new 介質波導與光纖eportfolio.lib.ksu.edu.tw/user/t/0/t094000004/repository... · 2010. 6....

第二章

介質波導與光纖

目錄

2-1 對稱平面介質板波導2-2 平面波導內的模色散與波導色散2-3 步級折射率光纖2-4 數值孔徑2-5 單模光纖內的色散2-6 位元率、色散、電以及光的帶寬2-7 斜射率 (GRIN) 光纖2-8 光吸收與散射2-9 光纖中的衰減2-10 光纖製造

2-1 對稱平面介質板波導

Lightn2

A planar dielectric waveguide has a central rectangular region ofhigher refractive index n1 than the surrounding region which hasa refractive index n2. It is assumed that the waveguide isinfinitely wide and the central region is of thickness 2a. It isilluminated at one end by a monochromatic light source.

n2

n1 > n2

Light

Light Ligh

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.1 一平面介質波導其中央矩形區域的折射率比周圍區域的折射率高。假設此波導為無限寬且中央區域的厚度為，並由單色光源照射其一端。

n2

n2

d = 2a

θθk1

Light

A

B

C

λ

β

κ

E

θn1

A light ray travelling in the guide must interfere constructively with itself topropagate successfully. Otherwise destructive interference will destroy thewave.


z

y

x

圖2.2 一個在波導中行進的光線必須跟它自己發生建設性的干涉以便能繼續傳播，要不然破壞性的干涉將使波受到破壞

波導條件

假設 k1 為在 n1 中的波向量 (wave vector)，即，其中 k 和為真空中的波向量和波長，則對建設性的干涉， A 和 C 間的相位差一定為的整數倍，

(1)

λπ /2 111 nknk == λ

π2)2(2)()( 1 πφφ mBCACkAC =−+=∆

為使波能沿著波導傳播，我們需要

以2去除 (2) 式，我們得到波導條件(waveguide condition)

(3)πφθλπ man mm =−⎥⎦

⎤⎢⎣⎡ cos)2(2 1

n 2

n 2

z2a

y

A

1

2 1

B

θθ

θA′

B′

Cπ−2θ 2θ−π/2

k1E

xn 1

Two arbitrary waves 1 and 2 that are initially in phase must remain in phaseafter reflections. Otherwise the two will interfere destructively and cancel eachother.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.3 兩個任意波1和2初始同相位，反射後仍須同相位；否則此二波將產生破壞性干涉並彼此相互抵消。

n2

z

a y

A

1

2

θθ

A′

C

kE

x

y

a−y

Guide center

π−2θ

Interference of waves such as 1 and 2 leads to a standing wave pattern along the y-direction which propagates along z.


圖2.4 波的干涉例如1和2將導入一個在方向固定不變且沿著傳播的波形。

n2

Light

n2

n1

y

E(y)

E(y,z,t) = E(y)cos(ωt ? β0z)

m = 0

Field of evanescent wave(exponential decay)

Field of guided wave

The electric field pattern of the lowest mode traveling wave along theguide. This mode has m = 0 and the lowest θ. It is often referred to as theglazing incidence ray. It has the highest phase velocity along the guide.


圖2.5 沿著波導之行進波的最低模的電場圖樣。該模具有以及最低的，且經常述說為光滑的入射線，沿著波導具有最高的相速度。

y

E(y)m = 0 m = 1 m = 2

Cladding

Cladding

Core 2an1

n2

n2

The electric field patterns of the first three modes (m = 0, 1, 2)traveling wave along the guide. Notice different extents of fieldpenetration into the cladding.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.6 沿著波導之行進波的前三個模的電場圖樣。留意包層內不同的場穿透範圍。

單模及多模波導

由 (3) 式我們可得到的一個表示式，然後應用內部全反射條件，，證明模數 m 必須滿足

式中稱為V-數目 (V-number)，它的大小由下列所定義

mθsin

cm θθ sinsin >

Low order modeHigh order mode

Cladding

Core

Light pulse

t0 t

Spread, ∆τ

Broadenedlight pulse

IntensityIntensity

Axial

Schematic illustration of light propagation in a slab dielectric waveguide. Light pulseentering the waveguide breaks up into various modes which then propagate at differentgroup velocities down the guide. At the end of the guide, the modes combine toconstitute the output light pulse which is broader than the input light pulse.


