide
Sapphire Silver HalideChalcogenide−Polyetherimide
Chalcogenide−Polyethersulfone
Solid Core
GuidingIndex
Single−Crystal
Crystalline
Hollow Waveguide
Attenuated Total
Reflection GuidingIndex Bandgap
Guiding
Bragg Fiber
Photonic CrystalFiber
Mat
eria
lG
uidi
ng T
ype
Stru
ctur
e
Figure 1.1: Classification of infrared fibers.
1.2.1 Solid-Core Fibers
Waveguiding in solid-core fibers obeys the principle of total reflection of light propagating in-side the core. Total reflection is caused by a difference in index of refraction between core- andcladding-material. Fibers transmitting light of wavelengths above 2µm can be manufacturedof glass or crystalline mateials. In Silica fibers, transmission range is limited by multiphononabsorption for large wavelengths and by Rayleigh scattering for short wavelengths. The trans-mission range of fibers can be increased when shifting multiphonon absorption towards higherwavelengths by employing heavy metal oxides, as in Fluoride fibers and Germanate fibers.
Flouride: Fluoride fibers show the lowest attenuation of all fibers transmitting in the mid-infrared. Interpolating intrinsic losses caused by Rayleigh-scattering and multiphononabsorption results in a theoretic value of attenuation of 0.24 dB/km at a wavelength of
CHAPTER 1. INTRODUCTION 3
Figure 1.2: Comparison of attenuation and wavelength-range of different types of infraredfibers (from [3]).
2.55µm, whereas the lowest measured value is about 0.45 dB/km [3]. Physical prop-erties of Fluoride fibers are inferior to those of Silica fibers. They are less durableand have less strength (Young’s modulus EFluoride = 54 GPa, ESilica = 73 GPa). Fur-thermore, the operating temperature range of Fluoride fibers is much lower becauseof the low glass transition point of Fluoride (TZBLAN = 265 ◦C, TSilica = 1175 ◦C).Most popular Fluoride glasses used for fiber fabrication are Fluorozirconate (ZBLAN:ZrF4−BaF2−LaF3−AlF3−NaF) and Flouroaluminate (AlF3−ZrF4−BaF2−CaF2−YF3).
Germanate: Better physical properties are shown by Germanate fibers, which have glasstransition temperatures up to 680 ◦C and an excellent durability. These fibers are basedon GeO2 and can guide light up to wavelengths of about 3 µm.
Chalcogenide: Chalcogenide fibers are usually based on one or more of the Chalcogene el-ements Sulfide, Selenide and Telluride. They are stable, durable, and insensitive tomoisture. In contrast to most infrared fibers, they can not transmit visible light. Mostof the Chalcogenide glasses show rather large values of the thermo-optic coefficient whichlimits power handling capabilities of the fiber [3].
1.2.2 Crystalline Fibers
Single-Crystal: Fibers made of sapphire show a transmission range of about 0.5 − 3 µm.Sapphire is an uniaxial crystal which gives the fiber excellent physical properties. It isvery hard and has a melting point higher than 2000 ◦C. Young’s modulus is much higherthan for any other fiber (ESapphire = 430 GPa), and the thermal expansion coefficientis about 10 times higher than that of Silica-fibers. Additionally, growth techniquesfor manufacturing this fibers need sufficiently more time than manufacturing of otherfibers [3].
Polycrystalline: There are a lot of halide crystals allowing for transmission in the infraredbut only silver- and thallium-halides have physical properties that allow extrusion into
CHAPTER 1. INTRODUCTION 4
a fiber. Silver-halide fibers are better than thallium-halide fibers for some reasons andwill be described in the following. Attenuation can be as low as 0.2 dB/m at 2.55 µmand transmission is possible nearly up to 20 µm. Disadvantages are low melting point,aging of the fiber, and photo sensitivity of the crystals. Additionally, they are corro-sive to many metals. Due to these facts, the fibers need a special coating as well asspecial connectors (e.g. gold). Moreover the tensile strength of this fibers is very low(Esilver-halide = 0.14 GPa) and exceeding a certain bending-radius can lead to permanentdamage and therefore higher attenuation of the affected region [3].
1.2.3 Hollow Waveguides
In hollow waveguides, light is propagating through an air core. Therefore, advantages of highlaser-power-thresholds, low insertion loss, and no end-reflections arise. Furthermore, hollowwaveguides show low beam divergence. Losses are indirect proportional to a3, where a givesthe bore radius. Drawbacks are high bending losses, which are indirect proportional to thebending radius R. Hollow waveguides can be realized as ATR-guides1 or as Leaky-guides [3].
ATR-guides: The refractive index of the inner wall material of ATR-guides is less than one.Together with the air-core (ncore = 1) a structure like in usual fibers (ncore > nclad)is achieved. Waveguiding works due to attenuated total reflection of light propagatinginside the core. Such a waveguide can be realized for instance with sapphire [3].
Leaky guides: In contrast to ATR-guides the refractive index of the inner wall material ofleaky guides is greater than one. Waves are guided due to reflection on the metallic innerwall. To minimize loss the inner wall of the waveguide is covered with a dielectric layer.The most popular structure is the Hollow Glass Waveguide (HGW), with inner layers ofsilver covered with silver iodide (see Figure 1.3). At 10 µm, losses are less than 0.5 dB/m
Silver iodide film
Glass substrate
Silver film
Polymer coating
Figure 1.3: Structure of a Hollow Glass Waveguide (from [4]).
for a HGW having a bore radius larger than 400 µm. HGWs are nearly single-mode(in waveguides with a bore radius less than 300µm only the LP01-mode propagates),because higher order modes suffer high attenuation and so in practice only the lowestorder modes propagate.
1(ATR . . . attenuated total reflectance)
CHAPTER 1. INTRODUCTION 5
1.2.4 Photonic Crystal Fibers
A novel kind of waveguides are Photonic Crystal Fibers (PCF). At present time PCFs trans-mitting above 2 µm are at an experimental stage and not commercially available. Figure 1.4shows index-guiding and bandgap-guiding PCFs.
Figure 1.4: Cross sections of photonic crystal fibers: index-guiding (left, from [5]) and bandgap-guiding (right, from [6]).
Index guiding: Waveguiding is realized as in solid-core fibers by creating a difference in indexof refraction between the core (solid, n > 1) and the cladding (microstructured) region.This is achieved by manufacturing a cladding region with air-holes which lower theeffective index of refraction. By varying size and number of the air-holes, the refractiveindex of the cladding area and thus also the difference of the refractive index of the coreand the cladding, can be chosen very precisely. Fibers with a high numerical aperture(up to 0.7) as well as fibers supporting single-mode operation over a wide wavelengthrange, or highly nonlinear fibers can be manufactured [7].
Bandgap guiding: By using special structures it is possible to create areas within a material,where light of a certain wavelength can not propagate. Such areas are realized around ahollow core so that light is confined to the core after being coupled into it. Due to thehollow core, high power levels can be transmitted without fiber damage or nonlinearities.There are no Fresnel reflections at the fiber ends [7].
1.3 Outline
Parameters allowing to characterize fibers are specified in Chapter 2. They are divided intophysical parameters and waveguide parameters. In Chapter 3 the results of a comprehensivemarket survey are presented. Information of all infrared fibers (transmitting light above 2 µm)offered presently, as well as information about the vendors, and a comparison of parameters ofthese fibers is presented. Chapter 4 gives a description of measurement methods for parametersimportant for deployment of fibers in space instruments. Technical feasibility of this methodswith presently existent labaratory equipment was especially taken into account.
Chapter 2
Identification of fiber parameters
The aim of this chapter is the identification of fiber parameters relevant and performance-critical for the possible applications mentioned in Chapter 1. Due to the different designs andguiding mechanisms of various infrared fibers, like step-index fibers, photonic crystal fibers,hollow fibers, Bragg grating fibers, etc., the detailed mathematical expressions of some fiberparameters may be different. If not stated otherwise, the remainder of this document will referto step-index fibers, which is appropriate for an application-oriented specification of importantparameters.
2.1 Physical parameters
2.1.1 Dimensions
Core/cladding diameter: The core diameter, dco, is twice the radial distance from the fiberaxis to the point where the index of refraction takes on the value it has in the cladding.The cladding diameter, dcl > dco, is twice the radial distance from the fiber axis to thepoint where the index of refraction becomes different from that in the cladding. Bothparameters are usually given in µm.
Index-of-refraction-profile: The radial profile of the index of refraction determines thewaveguiding properties of the fiber. In order to obtain wave guidance, the index ofrefraction in the core, nco, usually has to be higher than the index of refraction in thecladding, ncl. The index-of-refraction-profile for step-index fibers as a function of theradius r reads
n ={
nco : 0 < r < dco/2ncl : dco/2 < r < dcl/2
. (2.1)
The ratio
∆ =n2
co − n2cl
2n2co
(2.2)
is known as the relative refraction index difference.
If single-mode operation is aimed at, the upper bound for the core diameter is
dco <λV
π
1√n2
co − n2cl
, (2.3)
with a normalized frequency V = 2.405.
6
CHAPTER 2. IDENTIFICATION OF FIBER PARAMETERS 7
Core-cladding concentricity error: The radial distance between the geometric center ofthe core and the cladding is defined as core-cladding concentricity error.
Maximum fiber length: The maximum length of fiber, Lmax, which can be produced in onepiece is limited. Especially for infrared fibers, this length can be quite short (e.g. a fewmeters).
2.1.2 Mechanical parameters
Hardness: The hardness measures the resistance of the fibers’s material to indentation. Itcan be measured on the Moh’s and Vicker’s scale. The latter is a more quantitativemeasure, which measures the impression made using a pyramid-shaped diamond forcedinto the surface of a material. The result is given as the Vickers hardness number
VHN = 1854P
d2(2.4)
in kg/mm2, where P is the load in grams and d is the mean length of the indentation inmicrons. Moh’s scale characterizes the scratch resistance through the ability of a hardermaterial to scratch a softer. On this scale quartz (SiO2) has a hardness of 7, whereasdiamond (C) has a hardness of 10.
Hardness of a fiber material comes into play when preparing a fiber facet: In general,with a hard material it is easier to prepare a well-defined, smooth surface by polishing.It is also more scratch-resistant.
Tensile strength: The tensile strength of a fiber is the maximum amount of tensile stressthat it can be subjected to before it breaks. Tensile strength is measured in units offorce per unit area, i.e. Newton per square meter ([N/m2] or [Pa]).
Coefficient of elasticity: The relative elongation when subjected to an axial force (providedthe material is in the elastic region) is described by the coefficient of elasticity Young’smodulus E,
∆L
L=
1E
F
A, (2.5)
where ∆L is the absolute elongation, L is the fiber length, F is the applied force, and Ais the cross sectional area of the fiber. The coefficient of elasticity is therefore given inN/m2.
Minimum bending radius: When bending a fiber with less than the minimum bendingradius, it breaks.
2.1.3 Thermal parameters
Operating temperature range: The operating temperature range defines lower and uppertemperature limits within which the fiber can be operated.
Thermal expansion coefficient: The thermal expansion coefficient α gives the relativeelongation per temperature unit of a fiber,
∆L
L= α ∆T , (2.6)
CHAPTER 2. IDENTIFICATION OF FIBER PARAMETERS 8
where ∆L is the absolute elongation, L is the fiber length, and ∆T is the temperaturechange. The thermal expansion coefficient is given in K−1.
Thermo-optic coefficient: The thermo-optic coefficient (given in K−1) describes the changeof the index of refraction of a material due to a temperature change, dn/dT . This effectalso depends on the wavelength and on the absolute temperature. If light of high intensityis transmitted via the fiber, the thermo-optic effect can lead to self-focusing and thereforeto an additional intensity increase. This may lead to thermal damage of the fiber.
Temperature coefficient of optical length: The parameter 1L
d(nL)dT describes the temper-
ature dependence of the optical length, which is the product of the refractive index ofthe fiber’s material n and the geometrical length L of the fiber.
Thermal conductivity: The thermal conductivity of a fiber is equivalent to the quantity ofheat that passes in unit time through unit area of unit length of fiber, when its oppositefaces are subject to unit temperature gradient. Thermal conductivity is measured in[Wm−1K−1].
Laser damage threshold: The maximum light intensity (given in W/m2) which can betransported over a fiber without damaging it is defined by the laser damage threshold.
2.2 Waveguiding parameters
2.2.1 Transmission parameters
Mode field radius: The mode field radius w0 is the radial dimension, where the intensityof the fundamental mode drops to 1/e2 = 0.135 of its peak value. Close to single-modecutoff, the modefield radius is only slightly larger than the core radius. Two octavesabove the cutoff wavelength it increases substantially [8].
Fiber attenuation vs. bending radius: Generally, the fiber attenuation increases with de-creasing bending radius. The bend loss coefficient αB for the fundamental mode LP01,given in dB/m, as depending on the bend radius R is given by [9, 10]
αB =10
ln 102√
π(n2co − n2
cl(1 + b∆)2)γ3/2d2
co(n2co − n2
cl)√
RK21 (dcoγ/2)
exp(− 2γ3R
3k2n2cl(1 + b∆)2
), (2.7)
where k = 2π/λ is the wave number, b is the ratio of the integrated field in the core tothe total integrated field of the LP01 mode, K1 is a modified Hankel function, and withthe abbreviation
γ =√
n2clk
2b2∆2(1 + 2/b∆) . (2.8)
The total attenuation of a fiber is then
αtotal = α + αB , (2.9)
where α is the attenuation coefficient of the straight fiber. Figure 2.1 shows αB over Rfor a fiber with dco = 9.3 µm, ∆ = 0.4% at λ = 1550 nm.
CHAPTER 2. IDENTIFICATION OF FIBER PARAMETERS 9
Figure 2.1: Bending loss coefficient αB as a function of bending radius R.
Birefringence: Imperfections of the fiber geometry or mechanical stress cause unintendedbirefringence. However, birefringence can also be a desired fiber property, e.g. for po-larizing or polarization maintaining fibers. In a birefringent fiber, two principal axesfor linear polarized eigenmodes exist, allowing for propagation of decoupled waves atdifferent velocities.
Beat length: The beat length LB of a fiber is defined as the distance after which two com-ponents of a field polarized parallel and normal to the optical axis, and therefore expe-riencing different propagation constants due to birefringence, have a phase shift of 2π.After a length of ∆L the phase shift amounts to
∆ϕ = 2π∆L
LB. (2.10)
The beat length depends on the wavelength and on the refractive indices of the twoprincipal axes,
LB =λ
|ne − no|, (2.11)
where ne and no are the indices of refraction parallel and normal to the optical axis ofthe birefringent fiber. The beat length of a standard fiber may be in the range of severalmeters.
2.2.2 Wavelength parameters
Cut-off wavelength: Every mode of a fiber except the fundamental mode experiences acertain wavelength above which it can not propagate. The cut-off wavelength of a fiber,
CHAPTER 2. IDENTIFICATION OF FIBER PARAMETERS 10
λc, is defined as the wavelength above which only one mode – the fundamental mode –represents a valid solution for the wave equation. The cut-off wavelength for a step-indexfiber is given by
λc =dcoπ
V
√n2
co − n2cl , (2.12)
with a normalized frequency of V = 2.405.Since in practice the transition from single-mode to multi-mode operation is not abrupt,experimenters define the cut-off wavelength as that wavelength where the power propa-gating in the fiber is by 0.1 dB higher than the power of the fundamental mode.
Fiber attenuation vs. wavelength: To determine the wavelength range of a fiber, the fiberattenuation α(λ), usually given in dB/km, is presented in a diagram as a function of thewavelength. The shape of this curve depends on the fiber geometry and material.
Normalized frequency: The normalized frequency of a fiber is defined by
V =dcoπ
λ
√n2
co − n2cl. (2.13)
For single-mode operation, the normalized frequency must not be higher than 2.405. Thedesign criterion for a step-index fiber to be solely single-mode above a desired wavelengthλc is
dco
√n2
co − n2cl ≤ 0.766λc . (2.14)
2.2.3 Fiber coupling
Acceptance angle: When coupling into a fiber, the angle between incident light beams andthe fiber axis must be lower than
Θ = arcsin√
n2co − n2
cl (2.15)
in order to provide wave-guiding due to total reflection at the core-cladding boundary.
Numerical aperture: The numerical aperture is the sine of the acceptance angle,
NA =√
n2co − n2
cl . (2.16)
Effective numerical aperture: Due to imperfections during the manufacturing of the fiber,the actual numerical aperture may be slightly different from the theoretical one. In thiscase it is called effective numerical aperture.
Reflective loss: When coupling light into or out of a fiber, losses occur due to reflectionsat the fiber facet as a consequence of index-of-refraction differences of the propagationmedia within and outside the fiber (so-called Fresnel losses). The reflectivity of a beamentering the fiber parallel to the fiber axis is given by
R =(nm − nco)2
(nm + nco)2, (2.17)
where nm and nco are the indices of refraction of the medium outside the fiber and thefiber core, respectively.
