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istributed Bragg Reflector Lasers Abstract | Full Text: PDF (228K)

istributed Feedback Lasers Abstract | Full Text: PDF (210K)

ye Lasers Abstract | Full Text: PDF (250K)

lectronic Speckle Pattern Interferometry Abstract | Full Text: PDF (310K)

xcimer Lasers Abstract | Full Text: PDF (254K)

ree Electron Lasers Abstract | Full Text: PDF (210K


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HELPme /Engineering /Electrical and Electronics Engineering

iley Encyclopedia of Electrical and

ectronics Engineering

stributed Bragg Reflector Lasers

ndard Article

D. Roh1, R. B. Swint1, J. J. Coleman1

niversity of Illinoispyright 1999 by John Wiley & Sons, Inc. All rights

erved.

OI: 10.1002/047134608X.W6301

ticle Online Posting Date: December 27, 1999

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bstract

e sections in this article are

Dbr and Laser Basics

The Bragg Period

Edge-Emitting Single Frequency Lasers

Vcsel

Conclusion

ywords: bragg period; coupled mode theory; single frequency semiconductor lasers; reflectivity; DBR fabrications; VC

able DBRs

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J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering

Copyright c 1999 John Wiley & Sons, Inc.

DISTRIBUTED BRAGG REFLECTOR LASERS

One of the distinguishing characteristics of a laser, as opposed to other sources of light, is that its emission

consists very nearly of a single frequency, or color, of light. However, close inspection of the light emitted from

a simple semiconductor laser source reveals that its light output consists of several closely spaced frequencies

and thus its spectrum is not infinitely narrow. The characteristic of single-frequency emission is critical for

some applications, including optical communications and spectroscopy. One method of narrowing the emission

spectrum of a simple semiconductor laser source is to incorporate in the laser a structure that is capable o

selectively reflecting only one frequency of light. A distributed Bragg reflector (DBR) is just such a structure

Semiconductor lasers that have DBRs incorporated in them have single-frequency output. Emission spectra

from two semiconductor lasers, one with and one without a DBR, are shown in Fig. 1. While other single

frequency laser sources exist, semiconductor DBR lasers are preferred for many applications because they

are relatively simple, compact, and robust and operate over a large temperature and current range, whereas

alternative sources may be complex and bulky and require precise alignment.

The use of a DBR to make a single-frequency laser source is only one of the several ways that a DBR can

be used to improve or otherwise make possible certain operating characteristics of a semiconductor laser. This

article describes the basic operating principles of a DBR and specifically how it is implemented in two types o

semiconductor lasers: edge-emitting lasers and vertical cavity surface-emitting lasers. Design and fabrication

issues for both types of laser are presented, as well as some of the advantages afforded by each design.

Dbr and Laser Basics

The DBR Concept. When light crosses a boundary between two materials that have different indicesof refraction, ni, the light experiences a partial reflection given by

ADBR is a structure that has a change in its refractive index that is repeated several times in a set period

termed the Bragg period, . The periodic change in the refractive index causes multiple partial reflections that

add constructively to create a strong reflection. Figure 2 is a simplified picture of how these multiple partial

reflections can add to form a strong reflection. As will be shown later, this type of additive reflection is maximized

when the incident light has a wave-length that is equal to twice the period of the Bragg reflector, . ADBR isuseful in two respects: it can create a strong reflection, and the reflection created is wavelength specific, that

is, it reflects some frequencies of light while allowing other frequencies of light to pass through unreflected.

The Semiconductor Laser. Before developing further how a DBR can be used to improve a lasersperformance, it is important to have clear understanding of the fundamentals of laser operation. Three factors

are required for laser operation: an amplifying or gain medium, a resonant cavity for feedback, and some means

1


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2 DISTRIBUTED BRAGG REFLECTOR LASERS

Fig. 1. Optical spectra of InGaAsPInP ridge-waveguide lasers. Several longitudinal modes exist in the simple FabryPerot laser, whereas the DBR laser exhibits single-frequency operation.

Fig. 2. Simplified pictorial of how multiple partial reflections can add to create a strong effective reflection in a DBR witha period .

of excitation. In a semiconductor diode laser, recombination of electrons and holes in the diode junction results

in light emission, and a population inversion of these carriers provides optical gain. The resonant cavity for a

semiconductor laser is formed by an optical waveguide with partially transparent mirrors on either end. An

electric current flowing through the diode is the source of excitation. The onset of lasing action occurs when the

excited gain medium begins to create just enough light to offset the loss of light due to internal losses within

the cavity and the loss of light through the semitransparent mirrors. This condition is given by the equation


5/86

DISTRIBUTED BRAGG REFLECTOR LASERS 3

Fig. 3. A schematic diagram of (a) wavelengths at which FabryPerot modes exist, (b) the gain distribution in a semiconductor laser, and (c) the superposition of (a) and (b) showing the possible laser modes in a simple FabryPerot laser. Allthree graphs are plots as a function of wavelength.

where int is the internal loss, g is the gain, L is the length of the cavity, and R1 and R2 are power reflectivities

of the two semitransparent mirrors.

The frequency of the laser light is governed by the energy distribution the gain medium is capable of

providing and by the geometry of the resonant cavity. The cavity constrains the emission to discrete frequencies

of light, or FabryPerot modes, whose half-wavelengths will fit in the cavity an integral number of times. The

smaller the cavity, the greater the spacing between adjacent FabryPerot modes. Because the round-trip cavity

loss is fairly constant for different modes, the laser emission from a simple semiconductor diode laser, usually

called a FabryPerot laser, will consist of multiple FabryPerot modes that coincide with the highest gain ofthe material (see Fig. 3).

Edge-Emitting Lasers. Simple edge-emitting semiconductor lasers are formed by first growing a pla-nar optical waveguide and diode junction by a suitable epitaxial growth technique. The laser is completed when

the semiconductor is cleaved in two places to produce reflective facets that terminate the planar waveguide

Laser light propagates in the plane of the semiconductor wafer and is emitted from the facet formed by the


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Fig. 4. A schematic diagram of a simple FabryPerot semiconductor diode laser. Laser light propagates in the plane ofthe semiconductor wafer and is emitted from the facet formed by the cleave at the edge of the wafer.

cleave at the edge of the wafer. Figure 4 shows a diagram of a simple FabryPerot edge-emitting laser fabricated

in this fashion.The facets formed by the cleave reflect due to the change in the index of refraction between

the semiconductor (n 3.5) and the air (n 1). The simple mirrors formed by the cleave reflect almost all

frequencies of light equally well, and hence many frequencies can and do experience enough reflective feedback

to lase. By replacing one or both of the facet reflectors with DBRs, the feedback created by the reflection can

be made wavelength selective. Thus, only the frequency of light that experiences a strong reflection from the

DBR will have enough feedback to lase. The DBRs are formed by etching a grating in the semiconductor. The

area where material is removed from the etched portion of the grating will have an index of refraction different

from that of the unetched material, creating a periodicariation in the refractive index.

Vertical Cavity Surface-Emitting Lasers. Advances in epitaxial growth techniques have recentlymade possible an alternative laser design that promise to provide several advantages over the more traditional

edge-emitter laser. The geometry of the vertical cavity surface-emitting laser (VCSEL) is rotated 90 from

that of the edge-emitter, and light emits from the surface of the wafer, rather than from the edge (see Fig.