圖2.7 光在平板介質波導中的傳播圖例。光脈衝進到波導後分解成各種模態，然後以不同的群速度沿波導傳播下去。在波導末端，這些模合併並組成輸出的光脈衝，而且比輸入的光脈衝寬。

θθ

E⊥

By

Bz

z

y

O

θθ

B⊥

E// Ey

Ez

(b) TM mode(a) TE mode

B//

x (into paper)

Possible modes can be classified in terms of (a) transelectric field (TE)and (b) transmagnetic field (TM). Plane of incidence is the paper.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.8 可能的模態可用 (a) 橫向電場 (TE) 及 (b) 橫向磁場(TM)來分類。入射面為紙面。

2-2 平面波導內的模色散與波導色散

βm

ωSlope = c/n2

Slope = c/n1

TE0

ωcut-off

TE1

TE2

Schematic dispersion diagram, ω vs. β for the slab waveguide for various TEm. modes.ωcut ff　 corresponds to V = π/2. The group velocity vg at any ω is the slope of the ω vs. βcurve at that frequency.


圖2.10 圖示平板波導之各種TEm模的對的色散曲線圖。對應於，而在任意的群速度為在該頻率時對的曲線的斜率。

ωβ2/π=V ωω gv

β off-cutω

y

E(y)

Cladding

Cladding

Core

λ2 > λ1λ1 > λc

ω2 < ω1ω1 < ωcut-off

vg1

y

vg2 > vg1

The electric field of TE0 mode extends more into thecladding as the wavelength increases. As more of the fieldis carried by the cladding, the group velocity increases.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.11 當波長增加時，TE0模的電場伸展到包層越多。若越多的場被載於包層中，則群速度越增加。

2-3 步級折射率光纖

n

y

n2 n1

Cladding

Core z

y

rφ

Fiber axis

The step index optical fiber. The central region, the core, has greater refractiveindex than the outer region, the cladding. The fiber has cylindrical symmetry. Weuse the coordinates r, φ, z to represent any point in the fiber. Cladding isnormally much thicker than shown.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)圖2.12 步級折射率光纖 ( 示意圖 )。中央區，核心，具有比外圍區，包層，大的折射率。由於光纖為圓柱對稱，故其內任何一點 P 皆以 r 、

及 z 等座標表示。包層通常比所顯示的為厚。ϕ

本質上此為圓柱形的介質波導，其內部核心介質的折射率為 n1 比外部包層介質的折射率 n2大。歸一化折射率差(normalized index difference) 定義為∆

一個沿著光纖的導引LP模可用一個沿 z 的電場分佈的傳播來表示，此電場分佈 ( 或圖樣 ) 在垂直於纖軸的平面上，因此只和 r 和相關而與 z 無關。此外，由於存在著兩個邊界，所以它的特性是由和 m 兩個整數決定；因此在一個LP模中的傳播電場分佈是由給出，並表示為。故一個模可用

(1)

),( ϕrEϕ

l),( ϕrElm

lmLP lmLP)(exp),(LP ztjrEE lmlm βωϕ −=

Fiber axis

12

34

5

Skew ray1

3

2

4

5

Fiber axis

1

2

3Meridional ray

1, 3

2

(a) A meridionaray alwayscrosses the fibeaxis.

(b) A skew raydoes not haveto cross thefiber axis. Itzigzags aroundthe fiber axis.

Illustration of the difference between a meridional ray and a skew ray.Numbers represent reflections of the ray.

Along the fiber

Ray path projectedon to a plane normalto fiber axis

Ray path along the fiber

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)圖2.13 子午光線與斜光線之間的差異的說明。數字代表光線的反射。

E

r

E01

Core

Cladding

The electric field distribution of the fundamental modin the transverse plane to the fiber axis z. The lightintensity is greatest at the center of the fiber. Intensitypatterns in LP01, LP11 and LP21 modes.