CHAPTER 2. IDENTIFICATION OF FIBER PARAMETERS 11
Coupling efficiency: When coupling into a fiber (be it from free-space or from anotherfiber) the ratio of guided light power to total available light power is called couplingefficiency. The easiest way to couple a free-space beam into a fiber is to use a lens as afocussing element. In a breadboard setup with an approximately Gaussian input beamoptimum coupling is obtained, if the lens matches the modefield radius w0 of the beamin the focal plane to the modefield radius of the field propagating in the fiber [11, 12].For fixed lens and waveguide parameters, the coupling efficiency changes significantlywith changing wavelength. The maximum coupling efficiency can be obtained at single-mode cutoff, i.e. for V = 2.405, [13]. This theoretical maximum coupling efficiency1
between the LP01 mode propagating in the fiber and an Airy function at the input planeof the fiber amounts to η = 0.786 [14]. Additional reflective loss, due to the Fresnelreflection (2.17) at the fiber facet (see above), reduces this coupling efficiency unless anantireflective coating is used.
Output divergence angle: Optical waves exiting a single-mode fiber will experience diffrac-tion, depending on the mode field radius and the wavelength. Assuming a Gaussianintensity profile within the single-mode fiber, the full output divergence angle reads
ε =2λ
πw0. (2.18)
In case of a multi-mode fiber the output divergence angle is best characterized via thefiber’s numerical aperture. It is just twice the acceptance angle (see above).
2.2.4 Dispersion
Dispersion: The velocity of waves in a fiber depends on the wavelength. This leads to arelative delay of signal components at different wavelengths, corresponding to a temporalspread of the signal. This effect, called dispersion, compounds of chromatic dispersion(wavelength-dependent index of refraction and radial extension of the field in the fiber)and mode dispersion (due to propagation velocity differences of different modes).
Dispersion vs. wavelength: The chromatic dispersion coefficient, given in ps/(km·nm), ispresented in a diagram as a function of the wavelength.
Zero dispersion wavelength: The zero dispersion wavelength is the wavelength for whichthe chromatic dispersion coefficient vanishes.
1For calculating this coupling efficiency not an approximation but the exact field was used for the fiber’sfundamental mode.
Chapter 3
Market survey
From November 2004 to January 2005 I performed a thorough market survey concerning opticalfibers in the mid-infrared spectral range, with emphasis on the wavelength range from 2 to12 µm. Manufacturers and distributors for various types of fibers were contacted and askedfor offers and detailed specifications. While the focus was the European market, I eventuallyperformed a world-wide survey.
As outlined in Chapter 1, I distinguish between solid-core fibers, hollow waveguides, andphotonic crystal fibers.
The major information sources for my search were the Internet, the Laser Focus WorldBuyers Guide [15], and personal knowledge.
3.1 Fibers offered
Table 3.1 gives an overview of the IR fibers offered and provides main parameters as well asthe price and delivery time. From some companies offering several types of fibers (e.g. fiberswith different dimensions) I only asked for exemplary offers. To allow a comparison withthe characteristics of standard fibers, I added information provided by three representativemanufacturers of telecom fibers.
12
CHAPTER 3. MARKET SURVEY 13ty
pe
mate
rial
pro
duct
core
/cl
addin
gw
avel
ength
ven
dor
pri
cedel
iver
ydata
shee
tdia
met
erra
nge
tim
e[µ
m]
[µm
]E
UR
/m
[wee
ks]
solid-c
ore
fiber
Chalc
ogen
ide
C1
100/−
to1000/−
2−
10
Am
orp
hous
Mate
rials
96
3A
.7C
2100/−
to1000/−
d0.7−
7A
morp
hous
Mate
rials
A.7
CIR
fiber
250/300
2−
6A
RT
photo
nic
s85
2−
6A
.3C
IRfiber
340/400
2−
6A
RT
photo
nic
s105
2−
6A
.3C
IRfiber
400/440
2−
6A
RT
photo
nic
s115
2−
6A
.3C
IRfiber
500/550
2−
6A
RT
photo
nic
s135
2−
6A
.3IR
T-S
U50/170
to700/800
2−
5C
orA
ctiv
e2680f
2−
4A
.10
IRT
-SE
50/170
to700/800
2−
9C
orA
ctiv
eA
.10
Bej
ing
fiber
150/400
1−
6B
eijing
S-F
iber
Tec
hn.
A.6
Bej
ing
fiber
250/600
2−
12
Bei
jing
S-F
iber
Tec
hn.
A.6
Bej
ing
fiber
3100/600
2−
12
Bei
jing
S-F
iber
Tec
hn.
A.6
Bej
ing
fiber
450/400
2−
11
Bei
jing
S-F
iber
Tec
hn.
A.6
Flu
ori
de
SM
fluori
de
8.5
/122
0.5−
3.7
Fib
erLabs
153
1A
.15
MM
fluori
de
TFF
190/200
0.7−
2.5
Fib
erLabs
46
A.1
6M
Mfluori
de
GFF
140/200
to400/530
0.5−
4Fib
erLabs
46e
A.1
6SG
fiber
100/−
to700/−
0.4
5−
5In
frare
dFib
erSyst
ems
A.1
4M
IDIR
MM
fiber
50/−
to1000/−
0.3−
4.5
IRphoto
nic
sA
.2M
IDIR
SM
fiber
9/125
0.3−
4.5
IRphoto
nic
s226
8−
10
A.1
6.5
/125
Le
Ver
reFlo
ure
1325
<1
Ger
manate
HP
fiber
150/−
1−
3a
Infr
are
dFib
erSyst
ems
23–38c
A.1
3H
Pfiber
250/−
1−
3a
Infr
are
dFib
erSyst
ems
306
A.1
3H
Pfiber
450/−
1−
3a
Infr
are
dFib
erSyst
ems
421
A.1
3H
Pfiber
700/−
1−
3a
Infr
are
dFib
erSyst
ems
230–383j
A.1
3poly
cryst
allin
e-
Optr
an
MIR
200/300
to860/1000
4−
16
Cer
am
Opte
cA
.5si
lver
halide
Optr
an
MIR
300−
1000b
4−
16
Cer
am
Opte
cA
.5si
lver
halide◦
900/1000
3−
18
Infr
are
dFib
erSen
sors
745
4A
.12
silv
erhalide
�750×
750,1000×
1000i
2−
18
Infr
are
dFib
erSen
sors
A.1
2P
IRfiber
450/500
4−
18
ART
photo
nic
s190
2−
6A
.4P
IRfiber
630/700
4−
18
ART
photo
nic
s230
2−
6A
.4P
IRfiber
900/1000
4−
18
ART
photo
nic
s270
2−
6A
.4si
ngle
-cry
stal-
sapphir
e150−
425b
0.3−
3P
hotr
an
506h
2−
3A
.11
hollow
waveg
uid
eH
itach
ifiber
700
3−
12
Hitach
iC
able
A.9
HW
EA
/H
WC
A300−
1000
2.9−
12
Poly
mic
roTec
hnolo
gie
s387g
1−
2A
.8photo
nic
cryst
alfiber
Silic
aH
C-1
550-0
210.9
1.4
5−
1.6
5C
ryst
alFib
reA
/S
tele
com
fiber
Silic
aSM
F-2
8e
9/125
Corn
ing
0.0
3SM
09/125
9/125
j-fiber
0.0
26
<1
AllW
aveF
iber
9/125
ofs
0.0
44k
aacc
ord
ing
todia
gra
min
data
shee
tbno
claddin
gcm
inim
um
purc
hase
length
100
mdnot
available
bef
ore
mid
2005
eoffer
for
fiber
wit
hco
redia
met
er160
µm
f offer
for
fiber
wit
hco
re/cl
addin
gdia
met
er50/170
µm
incl
udin
gco
nnec
tors
and
coati
ng
gH
WE
Afiber
,opti
miz
edfo
rE
r:Y
AG
,offer
by
Optr
onis
Gm
bH
hoffer
for
fiber
wit
hco
redia
met
er250
µm
i square
wav
eguid
ej m
inim
um
purc
hase
length
10
mkoffer
from
Matt
ig-S
chauer
(Aust
ria)
Table 3.1: Overview of all fiber offers resulting from the market survey performed.
CHAPTER 3. MARKET SURVEY 14
3.2 Fiber vendors
Tables 3.2 and 3.3 present detailed contact information on fiber manufacturers and vendors,while Table 3.4 contains information on companies where I was unable to make contact.
Chalcogenide fibers with dimensions 400/500 µm, produced by ARTphotonics, are offeredby JT Ingram Sales & Marketing Co. for the price of 333 EUR for 2 m, including SMA con-nectors and protective tubing.
Photran single-crystal sapphire fibers with a core diameter of 250µm and PTFE (Poly-tetrafluoroethylene) buffer are offered by Laser Components (Germany) for the price of 823EUR/m.
Polycrystalline fibers with dimensions 400/500 µm and 630/700 µm, produced by ARTpho-tonics, are offered by JT Ingram Sales & Marketing Co. for the price of 449 EUR and 525EUR for 2 m, respectively, including SMA connectors and protective tubing. ARTphotonicsadditionally offers square PIR fibers with core/cladding dimensions from (450/500 µm)2 forthe price of 240 EUR/m to (900/1000 µm)2 for 240 EUR/m and bare core PIR fibers withdiameters from 500 µm to 1000 µm, for 130 EUR/m to 210 EUR/m. ARTphotonics fibers areadditionally offered by FiberWare.
The prices of all PIR fibers offered apply for products with moderate quality of core/claddingboundary, corresponding to an attenuation of 0.2− 0.8 dB/m at a wavelength of 10.6 µm.
I could not get in contact with Beijing S-Fiber Technology (China) who, on their homepage,claim to produce chalcogenide fibers. It is neither possible to send an email to the addressesposted on the homepage nor to get in contact by phone. Autex (Japan) did not respond to mymails. It is probably a distributor for Polymicro’s (USA) hollow fibers. I also did not succeedto get in contact with OmniGuide Communications Inc. (USA), probably a manufacturer ofhollow core photonic bandgap fibers.
In the search for photonic crystal fibers designed for the mid-infrared, I also contactedCrystal Fibre A/S (Denmark) but they responded that they only work with silica. The dis-tributor Oxford Electronics (UK) has a chalcogenide fiber in his program but cannot offer itat this time.
The fiber section of Saphikon (France) was moved to Photran (USA). BlazePhotonics Ltd.(UK) is now owned by Crystal Fibre A/S (Denmark).
CHAPTER 3. MARKET SURVEY 15
com
pany
addre
ssco
untr
yphone
fax
UR
Le-
Am
orp
hous
Mate
rials
Inc.
3130
Ben
ton
Garl
and,Tex
as
75042
USA
phone:
fax:
+1-9
72-4
94-5
624
(G.W
hale
y)
+1-9
72-2
72-7
971
(G.W
hale
y)
ww
w.a
morp
housm
ate
rials
.com
GregW
hale
y@
am
orphousm
ateria
ls.c
om
RayH
ilto
njr
@am
orp
housm
ate
rials
.com
ART
photo
nic
sG
mbH
Sch
warz
schildst
r.6
D-1
2489
Ber
lin
Ger
many
phone:
fax:
+49-3
0-6
789-4
153
+49-3
0-6
789-4
156
ww
w.a
rtphoto
nic
s.de
info
@art
photo
nic
s.de
Cer
am
Opte
cIn
dust
ries
Inc.
515A
Shaker
Rd.
East
Longm
eadow
,M
A01028
USA
phone:
fax:
+1-8
00-9
34-2
377
+1-8
60-7
47-4
487
(C.Sm
ith)
+1-4
13-5
25-1
112
+1-8
60-7
93-4
909
(C.Sm
ith)
ww
w.c
eram
opte
c.co
mSale
sEngin
eeri
ng@
Cer
am
Opte
c.co
mcheryl.sm
ith@
ceram
opte
c.c
om
Cer
am
Opte
cG
mbH
Sie
men
sstr
.44
53121
Bonn
Ger
many
phone:
fax:
+49-2
28-9
79670
+49-2
28-9
796799
CorA
ctiv
eH
igh-T
ech
Inc.
2700,Jea
n-P
erri
n,Suite
121
Queb
ec(Q
C)
Canada,G
2C
1S9
Canada
phone:
fax:
+1-4
18-8
45-2
466-2
19
(D.B
eik
o)
+1-4
18-8
45-2
609
(D.B
eik
o)
ww
w.c
ora
ctiv
e.co
msa
les@
cora
ctiv
e.co
min
fo@
cora
ctiv
e.co
mdavid
.beik
o@
coractive.c
om
Corn
ing
Inc.
One
Riv
erfr
ont
Pla
zaC
orn
ing,N
Y14831
USA
phone:
fax:
+1-6
07-7
86-8
125
+1-6
07-7
86-8
344
ww
w.c
orn
ing.c
om
/optica
lfiber
Cry
stalFib
reA
/S
Blo
kken
84,D
K-3
460
Bir
ker
ød
Den
mark
phone:
fax:
+45-4
348-2
800
(Gen
eral)
+45-4
348-2
820
(R.K
ris
tianse
n)
+45-4
348-2
801
(R.K
ris
tianse
n)
ww
w.c
ryst
al-fibre
.com
conta
ct@
cryst
al-fibre
.com
rek@
cryst
al-fibre.c
om
Fib
erLabs
Inc.
2-1
-15
Ohara
,K
am
ifukuoka,Saitam
a,
356-8
502
Japan
Japan
phone:
fax:
+81-4
9-2
78-7
829
(B.In
oue)
+81-4
9-2
63-9
328
(B.In
oue)
ww
w.fi
ber
labs.
co.jp
info
@fiber
labs.
co.jp
inoue@
fiberla
bs.
co.jp
Hitach
iC
able
,Ltd
.1-6
-1O
hte
mach
i,C
hiy
odaku,
Tokyo
100-8
166
Japan
Japan
phone:
fax:
+81-2
94-2
5-3
837
(A.H
ongo)
+81-2
94-4
3-7
487
(A.H
ongo)
ww
w.h
itach
i-ca
ble
.co.jp
hongo.a
kih
ito@
hit
achi-cable
.co.jp
Infr
are
dFib
erSen
sors
ImG
ille
sbach
tal33
52066
Aach
enG
erm
any
phone:
fax:
+49-2
41-6
5609
(L.K
uepper)
+49-2
41-6
5617
(L.K
uepper)
ww
w.ifs
-aach
en.d
e/42.0
.htm
lkuepper.ifs
@t-
online.d
eIn
frare
dFib
erSyst
ems
Inc.
2301-A
Bro
adbir
chD
r.,
Silver
Spri
ng,
MD
20904
USA
phone:
fax:
+1-3
01-6
22-9
546
+1-3
01-6
22-7
131
(A.T
chap)
+1-3
01-6
22-7
135
ww
w.infr
are
dfiber
syst
ems.
com
info
@in
frare
dfiber
syst
ems.
com
ale
xtchap@
infr
aredfibersystem
s.c
om
IRphoto
nic
sIn
c.248
Rue
Coro
tSuit
e212
Ile
des
Soeu
rs(V
erdun)
Montr
eal,
Canada,H
3E
-1K
9
Canada
phone:
fax:
+1-5
14-5
78-5
060
(E.G
eoffri
on)
+1-5
14-5
78-0
177
ww
w.irp
hoto
nic
s.co
min
fo@
irphoto
nic
s.co
megeoffrio
n@
irphoto
nic
s.com
Table 3.2: Contact information for fiber vendors. Telephone numbers and email addresses ofpersons with whom a personal contact was established are printed in bold face.
CHAPTER 3. MARKET SURVEY 16
com
pany
addre
ssco
untr
yphone
fax
UR
Le-
j-fiber
Gm
bH
ImSem
mic
ht
1D
-07751
Jen
aG
erm
any
phone:
fax:
+49-3
641-3
52-1
00
+49-3
641-3
52-1
01
ww
w.j-fi
ber
.com
info
@j-fiber
.com
Le
Ver
reFlo
ure
Cam
pus
Ker
Lann
F-3
5170
Bru
z,B
ritt
any
Fra
nce
phone:
fax:
+33-2
-9905-3
130
(G.M
aze)
+33-2
-9905-9
53
(G.M
aze)
lever
refluore
.com
info
@le
ver
refluore
.com
sale
s@le
ver
refluore
.com
ofs
2000
Nort
hea
stE
xpre
ssw
ay
Norc
ross
,G
eorg
iaU
SA
phone:
+1-8
88-3
42-3
743
+1-7
70-7
98-5
555
ww
w.o
fsoptics
.com
ofs
@ofs
optics
.com
Photr
an
LLC
13446
Pow
ay
Road,P
MB
#150
Pow
ay,
CA
92064
USA
phone:
fax:
+1-8
58-7
48-0
850
+1-6
19-5
07-4
455
(L.R
oth
rock)
+1-8
58-7
48-0
854
(L.R
oth
rock)
ww
w.p
hotr
an.c
om
sale
s@photr
an.c
om
roth
rock@
znet.
com
Poly
mic
roTec
hnolo
gie
s,LLC
.18019
N.25th
Aven
ue.
