Eindhoven University of Technology

MASTER

Design of grating structures to reduce longitudinal spatial hole burning in distributed feedbacklasers

Walraven, P.J.

Award date:1995

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FACULTEIT DER ELEKTROTECHNIEKTECHNISCHE UNIVERSITEIT EINDHOVENVAKGROEP TELECOMMUNICATIE

DESIGN OF GRATING STRUCTURESTO REDUCE LONGITUDINALSPATIAL HOLE BURNING IN

DISTRIBUTED FEEDBACK LASERS

door P.J. Walraven

Rapport van afstudeerwerk uitgevoerd van maart 1994 tot januari 1995.Aftudeerhoogleraar: Prof.Ir. G.D. KhoeOnder leiding van: Prof.Dr. B.H. Verbeek (Philips Nat. Lab.)

Dr.Ir. A.A.M. Staring (Philips Nat. Lab.)

DE FACULTEIT DER ELECTROTECHNIEK VAN DE TECHNISCHE UNIVERSITEIT EINDHOVEN

AANVAARDT GEEN VERANTWOORDELlJKHElD VOOR DE INHOUD VAN STAGE- EN

AFSTUDEERVERSLAGEN

Author(s) P.J. Walraven

Title Design of grating structures to reduce longitudinalspatial hole burning in distributed feedback lasers

Abstract

It is known that DFB laser characteristics, e.g. the linewidth and FM response, arenegatively affected by spatial hole burning, which is a result of the non-uniform fieldintensity distribution in the laser.

A laser simulation program was used to find grating structures that yield a flatter fieldintensity distribution than that of a uniform-grating DFB laser. The performance of theselasers with reduced longitudinal spatial hole burning was analyzed.

To verify the simulation results, a number of lasers of two selected grating designs weremeasured.

According to the simulations the effect of the grating design on the linewidth and FMresponse mainly results from the magnitude of the ",L product, rather than from theparticular type of grating used.

Keywords

DFB, laser, grating (structure), spatial hole burning.

Contents

1 Introduction

2 Distributed FeedBack lasers

2.1 Laser structure ....

2.2 Round-trip condition.

2.3 Rate equations

2.4 Laser spectrum

2.5 Grating structure .

2.6 Field distribution .

2.6.1 Coupled wave equations

2.6.2 Solution to coupled wave equations.

2.6.3 Facet reflections

2.7 DFB laser spectrum . .

2.8 Spatial and spectral hole burning

2.8.1 Spatial hole burning .

2.8.2 Spectral hole burning

2.9 FM response and FM efficiency

2.10 Uniform intensity distribution.

3 Simulation with CLADISS

4 Threshold simulation of various DFB lasers

4.1 Uniform DFB laser.

4.2 >..j4 DFB laser ...

4.3 Coupling coefficient modulated DFB laser

4.4 Partially corrugated DFB laser

4.5 Multiple phase shifted DFB laser

4.6 Corrugated pitch modulated DFB laser

5 Field intensity distribution at and above threshold

6 Above threshold simulations for several KL products

6.1 Simplified coupling coefficient modulated DFB laser

6.2 Partially corrugated DFB laser . . . . . . . . . . . .

ii

1

2

2

4

5

6

7

8

8

10

10

10

13

13

14

15

15

17

18

18

20

21

22

25

29

31

34

34

37

6.3 Overall conclusion of ",L variations . . . . . . . . . . . . . . . . . . . . . .. 39

7 Measurement results

7.1 CCM DFB laser measurements

7.2 PC DFB laser measurements

8 Conclusions

References

A Introduction to the CLADISS simulation package

B Example of parameter file for 1.5 /-Lm DFB lasers

C Example of parameter file for 1.3 /-Lm DFB lasers

iii

41

41

43

46

47

49

51

54

Acknowledgements

At the beginning of this report, I would like to express my thanks to ProUr. G.D. Khoeand Prof.Ir. B.H. Verbeek for giving me the opportunity of doing my graduation work inthe Philips Optoelectronic Center group at the Philips Research Labs., Eindhoven.