(a) The electric fieldof the fundamentalmode

(b) The intensity inthe fundamentalmode LP01

(c) The intensityin LP11

(d) The intensityin LP21


圖2.14 基模在垂直於光纖軸之橫向平面上的電場分佈。最大的光強度位在光纖的中央。所示為LP01、LP11 及 LP21 模的強度圖樣。

一般單模光纖具有遠小於較多模光纖的核心半徑以及較小的。如果光源波長足夠小，使得 V 超過2.405時，單模光纖將變成多模，即較高的模也將貢獻傳播。讓波長超過而使光纖變成單模的截止波長可由下式給出

(4)

∆ λ

cλ

405.2)(2 2/12221off-cut =−= nn

aVcλ

π

0 2 4 61 3 5V

b

1

0

0.8

0.6

0.4

0.2

LP01

LP11

LP21

LP02

2.405

Normalized propagation constant b vs. V-numberfor a step index fiber for various LP modes.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.15 一步級折射率光纖之各種LP模的歸一化傳播常數 b對 V 數目的曲線圖。

因LP模的傳播常數隨波導特性以及光源波長而定，所以方便上採

2-4 數值孔徑

Cladding

Coreα < αmax

AB

θ < θc

A

B

θ > θc

α > αmax

n0 n1

n2Lost

Propagates

Maximumacceptance angleαmax is that which just givestotal internal reflectionat thecore-claddinginterface, i.e.whenα=αmax thenθ=θc.Rays withα>αmax (e.g. rayB) become refracted andpenetrate the claddingandareeventuallylost.

Fiber axis

©1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.16 最大可接受角為剛好在核心-包層的界面上發生內部全反射，即當時，的光線 ( 即光線B) 則變成折射而穿透到包層，最後損失掉。

maxαmaxαα = max, ααθθ >= c

2-5 單模光纖內的色散

τt

Spread, �τ

t0

λ

Spectrum, �λ

λ1 λ2λo

Intensity Intensity Intensity

Cladding

CoreEmitterVery shortlight pulse

vg(λ2)vg(λ1)

Input

Output

All excitation sources are inherently non-monochromatic and emit within aspectrum, �λ, of wavelengths. Waves in the guide with different free spacewavelengths travel at different group velocities due to the wavelength dependenceof n1. The waves arrive at the end of the fiber at different times and hence result ina broadened output pulse.


圖2.17 所有的激發光源本質上皆為非單色光並發射出一頻譜波長。由於折射率 n1 為波長的函數，故波導中不同自由波長的波將以不同的群速度行進。波將以不同的時間到達光纖的末端，因而導致一個加寬的光脈衝。

λ∆

色散通常以單位長度的擴展表示並由下列給出

在 (1) 式中，由於有限的輸入頻譜，因而成為群延遲時間上的擴展。若為基模的傳播常數，則由定義

(3)

L/τ∆

01β

ωβτd

d 011 ==g

g v

0

1.2 1.3 1.4 1.5 1.61.1-30

20

30

10

-20

-10

λ (µm)

Dm

Dm + Dw

Dwλ0

Dispersion coefficient (ps km -1 nm-1)

Material dispersion coefficient (Dm) for the core material (taken asSiO2), waveguide dispersion coefficient (Dw) (a = 4.2 µm) and thetotal or chromatic dispersion coefficient Dch (= Dm + Dw) as afunction of free space wavelength, λ.


圖2.18 核心材料的材料色散係數、波導色散係數以及總或色彩色散係數為自由空間波長的函數。

)(SiO2 )( mD ( mD+= mch DD ( )wD

)

波導色散

如圖2.17，我們若使用一個具有頻譜之很短的光脈衝當作輸入，則因波導色散，輸出光脈衝單位長度的加寬或色散，，可由下列求得

(4)

λ∆

L/τ∆

λτ ∆=∆ || wDL

它是隨波導特性 ( 不瑣碎的方式 ) 而定，且在的範圍，可由下列近似給出

(5)

2.45.1

色彩色散或總色散

在一階近似時，此兩個色散效應可簡單地相加而使單位長度的總色散變成

(6)λτ

∆+=∆ || wm DDL

外形與偏振色散效應

如果隨波長改變，則光源中不同的波長將有不同的群速度並經不同的群延遲而導致脈衝的加寬。外形色散是色彩色散的一部分，因其隨輸入的頻譜變化

(7)

∆

λ∆

λτ ∆=∆ || pDL

Core

z

n1 x // x

n1 y // y

Ey

Ex

Ex

Ey

E

∆τ = Pulse spread

Input light pulse

Output light pulset

t

∆τ

Intensity

Suppose that the core refractive index has different values along two orthogonaldirections corresponding to electric field oscillation direction (polarizations). We cantake x and y axes along these directions. An input light will travel along the fiber with Exand Ey polarizations having different group velocities and hence arrive at the output atdifferent times