5). The feedback mirrors are formed by epitaxially grown DBRs, which consist of alternating layers of two

materials with different refractive indices. This method of creating a periodic change in refractive index is

clearly different from the etched grating utilized in edge-emitting lasers. The reason DBRs are used in each o

the lasers is also different. In edge-emitting DBR lasers, the grating provides a wavelength-selective mirror

which is useful because it constrains the laser to operate at a single frequency. VCSELs, on the other hand

operate at a single frequency because theresonant cavity is very short, usually only one wavelength long. While

the short cavity creates a single-mode operation, it also causes the gain path to be very short. Consequently

the mirror reflectivies must be very high in order to satisfy the requirements for lasing. In VCSELs, the DBRs

are used to obtain a mirrors with extremely high reflectivities.

The Bragg Period

A simplified model of wavelength-selective reflection can give insight into how a DBR works. Consider a strong

electromagnetic wave, which can be represented by the real part ofE0 ejkz, incident upon a structure of period

at z = 0 (see Fig. 6). Assume only a negligibly small part, of the incident wave is reflected back at each


7/86


Fig. 5. A schematic diagram of a VCSEL. The geometry of the VCSEL is rotated 90 from that of the edge emitter, andlight emits from the surface of the wafer. The feedback mirrors are epitaxially grown DBRs.

Fig. 6. A schematic diagram of light incident on a structure with a periodic refraction index. In order for the smalreflections to interfere constructively and provide a large effective reflection, the periodic structure must satisfy the Braggcondition, = m/2.

interface. The reflected wave at z = 0 can be expressed as the sum of the small reflections at each of the

interfaces

Note that the phase components of the individual reflected waves are integer multiples of 2k, where k isthe wave number (2/) of the propagating wave. For these small reflections to constructively interfere (sum

and provide a large effective reflection, 2k must equal an integer multiple of 2 radians. This model is not

strictly valid because we have ignored the fact that the magnitude of the incident wave, E0, decreases and that

the backward traveling reflections will be partially reflected in the forward direction again. Nevertheless, the

model leads to an important concept: a periodic structure can provide a wavelength-selective reflection when


8/86


the period, is equal to an integer multiple of half wavelengths

where we have used the fact that k = 2/ and defined = 0/n0. The parameters 0 and n0 are, respectively

the free-space wavelength and the effective index of the laser mode. The order of the grating is designated by

the integer m.

Edge-Emitting Single Frequency Lasers

Both distributed feedback (DFB) lasers and DBR lasers utilize Bragg reflectors to induce single-frequencyoperation. The distinction between DFB lasers and DBR lasers lies in the placement of the Bragg grating (see

Fig. 7). In a DFB laser, the grating that provides distributed feedback is placed along the entire length of the

laser, whereas in the DBR laser, the grating does not overlap the active region, and is used only at the end

of the cavity as a wavelength-selective mirror. In 1972, Kogelnik and Shank outlined the principles behind

the operation of DFB lasers using a coupled wave model (1). Coupled-mode theory explains the operation o

both DBR and DFB lasers; however, the lasers realize single-frequency operation by two distinctly different

methods. In a DFB laser, only modes that can propagate in the periodic structure will exist. Of the allowed

modes, the mode nearest the Bragg wavelength will lase. In a DBR laser, where the Bragg grating is used

as a reflector, modes that can propagate through the periodic structure will not experience any feedback and

therefore cannot resonate and will not lase. The cavity mode that experiences the strongest reflection from the

DBR will lase, assuming the mode overlaps the gain spectrum of the material. DFB lasers were demonstrated

in 1974 (1), and demonstration of DBR lasers followed in 1975 (2).

Coupled-Mode Theory.Coupling Coefficient. To create a high degree of wavelength selectivity, the periodic structure must

satisfy the Bragg condition, and it must effectively interact with the optical mode in the laser structure. Within

a laser cavity, there are both forward- and backward-propagating waves. These waves are coupled through

the distributed reflections within the periodic structure. The coupling coefficient describes the degree o

interaction between the forward- and backward-propagating waves.

The coupling coefficient can be determined by applying coupled-mode theory. Let us start with a periodi-

cally varying index of refraction profile and use the coordinate system defined in Fig. 6

Note that any index variation profile, n(z), can be expressed in a similar expression by the Fourier

expansion of the function that describes the index variation. By making the approximation that the variationsof the optical field in the x and y directions are negligible, the wave equation for the optical field along the laser

cavity ( z direction) can be written as


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Fig. 7. Schematic diagrams of a (a) DFB laser and (b) DBR laser, with a diagram of the optical field intensity inside thelaser superimposed. The feedback mechanism (grating) is distributed along the entire length of the cavity in a DFB laserbut is separated from the gain section in for DBR laser.

When n(z ) is squared, the term including ( n)2 can be neglected. Therefore

where = (2/)n0 and = (/)n.

The complex propagation constant is assumed to be very close to the Bragg propagation constant 0.

where is the detuning parameter that represents the separation of from the Bragg propagation constant

and 0 represents the gain or loss in the medium.


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Next, we assume that the solution for the field, E(z), can be written as the superposition of a forward- and

backward-propagating components, with propagation constant 0.

The assumptions of Eq. (10) will result in A(z) and B(z) being slowly varying functions of z.

Equations (9) and (11) can then be substituted into Eq. (7). The first term of Eq. (7) becomes

The second derivative terms, d2 A/dz2 and d2 B/dz2, can be neglected because, as mentioned before, A and

B are slowly varying functions

The second term of Eq. (7) becomes

where the Euler identity has been used and third-harmonic terms have been neglected.

Collecting terms with common phase components and utilizing the assumption that , result in thecoupled-mode equations

These equations show that the forward-propagating term A(z) is coupled to the backward-propagating

term, B(z), by , and vice versa.

Thus far, the periodic index variation has been assumed to be infinite in the x and y directions. However

in a laser structure,the gratings (the periodic structure) have a finite dimension. Therefore, only a portion ofthe optical mode overlaps the periodic index variation. The expression for the coupling coefficient now must

account for the spatial extent ( x direction) of the index variation


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Fig. 8. Schematic diagram of the coupling coefficient , as a function of grating duty cycle for three different orderedgratings. The coupling coefficient is larger for lower order gratings. For odd-order gratings, there is maximum coupling a50% duty cycle. For even-order gratings, a null exists at 50%.

Here, d(x) is the Fourier expansion of the periodic index variation. Therefore, to obtain a large coupling

coefficient , the optical mode and the periodic structure should overlap strongly [large E(x)], or the index

variation d(x) should be sufficiently large.

Depending on the order of the grating, different duty cycles are required to achieve maximum coupling

A duty cycle is the length of the high-index region within the period devided by the period. Figure 8 shows a

schematic diagram of how the coupling varies with the duty cycle. For odd-order gratings, there is maximum

coupling at 50% duty cycle. For even-order gratings, a null exists at 50% duty cycle. The coupling coefficient is

larger for lower-order gratings.

In summary, several factors must be considered to achieve the desired coupling coefficient: the placementof the gratings within the laser structure, the order of the gratings, and the duty cycle are all factors that affect

the coupling coefficient.

Reflectivity. The reflectivity of a periodic structure is determined from the coupled-mode equations. Notethat the coupled-mode equations are linear, first-order differential equations. Therefore, the general solutions

to the coupled-mode equations have the form of

Substituting Eqs. (18) and (19) into Eqs. (15) and (16), the coupled-mode equations, yields


12/86


Fig. 9. Reflectivity of lossless ( 0 = 0 ) DBR gratings for L = 100 m with = 100 cm1 and = 400 cm1. Note tha

larger yields a higher reflectivity and a wider stop band.