For valuable discussions on semiconductor lasers and laser modelling, I would like to thankmy coach Dr'!r. A.A.M. Staring, Dr. J.P. Weterings and Dr.Ir. M.F.C. Schemmann.

Also, I would like to thank Dr. J.J.M. Binsma for handing me subjects of investigationand providing lasers for measurement.

I also like to thank the people who made an extra effort to assist the final measurementsand results.

Last, but certainly not least, I thank everyone at the Philips Research Labs., who mademy stay here very enjoyable.

v

1 Introduction

Optical communication based on amplitude shift keying is already in use, but the trans­mission capacity can be increased if coherent transmission systems are used. A coherentsystem imposes several demands on a laser, concerning the linewidth and FM response.A laser capable of fulfilling these demands is the Distributed FeedBack (DFB) laser. TheDFB laser is known for its stable single mode operation and small linewidth.

A laser is much like a pn-diode but has an additional (active) layer inserted between thep- and n-Iayers. For a Fabry-Perot laser the for lasing necessary feedback is provided bythe facet reflections. For a DFB laser the feedback is frequency dependent and resultsfrom a grating structure near the active layer.

It is known that DFB laser characteristics are negatively affected by a non-uniform de­pletion of carriers, called spatial hole burning [1], which is a result of the non-uniformfield intensity distribution in the laser. Since the refractive index depends on the carrierdensity, the index profile becomes non-uniform, which affects the DFB modi. This canreduce the side mode suppression or even a mode jump might occur. The additional noisefrom the side modi enlarges the linewidth of the main mode.

According to [2] the field intensity distribution can be made uniform by modulating thecoupling coefficient of the grating structure. This analysis was confirmed by simulationscarried out with CLADISS, a laser simulation program. This solution however can onlybe approximated because of fabrication restrictions. Other possibilities to flatten the fieldintensity distribution using the grating structure were investigated in this report.

The grating structures found in several articles were simulated and accordingly optimized.Simulation gives the opportunity to analyze the influence of reduced longitudinal spatialhole burning, without the necessity of a time-consuming and expensive device fabricationprocess.

In chapter 2 a general introduction to the laser theory is given, followed by a treatment ofthe DFB laser. Chapter 3 deals with the information concerning the simulation programCLADISS. An extended treatment of grating design in DFB lasers and their simulation atthreshold is given in chapter 4. In chapter 5 the obtained field intensity distributions arecompared at threshold and for a much higher bias current. Simulation above thresholdof the various lasers showed similar results, therefore the dynamics of only two of theselasers are treated fully in chapter 6. Finally, in chapter 7 two DFB lasers with a flattenedfield intensity distribution were measured for a verification with the simulation results.

1

2 Distributed FeedBack lasers

In this chapter the theoretical foundation of the laser action is explained. After treatmentof the elementary of semiconductor lasers the Distributed FeedBack (DFB) laser is dis­cussed. The DFB laser is the main topic of this report and in particular the embeddedgrating structure.

2.1 Laser structure

A semiconductor laser is a diode with an optically active layer between the p and n dopedmaterials, see figure la.

PORWAAD CURRENT 1P-DOPED ACTIVE

REGION N-DOPED

P-llOPEO LAYER

ACTIVE LAYER

CONDUCTION .I 1BAND ~

electrons

N-,llOPEO LAYER

1a

VALENCE ----r'l"1h~(o:f.lle~s~1BAND _ /' 1,-----

~ V

b

Figure 1: a) Schematic view of a semiconductor laser diode and b) the energy band diagramof heterojunction laser.