圖2.19 假設核心折射率在相應於電場振盪方向 ( 偏振 ) 的兩個正交方向上的值不相同；我們讓 x 和 y 軸沿此二方向，則一沿著光纖行進的輸入光其 Ex 和 Ey 偏振具有不同的群速度因而以不同的時間到達輸出端。

20

-10

-20

-30

10

1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

30

λ (µm)

Dm

Dw

Dch = Dm + Dw

λ1

Dispersion coefficient (ps km -1 nm-1)

λ2

n

r

Thin layer of claddingwith a depressed index

Dispersion flattened fiber example. The material dispersion coefficient (Dm) for thecore material and waveguide dispersion coefficient (Dw) for the doubly clad fiberresult in a flattened small chromatic dispersion between λ1 and λ2.


圖2.20 色散平坦化光纖的例子。核心材料的材料色散係數以及雙包層光纖的波導色散係數導致和之間小而平坦的色彩色散。

)( mD

1λ 2λ)( wD

2-6 位元率、色散、電以及光的帶寬

t0

Emitter

Very shortlight pulses

Input Output

Fiber

PhotodetectorDigital signal

Information Information

t0

~2�τ1/2T

t

Output IntensityInput Intensity² τ1/2

An optical fiber link for transmitting digital information and the effect ofdispersion in the fiber on the output pulses.


圖2.22 一光纖連接以傳送數位訊息以及光纖中的色散對輸出脈衝的效應。

脈衝可傳送的最大位元率，或簡稱位元率 B ，大約為

(1)

)2/(1 2/1τ∆

2/1

5.0τ∆

≈B

t

Output optical power

∆τ1/2

T = 4σ1

0.50.61 2σ

A Gaussian output light pulse and some tolerable intersymbolinterference between two consecutive output light pulses (y-axis inrelative units). At time t = σ from the pulse center, the relativemagnitude is e-1/2 = 0.607 and full width root mean square (rms)spread is ∆τrms = 2σ.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)圖2.23 高斯輸出脈衝及兩連續輸出脈衝 ( y 軸為相對單位 ) 間之可容忍的碼間干擾。距脈衝中心為處的相對大小為，而全寬度均方根(ms) 延展為

at =607.02/1 =−e στ 2rms =∆

位元率 B 若以來表示則需兩連續輸出光脈衝之波峰間的分隔為 4 ，如圖2.23所示。因此，

(2)

σσ

σ25.0

≈B

如果 Dch 為色彩色散係數，則輸出光脈衝的均方根色散為，而乘積 BL ，稱為乘積值，並由下列給出

(3)

λσchLD

λσσ ||25.025.0

chDLBL =≈

體色散若以一個均方根色散表示則可由各個均方根色散求得

(4)

σ

2intramodal

2intermodal

2 σσσ +=

t0

Pi = Input light power

Emitter

OpticalInput

OpticalOutput

Fiber

PhotodetectorSinusoidal signal

Sinusoidal electrical signalt

t0f

1 kHz 1 MHz 1 GHz

Po / Pi

fop

0.10.05

f = Modulation frequency

An optical fiber link for transmitting analog signals and the effect of dispersion in thefiber on the bandwidth, fop.

Po = Output light power

Electrical signal (photocurrent)

fel

10.707

f1 kHz 1 MHz 1 GHz


圖2.24 用來傳送類比訊號的光纖連接以及光纖中的色散對帶寬的效應。

如果光纖的色散特性為高斯的，則

(5)σ19.075.0 ≈≈ Bfop

2-7 斜射率 (GRIN) 光纖

n1

n2

21

3

nO

n1

21

3

n

n2

OO' O''

n2

(a) Multimode stepindex fiber. Ray pathsare different so thatrays arrive at differenttimes.

(b) Graded index fiber.Ray paths are differentbut so are the velocitiesalong the paths so thatall the rays arrive at thesame time.

23


圖2.25 (a) 多模步級折射率光纖，光線路徑不同故光線以不同的時間到達；

nb

nc

O O'Ray 1

A

B'

B

θAθB

θB' Ray 2

M

θB' c/nb

c/na12

B''na

a

b

c We can visualize a graded indexfiber by imagining a stratifiedmedium with the layers of refractiveindices na > nb > nc ... Consider twoclose rays 1 and 2 launched from Oat the same time but with slightlydifferent launching angles. Ray 1just suffers total internal reflection.Ray 2 becomes refracted at B andreflected at B'.