In order for these equations to result in a nontrivial solution, the determinants of both matrices must

equal to zero. Making this assignment yields

Now, consider a periodic structure of length L with a forward traveling wave incident on it. For simplicity

assume that the strength of the incident wave, A(z = 0), is known, the structure is lossless ( 0 = 0 ), and

the backward traveling wave is zero at L, B(z = L) . These boundary conditions reduce Eqs. (18) and (19) to

a system of two equations and two unknowns. Using Eq. (22), it is possible to derive expressions for A(z) and

B(z) in terms of A(z = 0) . The reflectivity at z = 0 is then expressed as a ratio between the backward- and

forward-propagating components:

A plot of |r(0)|2 versus , the detuning parameter, for two different values of is shown in Fig. 9. The

region of high reflection near = 0 is called the stop band. The plot clearly shows that the reflectivity and

the width of the stop band increases with increasing . The reflectivity also increases with the length of the

grating, L.


13/86


Fig. 10. A schematic diagram of a holographic interference lithography setup. An interference pattern is formed when thetwo beams are brought together on the surface of the sample. The interference pattern is photolithographically transferredto the sample, which is spin-coated with photoresist.

Grating Fabrication. In 1975, Reinhart et al. used holographic interference and ion milling to createa third-order DBR grating. Since then, the fabricationand epitaxial technologies have improved steadily, and

these advances allow the design and fabrication of more sophisticated and complex devices.The small dimensions of the gratings, on the order of a few hundred nanometers, preclude the use

of conventional photolithography for their fabrication. Although recent advance have greatly reduced the

minimum feature size attainable by photolithography, two other methods are more common for gratings

fabrication today: holographic interference and direct-write electron-beam lithography.

A typical setup for holographic interference is shown in Fig. 10. The output of a laser is split into two

beams that are expanded and collimated. An interference pattern is formed when the two beams are brought

together on the surface of the sample. The interference pattern is photolithographically transferred to the

sample, which is spin-coated with photoresist. By choosing a laser with the proper laser wavelength () and

controlling the angles of the sample and beam incidence ( and ), it is possible to fabricate gratings with

different periods (pitches)

This simple technique has been used since the first fabrication ofDBR lasers. Because of its high through-

put, the holographic interference method is the most common fabrication technique used to produce DBR and

DFB lasers commercially. More complicated exposure schemes using multiple resist and phase shifting, among

others can be used to create gratings with more complex characteristics.

Electron-beam direct-write lithography is an alternative method for fabricating gratings. An electron

beam is used to write gratings on a sample spin-coated with a resist, typically polymethylmethacrylate (PMMA)

The accuracy of the period and duty cycle of the grating generated by electron beam direct-write lithography

depends on several factors, including the electron-beam current, the electron-beam size, and the scanning sys

tem. Although electron-beam direct-write lithography has been used togenerate gratings for high-performance

lasers, slow writing speed and high system cost limit its application in the commercial sector.Once gratings have been lithographically transferred into a resist, the next step is to etch the grating

pattern into the underlying semiconductor.Wet etching is a simple and easy process that causes little damage

to the semiconductor crystal. Precise etch depths can be achieved by utilizing selective wet etches. Lateral

dimensions can be much more precisely controlled by using dryetching techniques rather than using a wet

etch. However, dry etching can cause crystal damage that may need to be repaired before further processing.


14/86


The location of the gratings in the laser structure and the material system of the epitaxial layers determine

the subsequent processing. Typically,gratings are placed near the active region of the laser structure, where

the optical mode is strongest. Locating the grating near the peak of the optical mode creates strong coupling

but it requires that the epitaxial growth of the laserbe done in two steps, with the grating etch performed in

between the two growths. Because the optical mode interacts strongly with the grating, large variations in

the refractive index are not necessary [see Eq. (17)] and the depth of the gratings can remain small, which

is desirable when regrowth is necessary. Special care must be taken to preserve the shape of the gratings

during subsequent epitaxial growth because they can be deformed by mass transport. In the InPInGaAsP

material system, regrowth is fairly trouble-free when the sample is properly prepared. However, in the GaAs

AlGaAs material system, regrowth over gratings is can be problematic because of the highly reactive nature o

Al-containing compounds.

To circumvent this problem, aluminum-containing laser structures areusually grown in a single step

and gratings are etched on the surface of the laser. However, the placement of the gratings on the surface

reduces the amountof interaction between the optical mode and the grating because the optical mode is tightly

confined within the cladding layers, and only the tail of the optical mode can interact with the grating. As seen

in Eq. (17), to achieve an appreciable value for , a large index change in the grating structure is necessary to

compensate for the small overlap of the optical mode with the grating. To create this large change in refractiveindex, the gratings must be etched fairly deeply ( 0.8 m 1.0 m ) into the epitaxial layers. Because the grating

dimensions are only a few hundred nanometers and the etch depth may be a 1 m or more, the aspect ratio

of the grating is very large. The task of etching these large-aspect-ratio features into the semiconductor while

preserving the period, duty cycle, and shape is difficult to perform even with dry etching processes such as

reactive ion etching (RIE). More sophisticated dry etching techniques such as chemically assisted ion beam

etching (CAIBE) are often necessary to achieve the highly anisotropic etch demanded by the high-aspect-ratio

grating. DBR lasers with a thinner upper cladding, often called asymmetric cladding lasers, can be used to

circumvent this difficulty. Because the upper cladding is thinner, typically 0.3m to 0.4m, the field is stronger

at the surface and adequate coupling can be achieved even with a shallow grating etch ( < 0.25 m ).

Ridge waveguides, buried ridge waveguides, and buried heterostructures are some of the device configu-

rations to provide lateral confinement, both optical and electrical, necessary for improved performance of the

DBR laser.

Wavelength-Tunable DBR Lasers. For various applications such as wavelength-division multiplexingand light detection and ranging LIDAR spectroscopy, wavelength-tunable DBR lasers are highly desirable

It is possible to tune DBR lasers efficiently by injecting a current into the DBR section of the laser (3)

Current injection causes the refractive index of the semiconductor to change, which in turn changes the Bragg

wavelength of the grating, as seen in Eq. (5). Figure 11 shows a schematic diagram of a wavelength-tunable

DBR laser. The contact pads of the gain section and the tuning section of the laser are isolated so that each

section can be biased independently.

There are two mechanisms by which current injection changes the refractive index of a semiconductor.

Injected free carriers and band-filling effects cause a decrease in the index of refraction. This phenomenon is

referred to as the plasma effect and is described by

where n0 is the index of refraction, ne is the electron concentration, and me is the effective electron mass.

Current injection also causes heating of the laser structure, which creates in an increase in the index

of refraction. Therefore, injecting carriers to the DBR section can tune the output of a DBR laser to a longer

or shorter wavelength, depending on which mechanism dominates. The plasma effect increases as a function


15/86


Fig. 11. Schematic diagram of a tunable DBR laser showing the isolated contact pads of the gain section and the tuningsection of the laser so that each section can be biased independently. It is possible to tune DBR lasers efficiently by injectinga current into the DBR section of the laser.

of2. Thus, in the long-wavelength InP material system, current injection into the tuning section decreases

the Bragg wavelength. The heating mechanism dominates in the shorter-wavelength GaAs material system

resulting in an increase of the Bragg wavelength.

Tuning is not continuous with tuning current but is interrupted by mode hops. As the peak Bragg

reflection shifts, the lasing wavelength also shifts. When the peak shifts over far enough, an adjacent cavity

mode will experience a higher reflectivity. This selection of successive cavity modes causes mode hopping in the

wavelength tuning characteristic. The addition of a third phase controlling section can extend the continuous

tuning range (4). The tuning range is typically limited by the amount of index shift that can be achieved in the

mirror ( / = n/n ). A maximum tuning range of1% of the wavelength is common (5). Increased tuning

range can be achieved when more complex structures and tuning schemes such as superstructure gratings and

sampled gratings are employed (6,7).