Phoen
ix,A
rizo
na
85023-1
200
USA
USA
phone:
fax:
+1-6
02-3
75-4
100
+1-6
02-3
75-4
110
ww
w.p
oly
mic
ro.c
om
fiber
ware
Gm
bH
Born
hei
mer
Str
.4
09648
Mit
twei
da
Ger
many
phone:
fax:
+49-3
727-6
13335
+49-3
727-6
13336
ww
w.fi
ber
ware
.de
offi
ce@
fiber
ware
.de
JT
Ingra
mSale
s&
Mark
et-
ing
Co.
316
Harl
equin
Ct,
Ovie
do,Fl32765
USA
phone:
fax:
+1-5
61-5
73-6
533
+1-2
53-6
63-2
608
ww
w.jtingra
m.c
om
/Jim
@jt
ingra
m.c
om
Lase
rC
om
ponen
tsG
mbH
Wer
ner
-von-S
iem
ens-
Str
.15
82140
Olc
hin
gG
erm
any
phone:
fax:
+49-8
142-2
864-0
+49-8
142-2
864-1
1w
ww
.lase
rcom
ponen
ts.c
om
info
@la
serc
om
ponen
ts.c
om
Matt
ig-S
chauer
Gm
bH
Matz
ner
gass
e34
1140
Wie
nA
ust
ria
phone:
fax:
+43-1
-984-8
383-6
2(R
.B
inder)
+43-1
-984-8
383-5
0(R
.B
inder)
ww
w.m
att
ig-s
chauer
.at
r.b
inder@
matt
ig-s
chauer.a
tO
ptr
onis
Gm
bH
Honse
llst
r.8
D-
77694
Keh
lG
erm
any
phone:
fax:
+49-7
8-5
19126-3
4(D
.Schoch)
+49-7
8-5
19126-1
0(D
.Schoch)
ww
w.o
ptr
onis
.com
schoch@
optr
onis
.com
Oxfo
rdE
lect
ronic
sLtd
Pyra
mid
House
,59
Win
ches
ter
Road,
Four
Mark
s,H
am
psh
ire
GU
34
5H
RU
Kphone:
fax:
+44-1
420-5
61200
+44-1
420-5
61300
ww
w.o
xfo
rd-e
lect
ronic
s.co
msa
les@
oxfo
rd-e
lect
ronic
s.co
m
Table 3.3: Contact information for fiber vendors, continued. Telephone numbers and emailaddresses of persons with whom a personal contact was established are printed in bold face.Distributors are listed below manufacturers, separated by an empty line.
CHAPTER 3. MARKET SURVEY 17
com
pany
addre
ssco
untr
yphone
fax
UR
Le-
Aute
x16-5
Tom
ihis
a-c
ho,Shin
jyuku
Tokyo
162-0
067,Japan
Japan
phone:
fax:
+81-3
-3226-6
321
+81-3
-3226-6
290
ww
w.a
ute
x-inc.
co.jp
[sale
s32@
aute
x-inc.
co.jp]
Bei
jing
S-F
iber
Tec
hnolo
gy
A#
1006,T
ianyuan
Apart
men
tN
o.3
6,
South
GuangA
nM
enR
oad,
Xuanw
uD
istr
ict,
Bei
jing,Post
Code:
100054
Chin
aphone:
fax:
[+86-1
0-8
3522482]
[+86-1
0-6
3586031]
ww
w.s
-fiber
.com
.cn
[sfiber
@so
hu.c
om
][s
unhuim
ail@
vip
.sin
a.c
om
]O
mniG
uid
eC
om
munic
a-
tions
Inc.
One
Ken
dall
Square
Buildin
g100,3rd
Flo
or
Cam
bri
dge,
MA
02139
USA
phone:
fax:
+1-6
17-5
51-8
444
+1-6
17-5
51-8
445
ww
w.o
mni-guid
e.co
min
form
ation@
om
ni-guid
e.co
m
Table 3.4: Contact information for fiber manufacturers and vendors I failed to get in touchwith.
CHAPTER 3. MARKET SURVEY 18
3.3 Comparison of fibers offered
In the following more detailed information on the fibers listed in Table 3.1 is presented [2].Figure 3.1 shows the attenuation of the different fibers for three representative wavelengths,Fig. 3.2 provides an overview of the corresponding useful wavelength ranges. In the subsectionsto follow I list the detailed properties as extracted from the data sheets copied in AppendixA.
6
α[d
B/m
]
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
C1
C2
CIR
fiber
IRT-SU
IRT-SE
Beijin
gFibe
r1
Beijin
gFibe
r2
Beijin
gFibe
r3
Beijin
gFibe
r4
SMFluo
ride
fiber
MM
Fluo
ride
TFF
MM
Fluo
ride
GFF
SGfib
er
mid
IRMM
fiber
mid
IRSM
fiber
PIR
fiber
Opt
ranMIR
core/c
lad
silver
halid
efib
er�
silver
halid
efib
er◦
germ
anateHP
fiber
sing
lecrystal fi
ber
HW
EA
HW
CA
Hitachi
fiber�
��
��
���
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
��
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��
��
��
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��
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��
��-�chalcogenide
-�fluoride
-�polycrystalline
-�other
u
u
u uu u
u u u
u uu
u
u. . . 3 µm. . . 5 µm. . . 10.6 µm
w
Figure 3.1: Attenuation coefficient α for different wavelengths of the fibers offered.
CHAPTER 3. MARKET SURVEY 19C
1
C2
CIR
fiber
IRT
-SU
IRT
-SE
Bei
jing
Fib
er1
Bei
jing
Fib
er2
Bei
jing
Fib
er3
Bei
jing
Fib
er4
SMFlu
orid
efib
er
MM
Flu
orid
eT
FF
MM
Flu
orid
eG
FF
SGfib
er
mid
IRM
Mfib
er
mid
IRSM
fiber
PIR
fiber
Opt
ran
MIR
silv
erha
lide
fiber
�
silv
erha
lide
fiber◦
germ
anat
eH
Pfib
er
sing
lecr
ysta
lfib
er
HW
EA
HW
CA
Hit
achi
fiber
-
01
23
45
67
89
1011
1213
1415
1617
18
λ[µ
m]
6 ?other6 ?
polycrystalline
6 ?flouride6 ?
chalcogenide
Figure 3.2: Wavelength ranges of the mid-infrared fibers offered.
CHAPTER 3. MARKET SURVEY 20
3.3.1 Chalcogenide Fibers
pro
duct
C1
C2
CIR
Fib
erIR
T-S
UIR
T-S
E
mate
rial
As-
Se-
Te
As 2
S3
As 2
S3/A
s-S
Sulp
hid
eSel
enid
eco
mpany
Am
orp
hous
Mate
rials
Am
orp
hous
Mate
rials
ART
photo
nic
sC
orA
ctiv
eC
orA
ctiv
e
data
shee
tin
subse
ctio
nA
.7A
.7A
.3A
.10
A.1
0st
ruct
ure
core
/cl
ad
core
/cl
ad
core
/cl
ad
core
/cl
ad
core
/cl
ad
wavel
ength
range
[µm
]2−
10
0.7−
71.5−
62−
52−
9cu
t-off
wavel
ength
[µm
]co
re/cl
addin
gdia
met
er[µ
m]
100/−
to1000/−
100/−
to1000/−
200/250
to700/800
50/170
to700/800
50/170
to700/800
core
refr
act
ion
index
2.8
2.4
2.4
2.4
2.7
coating
mate
rial
double
poly
mer
dualco
at
acr
yla
tedualco
at
acr
yla
tem
inim
um
ben
din
gra
diu
s@
fiber
dia
met
er[m
m]@
[µm
]1
@100a
8@
500a
10
@750a
40
@1000a
1@
100a
17
@500a
30
@750a
40
@1000a
oper
ating
tem
per
atu
rera
nge
[◦C
]7
to127
ther
malex
pansi
on
coeffi
cien
t[1
0−
7/K
]235
241
ther
mo-o
pti
cco
effici
ent
[10−
5/K
]3
±0.9
tensi
lest
rength
[MPa]
916
@100a
483
@500a
469
@750a
427
@1000a
841
@100a
386
@500a
310
@750a
303
@1000a
lase
rdam
age
thre
shold
[W]
5100
@5.2
5µm
num
eric
alaper
ture
0.3
0.2
60.3
0fiber
att
enuation
@w
avel
ength
s[d
B/m
]@
[µm
]0.2−
0.4
@5.2
50.2−
0.4
@9.2
74−
5@
10.6
0.2−
0.4
@5.2
50.2
@(2−
4)
<0.2
<0.5
aco
redia
met
er
CHAPTER 3. MARKET SURVEY 21
pro
duct
Bei
jing
Fib
er1
Bei
jing
Fib
er2
Bei
jing
Fib
er3
Bei
jing
Fib
er4
mate
rial
As-
S/A
s-S
As-
Se-
Te/
As-
Se-
Te
GeS
eTe/
Ge-
As-
Se-
Te
As-
Se/
As-
Se
com
pany
Bei
jing
S-F
iber
Tec
hnolo
gy
Bei
jing
S-F
iber
Tec
hnolo
gy
Bei
jing
S-F
iber
Tec
hnolo
gy
Bei
jing
S-F
iber
Tec
hnolo
gy
data
shee
tin
subse
ctio
nA
.6A
.6A
.6A
.6st
ruct
ure
core
/cl
ad
core
/cl
ad
core
/cl
ad
core
/cl
ad
wavel
ength
range
[µm
]1−
62−
12
2−
12
2−
11
cut-
off
wavel
ength
[µm
]co
re/cl
addin
gdia
met
er[µ
m]
50/400
50/600
100/600
50/400
core
refr
act
ion
index
coating
mate
rial
min
imum
ben
din
gra
diu
s@
fiber
dia
met
er[m
m]@
[µm
]
oper
ating
tem
per
atu
rera
nge
[◦C
]th
erm
alex
pansi
on
coeffi
cien
t[1
0−
7/K
]th
erm
o-o
pti
cco
effici
ent
[10−
5/K
]te
nsi
lest
rength
[MPa]
lase
rdam
age
thre
shold
num
eric
alaper
ture
0.5
0.5
0.5
0.5
fiber
att
enuation
@w
avel
ength
s[d
B/m
]@
[µm
]0.2
@2.4
<0.5
@(1
.8−
3.7
)a
<1
@(4
.5−
6)a
<0.5
@8
<1
@(3
.7−
5.7
)a
<1.5
@(7−
10)a
3@
10.6
<1
@4
aacc
ord
ing
toth
edia
gra
min
the
data
shee
t
CHAPTER 3. MARKET SURVEY 22
3.3.2 Flouride
pro
duct
single
mode
Flu
ori
de
fiber
mult
imode
Flu
ori
de
fiber
TFF
mult
imode
Flu
ori
de
fiber
GFF
SG
fiber
mate
rial
HM
FG
-ZB
LA
NH
MFG
HM
FG
HM
FG
com
pany
Fib
erLabs
Inc.
Fib
erLabs
Inc.
Fib
erLabs
Inc.
Infr
are
dFib
erSyst
ems
data
shee
tin
subse
ctio
nA
.15
A.1
6A
.16
A.1
4st
ruct
ure
core
/cl
ad
core
/cl
ad
core
/cl
ad
core
/cl
ad
wavel
ength
range
[µm
]0.5−
3.7
b0.7−
2.5
0.5−
40.4
5−
5cu
t-off
wavel
ength
[µm
]2.3
c
core
/cl
addin
gdia
met
er[µ
m]
8.5
/122
190/200
140/200
to400/530
100/−
to700/−
core
refr
act
ion
index
coating
mate
rial
UV
cura
ble
resi
nja
cket
UV
cura
ble
resi
nja
cket
poly
mer
icbuffer
coating
min
imum
ben
din
gra
diu
s@
fiber
dia
met
er[m
m]@
[µm
]20
@190a
20
@150a
5@
100a
10
@200a
40
@400a
oper
ating
tem
per
atu
rera
nge
[◦C
]≤
250
ther
malex
pansi
on
coeffi
cien
t[1
0−
7/K
]th
erm
o-o
pti
cco
effici
ent
[10−
5/K
]te
nsi
lest
rength
[MPa]
lase
rdam
age
thre
shold
num
eric
alaper
ture
0.2
10.6
50.2
80.2
2
fiber
att
enuation
@w
avel
ength
s[d
B/m
]@
[µm
]<
0.0
3@
(0.5−
2.6
)b
<0.0
6@
(2.5−
3.5
)b
<0.5
@(3
.5−
4.1
)b
<0.0
3@
(0.7−
2.6
)b
<0.0
5@
(2.6−
3.5
)b
<0.5
@(3
.5−
4.2
)b
<0.0
5@
(1.5−
2.5
)b
<0.2
@(2
.5−
2.8
)b0.0
5@
2.5
aco
redia
met
erbacc
ord
ing
toth
edia
gra
min
the
data
shee
tcca
lcula
ted
from
fiber
dia
met
erand
num
eric
alaper
ture
CHAPTER 3. MARKET SURVEY 23
pro
duct
mid
infr
are
dm
ult
imode
fiber
mid
infr
are
dsi
ngle
mode
fiber
mate
rial
HM
FG
HM
FG
-ZB
LA
NH
MFG
com
pany
IRphoto
nic
sIR
photo
nic
sLe
Ver
reFlo
ure
data
shee
tin
subse
ctio
nA
.2A
.1st
ruct
ure
core
/cl
ad
core
/cl
ad
core
/cl
ad
wavel
ength
range
[µm
]0.3−
4.5
0.3−
4.5
cut-
off
wavel
ength
[µm
]≤
3.5
c2.5
core
/cl
addin
gdia
met
er[µ
m]
50/−
to1000/−
9/125
6.5
/125
core
refr
act
ion
index
coating
mate
rial
UV
cure
d,
dualacr
yla
te,
oth
er
UV
cure
d,
dualacr
yla
te,
oth
erm
inim
um
ben
din
gra
diu
s@
fiber
dia
met
er[m
m]@
[µm
]4
@125
4@
125
oper
ating
tem
per
atu
rera
nge
[◦C
]−
20
to80
−20
to80
ther
malex
pansi
on
coeffi
cien
t[1
0−
7/K
]100−
250
100−
250
ther
mo-o
pti
cco
effici
ent
[10−
5/K
]te
nsi
lest
rength
[MPa]
≥480
≥480
lase
rdam
age
thre
shold
num
eric
alaper
ture
≤0.3
≤0.3
0.3
fiber
att
enuation
@w
avel
ength
s[d
B/m
]@
[µm
]≤
0.5
@(2
.94,2.7
8,2.0
7,2.8
)≤
0.5
@(0
.5−
4.5
)
aco
redia
met
erbacc
ord
ing
toth
edia
gra
min
the
data
shee
tcca
lcula
ted
from
fiber
dia
met
erand
num
eric
alaper
ture
CHAPTER 3. MARKET SURVEY 24
3.3.3 Polycrystalline
pro
duct
PIR
fiber
Optr
an
MIR
Optr
an
MIR
Spec
tralG
rade
Silver
Halide
Fib
ers
Spec
tralG
rade
Silver
Halide
Fib
ers
mate
rial
silv
erhalide:
AgC
l:A
gB
rsi
lver
halide:
AgC
l:A
gB
rsi
lver
halide:
AgC
l:A
gB
rsi
lver
halide
silv
erhalide:
AgC
l:A
gB
rco
mpany
ART
photo
nic
sC
eram
Opte
cC
eram
Opte
cIn
frare
dFib
erSen
sors
Infr
are
dFib
erSen
sors
data
shee
tin
subse
ctio
nA
.4A
.5A
.5A
.12
A.1
2st
ruct
ure
core
/cl
ad
core
/cl
ad
core
core
core
/cl
ad
wavel
ength
range
[µm
]4−
18
4−
16
4−
16
2−
18
3−
18
cut-
off
wavel
ength
[µm
]co
re/cl
addin
gdia
met
er[µ
m]
300/500
to900/1000
200/300
to860/1000
300−
1000
750×
750a
1000×
1000a
900/1000
core
refr
act
ion
index
2.1
52.1
02.1
02.2
02.2
0co
ating
mate
rial
PE
EK
(Poly
Eth
erE
ther
Ket
one)
poly
carb
onate
or
Tef
zel
poly
carb
onate
or
Tef
zel
min
imum
ben
din
gra
diu
s10×
FD
b100×
FD
b100×
FD
b10×
FD
b10×
FD
b
oper
ating
tem
per
atu
rera
nge
[◦C
]−
270
to140
−60
to110
−60
to110
ther
malex
pansi
on
coeffi
cien
t[1
0−
7/K
]th
erm
o-o
pti
cco
effici
ent
[10−
5/K
]te
nsi
lest
rength
[MPa]
>100
100
100
>110
>110
lase
rdam
age
thre
shold
[kW
/cm
2]
12d
10d
10d
12d
num
eric
alaper
ture
0.2
5e
0.1
3−
0.3
5e
0.5
e<
0.4
2c
<0.2
6c
fiber
att
enuation
@w
avel
ength
s[d
B/m
]@
[µm
]0.1−
0.5
@10.6
<0.5
@(9−
12.5
)f
<1
@(5−
13)f
<0.6
@3.5
<0.3
@5
<0.2
@10.6
<1
@3.5
<0.6
@5
0.1−
0.3
@10.6
asq
uare
bFD
...fi
ber
dia
met
ercif
fiber
length
isgre
ate
rth
an
2m
dcw
CO
2Lase
reeff
ecti
ve
NA
f acc
ord
ing
todia
gra
min
data
shee
t
CHAPTER 3. MARKET SURVEY 25
3.3.4 Other IR fibersty
pe
Ger
manate
single
cryst
alfiber
hollow
waveg
uid
ehollow
waveg
uid
ehollow
waveg
uid
epro
duct
HP
Fib
ersa
pphir
eopti
cal
fiber
HW
EA
HW
CA
Hitach
ifiber
mate
rial
GeO
2Sapphir
ehollow
silica
waveg
uid
eE
rYA
Ghollow
silica
waveg
uid
eC
O2
hollow
silica
waveg
uid
eco
mpany
Infr
are
dFib
erSyst
ems
Photr
an
LLC
Poly
mic
roTec
hnolo
gie
sPoly
mic
roTec
hnolo
gie
sH
itach
iC
able
data
shee
tin
subse
ctio
nA
.13
A.1
1A
.8A
.8A
.9st
ruct
ure
core
/cl
ad
core
hollow
hollow
hollow
wavel
ength
range
[µm
]1−
3b
0.3−
32.9−
12
2.9−
12
3−
12
cut-
off
wavel
ength
[µm
]
core
/cl
addin
gdia
met
er[µ
m]
150/−
to700/−
150−
425
300−
1000
d300−
1000
d700d
core
refr
act
ion
index
coating
mate
rial
poly
imid
eacr
yla
teacr
yla
tem
inim
um
ben
din
gra
diu
s@
fiber
dia
met
er[m
m]@
[µm
]5
@150a
25
@400a
40
@500a
20
@150
30
@250
60
@325
80
@425
oper
ating
tem
per
atu
rera
nge
[C]
ther
malex
pansi
on
coeffi
cien
t[1
0−
7/K
]th
erm
o-o
pti
cco
effici
ent
[10−
5/K
]te
nsi
lest
rength
[MPa]
2800
lase
rdam
age
thre
shold
[W]
20c
1000
@10.6
µm
num
eric
alaper
ture
0.2
5≥
0.3
fiber
att
enuation
@w
avel
ength
s[d
B/m
]@
[µm
]0.7
@2.9
4≤
1@
2.9
61e−
2f@
2.9
60.5
e−
2.0
f@
10.6
<1.5
@(4
.5−
5.8
)<
2.5
@(7−
12)g
aco
redia
met
erbacc
ord
ing
todia
gra
min
data
shee
tc@
10
Hz
din
ner
core
dia
met
ere1000
µm
inner
core
dia
met
erf 3
00
µm
inner
core
dia
met
ergm
easu
red
wit
hin
coher
ent
light
(<0.4
8dB
/m
for
CO
2la
ser)
CHAPTER 3. MARKET SURVEY 26
3.3.5 Standard single mode telecommunication fibers and photonic crystalfibers for 1.5 µm
pro
duct
SM
F-2
8e
Sin
gle
mode
Opti
-ca
lFib
er09/125
AllW
aveF
iber
hollow
core
photo
nic
bandgap
fiber
HC
-1550-0
2
mate
rial
Silic
aSilic
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mpany
Corn
ing
j-fiber
ofs
Cry
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reA
/S
data
shee
tin
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ruct
ure
core
/cl
ad
core
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core
/cl
ad
mic
rost
ruct
ure
dw
avel
ength
range
[µm
]1.4
5−
1.6
5cu
t-off
wavel
ength
[µm
]1.2
61.1
9−
1.3
31.2
6
core
/cl
addin
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met
er[µ
m]
9/125
9/125
9/125
10.9
b
core
refr
act
ion
index
1.4
7a
1.4
7a
coating
mate
rial
min
imum
ben
din
gra
diu
s@
fiber
dia
met
eroper
ating
tem
per
atu
rera
nge
[◦C
]−
60
to85
−60
to85
−60
to85
ther
malex
pansi
on
coeffi
cien
t[1
0−
7/K
]th
erm
o-o
pti
cco
effici
ent
[10−
5/K
]te
nsi
lest
rength
[MPa]
700
700
700
lase
rdam
age
thre
shold
num
eric
alaper
ture
0.1
40.1
2fiber
att
enuation
@w
avel
ength
s[d
B/km
]@
[µm
]≤
0.3
5@
1.3
1≤
0.2
0@
.155
≤0.3
7@
1.3
1≤
0.2
4@
1.5
5≤
0.3
4@
1.3
1≤
0.2
1@
1.5
5≤
100
@(1
.45-1
.65)
aeff