If the diode is connected in the forward direction the electrons, respectively holes, areinjected from the n, respectively p, doped material into the active layer. The electronsoccupy the conduction Ee band while the holes fill the valence band E v of the active layer,see figure lb. Confinement of the carriers in the active layer is accomplished by an energydifference between the active and cladding layer bandgap. Such a junction between twosemiconductors, with a different bandgap energy, is called a heterojunction. Inherent tolaser action is the generation of photons, induced by carrier transitions between the energystates E e and E v , see figure 2. In figure 2a an electron-hole pair is generated by absorptionof a photon. The energy of such a photon is E = hv with h as Planck's constant and vthe optical frequency. For this effect to occur the photon energy must be at least equalto the bandgap energy Eg = Ee - E v • Generally, the electrons will fall back at randomto a lower energy state Ev and emit a photon of energy Eg , see figure 2b. This is calledspontaneous emission. The electron can also be stimulated to fall back and emit a photon.The stimulus is provided by the presence of a photon of energy E9 , see figure 2c. Withthe transition of the electron a photon is emitted, which has the same energy and is inphase with the incoming photon. If this process continues, a large coherent radiation fieldcan build up.

Increasing the current injection leads to a point where the electron concentration in the

2

a) absorption

b) spontaneous emi.sion

c) .timulated emi••ion

~=-hV~--I1T--_

Z"_lr-/\J\I'-hV

~_hV lr-- ~_ ::Figure 2: Schematic view of energy transitions with a photon represented as a wave duringa) absorption, b) spontaneous emission and c) stimulated emission.

conduction band exceeds the hole concentration in the valence band and population in­version is achieved. At this point the gain equals the loss. The loss consists of absorptionloss, mirror loss, i.e. the part of the light emitted from the facets, and non-radiative re­combination. Contributors to the latter are Auger recombination and recombination atimpurities and surface. The Auger recombination is a very important loss mechanism inlong wavelength lasers. It describes the recombination of carriers of which the recombi­nation energy is transferred to another carrier instead of a photon. This carrier is excitedto another energy state and when it relaxes back to equilibrium its energy is transmittedto lattice vibrations or phonons, i.e. it is converted into heat.

Increasing the current injection further, the probability of stimulated emission becomeshigher than the probability of absorption, providing the necessary gain for lasing. Inaddition a feedback mechanism is required to achieve laser operation. This can be obtainedby positioning the gain medium inside a resonant " Fabry-Perot" cavity, created by twoperfectly parallel partially reflective mirrors. In fact, the cleaved end facets of a laser chipact as such mirrors having a reflection coefficient of about 30 %.

The active layer of 1.3 and 1.5 /Lm wavelength lasers is made of the quaternary materialInGaAsP. An interface between the InGaAsP active layer and a InP cladding layer can bemade almost without imperfections which improves the laser efficiency. The compoundsGaAs and InP are direct band-gap materials. Indirect band-gap materials, such as Si or Ge,are avoided, because their electron recombination involves not only a change of energy butalso a change of momentum. As a result recombination occurs by non-radiative processes.

3

2.2 Round-trip condition

Lasers suffer from non-linearities because of the non-unifQrm distribution of the injectedcurrent. With an additional process step the active layer can be confined, next to thetransverse direction, in the lateral direction, see figure 3. The confinement of carriersimproves the current distribution and results in better current characteristics, such as alinear light-current dependence. These lasers are called buried-heterostructure semicon­ductor lasers.

substrate

transverse

x I / :ongitudiDal

Llateraly

Figure 3: Schematic view of index-guided semiconductor laser.

When the laser reaches the population inversion point the lasing condition is satisfied. Away of defining this lasing condition is to say that the gain of wave travelling back andforth between the facets equals one. This leads to the round-trip condition [3]

J RfR,. exp( -j2(3L) = 1 (1)

where (3 is the propagation constant, L the laser length and Rf respectively R,. the re­flection coefficients of the front and rear facet. The propagation constant is defined asfollows

(3 = kon + jao (2)

with ko = 27T/ >'0 the wavenumber in vacuum, n the refractive index and 00 the net fieldgain per unit length.

If (3 is inserted in the round-trip condition, the condition can be divided into a conditionfor the amplitude

and a condition for the phase

JRfR,. exp( -200 L) =1

exp(2jkonL) = 1

(3)

(4)

with the solution 2konL = m27T and m an integer. Increasing the forward current willincrease the gain until the round-trip gain and phase are satisfied and threshold is reached.Below threshold spontaneous emission is dominant, above threshold the output is deter­mined by stimulated emission. The current at which the round-trip condition is satisfiedis called the threshold current.