Integrated DBR lasers. Because the gratings eliminate the need for cleaved facets, and the reflectivitycan be controlled by the length, depth, and order of the grating, it is possible to design and fabricateDBR lasers

with monolithically integrated waveguides, modulators, and amplifiers. The separation of the active and grating

sections of the laser enables the laser to be interconnected with other optical components using a continuous

waveguide that permits high optical coupling between the source and these components. The laser structurecan be optimized for improved performance with these devices by smoothly integrating regions with differen

bandgaps. One technique for achieving in-plane bandgap tuning within a single epitaxial growth is selective

area epitaxy (SAE). For example, Lammert et al. have demonstrated an electroabsorption modulator integrated

with a DBR laser utilizing SAE (8). The bandgap of the modulator section is designed to be larger than the

bandgap of the laser. Therefore, the modulator is transparent until a modest reverse bias is applied to shift the

absorption peak to extinguish the output signal from the DBR laser.

Vcsel

The concept of the VCSEL, a surface-emitting diode laser formed by sandwiching a pn junction between two

epitaxially grown DBR mirrors, was initially conceived by Soda et al. at the Tokyo Institute of Technology in

1979 (9). The VCSEL, although requiring more complex and exacting crystal-growth processes, has severaladvantages over the edge-emitting laser. Aside from the more complicated epitaxial growth, the VCSEL is a

more attractive candidate for manufacturing. Because the VCSEL does not require etched or cleaved facets

these devices can be fully tested at the wafer level, before committing to further processing steps. It is also

much smaller than an edge-emitting laser, so more devices can be produced from each wafer. The all planar

processing of the VCSEL also facilitates integration of the VCSEL with other electronic devices.


16/86


The attribute of surface emission, in addition to eliminating the need for cleaved facets, makes possible the

fabrication of two-dimensional arrays of lasers, which lends itself to applications in parallel communications

Or, by allowing the growth thickness to change across the wafer, each VCSEL in the array can be made to lase

at a slightly different frequency, which allows for wavelength-division multiplexing (WDM).

One serious drawback of the edge-emitting laser is its highly elliptical and astigmatic beam pattern

which arises from the aspect ratio of the lasers aperture (thin and wide). Such a beam pattern requires the

use of additional optics in many applications, such as coupling to an optical fiber. There is much more control

over the design of the aperture and beam pattern of the VCSEL, and consequently the emission beam pattern

has much better characteristics.

The smaller size of the VCSEL improves operating performance because of smaller drive currents, capaci-

tances, and power requirements. Moreover, because the cavity of the VCSEL is very short, only one longitudina

mode can exist, so the emission is inherently single longitudinal mode. A drawback of the small size is that the

VCSEL output power is small as well.

VCSEL Design. Because the gain path in a VCSEL is very short (twice the length of the cavity, typically2 ), the reflectivity of the cavity mirrors must be extremely high ( >99% ) to satisfy the requirement for lasing

where u and l are the total field reflectivities of the upper and lower mirrors, L is the length of the cavity, and0 is the gain coefficient. The equation for the net reflectivity of a VCSEL DBR mirror is given by the formula

for a plane wave experiencing multiple reflections and is found in many textbooks

Here i is the net field reflectivity at layer i, i is the propagation constant in layer i, li

eff is the effective

thickness of layer i, and ri is the local reflectivity between the layers i and i+1.

In order to make large, two conditions are required: (1) a large number of quarter-wavelength-thick

layers in the Bragg reflector, and (2) two materials with contrasting indices of refraction out of which to make

the pairs. Because the VCSEL has only one longitudinal mode, which is determined by the length of the cavity

the cavity length must be grown with great precision to attain the desired wavelength. The length must be

such that the resulting mode overlaps the gain spectrum and the stop band of the DBR.

Mirror Fabrication. The VCSEL is perhaps the most challenging optoelectronic structure to be created bycrystal-growth techniques. While the concept for the VCSEL has been around for a long time, its performance

had been limited largely due to the complexity of mirror fabrication.

InGaAs and AlGaAs lasers, which operate at shorter wavelengths (800 nm to 1100 nm), utilize AlAs

GaAs DBRs. AlAs and GaAs have large differences in their indices of refraction and are almost perfectly latticematched, which makes them ideal for use in a DBR. AlAsGaAs mirrors, as semiconductor materials, can be

doped to allow current to flow directly through them to the active region of the laser. Even though the AlAs

and GaAs have strongly contrasting indices of refraction, more than 20 pairs are needed in the DBR to obtain

the necessary reflectivity. The multiple abrupt heterointerfaces in the mirror can create a significant electrical

resistance, which leads to heating and higher power requirements. This effect can be reduced by compromising


17/86


to some degree on optical design. By grading the composition and heavily doping the heterointerfaces this

series resistance can be reduced and overall performance of the VCSEL is improved (10).

Lasers based on InP-based material systems, which provide the longer wavelengths suitable for use in

optical communications, lack semiconductor materials that are both lattice matched and have sufficient contrast

in their indices of refraction to be good candidates for materials in a DBR. Without a substantial difference

in refraction indices, the number of DBR pairs required poses problems both in the precision of the extended

growth and with incurred diffraction losses. One solution has been to use dielectric materials having disparate

refraction indices, such as ZnSeCaF2 or TiO2ZnO2, in the Bragg reflector in place of semiconductors. Because

of the insulating nature of these dielectrics, this technique leads to problems in making electric contacts and

with heat dissipation. Another solution has been to use the same AlAsGaAs DBRs that are used to make

VCSELs at the shorter wavelengths. While AlAsGaAs mirrors cannot be grown directly on a material to which

it is not lattice matched, such as InP, it can be grown separately and then later fusion bonded onto another

material (10). Fusion bonding is a process using heat and pressure to adhere two semiconductors together.

Lateral Confinement. Another design aspect that has received a great deal of attention is the definitionof the lateral dimensions of the VCSEL. Lateral definition of the cavity is needed both to efficiently funnel

carriers to the active region and to provide confinement for the optical mode. Several techniques have been

used for this process. One method is simply to etch away all the surrounding material from the VCSEL, leavinga so-called air post VCSEL. This provides strong electrical and optical confinement. A disadvantage of this

technique is that the resulting morphology is nonplanar, making placement of electric contacts difficult. In a

second technique, rather than etching away the surrounding material, it is rendered electrically insulating by

ion bombardment. This technique has proved to be highly reliable and is currently used to produce VCSELs

commercially. For VCSELs using AlAsGaAs mirrors, selective oxidation is a recently developed technique

that has proved most successful in creating small apertures, leading to smaller devices with lower threshold

currents and higher efficiencies (11). In selective oxidation, aluminum-containing layers of the DBR mirror are

oxidized, providing both electrical and optical confinement. Holes are etched in the perimeter of the VCSEL

and the VCSEL is placed in a steam environment at elevated temperatures. Oxidation initiates from the etched

holes, creating a ring of oxide, the center of which forms the aperture of the VCSEL. The aperture size can be

closely controlled by how much material is allowed to oxidize.

Conclusion

Both edge-emitting DBR lasers and VCSELs are important laser sources for a variety of applications ranging

from optical communications to spectroscopy. Because of their advantages over traditional FabryPerot semi-

conductor lasers, significant resources have been directed towards active research and development of both

laser structures.