ecti
ve
gro
up
index
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bin
ner
core
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met
er
Chapter 4
Measurement methods
In this chapter measurement methods for the following fiber-parameters are described:
• Attenuation vs. wavelength
• Attenuation vs. bending radius
• Minimum bending radius
• Cut-off wavelength
• Mode field diameter
• Effective numerical aperture
• Output divergence angle
• Coupling efficiency
• Chromatic dispersion
• Temperature coefficient of optical length
• Coefficient of elasticity
When selecting measurement methods I paid special attention to the feasibility of performingthe experiments with the equipment available in the optical labaratory of the Institute ofCommunications and Radio-Frequency Engineering.
4.1 Attenuation vs. wavelength
Attenuation of fibers can be characterized by the attenuation-coefficient α(λ), which gives theattenuation per unit length [dB/m], as:
P (z) = P (0) 10−αz
10 , (4.1)
where P (0) is the power directly at the beginning of the fiber and P (z) is the power at thelength z of the fiber.
27
CHAPTER 4. MEASUREMENT METHODS 28
The attenuation coefficient α is not defined for the total transmitted power, but for thepower carried by a certain mode. In general, different modes experience different attenuationcoefficients. Therefore, and due to mode-coupling, the attenuation coefficient depends onthe fiber-length z. However, after a certain fiber-length, a steady-state or equilibrium modedistribution (EMD) is established, which means that the ratio of power carried by the eachmode relative to a reference mode, no longer depends on the fiber-length z.
Provided such an EMD can be obtained, the loss-coefficient α of the total transmittedpower can be measured [16]. A steady-state distribution emerges after a certain fiber-length,either when the power carried by higher order modes is attenuated to a negligible extent(because of the higher α for these modes) or due to mode coupling, if present in considerablestrength. Since the test fibers are very short (a few meters), this is not feasible. There aretwo methods for obtaining an EMD in short fiber pieces:
• In the mechanical method an EMD is established by enforcing strong mode-coupling withmode-scramblers or by using mode filters.
• The optical method is based on a limited launch numerical aperture, which means tocreate an input-beam, which fills only 70% of the core diameter and 70% of the numericalaperture of the fiber, so that the excitation of higher-order modes, leaky modes, andcladding modes is avoided.
The optical method suits best for the measurement of, usually short, IR-fibers, due tocertain limitations of the mechanical method in measurement of short fibers.
Attenuation measurement of singlemode fibers can be done by the well known cut-backtechnique, whereas the attenuation coefficient of multimode fibers can be measured best bythe taper based technique, where a hollow glass taper is used to create an EMD in the fiberunder test.
4.1.1 Cut-back technique
The cut-back technique is the reference test method for attenuation measurement recom-mended by the ITU [17]. It is preferable for attenuation measurement of singlemode fibers.
First step is to measure the output-power of the fiber P2. Then the fiber is cut to thecut-back point (which could be 2m from the launching point, for instance), and the output-power P1 at the cut-back point is measured, without changing the launching conditions. Sothe measurement is independent from the launching conditions. The attenuation coefficient αcan then be calculated as
α =10z
logP1
P2, (4.2)
where z is the length fiber piece cut off. The measurement can be done either for some specificwavelengths or over a wavelength-range. Figure 4.1 shows a measurement-setup for measuringα over a wavelength-range. The wavelength is selected by a monochromator. The signal ismodulated and a chopper is used, together with a lock-in amplifier, to improve the signal tonoise ratio. By coupling with a fiber or by a suitable system of optics it can be assured thatonly the fundamental mode is excited in the fiber. The propagation of higher-order modesthrough the cut-back length, is prevented by by a mode filter (higher-order modes can beremoved by a bend of the fiber, for example), while cladding modes are removed by a claddingmode stripper. The measurement should be done at the same temperature for all wavelengths.
CHAPTER 4. MEASUREMENT METHODS 29
Figure 4.1: Measurement setup for the cut-back method (from [17]).
4.1.2 Taper-based technique
The following is based on the article: “Attenuation Measurement of Infrared Optical Fibersby Use of a Hollow-Taper-Based Coupling Method” by Ilko K. Ilev et. al. [18]. In the measure-
Figure 4.2: Measurement setup for the taper-based technique (from [18]).
ment setup shown in Figure 4.2, the optical method is used to create an EMD-state and theattenuation coefficient is determined through power measurements in front of the input-endand behind the output-end of the fiber. In this setup a hollow taper is used, due to certainadvantages, as explained in the following.
The taper is made of Pyrex-glass with 3.5 mm input diameter, and 250µm output diam-eter, and a length of 120 mm. This ensures a cone angle of less than 1◦, so that grazingincidence is achieved. Therefore, reflectance coefficients are very high (close to 100%), andalso wavelength-independent, so that measurements can be performed over a wide wavelength-range. In contrast to a conventional lens there are no problems in finding the optimum point
CHAPTER 4. MEASUREMENT METHODS 30
for coupling in.
Figure 4.3: Intensity distribution at the input (a) and at the output (b) of the taper (from [18]).
The taper has a very low output numerical aperture (about 0.033) and its output diametershould be chosen smaller than the fiber core, to satisfy the conditions for a limited launchnumerical aperture. Furthermore, the taper forms a smooth, Gaussian-shaped, laser beamprofile (inside the taper occurs an intensive conversion of higher order modes into leaky modesbecause of the grazing incidence). Figure 4.3 shows the measured intensity distribution at theinput and at the output of the taper.
Altogether, the use of the taper ensures that lower-order modes are excited predominately,and thus a proper EMD-state is achieved. In order to confirm this, Figure 4.4 shows thefar-field intensity distributions measured after a 1m hollow fiber, using taper-to-fiber couplingand lens-to-fiber coupling. The output-intensity after taper-to-fiber coupling shows low-ordermodes around the fiber-axis, while the output-intensity after fiber-to-lens coupling is strongmultimodal.
Figure 4.4: Far-field intensity distributions measured after a 1 m hollow fiber, using taper-to-fiber coupling (a) and lens-to-fiber coupling (CaF2-lens, focal length f=100 mm) (b) (from [18]).
The attenuation coefficient can be calculated after measuring the power P0 at the taperoutput, and the power at the fiber output P1, as:
α =10z
logP0
P1(4.3)
A broadband, tunable laser-source has to be used to measure the attenuation coefficient independence on the wavelength. If the attenuation of solid-core fibers is measured, a correction
CHAPTER 4. MEASUREMENT METHODS 31
for the Fresnel-reflections R at both fiber-ends has to be done. For that purpose the Fresnel-relation (see Section 2.2.3) can be used (n gives the index of refraction of the fiber):
R =(
n− 1n + 1
)2
(4.4)
If the fiber is sufficient long, a cut-back measurement can be done instead of this correction.For measurements made with a fluoride-glass fiber with a core diameter 250 µm, a length
of 1 m, and an attenuation of about 1 dB/m, the difference of the attenuation-coefficient mea-sured with the conventional cutback-method, and the attenuation-coefficient measured withthe taper-based method was as low as 0.05 dB/m.
4.2 Attenuation vs. bending radius
The bending-induced attenuation can be determined as follows: First the power P1 at theoutput-end of the straight fiber is measured. Then a part of the fiber with the length Lw iswound up on a cylinder with the radius r0 and the power P2 is measured at the output-end ofthe fiber. The bending-induced attenuation in [dB/m] is then
αB(r0) =10Lw
logP1
P2. (4.5)
A diagram attenuation vs. bending can be obtained by using several cylinders with differentdiameters and measuring αB for each value of r0.
4.3 Minimum bending radius
The minimum bending radius of a fiber can be determined using the setup shown in Figure4.5. The distance D, between the two face-plates, is slowly decreased, until the fiber breaks.The breaking-point Dbreak could be determined by use of an acoustic sensor. Since the fiber is
Figure 4.5: Schematic diagramm of the bending technique for breaking fibers (from [19]).
CHAPTER 4. MEASUREMENT METHODS 32
not bent to a semi-circle by this device, the bending radius at the breaking-point Rbreak (thispoint is exact between the two face-plates, at D/2), is less than Dbreak/2. It can be calculatedfrom [19].
Rbreak =1
1.198Dbreak − d
2, (4.6)
where d is the overall fiber diameter (including any coating material). Because the strengthof the fiber is not distributed uniformly over the fiber-length (due to material imperfections),a series of measurements should be done, followed by a statistical evaluation of the obtainedresults.
4.4 Cut-off wavelength
The cut-off wavelength λc depends not only on fiber geometry and refractive indices of coreand cladding, but also on length, bending, and mechanical stress of the fiber. With respectto these facts, cut-off wavelength is defined as the wavelength, where the power propagatingthrough the fiber is by 0.1 dB higher than the power transported by the fundamental mode, ifthe fiber is 2 m long and has a loop with a radius of some 140 mm [17].
4.4.1 Transmitted power technique
Assuming that the same power of the LP01 mode and of the LP11 mode is coupled into afiber, the power Ptest(λ), measured at the output of this fiber, will decrease significantly if thewavelength of the light goes beyond λc, because the LP11 mode can only propagate for λ ≤ λc.In the transmitted power technique the cut-off wavelength is determined from that change ofPtest(λ).
In order to remove the influence of the wavelength-dependent attenuation of the fiber onthe determination of λc, the power Ptest(λ), measured at the output-end of the fiber undertest, is referred to the power Pref(λ), measured at the output-end of a reference fiber, as
R(λ) =Ptest(λ)Pref(λ)
. (4.7)
The testfiber should have a length of 2 m, and a loop with a radius of 140 mm. As areference fiber either the same fiber with an additional loop (single bend attenuation), or amultimode fiber (power-step) can be used (see Figure 4.6).
Single bend attenuation
Within the single bend attenuation method the reference power Pref(λ) is measured as afunction of the wavelength at the output-end of the testfiber, in which an additional loop wasinserted. The radius r of this loop has to be small enough to ensure, that the power intensitytransmitted by the LP11 mode is radiated off, so that only the fundamental mode LP01 canpropagate in the reference fiber. At wavelengths near λc, R(λ) gives the ratio of the powertransmitted over the testfiber (i.e. the power transmitted by the LP01 mode for λ > λc, andby the LP01 mode and the LP11 mode for λ ≤ λc) to the power transmitted over the referencefiber (that is the power transmitted by the fundamental mode LP01). The cut-off wavelengthcan then be determined as the lowest wavelength, for which R(λ) = 0.1 dB (see Figure 4.7).Figure 4.8 shows that the exact value of the loop radius r does not affect the determinationof λc.
CHAPTER 4. MEASUREMENT METHODS 33
claddingmode stripper
launching system PD
testP
refP
refP
claddingmode stripper
launching system PD
(b)
multimode fiber
claddingmode stripper
launching system PD
loopadditional
(a)testfiber
testfiber
Figure 4.6: Measurement setup: Single bend attenuation (a), power step (b) (from [20]).
The measurement of a Fluoride fiber is reported in [22]. The intensity P1 has been measuredfrom the straight fiber, and Pref has been measured from the same fiber having a loop withr = 40mm.
The advantage of the single bend attenuation method is that there is no change in couplingbetween the two measurements.
Power step
In the power step method Pref(λ) is measured at the output-end of a multimode fiber, in orderthat both, the LP01 mode and the LP11 mode can propagate in the reference fiber [21]. Thespectral attenuation characteristic of this fiber should be similar to that of the testfiber. Atwavelengths near λc, R(λ) gives the ratio of the power transmitted over the testfiber (i.e. thepower transmitted by the LP01 mode for λ > λc, and by the LP01 mode and the LP11 modefor λ ≤ λc) to the power transmitted over the reference fiber (that is the power transmittedby the LP01 mode and the LP11 mode). Cut-off wavelength can then be determined as thelowest wavelength, where R(λ) is 0.1 dB above its minimum value (see Figure 4.9) [17].