The gain in a semiconductor laser depends on the composition of the active layer and hasits peak for a photon energy near the band-gap energy E g , see figure 4.

4

GAIN

LOSS

~/ hv

Figure 4: Gain in a semiconductor laser.

If the photon energy hv exceeds the bandgap energy E g and the carrier injection is suf­ficiently large then population inversion is achieved. For a semiconductor laser this gainregion can be, using E = he/.x, tens of nanometers. The carrier density N in the activelayer is used as a parameter. An increase in carrier density increases the maximum gain,see dotted line in figure 4.

2.3 Rate equations

The total behavior of the laser discussed until now can be summarized in the rate equationsfor carriers and photons [4, 5].

carriersaN(z, t) I(t) N(z, t)

- vgg(z)S(z, t) (5)=at qV TN

photonsas(z, t) T/N(z, t) S(z, t)

(6)at

- + vgg(z)S(z, t)TN Tp

The variation in time t of the carrier density N depends on three terms, see equation 5.First there is the so called pumping term, i.e. carriers with a unit charge q are generatedby injecting a current I into the active layer, with volume V. The current is assumed tobe uniformly distributed in the longitudinal direction. The second and third term are thecontributions of the carriers that recombine spontaneously and by stimulated emission,respectively. Both terms decrease the number of carriers. The spontaneous recombinationdepends on the number of carriers and the carrier lifetime TN inside the active layer. Thestimulated recombination is calculated from the number of photons S and the gain factorin the active layer. This gain factor which is the gain per unit time is composed of thegain per unit length 9 and the group velocity vg in the active layer.

Contributions to the time dependent variations of the photon density are the spontaneousand stimulated emission and the absorption of photons, see equation 6. The fraction ofspontaneous emission that actually contributes to the coherent wave is given by '7. Thespontaneously emitted photons depend further on the number of carriers and the carrier

5

lifetime in the active layer. The center term is the decrease of the photons and depends onthe number of photons and the photon lifetime Tp in the active layer. The photon lifetime

. Tp is the inverse decay rate, which depends on the absorptiQI! by the cladding layers andthe facet reflection.

2.4 Laser spectrum

The spectrum of a Fabry-Perot semiconductor laser is very wide. This is easily explainedby the gain curve of such a laser. There is a large region that (nearly) meets the round-tripcondition, Le. gain=loss, see figure 5.

GAIN

LOSS --------~-~-~~-~---------

LONGI'l'OD:INALMODES

FREQUENCY

Figure 5: Schematic view of the gain curve of a semiconductor laser diode.

For a Fabry-Perot the round-trip condition can be used to calculate the mode distance,Le. the distance between two adjacent modi, and determine the number of modi. Withthe round-trip phase solution 2konL = m27r and using v = CiA with c the speed of lightin vacuum and A = 27rlko it follows that

m2c m1c cD..v = V2 - VI = -- - -- = --

2Ln 2Ln 2Ln(7)

with m2 = m1 + 1. The mode distance in wavelength is

c c c A2D..V6.A = A2 - Al = - - - = -(112 - Ill) ::::: --

112 III 111112 C(8)

and using 6.11 = c/2Ln this becomes

D..A A=

A 2Ln(9)

For a Fabry-Perot laser, with c = 3 . 108 mis, L = 250 /.lm and n = 3.0 the frequencydifference is D..v = 200 GHz. The mode spacing with A = 1.5 /.lm becomes D..A = 1.5 nm.Compared with data about the width of the gain curve [3], the spectrum is multi-mode.In optical communication systems this broad spectrum of several modi prohibits fast datatransmission. A signal that travels through a fiber broadens, because the propagation

6

velocity in the fiber is frequency dependent. This behavior of fibers is called dispersion.The wider the laser spectrum the sooner the data degenerates. Ideal would be a spectrumconsisting of just one mode with a small mode width. If one of the modi is favored abovethe others, that is the gain difference is large enough, it is possible to produce a singlemode laser. This can be done by making the feedback frequency dependent to enforcemode discrimination. A laser using this method is the Distributed FeedBack (DFB) laser.