The single-longitudinal-mode operation of DBR lasers is a major advantage over FabryPerot lasers. In

addition, because the cavity is defined by gratings rather than a cleave, DBR lasers can be monolithically inte

grated with other optoelectronic components. The ability to tune the output wavelengths by current injectionmakes DBR lasers excellent candidates for wavelength-division multiplexing (WDM) applications.

Compatibility with current integrated-circuit fabrication technologies, the possibility of two-dimensiona

array configurations, and on-wafer testing enable inexpensive fabrication and packaging ofVCSELs. As VCSEL

technology matures, the numerous advantages of the VCSEL design will undoubtedly allow it to displace light

emitting diodes and edge-emitting lasers in some extisting applications as well as to foster new applications.


18/86


BIBLIOGRAPHY

1. H. Kogelnik C. V. Shank, Coupled-wave theory of distributed feedback 011lasers, J. Appl. Phys., 43: 23272335, 1972

2. F. K. Reinhart, R. A. Logan, C. V. Shank, GaAsAl xGa1-x As injection lasers with distributed Bragg reflectors, Appl

Phys. Lett., 27: 4548, 1975.

3. S Murata, I. Mito, K. Kobayashi, Spectral characteristics for a 1.5 m DBR laser with frequency-tuning region, IEEE

J. Quantum Electron., QE-23: 835838, 1987.

4. S Murata, I. Mito, K. Kobayashi, Over 720 GHz (5.8 nm) frequency tuning by a 1.5 m DBR laser with phase and

Bragg wavelength control region, Electron. Lett., 23: 403405, 1987.

5. Y. Kotaki H. Ishikawa, Wavelength tunableDFB andDBR lasers for coherentoptical fibre communications,IEE Proc.-J

138: 171177, 1991.

6. Y. Tohmori,, et al. Broad-range wavelength tuning in DBR lasers with super structure grating (SSG), IEEE Photon

Technol. Lett., 5: 126129, 1993.

7. V. Jayaraman,, et al. Extended tuning range in sampled gratingDBR lasers, IEEE Photon. Technol. Lett., 5: 489491

1993.

8. R. M. Lammert,, et al. MQW wavelength-tunable DBR lasers with monolithically integrated external cavity electroab

sorption modulators with low-driving voltages fabricated by selective-area MOCVD, IEEE Photon. Technol. Lett., 8

797799, 1996.

9. H. Soda,, et al. GaInAsP/InP surface emitting injection lasers, Jpn. J. Appl. Phys., 18: 23292230, 1979.

10. Y. Ohiso, et al. T. Kurokawa, Long-wavelength (1.55-um) vertical-cavity lasers with InGaAsP/InP-GaAs/AlAsDBRs by

wafer fusion, IEEE J. Quantum Electron., 34: 1904711913, 1998.

11. W. W. Chow,, et al. Design, fabrication, and performance of infrared and visible vertical-cavity surface-emitting lasers

IEEE J. Quantum Electron., 33: 18101824, 1997.

READING LIST

G. P. Agrawal (ed.), Semiconductor Lasers: Past, Present, and Future, Woodbury, NY: American Institute of Physics, 1995

J. Buus, Single Frequency Semiconductor Lasers, Bellingham, WA: SPIE Optical Engineering Press, 1991.

H. Casey M. Panish, Heterostructure Lasers, New York: Academic, 1978.

K. D. Choquette, Vertical-cavity surface emitting lasers: moving from research to manufacturing, Proc. IEEE, 85: 1730

1739, 1997.

L. A. Coldren S. W. Corzine, Diode Lasers and Photonic Integrated Circuits, New York: Wiley, 1995.K. S. Giboney, L. B. Aronson, B. E. Lemoff, The ideal light source for datanets, IEEE Spectrum, 35: 4353, February 1998

T. L. Koch U. Koren, Semiconductor photonic integrated circuits, IEEE J. Quantum Electron, 27: 641653, 1991.

S. D. ROH

R. B. SWINT

J. J. COLEMAN

University of Illinois


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20/86

DISTRIBUTED FEEDBACK LASERS 705

Emission spectrum of FP lasers can be considerably nar-

rowed by providing wavelength-selective feedback. In DFB la-

sers, such a wavelength-selective feedback is provided within

and throughout the laser cavity. This type of feedback can

also be provided by wavelength-selective mirrors. Such a la-ser is called the distributed bragg reflector (DBR) laser. The

DBR laser is a diverse subject in itself and will not be dis-

cussed here. FP lasers that are externally stabilized using a

grating to provide wavelength-selective feedback also fall into

this category. The external grating may also be written on the

fiber used to couple light out of a diode laser in a package.

Frequency-tunable lasers can be made using external grat-

ings. The wavelength of the feedback into the laser cavity is

DISTRIBUTED FEEDBACK LASERS adjusted by changing the orientation of the grating with re-spect to the laser cavity and, by continually changing the ori-

Distributed feedback (DFB) lasers are a special class of semi- entation of the grating, the laser output can be tuned over a

wide range of frequencies.conductor diode lasers. They have found widespread applica-

tion in fiber optic telecommunication systems, where they are

essential for the operation of long-haul fiber links. DFB lasers

have a much narrower wavelength emission spectrum com- DFB DEVICE STRUCTURE AND MATERIAL CHARACTERISTICSpared to the conventional diode lasers, and they emit lightessentially at a single wavelength. For this reason they are Electrically, semiconductor lasers are equivalent to p n junc-

tion diodes. They are composed of a vertically (or laterally)also referred to as single frequency lasers. Diode lasers oper-

ate on the same amplification of stimulated emission princi- stacked p and n heterojunction sandwich. The excitation is

provided by injecting electrical current in a forward-biasedple as other laser systems. To achieve this light amplification,

lasers are composed of a gain medium inserted between two configuration. The current flow is bipolar, that is, the current

transport is composed of both electrons and holes. The hetero-mirrors. The mirrors provide the positive feedback needed to

initiate laser action, as external excitation is applied to the junction is necessary to confine the bipolar carriers in the

same spatial location for efficient recombination, thereby re-active medium. This configuration of an active region and

mirrors is referred to as the laser cavity. The mirrors are gen- ducing the threshold necessary to overcome cavity losses for

laser action. An electron recombines with a hole to produce aerally not completely reflecting, so some amount of light leaks

out and is collected as output from the cavity. As the active photon. The first-generation diode lasers were of the homo-

junction type and required very large pump excitation for la-medium is excited, or pumped, the excitation is converted to

light by the gain medium. The light begins to propagate ser action.

Figure 1 shows a drawing of a modern buried heterostruc-within the cavity formed by the mirrors and the optical field

starts to build up in intensity. Laser action begins once there ture DFB semiconductor laser diode. Buried refers to the

fact that the p n heterojunction gain region of the laser hasis enough light to overcome the cavity and mirror losses.