Measurement setup
The wavelength-range of the light source has to be large enough for cut-off wavelength deter-mination, and the linewidth should not extend 10 nm (FWHM). The signal to noise ratio canbe improved by modulating the source in combination with a lock-in amplifier. The couplingshould ensure that the same amount of power is carried by the LP01 mode and the LP11 mode.This could be done by coupling in with a multimode fiber, or by coupling in with a large spotsize and numerical aperture [17]. If the power step method is used, leaky modes should beavoided, because they can induce ripples in R(λ), and thus complicate the determination ofthe cut-off wavelength.
CHAPTER 4. MEASUREMENT METHODS 34
Figure 4.7: R(λ) for r = 30mm (from [21]).
Figure 4.8: R(λ) for r=10, 20, 30, 50mm (from [21]).
4.5 Mode field diameter
The mode field diameter (MFD) characterizes propagation properties of singlemode fibers,as are, e.g., loss due to macrobendings, microbendings, or connectors. Additionally, cut-offwavelength or chromatic dispersion can be determined if the spectral behavior of the MFD isknown. The mode field diameter can be determined from a scan of the near-field or far-field,of the light exciting the fiber, or from several measurements of the far-field power behind acircular aperture (located behind the output-end of the fiber) with different diameters at eachmeasurement (variable aperture technique).
4.5.1 Theoretical background
The MFD can be determined either in the near-field or in the far-field (see Figure 4.10). The
CHAPTER 4. MEASUREMENT METHODS 35
Figure 4.9: Power Step Method: R(λ) (from [17]).
R
0
P
0’r
near−field planefar−field plane
zθ
Figure 4.10: Near- and far-field geometries (from [23]).
near-field MFD, dn, can be calculated according to the Petermann I definition
dn = 2√
2
√√√√√√√∞∫0
r3 dr
∞∫0
E2(r) r dr
, (4.8)
where E2(r) gives the radial intensity distribution in the near-field, whereas the far-field MFD,df, can be calculated using Petermann II definition
df =2√
2wff
, with wff =
√√√√√√√∞∫0
F 2(p) p3 dp
∞∫0
F 2(p) p dp
, (4.9)
CHAPTER 4. MEASUREMENT METHODS 36
where p = k sin(θ) with k = 2πλ , and F 2(p) gives the intensity distribution in the far-field [23].
The far-field MFD can be calculated from F 2(θ), after substituting p in (4.9):
df = 2√
2π
λ
√√√√√√√√√π2∫0
F 2(θ) sin3(θ) cos(θ)dθ
π2∫0
F 2(θ) sin(θ) cos(θ)dθ
. (4.10)
The intensity in the far-field F 2(p) can be derived from the near-field intensity E2(r) byuse of the Hankel transform1. Therefore, the near-field MFD can be calculated from theintensity-distribution in the far-field (4.11), and the far-field MFD can be calculated from theintensity-distribution in the near-field (4.12).
dn = 2√
2
√√√√√√√∞∫0
[dF (p)
dp
]2p dp
∞∫0
F 2(p) p dp
(4.11) df = 2√
2
√√√√√√√∞∫0
E2(r) r dr
∞∫0
[dE(r)
dr
]2r dr
(4.12)
The near-field MFD is at least equal the far-field MFD: df ≤ dn. For Gaussian intensitydistributions2 both MFD definitions are equal df = dn = 2
√2w, and at r = dn
2 the intensitydrops to 1
e2 of its maximum [23].It is important for the measurement of the MFD, that only the fundamental-mode is
propagating inside the fiber. This can be guaranteed by a mode-filter, or by a sufficient smallloop of the fiber.
4.5.2 Far-field scan
The far-field intensity F 2(θ) as a function of θ is scanned by a flexible detector (see Figure4.11), and the MFD can then be calculated using (4.10). The detector should be moved in
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LD
filtercladding modefiber
R
θ
photodiode
Figure 4.11: Measurement setup: Far-field scan (from [23]).
fixed steps not greater than 0.5◦ and the dynamic range of the measurement has to be at least1F (p) =
∫∞0
E(r)J0(rp)rdr = 1√2π
H{E}(p)
2E(r, w) = Ae− r2
2w2 .
CHAPTER 4. MEASUREMENT METHODS 37
50 dB. The angular region in the far-field, covered by the active area of the detector, must notbe too large. That can be assured by placing the detector at a distance R from the fiber endgreater than 40 d b
λ , where d is the expected MFD, and b is the diameter of the active area ofthe detector [17].
4.5.3 Near-field scan
The near-field intensity E2(r) at the output-end of the fiber is magnified by a suitable lens,and then scanned by a flexible detector (see Figure 4.12). The far-field MFD can be calculatedthrough (4.12). The active area of the detector must not be too large and the detector has tobe adjustable precisely. Furthermore, the aperture of the lens should be at least 0.5 to avoidspatial cutoffs [17].
����������������������������������������������������������������������������������������������������
����������������������������������������������������������������������������������������������������
������������������������������������������������������������������������������������������������������������������������������������������������������������������
������������������������������������������������������������������������������������������������������������������������������������������������������������������
LED
modestripper
fibreunder
test
40 xOBJ Scanning
fibre
detector
Figure 4.12: Measurement setup: Near-field scan (from [23]).
4.5.4 Variable aperture technique
In the variable aperture technique the far-field power P (θ ≤ θ0) of the light exiting the fiberis measured for the circular area θ ≤ θ0, where θ is the angle between the light-beam and thefiber axis (see Figure 4.13). The measurement of P (θ ≤ θ0) is performed by placing a circular
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������������
��������������������
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���������
������������
������������
������������
������
������
������������
� � �
���
D 0
P
x
zθ 0
Figure 4.13: Variable Aperture Technique (from [23]).
aperture with the radius x = D tan θ0 in the distance D from the output-end of the fiber, and
CHAPTER 4. MEASUREMENT METHODS 38
focusing the light passing the aperture onto a detector (see Figure 4.13). The center of theaperture has to be located on the fiber-axis z.
The measurement is performed for at least 12 different apertures corresponding to anglesin the range of 0.02 ≤ sin θ0 ≤ 0.25 (≤ 0.4 for dispersion shifted fibers). It is not necessary toperform measurements for higher values of θ0, since the intensity of the light is very low forhigher values of θ.
The MFD can then be calculated as
df =λ
πD
{∫ ∞
0
[1− P (x)
Pmax
]x
(x2 + D2)2dx
}− 12
, (4.13)
where P (x) = P (θ ≤ θ0) and Pmax is the power measured from the setup with the largestaperture used in the measurements. Equation (4.13) can be obtained by integrating (4.10)and assuming small angles θ [17].
4.6 Effective numerical aperture
The effective numerical aperture NA is defined as the sine of the angle θ, at which the far-field intensity of the light exciting the fiber has dropped to 5% of its maximum value (seeFigure 4.14). It can be determined by the far-field method. First step is to aquire the far-field
Figure 4.14: Determination of the numerical aperture from far-field radiation pattern (from[24]).
intensity pattern I(θ) of the fiber output end as a function of θ (see Section 4.5.2). The fibershould be 2 m long, and excited by an overfilled launch in order excite all possible guidedmodes. This means, that the launch spot intensity is uniformly distributed over the core, andthe launch numerical aperture exceeds the numerical aperture of the fiber [24]. The numericalaperture can then be calculated as
NA = sin∆θ
2, (4.14)
where ∆θ is the angular region where the output intensity is higher than 5% of its maximumvalue (see Figure 4.14).
The theoretical numerical aperture could also be determined from the measured index ofrefraction profile of the fiber, as described in [24].
CHAPTER 4. MEASUREMENT METHODS 39
4.7 Output divergence angle
The output divergence angle ε characterizes the diffraction of light leaving a fiber. The outputdivergence angle of a singlemode fiber can be determined as follows: The radial distances r1
and r2, at which the light-intensity drops to 1/e2 of its maximum value, are measured at the
fiberε
r 2
r 1
L2
L1
Figure 4.15: Measurement of the output divergence angle.
distances L1 and L2 from the fiber-end, using the results of a far-field scan (see section 4.5.2).Then the output divergence angle ε can be calculated from
tan ε =r2 − r1
L2 − L1. (4.15)
It is essential that only the fundamental mode propagates in the fiber. This can be realizedby means of a fiber loop.
If the mode field diameter df is known, only one measurement (r1 at the distance L1 fromthe fiber-end) has to be performed, and ε can be calculated from
tan ε =r1 −
df
2
L1. (4.16)
The output divergence angle of a multimode fiber can be calculated from the numericalaperture NA of the fiber (see Section 4.6), as
ε = arcsin(NA) . (4.17)
4.8 Coupling efficiency
The coupling efficiency can be determined by making two measurements: First the power P1
of the light (this can be a free space beam or light guided in a fiber) that should be coupledin, is measured. Then the light is coupled into the fiber and the power P2 at the output-endof this fiber is measured. It has to be assured that neither cladding modes nor leaky modescan propagate as far as to the output-end of the fiber. This could be done by a cladding
CHAPTER 4. MEASUREMENT METHODS 40
mode stripper and a fiber loop (with a diameter small enough to remove leaky modes andlarge enough not to increase the fiber’s attenuation). When taking the influence of the fiberattenuation α, given in [dB/m], into account, the coupling efficiency reads
η = 10αLfib/10 P2
P1, (4.18)
where Lfib is the length of the fiber. In order to keep this influence small the piece of fiberused for this measurement should be as short as possible. Since the coupling efficiency changessignificantly with wavelength, the measurements have to be performed separately for desiredspecific wavelengths or, more general, over a wavelength-range.
4.9 Chromatic dispersion
Method Principledirect techniques turning point analysis
non-Fourier-transform center wavelength against air-path lengthmethods indirect techniques shift of center wavelength for increase of op-
tical path-lengthFourier-transform Fourier-transformation of the interferogrammethods
Table 4.1: Overview of measurement techniques of chromatic dispersion [25,26]
Chromatic dispersion of fibers can be measured with various methods. However, interfer-ometric methods, where the fiber is in one the arms of the interferometer, have to be used toobtain accurate results if only very short pieces of fiber are available (e.g. a few meter), as itis the case for most of the fibers designed for transmitting light with wavelengths above 2 µm.These methods can be divided into non-Fourier-transform methods and Fourier-transformmethods (see Table 4.9). In non-Fourier-transform methods the output-intensity of the in-terferometer is measured at several wavelengths, either at constant or at variable differencesbetween air-path-length and fiber-path-length. A tunable laser source or a monochromatoris necessary to perform wavelength dependent measurements. In Fourier-transform methods,measurements are done over a broad spectral range, without selecting discrete wavelengths,for varying differences between air-path-length and fiber-path-length.
Chromatic dispersion D(λ) and dispersion slope S(λ) coefficients of the fiber can be deter-mined from the effective group index of the fiber ng(λ), from the effective index of refractionof the fiber n(λ), as well as from the group propagation time τfib(λ) in the fiber, as [27,25]:
D(λ) =dng(λ)c dλ
=1lfib
dτfib(λ)dλ
= −λ
c
d2n(λ)dλ2
, (4.19)
S(λ) =dD(λ)
dλ= −λ
c
d3n(λ)dλ3
+1λ
D(λ) . (4.20)
4.9.1 Non-Fourier-transform methods
The following text is based on the article “Interferometric Chromatic Dispersion Measurementson Short Lengths of Monomode Optical Fiber” by P. A. Merritt et al. [25].
CHAPTER 4. MEASUREMENT METHODS 41
Within this measurement method the light of a source is split-up into two beams, whichthen propagate either through the air-arm or through the fiber-arm of a Mach-Zehnder in-terferometer (see Figure 4.16). After superimposing the two beams, the intensity Iout(λ) isobtained at the detector. It is significantly depending on the wavelength of the light, as wellas on the difference in optical path length between the air-arm and the fiber-arm. Figure4.17 shows Iout(λ) at a certain optical path length difference as a function of the wavelength.Chromatic dispersion can be extracted from measurements of Iout(λ), either at a constantoptical path length difference (direct techniques), or at varying optical path length differences(indirect techniques).
Theoretical background
The principle configuration of the interferometer is shown in Figure 4.16. One arm of theinterferometer contains the device under test, i. e. a short fiber piece with length lfib about1 m, of which the chromatic dispersion is measured, while the other path leads through air.
The interference fringes shown in Figure 4.17, from which the chromatic dispersion willbe extracted, are a consequence of different propagation properties in the air and in the fiber.There are also air-paths in the fiber-arm, lair, fiber-arm, which have to be subtracted from thelength of the air-arm, in order to obtain the path-length, corresponding to the fiber-pathlength, and therefore, contributing to the interference fringes:
lair = lair-arm − lair, fiber-arm . (4.21)
The difference in optical length between the fiber-path and the air-path, OPD (optical pathlength difference), is then
OPD = lair − n(λ) lfib . (4.22)
At a fixed wavelength λ, a change in air-path length of ∆L, leads to a change in optical pathlength difference of ∆OPD.
fibercoupler
variableair path
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detectorbroadbandsource
mono−chromatortestfiber
air−arm
fiber−arm
Figure 4.16: Simplified measurement setup with a Mach-Zehnder Interferometer [25].
The light emitted by the source is split up by a beamsplitter, then propagates throughthe two arms, and is finally combined by a second beamsplitter. Superimposing the intensityof the fiber-path Ifib(λ) and of the air-path Iair(λ), we obtain the output-intensity of theinterferometer
Iout(λ) = Iair(λ) + Ifib(λ)− 2√
Iair(λ) Ifib(λ) cos[2π
λ(lair − lfib n(λ))
]. (4.23)
CHAPTER 4. MEASUREMENT METHODS 42
Expanding for the effective index of refraction of the fiber a taylor series around λ
n(λ) = n + (λ− λ)dn
dλ
∣∣∣∣λ
+(λ− λ)2
2!d2n
dλ2
∣∣∣∣λ
+(λ− λ)3
3!d3n
dλ3
∣∣∣∣λ
+ . . . , (4.24)
we get
Iout(λ) = Iair(λ) + Ifib(λ)− 2√
Iair(λ) Ifib(λ) cos
[2π
λ
(lair − lfib
(n− λ
dn
dλ
∣∣∣∣λ
))−
−2π lfib
(dn
dλ
∣∣∣∣λ
+(λ− λ)2
2!λd2n
dλ2
∣∣∣∣λ
+(λ− λ)3
3!λd3n
dλ3
∣∣∣∣λ
+ . . .
)]. (4.25)
Here λ is the so called center-wavelength, at which the group propagation time τ is equalin both arms of the interferometer. This is equivalent to setting zero the first term inside thecosine-function of (4.25):
τair − τfib = lair1c− lfib
1c
(n− λ
dn
dλ
∣∣∣∣λ
)︸ ︷︷ ︸
ng(λ)
= 0 , (4.26)
where c is the velocity of light in vacuum. Around this wavelength, Iout(λ) is cosinusoidalwith decreasing cycle duration, moving both above and below λ. A schematic representationis shown in Figure 4.17. The envelope of this function is due to the spectral characteristic ofthe source. Techniques for extracting dispersion coefficient and slope coefficient from these
λ1 λ2 λ λ3 λ4
I out
λ
Figure 4.17: Schematic representation of Iout around λ (from [25]).
interferometric fringes can be divided into direct and indirect techniques. Direct techniques usedata measured at a constant optical path length difference (OPD), whereas indirect techniquesrequire data measured at varying optical path length differences.
Direct techniques
Chromatic dispersion can be obtained by determining two wavelengths λ1 and λ2 of minimaof Iout(λ), which are separated by M intensity cycles of Iout(λ), and which are located on the
CHAPTER 4. MEASUREMENT METHODS 43
same side of λ (turning point analysis; see Figure 4.17). Consequently, 2πM is added to theargument of the cosine in (4.25), and (4.27) can be obtained by subtracting the argument ofthe cosine in Iout(λ2) from the argument of the cosine in Iout(λ1)3:[
(λ1 − λ)2
λ1− (λ2 − λ)2
λ2
]12!
d2n
dλ2
∣∣∣∣λ︸ ︷︷ ︸
A
+
[(λ1 − λ)3
λ1− (λ2 − λ)3
λ2
]13!
d3n
dλ3
∣∣∣∣λ︸ ︷︷ ︸
B
=2πM
lfib. (4.27)
Chromatic fiber dispersion is characterized by (4.19) and part A of (4.27). It can be calculatedeither directly from (4.27) by neglecting part B, and thus assuming S(λ)|
λ� D(λ)|
λ, or more
accurate by determining another two wavelengths of minima of Iout(λ), which yields anotherequation of the form of (4.27). We then obtain two equations with two unknown variables,from which D(λ) and S(λ) can be calculated by employing (4.19) and (4.20).