圖2.26 我們可藉由想像一個層狀的介質，其層折射率為，而瞭解斜射率光纖。考慮兩個靠近的光線1及2，以相同的時間但不同的發射角由O發射。光線1正好遭到內部全反射，而光線2先在 B 折射而後在反射。

…cba nnn >>

B′

n decreases step by step from one layerto next upper layer; very thin layers.

Continuous decrease in n gives a raypath changing continuously.

TIR TIR

(a) A ray in thinly stratifed medium becomes refracted as it passes from onelayer to the next upper layer with lower n and eventually its angle satisfies TIR(b) In a medium where n decreases continuously the path of the ray bendscontinuously.

(a) (b)


圖2.27 (a) 薄層狀介質中的光線當它由一層通過下一個折射率 n 較低的上層時變成折射直至最後它的角度滿足TIR；(b) 在 n 連續減少的介質中，光線的路徑為連續彎曲。

2-8 光吸收與散射

Medium

kAttenuation of light in thedirection of propagation.


z

E

圖2-28 光在傳播方向的衰減。

z

A solid with ions

Light directionk

Ex

Lattice absorption through a crystal. The field in the waveoscillates the ions which consequently generate "mechanical"waves in the crystal; energy is thereby transferred from the waveto lattice vibrations.


圖-29 通過晶體的晶格吸收。波內的場使離子振盪，結果在晶體中產生“機械的”波，於是能量由波傳到晶格振盪。

Scattered waves

Incident wave Through wave

A dielectric particle smaller than wavelength

Rayleigh scattering involves the polarization of a small dielectricparticle or a region that is much smaller than the light wavelength.The field forces dipole oscillations in the particle (by polarizing it)which leads to the emission of EM waves in "many" directions sothat a portion of the light energy is directed away from the incidentbeam.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)圖2.30 瑞利散射涉及一個遠小於光波長的小介電粒子或小區域的極化。場迫使介質中的電偶極振盪導致電磁波在“很多”方向發射，以致於一部分的光能由入射光束偏離。

2-9 光纖中的衰減

0.05

0.1

0.51.0

5

10

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Latticeabsorption

Rayleighscattering

Wavelength (痠)

Illustration of a typical attenuation vs. wavelength characteristicsof a silica based optical fiber. There are two communicationschannels at 1310 nm and 1550 nm.

OH-absorption peaks

1310 nm

1550 nm


圖2.31 典型矽玻璃光纖之對波長的衰減特性的例子。在1315nm及1550nm處有兩個通訊通道。

在單組成玻璃中因瑞利散射形成的衰減的表示式可由下列近似給出

(5)

Rα

fBTR Tkn βλπα 224

3

)1(38

−≈

Escaping wave

θ θ

θ′ < θ

θθ > θc θ′

Microbending

R

Cladding

Core

Field distribution

Sharp bends change the local waveguide geometry that can lead to wavesescaping. The zigzagging ray suddenly finds itself with an incidenceangle θ′ that gives rise to either a transmitted wave, or to a greatercladding penetration; the field reaches the outside medium and some lightenergy is lost.


圖2.32 由銳利彎曲而改變局部的波導形狀而導致波的逃脫。彎曲的光線突然發現它自己以一個入射角入射而引起一個透射波或是一個較大的包層穿透；場到達外側的介質並損失部分的光能。

0 2 4 6 8 10 12 14 16 18

Radius of curvature (mm)

10−3

10−2

10−1

1

10

102

αB (m-1) for 10 cm of bend

λ = 633 nmλ = 790 nmV = 2.08V = 1.67

Measured microbending loss for a 10 cm fiber bent by different amounts of radius ofcurvature R. Single mode fiber with a core diameter of 3.9 µm, cladding radius 48 µm,∆ = 0.00275, NA = 0.10, V = 1.67 and 2.08 (Data extracted and replotted from A.J.Harris and P.F. Castle, IEEE J. Light Wave Technology, Vol. LT14, pp. 34-40, 1986;see original article for discussion of peaks in αB vs. R at 790 nm).