In a typical laser cavity, the feedback from the mirrors is been completely surrounded by another material. This mini-

mizes the material index variation adjacent to the active re-broadband and is not wavelength selective. A passive cavity,

that is, in the absence of the gain region, is a resonator which, gion, and it has some desirable waveguide properties for the

optical mode within the cavity. The wavelength-selective feed-in principle, will support an infinite number of oscillating

modes. In a laser, the wavelength of operation depends on the back in the cavity is provided by the mode index or gain/ loss

variations caused by the grating etched into the semiconduc-range of wavelengths over which the active medium can pro-

vide useful gain. Diode lasers of this type are referred to as tor material. InP/In1xGaxAsyP1y material alloy combination

is typically used to make DFB lasers for telecommunicationFabryPerot (FP) lasers. They generally operate at several

different wavelengths or longitudinal (the direction along the applications. Lasers made of this material combination emit

light in the 1.2 m to 1.6 m wavelength. Although DFB la-cavity) modes. This type of laser is acceptable for many appli-

cations except in those where the dispersion in the optical sers have been made from other material systems, most are

from GaAs/AlxGa1x. As alloys emitting light in the 0.75 mfiber becomes detrimental. The mode index (which is a combi-

nation of the material refractive index and contributions from to 0.85 m region, these have not found use in long-distance

data transmission due to the loss and dispersion characteris-the waveguiding structure) of the optical fiber varies as afunction of the wavelength of light propagating in it. This tics of the commonly used silica optical fiber. This discussion

will only be concerned with the InP based or, more commonlyvariation in index, which is commonly referred to as fiber dis-

persion, causes different wavelengths to propagate down the called, the long-wavelength DFB lasers.

Figure 1 also shows the conduction band energy diagramoptical fiber at different speeds. When the laser signal, which

is composed of several different wavelengths from a FP laser of three possible types of active regions. In all three cases the

light-emitting layer, the one in the middle (usually made oftransmitter, reaches the receiver, after traveling some dis-

tance in the optical fiber, it is spread out in time. This results the InGaAs alloy) has the lowest bandgap energy. The outer-

most cladding regions are usually composed of InP and thesein signal distortion, called the intersymbol interference, and

severely limits the transmission distance of fiber optic sys- layers have the largest bandgap energies. This combination

of materials with different bandgap energies to form the p ntems. To limit dispersion-induced distortion, one needs a laser

source with a narrow emission spectrum. junction is referred to as a heterojunction. In a homojunction

J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright# 1999 John Wiley & Sons, Inc.


21/86

706 DISTRIBUTED FEEDBACK LASERS

Figure 1. Cut-away drawing of a buried het-

erostructure DFB laser. The active region is

the layer above the grating. The doping se-

quence for the laser structure is p-active re-

gion-n from the top to bottom. The sequence

for the burying structure is the reverse. In

addition to providing good waveguiding prop-

erties, the reverse doping sequence of the

burying structure forms a current blocking

region, thereby channeling the injected cur-

rent, under forward bias, directly into the ac-

tive region. The details of the active region

conduction band energy structure are also

shown. The material layer between two

quantum wells is called the barrier. The

width of the layer between the outer cladding

and the first quantum well is usually varied

to provide maximum overlap between the

quantum wells and the optical mode in the

cavity. This type of design is called the sepa-

rate confinement heterostructure. The total

width of the confinement heterostructure (allthe layers between the outer InP cladding

layers) is about 0.2 m (of the order of the

p contact electrode

n-InP

n contact electrode

p-InP

n-InP

InP

DFB grating

Acti ve region Longi tudinal direct ion

InGaAsP cap layer

InGaAsP

InGaAsP orInGaAs

Dielectric layer

Buried heterostructure

Increasingindex

Increasingenergy

Bulk Single quantum well Multiple quantum well

width of the bulk active region).

laser, the cladding and active regions have the same bandgap The very strong interest in the 1.5 m region is also due

to the ready availability of erbium-doped fiber amplifiersenergies and no electric potential is present to confine the car-

riers and facilitate their recombination. In Fig. 1, it is easy to (EDFA) for boosting signals at this wavelength. Similarly,

praseodymium-doped fiber amplifiers (PDFA) can be used tovisualize the carriers tumbling down the energy potential of

the active region to the lowest level before recombining to boost signals in the 1.3 m wavelength region. The amplifi-

cation bands for both wavelength regions have been superim-emit light. In the bulk active region, the layer width is typi-

cally between 0.1 m and 0.2 m. In this case, the carriers posed on the fiber attenuation characteristics in Fig. 2.

are unconfined in all three dimensions. As the width of the

active layer (the smallest bandgap layer in Fig. 1) shrinks to

about 0.01 m, the carriers are quantum mechanically con-

fined in the direction of the smallest dimension, but are free

to move in the plane vertical to the paper. These are called

quantum well lasers. Quantum well lasers can either have

single or multiple wells. InP lasers, in general, tend to have

multiple quantum wells (between 4 and 7). Although the clad-

ding regions are p and n doped, the active region proper is

nominally undoped. The active region is grown such that it is

lattice matched to all the other layers. Doping and strain (by

deliberate lattice mismatching of the active region) may be

introduced into the active region. If done correctly, strained

quantum well lasers and lasers with moderately doped active

regions have a number of useful properties, like lower thresh-

old current, narrower linewidth, and higher direct modula-

tion bandwidth.

Figure 2 shows the attenuation characteristics of the silica

fiber most commonly used in fiber optic transmission. Theminimum in the loss characteristics occur at about the

1.55 m wavelength, and hence, the relevance of DFB lasers

emitting at this wavelength. The window at 1.3 m wave-

1.3 m window

1.5 m window

100

10

1

0.10.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

Wavelength ( m)

Loss(dB/km)

length is traditionally significant because the dispersion of theFigure 2. Attenuation characteristics of the silica fiber which is com-standard step index optical fiber goes to zero at this wave-monly deployed in the ground. The loss minimum occurs at around

length (technically, it is the first-order dispersion term that1.55 m wavelength. The peaks in the absorption curve near the 1.3

goes to zero at this wavelength, but dispersion has otherm region is due to the hydroxyl ions (water), which are incorporated

higher-order terms that then become significant). In modern as impurities in the fiber during fabrication. The optical transmissionfibers this wavelength, also call the zero dispersion wave- windows at 1.3 m and 1.5 m wavelengths are also shown. Theselength, can be tailored to match the loss minimum at 1.55 m. lines are merely to show the bandwidth of the windows and are not

indicative of any loss values.This type of optical fiber is called the dispersion shifted fiber.


22/86


WAVELENGTH DIVISION MULTIPLEXING where k20 200 is the propagation constant in the vacuum

and the complex permittivity, tot, of the medium has been

The fiber has a very large bandwidth for signal transmission. written as a sum of its real and imaginary parts. Consider a

nonmagnetic dielectric medium, 0. If the refractive indexThe advent of fiber-based optical amplifiers and other fiber-

based devices has made it possible to realize this bandwidth of the medium is n and the gain in the medium is (in unitsof inverse length), then the complex refractive index of theover very large transmission distances. One way of utilizing

this huge bandwidth is to use wavelength division multi- medium, ntot, can be written as

plexing (WDM). Since it is impossible, at least for the present

generation of electronics, to take full advantage of all the us-

able fiber bandwidth, WDM systems employ lasers at severalntot = n+ j

2(3)

different wavelengths, each carrying a high-speed data signal.Assuming that the gain is small over distance of the order ofThis is analogous to the subcarrier division multiplexed sys-a wavelength, /2 n,tems in the microwave domain. For instance, the conventional

amplification band in the EDFA is about 32 nm wide. Current

commercial transmission systems can accommodate signals tot = n2tot n

2 + jn

(4)

spaced at 100 GHz or 0.8 nm apart for a total of 40 channels.