To determine the wavelengths of the minima of Iout(λ) the wavelength-spectra should besmoothed to remove noise, and then differentiated.
Indirect techniques
• Chromatic fiber dispersion can be determined by measuring the center-wavelength λ asthe air-path length is varied (l′air = lair +∆lair). Following (4.26), the group propagationtime in the fiber τfib at the wavelength λ = λ reads
τfib(λ) = τair =1c(lair + ∆lair) . (4.28)
The chromatic dispersion coefficient of the fiber can be calculated as (cf. (4.19))
D(λ) =1lfib
dτfib(λ)
dλ. (4.29)
• The chromatic dispersion coefficient can be obtained for a specific wavelength (λ =λ0 + ∆λ/2), by measuring the shift of the center-wavelength λ, after an incrementalincrease of the optical path length difference ∆OPD. Since the change of the grouppropagation time of the fiber τfib = ∆OPD/c, the chromatic dispersion coefficient of thefiber is given by (see (4.19))
D
(λ0 +
∆λ
2
)=
1lfib
∆τ
∆λ=
1lfib
∆OPD
c ∆λ. (4.30)
Resolution
The following resolutions can be obtained by extrapolating the values of fiber-pieces of 1mlength: Using the indirect technique of differentiating group delay data leads to a resolutionvalue of 2 ps/(nm·km). More accurate results are obtained using direct techniques. Turningpoint analysis gives a resolution of 0.8 ps/(nm·km).
Measurement setup
The setup is based on the Mach-Zehnder interferometer shown in Figure 4.16. Some additionalcomponents are necessary to allow for automatic measurements. The complete measurementsetup as suggested in [25] is shown in Figure 4.18.
3Here we assumed that the Taylor expansion is confined to the first three terms.
CHAPTER 4. MEASUREMENT METHODS 44
Figure 4.18: Measurement setup (from [25]). (P. . . polarizer, λ/4. . . quarter-waveplate,λ/2. . . half-waveplate, MS. . . mirror, BS. . . beamsplitter, GT. . . Glan-Thompson polarizer,IF. . . interference filter, OS. . . optical shutter, PZTM. . . piezoelectric translated mirror,APD. . . avalanche photodiode detector, SF. . . spatial filter, TF. . . test fiber)
A LED with full width half maximum bandwidth of 50 nm is used as a broadband lightsource. The output beam is spatially filtered by a singlemode fiber before entering the interfer-ometer. The beam exiting the interferometer passes a monochromator where the wavelengthis selected in 0.2 nm steps, and then the intensity is measured by an avalanche photodiode.Due to the low light level after the input fiber, synchronous detection is used to increase thesignal to noise ratio.
A HeNe-Laser beam is aligned coaxially to the LED beam for path-length stabilization,which is done by piezoelectric controlled mirror movement. An additional mirror togetherwith a shutter is used to measure the spectral profile of the LED simultaneously.
The measurement is performed over a wavelength range from 780−910 µm in 0.2 nm steps.
4.9.2 Fourier-transform methods
The description of the following method is based on the article: “Three Ways to Implement In-terferencial Techniques: Application to Measurements of Chromatic Dispersion, Birefringence,and Nonlinear Susceptibilities” by P.-L. Francois et al. [26].
The output-intensity, obtained by the experiment described in section 4.9.1, depends on thewavelength λ and the air-path length lair. In the following method, the intensity is measuredover the whole wavelength-range of the broadband source at once. From the measured interfer-ograms the chromatic dispersion of the fiber can be extracted by use of Fourier-transformation.
By integrating (4.23) over the whole frequency spectrum we obtain the proportion
Iout(lair) ∝∫ ∞
0R(ω) cos
[2π
λ(lair − lfib n(λ))
]dω . (4.31)
Source characteristic and transfer functions of the fiber-path and of the air-path are combined
CHAPTER 4. MEASUREMENT METHODS 45
in the real valued function R(ω). After substituting the argument of the cosine-function
2π
λ[lfib n(λ)− lair] = β(ω)lfib −
2π
λlair = β(ω)lfib −
ω
clair , (4.32)
where c is the velocity of light in vacuum and β = 2πλ n(λ) is the propagation constant of the
fundamental-mode in the fiber, we obtain
Iout(lair) ∝∫ ∞
0R(ω) cos
[β(ω)lfib −
ω
clair
]dω . (4.33)
Eventually, the phase of the cosine-function is also changed by effects like abberation. If thesephase-changes are not negligible, the substitution β(ω)lfib := β(ω)lfib + Φ(ω) has to be done4.
Since the fields arriving at the detector are real quantities, R(ω) is a symmetric functionand β(−ω) = −β∗(ω). Therefore, (4.33) can be written as
Iout(lair) ∝∫ ∞
−∞R(ω) ej[β(ω)lfib−ω
clair] dω , (4.34)
which is equivalent to the inverse Fourier-transform:
Iout(lair) ∝ F−1
{R(ω) ejβ(ω)lfib
}(lairc
). (4.35)
Therefore β(ω)lfib can be determined from the Fourier-transform of Iout(lair/c) up to an ad-ditive constant. The variations of the effective index of refraction n(λ) can then be obtainedfrom n(λ) = λ
2πβ(λ), and chromatic dispersion can be calculated as (of (4.19))
D(λ) = −λ
c
d2n(λ)dλ2
= −λ
c
d2
dλ2
[λ
2πβ
]= − λ
2πc
d2(λβ)dλ2
= (4.36)
= − λ
2πc
d
dλ
(β + λ
dβ
dλ
)= − λ
2πc
(2dβ
dλ+ λ
d2β
dλ2
).
Zero-dispersion wavelength corresponds to the inflexion point of the variations of the effectiveindex of refraction.
Measurement technique
The measurement setup is shown in Figure 4.19. The broadband source is realized by ahalogen lamp, and the subsequent filter ensures λ > 1.2 µm. A lock-in amplifier togetherwith a chopper is used to improve the signal-to-noise ratio. Lead-in fiber and mixing fiberare singlemode fibers. Even if several modes are transmitted over the test fiber, only thefundamental LP01 mode contributes to the interferences, because there is little transfer fromhigher order modes in the testfiber to the LP01 mode in the mixing fiber.
Iout(lair) is measured, while lair is changed in steps of 0.2 µm. Figure 4.20 shows measuredinterferograms for different types of fibers5.
The amplitude of the Fourier-transform of Iout(lair), and the variations of the effectiveindex of refraction, which is derived from the phase of the Fourier-transform of Iout(lair), areshown in Figure 4.21. The wavelength-region of interferences, and thus the region in which
CHAPTER 4. MEASUREMENT METHODS 46
amplifierlock−incomputer
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���������������������
���������������������
��������������������
detectorfiber
mixing halogen lamp
testfiberlead−infiber
chopper
couplerfiber
variableair path
Figure 4.19: Measurement setup [26].
0 50 100 150 200 0 200 400 600 800
SEGCOR fiber
0 200 400 600 800 1000
QC Fiber fluoride glass fiber
Variation of lair [ µm]
Figure 4.20: Measured interferograms of QC fiber, SEQCOR fiber, and fluoride glass fiber(from [26]).
1.6 1.8 2.01.80
4
8−5
effe
ctiv
e in
dex
0
2
4
0
2
4
6
1.31.3
Am
plitu
de
1.5 1.7
vari
atio
ns (1
0 )−5
1.5 1.7
Am
plitu
de
1.3 1.5 1.7
effe
ctiv
e in
dex
vari
atio
ns (1
0 )−5
1.3 1.5 1.7
Am
plitu
de
1.6 2.0
effe
ctiv
e in
dex
vari
atio
ns (1
0 )6
(c)Wavelength [µm]
-5
0
2
4
6
1.3
Wavelength [µm](b)
Wavelength [µm](a)
Figure 4.21: Amplitudes of the Fourier-transform of Iout(lair) and variations of the effectiveindex of refraction, derived from the phase of the Fourier-transform of Iout(lair), of QC fiber(a), SEQCOR fiber (b), and fluoride glass fiber (c) (from [26]).
chromatic dispersion can be determined, can be seen from these diagrams. A comparisonof the dispersion-spectra obtained with the Fourier-transform method, and the dispersion-spectra obtained from measurements with non-Fourier-transform methods (see [26]), is shownin Figure 4.22.
4The effects of aberrations of the optics on the phase are represented by Φ(ω); this substitution has to bedone in the functions derived from (4.33) too.
5dispersion-flattened (quadruply-clad) QC fiber, dispersion-shifted (segmented core) SEQCOR fiber, and afluoride glass fiber
CHAPTER 4. MEASUREMENT METHODS 47
1.4 1.6 1.8 2.0
fluoride fiberSEGCOR
QC
−20
−10
0
10
Dis
per
sion[ p
skm
nm
]
Wavelength [µm]
Figure 4.22: Comparison of the dispersion-spectra obtained with the Fourier-transform method(thick lines) and the dispersion-spectra obtained with mode delay measurements from theinterferogram-envelopes (thin lines) (from [26]).
A different measurement-setup for Fourier-transform measurements using fiber-couplersinstead of bulk optics is presented in [28].
4.10 Temperature coefficient of optical length
The following is based on the article: “Heterodyne Interferometric Measurement of the Thermo-Optic Coefficient of Single Mode Fiber” by S. Chang et al. [29].
In the described method the temperature of a fiber Fabry-Perot interferometer (FFPI),built up from the test-fiber, is varied, in order to determine the temperature coefficient ofoptical length 1
Ld(nL)
dT , from the temperature dependent output-signal and the wavelength ofthe source.
The authors of the article claim that measurements with the common used method of theangle of minimum deviation (AMD) [30] are only accurate to the order of 10−4 K−1, whereastemperature coefficients of optical length of fibers are about one or two decades lower, so thatthe described method has to be used in order to obtain accurate results.
The interferometer is fabricated from the fiber, of which the temperature coefficient ofoptical length shall be determined. Its length is 12 mm and the end-faces are coated withsingle layer TiO2, with a reflectivity of 3 − 4%. The interferometer is surrounded by a tube,in contact with a thermo-electric cooler for temperature control.
Figure 4.23 shows the measurement-setup. The light-source is a strained layer quantumwell DFB diode laser module, providing a stable output wavelength (1558 nm) with 0.8MHzline width. There is also an isolator integrated in this module. The laser is modulated by a veryweak rf-current, with a modulation frequency of ωm = 280 MHz, which yields a modulationindex β � 1. The spectrum of the obtained signal contains three components, which are thecarrier frequency ω0, and two side-band frequencies ω0 + ωm, and ω0 − ωm. The optical field
CHAPTER 4. MEASUREMENT METHODS 48
Figure 4.23: Setup for interferometric measurement of the thermo-optic coefficient (from [29]).
at the output of the laser diode is
E(t) ≈ E0
{J0(β)ejω0t + J1(β)ej(ω0+ωm)t + J−1(β)ej(ω0−ωm)t
}, (4.37)
where Jk(β) with k ε {0,±1} is the Bessel function. The signal propagates through a 2 × 2coupler, with 50% coupling ratio, into a Fabry-Perot interferometer sensor. Index matchingoil at the other output-end of the coupler ensures, that no light is reflected back from thatend-face.
The effect of the resonator on the signal is represented by the complex reflection functions
Tk(ωk) = e−δk−jϕk with ωk = ω0 + kωm, k = 0,±1 , (4.38)
where δk is the amplitude attenuation and ϕk is the optical phase shift at ωk. For β � 1 thesignal leaving the interferometer is
Er(t) ≈ E0
{T0(ω0)ejω0t + T1(ω1)
β
2ejω1t − T−1(ω−1)
β
2ejω−1t
}. (4.39)
Via the coupler the signal arrives at the photodetector, where the intensity is given by
I(t) ≈ E20eδ0β
{[e−δ1 cos(ϕ0 − ϕ1)− e−δ−1 cos(ϕ−1 − ϕ0)
]cos(ωmt)
+[e−δ−1 sin(ϕ−1 − ϕ0)− e−δ1 sin(ϕ0 − ϕ1)
]sin(ωmt)
}. (4.40)
The output of the photodetector is amplified, and filtered by a bandpass with center frequencyωm. Afterwards it is mixed with the signal modulating the source. The signal at the outputof the mixer is
V (t) ∝ E20eδ0β
{[e−δ1 cos(ϕ0 − ϕ1)− e−δ−1 cos(ϕ−1 − ϕ0)
]cos(ωmt) sin(ωmt)
+[e−δ−1 sin(ϕ−1 − ϕ0)− e−δ1 sin(ϕ0 − ϕ1)
]sin2(ωmt)
}. (4.41)
CHAPTER 4. MEASUREMENT METHODS 49
It is then filtered by a lowpass in order to obtain dc-signal related to the phase shift differencebetween the carrier and the side bands
V (ϕk, δk) ∝12E2
0 eδ0β[e−δ−1 sin(ϕ−1 − ϕ0)− e−δ1 sin(ϕ0 − ϕ1)
]. (4.42)
The amplitude attenuation and the phase shift caused by the interferometer are
e−δk =r√
(1− cos θk)2 + sin2 θk√(1− r2 cos θk)2 + (r2 sin θk)2
and (4.43)
ϕk = arctan[
sin θk
1− cos θk
]+ arctan
[r2 sin θk
1− r2 cos θk
]. (4.44)
The output signal V (ϕk, δk) becomes zero, if δ−1 = δ1 and sin(ϕ−1 − ϕ0) = sin(ϕ0 − ϕ1).This is the case, if the resonators resonance frequency is equal to the carrier frequency ω0.The phase shift θ of the signal after a round-trip in the resonator, and thus the resonancefrequency of the resonator, can be modified by changing the resonator temperature T , becausethe refractive index n as well as the resonator length L/2 is depending on the temperature:
θ =nLω
c= 2π
nL
λ. (4.45)
Both simulation and experimental results show that the output signal oscillates periodicallywith the temperature (see Figure 4.24). Differences between simulation and experimental
Figure 4.24: Output signal V (ϕk, δk) vs. temperature: The results of the theoretical simulationare shown by the line, and the experimental results are shown by dots (from [29]).
results arise from doping material differences in the simulation model and the measured fiber.During one oscillation period ∆T , the signal in the resonator experiences a 2π phase change,so that together with (4.45) the following equation is obtained:
d(nL)dT
∆T = λ0 . (4.46)
The obtained results have to be related to L, in order to make them independent of the usedresonator length and the temperature coefficient of optical length is
1L
d(nL)dT
∆T =1L
λ0 . (4.47)
CHAPTER 4. MEASUREMENT METHODS 50
The temperature coefficient of optical length can be calculated from the oscillation period ∆Tand the wavelength of the carrier λ0.
With a measured oscillation period of ∆T = 6.51 ◦C the temperature coefficient of opticallength is 9.92 · 10−6 K−1 for a Corning singlemode fiber with n = 1.4488. The temperaturecoefficient of optical length of a Amorphous Materials chalcogenide glass fiber, calculated fromdata provided by the manufacturer, is 9.58 · 10−5 K−1, and of a sapphire fiber, calculated fromdata from [3], is 2.3 · 10−5 K−1.
For measurements at higher wavelengths, as it is necessary for infrared fibers, the coatingof the resonator has to be changed.
4.11 Coeffiecient of elasticity
The coefficient of elasticity (Young’s modulus E) can be determined by a tensile test. Thetensile stress σ = F
A0, applied to fiber in axial direction, is continuously increased until the
fiber breaks, while the elongation ∆L of the fiber the fiber is measured. With the strain
ε =l − l0
l0=
∆l
l0(4.48)
of a fiber, a stress-strain diagram as shown in Figure 4.25 can be obtained [31]. The forceapplied to the fiber is given by F , while A0 and l0 are the original cross sectional area andlength of the fiber. If the applied stress is less than σE , it is proportional to the strain of the
Figure 4.25: Stress-strain curve (from [31])
fiber by the factor of E. Therefore Young‘s modulus can be calculated from the linear part ofthe diagram as
E =FA∆ll0
. (4.49)
Some coefficients of elasticity of infrared fibers are: ESapphire = 430 GPa, EFluoride =54 GPa, Echalcogenide = 21.5 GPa, and Esilver-halide = 0.14 GPa [3]. Therefore, applying 25% of
CHAPTER 4. MEASUREMENT METHODS 51
its tensile strength to a 1 m chalcogenide fiber (see Section 3.3.1) would result in an elongationof
∆l =25 MPa21.5 GPa
· 1 m = 0, 0012 m . (4.50)
Chapter 5
Outlook
With the data obtained from the market survey (see Chapter 3), the fibers which fit best tothe requirements of the applications described in Chapter 1 have been selected, and samplesof a few meter of each of those fibers have been bought.