From S.O. Kasap, Optoelectronics and Photonics: Principles and Practices (Prentice Hall)

圖2.33 10cm長的光纖以不同的曲率半徑彎曲所測量到的微彎曲損失。單模光纖的核心直徑為3.9um，包層半徑為48um, , NA=0.11, 及2.08。

004.0=∆67.1≈V

2-10 光纖製造

Preform feed

Furnace 2000蚓

Thicknessmonitoring gauge

Take-up drum

Polymer coater

Ultraviolet light or furnacefor curing

Capstan

Schematic illustration of a fiber drawing tower.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.34 光纖抽絲塔之圖解說明。

Protective polymerinc coating

Buffer tube: d = 1mm

Cladding: d = 125 - 150 µm

Core: d = 8 - 10 µmn

r

The cross section of a typical single-mode fiber with a tight buffertube. (d = diameter)

n1n2


圖2.35 具有一個堅固緩衝管的典型單模光纖的橫切面。(d=直徑)。

Vapors: SiCl 4 + GeCl 4 + O 2

Rotate mandrel

(a)

Deposited sootBurner

Fuel: H 2

Target rod

Deposited Ge doped SiO 2

(b)

Furnace

Porous sootpreform with hole

Clear solidglass preform

Drying gases

(c)

Furnace

Drawn fiber

Preform

Schematic illustration of OVD and the preform preparation for fiber drawing. (a)Reaction of gases in the burner flame produces glass soot that deposits on to the outsidesurface of the mandrel. (b) The mandrel is removed and the hollow porous soot preformis consolidated; the soot particles are sintered, fused, together to form a clear glass rod.(c) The consolidated glass rod is used as a preform in fiber drawing.


圖2.36 OVD以及光纖抽絲所需預形體準備的圖解說明。(a) 燃燒器火焰中的氣體反應產生玻璃煙灰並沉積在心軸的外表面；(b) 心軸移走且中空多孔的煙灰預形體被固化，即煙灰顆粒昇華、熔化在一起而形成一個透明的玻璃棒；(c) 所固化的玻璃棒當作光纖抽絲的預形體。

vg (m/s)

ω (1/s)

TE0

TE1

2.08×108

2.07×108

2.06×108

2.05×108

0 1×101 5 2×1015 3×101 5

ωcut-off = 2.3×1014

TE4

c/n2

c/n1

Group velocity vs. angular frequency for three modes for a planar dielectric waveguidewhich has n1 = 1.455, n2 = 1.44, a = 10 µm (Results from Mathview, Waterloo Maplemath-software application). TE0 is for m = 0 etc.


0

0.5

1

1.5

0 1 2 3V - number

V[d2(Vb)/dV2]

[d2(Vb)/dV2] vs. V-number for a step index fiber (after W.A. Gambling etal., The Radio and Electronics Engineer, 51, 313, 1981)


圖2.38 一步級折射率光纖之對 V 數目的關係曲線。]/)([ 22 dVVbdV

n2

n1

O O'

B'

AB

Ray ARay B θA θA

θB'

θB'

θB

θB '

y = 0

y = δ/2δ/2

Medium 1

Medium 2

n3 Medium 3 δ

δ

y = 3δ/2

y = 5δ/2

θB'

θB

B''

Step-graded-index dielectric waveguide. Two rays are launched fromthe center of the waveguide at O at angles θA and θB such that ray Asuffers TIR at A and ray B suffers TIR at B'. Both TIRs are at criticalangles.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.39 步級-斜射率介質波導。兩條光線由波導中心的 O 點分別以角度及發射，使光線 A 在 A 點歷經TIR而光線 B 在點歷經TIR。兩個TIR均在臨界角。

Aθ Bθ B′

0.5P

O'O

(a)

0.25P

O

(b)

0.23P

O

(c)

Graded index (GRIN) rod lenses of different pitches. (a) Point O is on the rod facecenter and the lens focuses the rays onto O' on to the center of the opposite face. (b)The rays from O on the rod face center are collimated out. (c) O is slightly away fromthe rod face and the rays are collimated out.


第二章目錄2-1 對稱平面介質板波導2-2 平面波導內的模色散與波導色散2-3 步級折射率光纖2-4 數值孔徑2-5 單模光纖內的色散2-6 位元率、色散、電以及光的帶寬2-7 斜射率 (GRIN) 光纖2-8 光吸收與散射2-9 光纖中的衰減2-10 光纖製造

new 介質波導與光纖eportfolio.lib.ksu.edu.tw/user/t/0/t094000004/repository... · 2010. 6....

Documents