Each of these channels run at the SONET (Synchronous Opti-The expression for k2 in Eq. (2) can then be written as

cal Network) OC-48 standard data rate of 2.48832 Gbit/s for

an aggregate data rate close to 100 Gbit/s. There are propos-

als to halve the channel spacing and quadruple the data ratek2 = k2

0

n2

1 + j

n

= k2

0

n(z)2

1 + j2(z)

k0n(z)

(5)

for an eightfold increase in data throughput to 800 Gbit/s in

a single silica fiber. This data throughput can be further en-where k0 2/. In a DFB structure, both n and vary peri-hanced with the new generation EDFAs, which, in laboratoryodically, and they are taken to be a function of the z coordi-

tests, have demonstrated as much as 80 nm bandwidth in thenate, that is, the longitudinal direction in the laser. The peri-

1.5 m wavelength region. As the wavelengths are packedodic spatial variation of the index and gain along the z

together for higher and higher data throughput, the termdirection in a DFB laser cavity can be written as

dense WDM (DWDM) systems is coming into common usage.

Modern-day DWDM systems increasingly need DFB lasers

with tighter wavelength control and higher spectral purityn(z) = no +n cos(20z)

(z) = o + cos(20z)(6)

(this translates to a requirement for narrow linewidth or low

phase noise DFB lasers) for proper implementation. The ulti-where 0 is the propagation constant of the waves at themate limit to DWDM systems is the coherent transmissionBragg condition. If 0 is the period of the distributed feedbacksystem.structure, 0 /0. At the Bragg condition,A review of the current state-of-the-art in components for

optical fiber telecommunication systems may be found in the

two volume set edited by Kaminow and Koch (1). Two good 0 0

= 2/n0

(7)

textbooks in the area of semiconductor lasers are by Coldren

and Corzine (2), and Agrawal and Dutta (3).which implies that the spatial periodicity, 0, is equal to half

the wavelength of the light in the medium, (/2) /n0. This is

an important result for all devices that depend on some formANALYTIC TREATMENTof a distributed reflector for their operation. Although this re-

sult has been assumed here, it can shown to be true usingDistributed Feedback ModelFourier analysis of wave propagation in periodic structures

Detailed analysis of a DFB laser is complicated, and is only(2). Substituting Eq. (6) into Eq. (5), one obtains the following

possible using numerical techniques. We present an analyticexpression for the propagation constant:

model which explains all major properties of DFB lasers with-

out having to use numerical techniques. We follow the analy-

sis used in the seminal paper on this subject by Kogelnik and k2 2 + 2j0 + 4

n

+ j

2

cos(20z) (8)

Shank (4). The idea is not to replicate their work, but to pro-

vide an overview of the analysis and also supply a number of

In deriving the expression for k in Eq. (8),

k0n0 and ismissing steps in the derivation that may prove useful to the assumed that n n0, 0, and 0 0. Equation (8) canreader. Starting point of the analysis is the scalar wave equa-

be rewritten in terms of a coupling constant astion for the electric field.

E2

z2+k2E = 0 (1)

where E is the complex amplitude of the electric field. This

k2 2 + 2j0 + 4 cos(20z)

= 2 + 2j0 + 2 (e2j0 +e2j0 )

r + ji = n

+ j

2

(9)

field varies with angular frequency . The propagation con-

stant, k, can be written as The coupling constant defines the strength of the feedback

provided by the gratings in the DFB laser. The expression for

k2 can then be substituted into the scalar wave, Eq. (1).k2 = 2 = 200(r + ji) = k

20(r + ji ) (2)


23/86


Coupled Wave Description conditions at the facet play a large role in the steady-stateevolution of the optical field within the laser cavity. To sim-

The scalar wave equation, in principle, will have an infiniteplify the analysis here, assume that both facets are anti-re-

set of solutions each corresponding to a certain diffraction or-flection coated, that is, the forward-propagating wave is not

der of the propagating wave. Consider the lowest-order solu-

reflected at the right-hand-side facet (thus not contributing totion to the equation close to the Bragg frequency. This corre-the initial value of the backward-propagating wave) and the

sponds to a forward -and-backward traveling wave. In thebackward-propagating wave is not reflected at the left-hand-

absence of any perturbation, these basic modes of the wave-side facet (thus not contributing to the initial value of the

guide are orthogonal and do not couple, but in the presenceforward-propagating wave). These boundary conditions can be

of index and/ or gain variations in the laser cavity they scatterwritten as

into one another and form the basis of the coupled wave de-

scription of the DFB laser. The sum of the complex ampli- R(L/2) = S(L/2) = 0 (15)tudes of the forward-and-backward traveling waves, which

will form the trial solution to the wave equation, is written asHere it has been assumed that the total cavity length is L

extending from z L/2 to z L/2. In a FP laser, theE(z) = R(z)ej0z + S(z)ej0z (10)

cleaved, uncoated, semiconductor crystal facets provide about

30% power feedback, which initiates and sustains laser actionSubstituting Eq. (9) and Eq. (10) into Eq. (1),

by overcoming the losses with the cavity. For all practical

purposes, this feedback is uniform over all frequencies and

such a laser is not wavelength selective. In the DFB struc-ture, only frequencies at or close to the Bragg frequency will

be supported by the cavity. If there is additional feedback

from the facets (cleaved and uncoated) of the DFB laser, then

the natural FP modes of the laser cavity will not be com-

2R

z2 2j

0

R

z 2

0

R+ 2R+ 2j0

R+ 2 S

ej0z

+

2S

z2+ 2j0

S

z 20 S+

2S+ 2j 0S+ 2R

ej0z

+ 2Re3j0z + 2 Se3j0z = 0 (11)pletely suppressed, leading to poor single-mode oscillation

characteristics.Since it has been assumed that the perturbations in the gainThe wave equations in Eq. (14) can be rewritten asand index of the medium are small, 2R/z2 and 2S/z2 can

be neglected. If the coefficients of each of the harmonic compo-

nents are independently set to zero, one obtains a pair of cou-

pled-wave equations:

2R

z2 [ 2 + (0 j)

2]R = 0

2S

z2 [ 2 + (0 j)

2]S = 0

(16)

The general solution of these equations is of the form:

R

z+

0

0R j

2 2020

R = j

0S

S

z+

0

0 S

j

2 20

20

S=

j

0 R

(12)

R = r1ez + r2e

z

S = s1ez +s2e

z(17)

When the deviation from the Bragg frequency is small, the

coupled wave equation can be simplified by setting /0 1.where the complex propagation constant is given by

A normalized frequency deviation parameter, , is then de-

fined as2 = 2 + (0 j)

2 (18)

If is real then R and S will be purely evanescent waves and =

2 20

20

0 =no( 0)

c(13)

if is imaginary then R and S will form a standing wave

within the cavity. Since it has been assumed that the deviceWith these simplifications, the coupled wave equations reduce is symmetric, the solutions will be such that E(z) E(z)to and E(z) E(z). Using this and the boundary conditions,

the solutions may be written as

R(z) = sinh[ (z+L/2)] = (e (z+L/2)

e (z+L/2)

)/2S(z) = sinh[ (zL/2)] = (e (zL/2) e (zL/2))/2

(19)

R

z+ (0 j)R = jS

S

z+ (0 j)S = jR

(14)

where is the deviation of the oscillation frequency from These equations describe the longitudinal distribution of the

optical modes within the laser cavity. The forward-travelingthe Bragg frequency 0. At the Bragg frequency, 0.

The coupled wave equations describe a forward-propagat- wave, R(z), builds up from zero at the left-hand end of the

cavity at z L/2 to its maximum at the right-hand end ofing wave that is first amplified by the medium. This wave is

then scattered by the grating at frequencies close to the Bragg the cavity at z L/2, and likewise the backward-traveling

wave, S(z), from the opposite end of the cavity.frequency into the backward-propagating wave. This scat-

tered wave reinforces the backward-propagating wave in the Now to determine the set of eigenvalues for the cavity

structure: This can be done by substituting Eq. (19) [takingcavity. Likewise, some of the backward-propagating wave is

scattered into the forward-propagating wave. The boundary the negative solution for S(z)] into Eq. (14). The sum and dif-


24/86


ference of the resulting equations are taken and the common The phase condition is central to the operation of the vari-

terms are eliminated. The results is as follows: ous classes of DFB lasers. The implications of the phase con-

dition are listed below.