The next step will be the verification of the characteristics provided by the vendors inthe datasheets and the measurement of the parameters which have not been specified by thevendors, using the measurement methods described in Chapter 4.
As a first measurement, the transmission and the output intensity distribution of a hollowglass taper for attenuation measurement of multimode fibers, as described in Section 4.1.2,has been determined.
52
Appendix A
Data sheets
A.1 IR Photonics: MID-infrared single mode fiber
53
APPENDIX A. DATA SHEETS 54
A.2 IR Photonics: MID-infrared multi mode fiber
APPENDIX A. DATA SHEETS 55
A.3 ARTPhotonics: CIR fiber
2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,00
200
400
600
800
1000
Atte
nuat
ion,
dB
/km
Wavelength, µm
CIR-fiber Chalcogenide IR-glass fiber
remote IR spectroscopy 1.5 - 6µm
flexible pyrometry & IR-imaging
Er:YAG-laser power delivery
Chalcogenide InfraRed (CIR-) glasses based on As-S-composition are the best for fiber optic in 2 – 6 µm range of spectra. Thereby CIR-fibers transmit IR-radiation in the gap between silica glass fibers (0.2 – 2.4µm) and Polycrystalline InfraRed (PIR-) fibers (4 – 18µm). CIR-Fibers are drawn in core-clad structure with double polymer coating and characterized by a low optical losses and high flexibility. The innovative glass purification process provides the attenuation spectra free from OH- absorption band at 3µm and thus it enables CIR-fibers to be used for Er:YAG laser power delivery
FEATURES •..... high transmittance from 2 µm up to 6 µm •..... suitable for Er:YAG - laser power delivery •..... optical losses 0.2 dB/m at 2 - 4 µm •..... double polymer coating for high flexibility •..... durable cables with SMA-connectors
APPLICATIONS Flexible delivery for Er:YAG - laser flexible IR-imaging systems remote non-contact pyrometry in the 200-600K range fiber probes for remote process IR - spectroscopy
FIBER SPECIFICATION Transmission range .................................1.5 - 6 µm Core/Clad structure .................................As2S3/As-S Core/Clad diameter .................................200-700 / 300-800 µm Numerical Aperture………………………..0.3 Core refractive index ...............................2.4 Protective coating ....................................Double polymer Ambient temperature range.....................280 – 400 K
Advanced Research &
Technology in
APPENDIX A. DATA SHEETS 56
A.4 ARTPhotonics: PIR fiber
€F® PIR - fibers Polycrystalline Core/Clad fiber for Mid-infrared spectrum (4-18µm) from a Silver Halide solid solution The development of specialty fibers for the Mid-Infrared region has resulted in a unique product – Core / Clad Polycrystalline Infra-Red (PIR-) fibers. PIR fibers are non-toxic, very flexible, transparent across a broad spectral region 4 –18 µm and capable of operating over the wide temperature range of −270 °C up to +140 °C. They are manufactured in a core/clad structure of superior quality from pure AgCl: AgBr solid solution crystals using an innovative vacuum extrusion method. They possess by no aging effect compared to an alternative bare core fiber. The range of €F®-PIR-fiber cables are available with a durable PEEK polymer jacket and terminations using either an SMA – type connector with a Ti or polymer ferrule or special one, manufactured on customer request. A wide variety of different optical coupling units can also be designed & fabricated for specialized customer requirements.
High transmittance from 4 µm up to 18 µm. 50 W.
st).
Suitable for CO2 - laser power delivery up to
4,0 6,0 8,0 10,0 12,0 14,0 16,00
500
1000
1500
2000
2500
Wavelength, µm
Atte
nuat
ion,
dB
/km
Low Attenuation at 10.6 µm (0.1-0.5 dB/m). Fiber diameters from 0.3 to 1.0 mm (on requeFiber lengths up to 20 m (for 0.5 mm diameter). No aging effect
Flexible delivery system for CO and CO2 laser. Flexible IR-imaging systems.
range. , in-vivo and process IR - spectroscopy.
Remote non-contact pyrometry in the 100-600KFiber probes for remote in-line
Fiber diameter (standard) ................................... 400/500, 630/700, 900/1000 µm ................................. 4-18 µm
0.1-0.5 dB/m
MPa meter]
ber Diameter]
Transmission range............Attenuation at 10.6 µm.......................................Refractive index ................................................. 2.15 Effective NA....................................................... 0.25 Laser Damage Threshold for cw CO2-laser........ >12 kW/cm²
Melting point ...................................................... 415°CTensile strength .................................................. >100 Minimum Bending Radius (fixed)...................... 10×[Fiber DiaMinimum Elastic Bending Radius...................... 100×[Fi
APPENDIX A. DATA SHEETS 57
€F® PIR - cables
CABLE SPECIFICATIONS • Core/clad PIR-fibers are protected by a loose PEEK-jacket (PolyEtherEther-
Ketone) to provide stiff, flexible and hermetic protection against mechanical, photoinduced and chemical damage over a wide temperature range (up to 250°C)
• Standard fiber/cable diameters are listed below. Other fiber diameters in 0.3 –
1.5mm range are also available upon the request for special fabrication:
Fiber core/cladding diameter *) (µm) Jacket’s inner/outer diameter (µm) 400 / 500 750 / 1590 630 / 700 1400 / 3175
900 / 1000 1400 / 3175 *) other diameter are available in 300 – 1000 µm range on request (10m min order)
• Cable termination with a special Ti-ferrule SMA-connector:
for low power (spectroscopy & radiometry) applications for high laser power delivery – free standing fiber end standard cable length – 1m & 2m
• PIR-fiber end-surface treatment: Cutting.....................low cost, high performance - standard Polishing..................for special application, including AR-coating – on request SMART...................for reduced reflection of high CO2-laser intensity – on request
OPTIONS
- accessory kits for remote spectroscopy with FTIR, QCL and TDL-spectrometers - pig-tailing of IR-detectors: TE- & LN-cooled MCT, PbSe, thermopiles, etc.
1 – PIR 400/500 after 2.5 year storing (red) 2 – PIR 600/700 after 2.5 year storing (purple) 3 – PIR 400/500 after 1 month storing (green)
PIR 600/700
PIR 400/500
Attenuation at 10.6µm in core/clad PIR-fibers measured within 28 months storage after extrusion
APPENDIX A. DATA SHEETS 58
A.5 CeramOptec: Optran MIR
CeramOptec is unique in its ability to manufacture fiber optic CO2 laser delivery systems and MIRoptical fiber commercially. CeramOptec’s flexible fiber optic delivery systems for CO2 lasers offer anadvantage over articulated arms—the typical delivery system for CO2 lasers—which are often rigidand cumbersome. Optran MIR optical fibers are the finest quality laser fibers for everything frommedical treatments to FT-IR spectroscopy (4 – 16 µm).
Features
■ Optimized for CO and CO2 lasers■ Low attenuation in the MIR region■ Non-brittle and very flexible■ Non-hygroscopical material■ High numerical aperture■ Reliable coupling accessories available■ Core/Clad or Bare Core design
Applications■ Medical
CO2 Laser Delivery■ Industrial/Scientific
FT-IR spectroscopy PyrometryLaser marking Remote, non-contact, temperature controlIR imagingLaser surface treatment
Physical PropertiesCrystal of solid solution: AgCl : AgBrSpecific weight: 6.39 g/cm3
Melting point: 412˚Tensile strength: 100 MPaWork temperature: -60˚ to +110˚CMinimum bend radius: R = 100 x Ø fiber
Optical PropertiesTransmission range: 4 to 16 µmRefractive index (core): 2.1Practical NA: 0.5 (bare core)
0.35 (core/clad)0.25 (core/clad)0.13 (core/clad)
Damage threshold (CO2 CW): 10 kW/cm2
Reflective loss (l = 10.6 µm) 25%
Innovative Fiber Optics...Every Step of the Way™
OPTRAN® MIR FIBERS
Transmission 80%
90%
3 4 5 6 7 8 9 10 11 12 130.0
0.5
1.0
1.5
2.0
2.5
3.0
Wavelength (um)
Atte
nuat
ion
(dB
/m)
Optran MIR
APPENDIX A. DATA SHEETS 59
Please contact our Sales Engineering representatives:North AmericaCeramOptec Industries, Inc.515A Shaker Road; East Longmeadow, MA 01028Tel: 800-934-2377
413-525-0600Fax: 413-525-1112Email: salesengineering@ceramoptec.comWest Coast OfficeTel: 408-362-0100Fax: 408-629-1657Email: salesengineering@ceramoptec.comEuropeCeramOptec GmbHSiemensstr. 44; 53121 Bonn, GermanyTel: +49 (0) 228-979670Fax: +49 (0) 228-9796799Email: info@ceramoptec.de
Innovative Fiber Optics...Every Step of the WayCeramOptec was founded in 1986 and today is a global leader in the production of stock and custom silica / silica, plastic-clad silica, and hard polymer-clad silica optical fibers; fused capillary tubing; DPSS lasers; diode modules; and low loss bundles and assemblies for UV, VIS, and IR transmission, medical laser delivery, sensors, plasma fusion, and spectroscopy. With several facilities worldwide, we are able to provide our customers with local, prompt, and reliable service and products. By maintaining complete control over the entire manufacturing process—from preformmanufacturing to finished fiber product—we are able to provide the highest quality control, custom solutions, and competitive pricing to our customers.Please visit http://www.ceramoptec.com for more information.CeramOptec is a subsidiary of biolitec™ AG.Please visit http://www.biolitec.com for more information.
Bare Core
Product Code Ø Core (µm) ± 2% Ø Loose Tube (µm) ± 2% Max. Length (m)MIR 300 300 700 20MIR 500 500 1000 10MIR 700 700 1500 10MIR 1000 1000 2000 10
Product Code Ø Core (µm) ± 2% Ø Clad (µm) ± 2% Ø Jacket (µm) ± 5% Max. Length (m)MIR 200/300 BPLC 200 300 400 10MIR 400/500 BPLC 400 500 700 10MIR 600/700 BPLC 600 700 900 10MIR 860/1000 BPLC 860 1000 1300 5
ML-127 REV. A (05/03)©2003 CeramOptec Industries, Inc.
Optran MIR—Bare Core Design
Mixed Silver Halide
Surrounding Air Functions as Cladding
Loose Polymer Tube(Polycarbonate or Tefzel®)
Optran MIR—Core/Clad Design
Mixed Silver Halide
Mixed Silver Halide
Loose Polymer Tube(Polycarbonate or Tefzel®)
Core/Clad
Notes:
NA is measured at the 95% intensity angle.
CeramOptec strives to ensure the accuracy of all information provided; however, we imply no warranties and disclaim any liability in connection with the use of this information.
Tefzel® is a registered DuPont product.
APPENDIX A. DATA SHEETS 60
A.6 Beijing S-Fiber Technology: Infrared Fiber
APPENDIX A. DATA SHEETS 61
APPENDIX A. DATA SHEETS 62
A.7 Amorphous Materials: C1, C2
IR Fibers
containing ultra violet.
TABLE 1 PROPERTIES OF AMI CORE GLASSES AND FIBERS
CORE GLASS As-Se-Te (Cl) As2S3 (C2)
Glass Transition Temperature °C 136 180
Softening Point °C 170 208
Thermal Expansion ∆L/Lx106/ºC 23.5 21.4
Refractive Index @ 4 µm
@ 10 µm
Value 2.82
2.81
Value 2.41
2.38
Thermal Change in Index xl05/°C +3 ± 0.9
Fiber Absorption From Transmission / Maximum Laser Power Transmitted.
@ 5.25 µm, db/m 0.2-0.4 5<10 w 0.2-0.4 > 100 w
@ 9.27 µm, db/m 0.2-0.4 5<10 w ----
@ l0.6 µm, db/m 4-5 5 w ----
Bend To Break Radius (cm) / Tensile Strength (psi) @ 40 Mpa/s Strain Rate
lOOO µm Core 4 62,000 4 44,000
750 µm Core 1 68,000 3 45,000
500 µm Core 0.8 70,000 1.7 56,000
<l00 µm Core 0.1 133,000 0.1 122,000
( Measurements courtesy of Tom Loretz of CES)
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APPENDIX A. DATA SHEETS 63IR Fibers
Numerical Aperture* 0.6-0.7 (± 40-50°) O.5-O.6 (± 35-40°)
(Measured at the 90 % point using variable iris while detecting energy from a heated surface. Large value results because of Fresnel reflection I refraction at oblique angles of incidence by the high refractive index core glass.)
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IR Fibers
SPOOLED FIBER FIBER CONNECTOR
GLASS CLAD IR FIBER PRICE LIST PRICE, DOLLARS PER METER
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APPENDIX A. DATA SHEETS 64
A.8 Polymicro: HWCA, HWEA
Polymicro Technologies > Products and Technologies > Optical Fibers > HOLLOW SILICA Waveguide, IR Applications
Products > Optical Fibers > HOLLOW SILICA Waveguide (HSW™), IR Applications
HOLLOW SILICA Waveguide (HSW™)- IR Applications HW
Hollow Silica Waveguide: Usage Guide and Test Process Overview
Characteristics
❍ Wavelength Range 2.9 µm past 10.6µm ❍ High Laser Damage Threshold: > 1000W of 10.6µm ❍ Strong and Flexible ❍ Non-Toxic: Sterilizable * ❍ Low Insertion Loss ❍ No End Reflection ❍ Transmission Optimized for CO2 or Er:YAG wavelengths
* The end manufacturer is responsible for bio-compatibility and sterilization testing and validation studies.
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APPENDIX A. DATA SHEETS 65
Polymicro Technologies > Products and Technologies > Optical Fibers > HOLLOW SILICA Waveguide, IR Applications
Terminations Available
Poly-Lok™:
❍ Removable, reusable connectors, ideal for prototyping ❍ SMA (905), SMA (906), STII, and FC (STII and FC not available for 1000µm bore) ❍ Not for permanent installations
Permanent SMA (905), SMA (906), STII, and FC:
❍ Waveguide protrudes 1 to 2 mm from connector endface
This product is licensed and manufactured under the following patents: US: 5,440,664; 5,567,471; 4,930,863; 5,497,440; and 5,605,716; Israel: 86296; 105956; and 111904; Europe: 0344478.
LEGAL NOTICES | PRIVACY POLICYWed, 26 May 2004 15:35:28 GMT
Copyright © Polymicro Technologies, LLC. 1995 - 2003. All Rights Reserved18019 N. 25th Avenue.
Phoenix, Arizona 85023-1200 USA 602-375-4100 Main602-375-4110 Fax
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APPENDIX A. DATA SHEETS 66
A.9 Hitachi: hollow fiber
Lamp Monochromator Detector(HgCdTe)
controller Lock-in Amp
Chopper
Computer Plotter
ZnSe Lensf=1”
ZnSe Lensf=1.5”
2 4 6 8 10 120
5
10
15
Wavelength (μm)
Tran
smis
sion
Los
s (dB
)
Infrared spectral attenuation of the hollow fiber
APPENDIX A. DATA SHEETS 67
A.10 CoreActive: IRT-SU, IRT-SE
Mid-Infrared Transmission Optical Fiber
CorActive delivers a full range of Infrared Transmission (IRT) optical fibers to address the beam delivery requirements for wavelengths in the mid-Infrared spectrum from 2.0 to 9.0 µm. CorActive’s family of Infrared Transmission Fiber products have been designed specifically to provide ultra low loss optical transmission in the mid-Infrared spectrum. The high optical quality and low loss characteristics of CorActive’s IRT optical fibers will enable performance enhancements of many existing applications that have relied on free space optics, low quality fiber or other beam delivery methods. A proprietary optical fiber manufacturing method ensures that fiber impurities and optical defects are removed prior to fiber drawing. This ensures the lowest loss and highest quality optical transmission of mid-IR wavelengths in the 2.0 to 9.0 µm range.
Ultra Low Loss High Power Capacity High Nonlinearity Bend/Polarization Insensitive
Robust Mechanical Properties Rare Earth Doping Available Designed for Military Applications by the U.S. Naval Research Laboratory
CorActive IRT Product Features and Benefits
IRT Product Features Customer Benefits Superior Beam Quality World leading fiber quality enables new fiber based mid-IR applications Proprietary Manufacturing Process Ensures highest optical quality by eliminating impurities and defects High Power Capacity Enables high power beam delivery of mid-IR wavelengths Consistent Reproducibility Reduces manufacturing costs and increases production yield Broad Product Family Ensures the most effective fiber choice for your application IRT Fiber Applications CorActive’s IRT optical fiber has been designed for high performance and demanding applications such as: - Infrared Counter Measure (IRCM) - IR Imaging Fiber Bundle (FLIR) - Er:YAG Laser Beam Delivery (3.0 µm) - IR Spectroscopy
Leading Low Loss IR Fiber Superior High Power Handling
Spectral Attenuation
012345678
1 3 5 7 9 11
Wavelength (um)
Atte
nuat
ion
(dB/
m) IRT-Se
IRT-Su
Peak Power Density: 1.1 GW/cm2 (27kW)
0
0.5
1
1.5
2
0 0.5 1 1.5 2 2.5 3
Pin (W)
Pout
(W)
APPENDIX A. DATA SHEETS 68
Mid-InfraredTransmission Optical Fiber
Fiber Specifications
IR Transmission Fiber IRT-SU IRT-SE
Core/Clad Structure Materials Sulphide Selenide
Optical Properties
Transmission Wavelength Range (µm) 2-5 2-9 Core Refractive Index 2.4 2.7 Numerical Aperture (nominal) 0.26 0.30 Nominal Attenuation (dB/m) <0.2 <0.5
Physical & Geometric Properties
Core Diameter (µm) 4-700 ± 3% Cladding Diameter (µm) 80-800 ± 3% Cladding Non-circularity (%) <2 Core/Clad Concentricity Error (µm) <5 Protective Coating Composition Dual Coat Acrylate
Environmental Properties
Chemical Insensitivity Insoluble in water, concentrated hydrochloric acid, non-oxidizing acids, gasoline, toluol, alcohol and acetone
Advanced Cable Manufacturing Process Advanced Cable Manufacturing Process
In our continuing effort to bring our customers the best service possible, CorActive utilizes a proprietary cable manufacturing process, which ensures optimal Anti-Reflective coating application. In our continuing effort to bring our customers the best service possible, CorActive utilizes a proprietary cable manufacturing process, which ensures optimal Anti-Reflective coating application.
IRT Cable Sheathing FC High Reliability Connector
Printed in Canada Copyright© 2004 CorActive High-Tech Inc. All rights reserved
APPENDIX A. DATA SHEETS 69
A.11 Photran LLC: Sapphire optical fiber
Sapphire Fiber Specifications
The Sapphire Fiber Advantage
● Biocompatiable, nontoxic, USP Class VI approved - passes both implant and elution test protocols
● High transmission from visible to beyond 3 micron wavelength.
● Flexible - bend radius as low as 20mm for 150 micron fiber diameter.
● High Strength - 400,000 psi/2.8 GPa - use of PTFE buffer further improves durability and handling.
● High laser damage threshold (1200 J/em2) and high melting point (2053ºC) enable high repetition rates and average power.
Sapphire Optical Fiber Specifications
(Typical Specifications)
Fiber Core Diameter (microns) 150 250 325 425
Buffer Diameter (microns) 400 450 650 750
Effective NA 0.12 0.12 0.12 0.12
Transmission (per meter) 80% 80% 80% 80%
Minimum Bend Radius (mm) 20 30 60 80
Length-Maximum Standard 2 meters 2 meters 2 meters 2 meters
Length-Maximum Special Order 4 meters 4 meters 4 meters 4 meters
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APPENDIX A. DATA SHEETS 70
A.12 Infrared Fiber Sensors: Spectral grade Silverhalide fibers
Core/Clad Fibers
Fiber diameter 900/1000µm (other diameters on request)Transmission range 3− 18 µmAttenuation at 10.6 µm 0.1− 0.3 dB/mAttenuation at 5µm < 0.6 dB/mAttenuation at 3.5 µm < 1 dB/mEffective NA (L>2 m) < 0.26Laser Damage Threshold for cw CO2-laser 12 kW/cm2
No ageing
Core Only Fibers
Fiber diameter 750 µm × 750 µm and 1 mm × 1 mm(other diameters on request)
Transmission range 2− 18 µmAttenuation at 10.6 µm < 0.2 dB/mAttenuation at 5µm < 0.3 dB/mAttenuation at 3.5 µm < 0.6 dB/mEffective NA (L>2m) 0.42No ageing
Refractive index (core) 2.2Melting point 420 ◦CTensile strength >110 MPaMinimum Inelastic Bending Radius 10 × Fiber DiameterMinimum Elastic Bending Radius 100 × Fiber Diameter
APPENDIX A. DATA SHEETS 71
A.13 Infrared Fiber Systems: HP fiber
IFS, Inc. Product 1
Applications:
• Dentistry
• Dermatology
• Ophthalmology
• General Surgery
• Orthopedics
Features:
• GeO2 – based glass
• High Power Handling
• Excellent Flexibility and Strength
• Glass Clad – No Bending Loss
• Low Optical Loss
• Non-Toxic
A key component to the Er:YAG, YSGG or Ho:YAG mid-infrared laser system is the optical fiber, which is used to transmit the laser power from the laser to the patient. Since conventional silica glass fibers cannot transmit in the infrared, a special fiber (HPTM fiber) made from Germanium Oxide (GeO2) – based glass was
developed by IFS, Inc. Fiber can handle up to 20 Watts of laser power for applications in dermatology, dentistry, ophthalmology, orthopedics and general surgery and is being sold worldwide to numerous laser companies. There are no other reliable fibers on the market for these types of applications and with today’s production volumes, IFS is a leading supplier of specialty HPTM fiber for mid-infrared medical lasers.
[ Home ] [ Up ] [ HP Fiber Specs ]
Infrared Fiber Systems, Inc. * Phone: (301)-622-9546 * Fax: (301)-622-7135 * info@infraredfibersystems.com
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APPENDIX A. DATA SHEETS 72
IFS, Inc. Product 1
Typical Specifications
Input Power @10 Hz 20.0 W (at least)
Loss at 2.94 µm 0.70 dB/m
Loss in visible region 1.00 dB/m (or less)
Output NA 0.12 (@ input NA=0.08)
Max acceptance NA 0.25
Available Core sizes 100 – 700 µm
Toxicity Passes Agar Overlay cytotoxicity and Dermal Sensitization tests
Core Size
Minimum Bend Radius
150 µm 0.5 cm
400 µm 2.5 cm
500 µm 4.0 cm
[ Home ] [ Up ]
Infrared Fiber Systems, Inc. * Phone: (301)-622-9546 * Fax: (301)-622-7135 * info@infraredfibersystems.com
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APPENDIX A. DATA SHEETS 73
A.14 Infrared Fiber Systems: SG fiber
Features:
• Low Optical Loss
• Multispectral Transmission
• Good Flexibility and Strength
• Glass Clad – No Bending Loss
• Perfect Matrix for Rare-Earth Doping
Applications:
• IR Imaging
• Fiber Lasers
• Fiber Amplifiers
• Temperature Sensing
• Remote Spectroscopy
IFS offers Heavy Metal Fluoride glass fibers (SGTM fiber) for use in a variety of industrialand scientific sensor systems such as temperature sensing and remote chemical analysis. Thesefibers transmit from the ultraviolet through 5µm in the mid-infrared. They can be furnishedas single fibers, cables or bundles. Infrared imaging bundles have been supplied to the Navyand to NASA as well as to the private companies. We have also developed fiber optic probesfor use with our AOTF spectrometer for remote and in-situ sensing applications.
APPENDIX A. DATA SHEETS 74
IFS, Inc. Product 2
Typical Specifications
Optimal Transmission Range 0.45 µm to 5.0 µm
Minimum Loss at 2.5 µm 0.05 dB/m
Max Operating Temperature 250 oC
Output NA 0.22
Available Core sizes 100 – 700 µm
Core Size
Minimum Bend Radius
100 mm 0.5 cm
200 µm 1.0 cm
400 µm 4.0 cm
[ Home ] [ Up ]
Infrared Fiber Systems, Inc. * Phone: (301)-622-9546 * Fax: (301)-622-7135 * info@infraredfibersystems.com
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APPENDIX A. DATA SHEETS 75
A.15 FiberLabs Inc.: SMFF
Fluoride Fiber SMFF
EnglishJapanese
Fluoride Glass Fiber - SMFF(Single Mode Fluoride Fiber) & Fiber-Module
=> SMFF(Single Mode Fluoride Fiber)
Rare earth doped SMFF enable to get high efficiency emissions easily, and are used for fiber lasers, optical amplifiers, and so on. Fiber module with pig-tail of silica fibers are also available.
Loss Spectra & Wavelength of Emission
SMFF Typical Fiber Parameters
DopantConcentration
ppm molNA
CoreDiameter
um
CladdingDiameter
um
Custom Fiber Price(US$)
Pr,Nd,Ho,Er,Tm,Yb, etc.
500 ~ 30,0000.150.200.27
2 ~ 12 123+/-3$8,000~
$20,000 /lot
Fluoride Fiber in Stock
=> Fluoride Fiber Module
Fiber module with pig-tail of silica fibers can be easily connected to other silica fibers. The hermetic sealed module can be used under the condition of high temperature and high humidity.
Insertion Loss Return Loss Output Fiber Size(mm)Operating
Temperature
Less than 1.5dB Less than -50dB SMF 15(H)X150(W)X100(D) -10 ~ 45 C
Request Sheet (Information, Quotation, Order, etc.)
HOME / Products / About FiberLabs / R&D / Information / Site-Map
Copyright(C) FiberLabs Inc. All Rights Reserved.
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APPENDIX A. DATA SHEETS 76
A.16 FiberLas Inc.: MMFF
Fluoride Fiber MMFF
EnglishJapanese
Fluoride Glass Fiber - MMFF(Multi Mode Fluoride Fiber)
=> MMFF(Multi Mode Fluoride Fiber)
MMFF have a broad transmission wavelength range from visible to infrared rays. There are two types of MMFF, depending on the applications. GFF series, which have longer transmission wavelength up to 4.0um, are suitable for IR spectrum guides. TFF with higher NA are appropriate for NIR spectrum transmission.In addition to the form of resin jacket fibers, single core and bundled cables are also available.
Loss spectra GFF-xxx*500nm to 4.0 um transmission range*20mm bend radius for GFF-150(proof test)*Custom-made fibers available
TFF-190*700nm to 2.5um transmission range*20mm bend radius(proof test)*Customized fiber bundles available
DCFF Typical Fiber Parameters
Part #Core Diameter
(um)Cladding Diameter
(um)Buffer(um)
NA JacketPrice(US$)
GFF-160/200-450 160 200 450 +/-10%
0.28UV
CurableResinJacket
$60.00/m
GFF-240/300-450 240 300 450 +/-10% $125.00/m
GFF-320/400-550 320 400 550 +/-10% $200.00/m
GFF-400/500-650 400 500 650 +/-10% $300.00/m
TFF-190/200-450 190 200 450 +/-10% 0.65 $60.00/m
Fluoride Fiber in Stock
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Bibliography
[1] M. Pfennigbauer, F. Fidler, W. Leeb, and U. Johann, “TN1: Survey of instrument op-portunities, Contract ESA/ESTEC/18514/04/NL/PA, Technical Note 1,” 30.11.2004.
[2] M. Pfennigbauer, F. Fidler, W. Leeb, and M. Dirnwoeber, “TN3: Market survey, ContractESA/ESTEC/18514/04/NL/PA, Technical Note 3,” 2004.
[3] J. A. Harrington, “Infrared fiber optics,” Handbook of Optics, Vol.3, ed. M. Bass, NewYork: McGraw-Hill, 2000.
[4] J. A. Harrington, “Hollow-glass waveguides have unique properties,” Laser Focus World,pp. S8–S10, August 2004.
[5] Crystal Fibre A/S. (2005, March). [Online]. Available: http://www.crystal-fibre.com/products/airguide.shtm
[6] Crystal Fibre A/S. (2005, March). [Online]. Available: http://www.crystal-fibre.com/products/nonlinear.shtm
[7] J. Eichenholz, “Photonic-crastal fibers have many uses,” Laser Focus World, pp. S5–S7,August 2004.
[8] O. Wallner, W. R. Leeb, and R. Flatscher, Design of spatial and modal filters for nullinginterferometers, Proceedings of SPIE, Vol. 4838, 668-679, 2003.
[9] D. Marcuse, Curvature loss formula for optical fibers, Journal of Optical Society of Amer-ica, Vol. 66, pp. 216-220, 1976.
[10] A. J. Harris and P. F. Castle, “Bend loss measurements on high numerical aperture single-mode fibers as a function of wavelength and bend radius,” J. Lightwave Technol., vol. 4,no. 1, pp. 34–40, 1986.
[11] W. D. Heacox and P. Connes, “Optical fibers in astronomical instruments,” The Astron-omy and Astrophysics Review, Vol.3, pp. 169-199, Springer-Verlag, 1992.
[12] M. Nisoli, S. Stagira, S. D. Silvestri, O. Svelto, S. Sartania, Z. Cheng, G. Tempea, C. Spiel-mann, and F. Krausz, Toward a Terawatt-Scale Sub-10-fs Laser Technology, IEEE Journalof Selected Topics in Quantum Electronics, Vol. 4, No. 2, pp. 414-420, 1998.
[13] O. Wallner, “Modal filtering of optical waves,” Doctoral Thesis, Institute of Communica-tions and Radio-Frequency-Engineering, Vienna University of Technology, 2004.
[14] O. Guyon. (2002) Wide field interferometric imaging with single-mode fibers. [Online].Available: http://www.edpsciences.org/articles/aa/abs/2002/19/aa2299/aa2299.html
77
BIBLIOGRAPHY 78
[15] Optoelectronics Industry Sourcebook 2004 Buyers Guide. Nashua, New Hampshire USA:LaserFocusWorld, 2004.
[16] D. Marcuse, Principles of Optical Fiber Measurements, 1st ed. New York, New YorkUSA: Academic Press, Inc., 1981.
[17] ITU-T G.650.1: Definitions and test methods for linear, deterministic attributes of single-mode fibre and cable, Prepublished Recommendation, International TelecommunicationUnion, 2004.
[18] I. K. Ilev, R. W. Waynant, and M. A. Bonaguidi, “Attenuation measurement of infraredoptical fibers by use of a hollow-taper-based coupling method,” Applied Optics, vol. 39,no. 19, pp. 3192–3196, July 2000.
[19] M. J. Matthewson, C. R. Kurkjian, and S. T. Gulati, “Strength measurement of opticalfibers by bending,” Journal of the American Ceramic Society, vol. 69, no. 11, pp. 815–821,November 1986.
[20] G. Cancellieri, Single-Mode Optical Fiber Measurement: Characterization and Sensing,1st ed. Norwood, Massachusetts USA: Artech House, Inc., 1993.
[21] D. L. Franzen, “Determining the effective cutoff wavelength of single-mode fibers: Aninterlaboratory comparison,” Journal of Lightwave Technology, vol. LT-3, no. 1, pp. 128–134, February 1985.
[22] Y. Ohishi, S. Mitachi, and S. Takahashi, “Fabrication of fluoride glass single-mode fibers,”Journal of Lightwave Technology, vol. LT-2, no. 5, pp. 593–596, October 1984.
[23] M. Artiglia, G. Coppa, P. di Vita, M. Potenza, and A. Sharma, “Mode field diametermeasurements in single-mode optical fibers,” Applied Optics, vol. 7, no. 8, pp. 1139–1152,August 1989.
[24] D. L. Franzen, M. Young, A. H. Cherin, E. D. Head, M. J. Hackert, K. W. Raine, andJ. G. N. Baines, “Numerical aperture of multimode fibers by several methods: Resolvingdifferences,” Journal of Lightwave Technology, vol. 7, no. 6, pp. 896–901, June 1989.
[25] P. A. Merritt, R. P. Tatam, and D. A. Jackson, “Interferometric chromatic dispersionmeasurements on short lengths of monomode optical fiber,” Journal of Lightwave Tech-nology, vol. 7, pp. 703–716, 1989.
[26] P.-L. Francois, M. Monerie, C. Vassallo, Y. Durteste, and F. R. Alard, “Three ways to im-plement interferencial techniques: Application to measurements of chromatic dispersion,birefringence, and nonlinear susceptibilities,” Journal of Lightwave Technology, vol. 7,no. 3, pp. 500–513, March 1989.
[27] G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. New York USA: John Wiley& Sons, Inc., 2002.
[28] Y. Noh, D. Kim, S. Oh, and U. Pack, “Lasers and electro-optics, 1999. cleo/pacific rim’99. the pacific rim conference on,” vol. 3, 1999, pp. 599–600.
BIBLIOGRAPHY 79
[29] S. Chang, C.-C. Hsu, T.-H. Huang, W.-C. Chuang, Y.-S. Tsai, J.-Y. Shieh1, and C.-Y.Leung, “Heterodyne interferometric measurement of the thermo-optic coefficient of singlemode fiber,” Chinese Journal of Physics, vol. 38, no. 3, pp. 437–442, June 2000.
[30] D. Gettemy, W. Harker, G. Lindholm, and N. Barnes, “Some optical properties of KTP,LiIO3, and LiNbO3,” Journal of Quantum Electronics, vol. 24, no. 11, pp. 2231–2237,November 1988.
[31] G. Fasching, Werkstoffe fuer die Elektrotechnik, 3rd ed. Vienna Austria: Springer-VerlagWien New York, 1994.
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