1. The cavity resonances are spaced approximately c/2n0Lapart. This is like any other two mirror, FabryPerot

laser cavity of length L.

2. Most conventional DFB lasers are purely index coupled,

that is, , i 0. The lowest-order solution occurs for

[e L/2 +e L/2]+ (o j)[e L/2

e L/2]

= j[e L/2 e L/2]

[e L/2 e L/2]+ (o j)[e L/2

+e L/2]

= j[e L/2 +e L/2]

(20) q 1, 0 where v1 vo c/4n0L, vo vo c/4n0L.

There is no solution at the Bragg frequency (vo), andEquation (20) can be again simplified by taking their sum and hence one has the problem of two degenerate modes indifference, to obtain Eq. (21): a conventional DFB structure, which are both equally

likely to dominate unless something is done to break

this degeneracy.

3. One way around the problem of two degenerate modes

(0 j) = jeL

+ (0 j) = jeL

(21)

is to introduce a /4 additional phase shift within theThese equations can then be combined into one to obtain the cavity. For the index-coupled case, that modifies the

complex transcendental equation for , which can then be nu- phase condition as follows:merically solved for the modes of the DFB structure. Each

of these modes has its own threshold and lasing frequency

corresponding to a particular cavity length and coupling

v vo

(c/2n0L)= q+ 1

strength of the grating.

Now there is a resonance at the Bragg frequency, v1 Approximate Solutions

v0. This shift is introduced in the grating structure, and

for symmetry reasons, it is usually done in the middleSeveral important results can be obtained without having toof the laser cavity during fabrication.resort to a numerical solution of Eqs. (21). Invoke what is

known as the high gain approximation to obtain these results. 4. The second solution is to fabricate a gain (or loss) cou-The expressions for given in Eq. (18) can by simplified by pled DFB laser instead of the conventional index cou-

using the high gain approximation, that is, 0 ( r pled one. In this case, n, r 0. This modifies theji n/ j/2). phase condition as follows:

0 j (22) v vo

(c/2n0L)= p+ q+ 1

Substituting Eq. (22) into the second expression in Eq. (21),

where p and q are integers such that p, q .2(0 j) = je(

0j)L (23)

Again there is a resonance at the Bragg frequency,

v0,1 v1,0 vo. Generally, most gain-coupled DFB la-Although the right-hand side of Eq. (23) is strictly negative,sers also have some amount of index coupling.if one were to repeat the analysis starting at Eq. (19), taking

5. The phase condition has been derived for a symmetricthe positive solution for S(z), the result would be the positivecavity. In practice, lasers with cleaved facets are seldomsolution for the right-hand side of Eq. (23). Equation (23) can

symmetric, and there is a good chance that one of thethen be solved to obtain the approximate solutions of the

modes of the DFB structure. two degenerate modes will have a more favorable phase

First derive the phase condition that must be satisfied by condition. Although one of the modes will dominate and

the lasing modes in the cavity. This can be done by comparing lase, it is not possible a priori to determine the lasingthe phase of both sides of Eq. (23). wavelength, and this particular mode may not have a

high discrimination under all operating conditions. The

second mode is usually not completely suppressed, andmay dominate under a slightly different operating con-

tan1

0

= tan1

ir

L (24)

dition, for instance, a different bias current or tempera-Near the Bragg frequency, one can assume 0. After sub- ture. Cleaved facets thus lead to poor single-mode yieldsstituting for from Eq. (13), Eq. (24) can be simplified to in DFB lasers. Commercially, the front facet of a DFB

laser is usually anti-reflection coated and the rear facet

is high reflection coated. This breaks the mode degener-

acy leading to a better single-mode performance. This

also results in a higher front facet output power (com-

pared to the cleaved facet case, where both the front

q+1

2

= tan1

i

r

2n0 (v vo )

cL

v vo

(c/2n0L)= q+

1

2+

1

tan1

i

r

(25)

and back facets both have equal reflectivities), which is

essential for practical applications.where 2v and q is an integer such that q .


25/86


Similar to the phase condition, the absolute value of Eq. (23)

is used to obtain the threshold condition for the DFB laser.

4(20 + 2) = e20L (26)

From Eq. (26) it can be seen that for a fixed value of, as the

frequency deviation from the Bragg frequency increases, the

threshold gain o also increases. This indicates that a larger

gain is required for the higher-order modes to lase and, hence,

the mode selectivity of the DFB lasers.

DEVICE CHARACTERISTICS

Light/Current Characteristics

Figure 3 shows the static light/current (L/I) and voltage/cur-

TEC

GRIN lens

Strain relief

Isolator

Ball lens

Back facet monitor

rent (V/I) characteristics of a packaged DFB laser. The gen-Figure 4. Cut-away drawing of a DFB laser in a butterfly styleeral form of the curves is similar to other semiconductor la-package. The laser diode itself is a small speck to the rear of thesers. This particular DFB laser is meant for high-power fiberball lens. The ball lens makes the spatial emission pattern of the DFBcoupled applications and has a threshold current of 60 mA

laser more symmetric. This is followed by the isolator and GRIN lensand an operating voltage of about 1.5 V. The V/I characteris-before the fiber. Strain relief prevents the misalignment of the fiber-

tics is similar to an electronic diode, and shows an exponen-coupling mechanism when the package pigtail is stressed during han-

tial dependence of the injected current on applied voltage. dling.The DFB laser in Fig. 3 is capable of operating at fiber cou-

pled output powers as high as 50 mW.more uniform output spatial emission) and coupling lens de-DFB laser packaging styles vary from one manufacturer tosign. Typically, a combination of a ball lens next to the laseranother and the details are often trade secrets. Although thefacet (to correct any residual asymmetry in the emission pro-details may be different, there are three essential goals in anyfiles in the lateral and transverse directions to the facet) andDFB package. The first is temperature stability. Single-modea graded index (GRIN) lens at the entry point to the outputcharacteristics of DFB lasers are very sensitive to tempera-fiber is used to couple light from the diode into the opticalture variations. The parameter of major concern is the varia-fiber.tions in the emission wavelength with temperature. Most

The third goal is to minimize the reflection of light backhigh-end DFB lasers are packaged with a thermoelectricinto the laser. As seen in the previous section, the wavelengthcooler (TEC) for stabilizing the temperature.stability of the DFB laser is governed by the wavelength-se-The second goal is high coupling efficiency. Output power

lective feedback provided by the grating structure. Any otherfrom the laser diode is expensive and careful attention is paidspurious reflections, from the laser facet or from an externalto maximize the amount of light that is coupled into a single-component in the fiber optic link, will lead to poor single-modemode optical fiber pigtail. In manufacturing, fiber couplingperformance. Back reflection is minimized by properly anti-efficiencies in the range of 60% can be obtained. This isreflection-coating the lens surfaces and including an isolatorachieved by a combination of laser diode design (to obtain ain the package. Isolator is an optical device that allows light

to be transmitted in one direction with very low loss, and es-

sentially prevents light transmission in the reverse direction.

The isolator may be placed after the ball lens and before the

GRIN lens.

Figure 4 shows a dr

[john g. webster (editor)] 50.quantum electronics(bookos.org)

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