2.5 Grating structure

In a DFB laser the feedback not only comes from the facets, but mainly from a gratingstructure close to the active layer, see figure 6.

p

ACTIVE LAYER

GRATING STRUCTURE

N>light waveintensity

Figure 6: Schematic view of a Distributed FeedBack laser diode and the intensity of thelight wave.

The feedback or reflections from the grating structure are distributed throughout the laser.Because of the different material composition on both sides of the grating, the structurehas an alternating refractive index in the longitudinal direction of the laser. The gratingstructure couples the forward and backward propagating waves in the laser. The modeselectivity depends on the period of this structure. For coherent coupling between oppositewaves the period of the grating structure must be half the mode wavelength inside themedium.

. . d A oXgratmg perlO = = '2 (10)

This condition, called the Bragg condition for the grating period, originates as follows.Assume the waves propagate through material with an alternating refractive index neff ±b.n, see figure 7. If the distance between the junctions is A/2 and having the reflectionalternate at every junction the waves with a wavelength oX = 2A add up. The part that isreflected at the junctions joins up with the counter-running wave. This process is calledbackward Bragg reflection.

7

L/2-L/2

lonllitu4iual <Iirection & _

Figure 7: Schematic view of propagating waves through laser cavity.

The fact that the waves are amplified combined with the backward Bragg reflection resultsin waves that are built up running towards the facets. The forward and backward runningwaves are drawn in figure 7, with L the longitudinal length.

The effective index variation can be best described by the following periodic structure [6]

n(z) = neff + Lln cos(2,8oz + n) (11)

(12)

with ,80 = 7r/ A the Bragg propagation constant and n the phase of the grating.

The intensity of the light wave has its maximum at the active layer and drops towardsand into the cladding layers, see figure 6. Therefore the distance between the active layerand grating structure has its influence on the coupling between the forward and backwardwave. The non-linearity of the light intensity distribution makes the coupling non-linearwith regard to an index amplitude variation, Lln.

2.6 Field distribution

An analysis of the laser modi and the resulting field distribution is essential to the mainpurpose of this work. A uniform field distribution means an efficient use of the total cavityand a uniform reaction on current modulations throughout the cavity.

2.6.1 Coupled wave equations

The mathematical description of the laser modi is based on the time independent waveequation [4, 6]

8

with k the wavenumber.

In buried-heterostructure lasers the active layer is surrounded transversely and laterallyby lower refractive index cladding layers. This refractive index difference is a measure forthe index guiding of lasers. For example the strong index-guided semiconductor laser asin figure 3. Because of the strong refractive index step the active layer dimension can bedetermined accurately. If the dimensions of the active layer are of a predefined size, onlya single transverse and lateral mode is supported by the passive waveguide. Equation 12then becomes

(13)

with E = Eo exp(jkz) an electrical field solution and ko = 271'"/>'0 the wavenumber invacuum and n(z) as in equation 11.

The effect of the grating structure on the field distribution can be dealt with by repre­senting the refractive index as an effective index with a small perturbation, according toequation 11. The wavenumber is then written as

kon(z) = kOneff + ko~ncos(2,8oz + f2)

After squaring kon(z) and assuming that ~n ~ neff this becomes

(14)

(15)

with ,8 = kOneff the wave propagation constant and K = 71'"~n/>'0 the coupling constant,which is a measure for the strength of the Bragg reflection.

Assuming there is a forward and backward propagating wave in the longitudinal directionand the propagation constant ,8 is close to the Bragg propagation constant ,80 accordingto ,8 = ,80 + ~(3, then the general solution of equation 13 becomes

E(z) = R(z) exp( -j,8oz) + S(z) exp(j,8oz) (16)

with R(z) = E, exp(j~{3z) and S(z) = Eb exp(-j~,8z) the amplitudes of the forwardrespectively backward propagating waves. The Bragg deviation is expressed in a real andimaginary part,

~,8 = c5 + jero (17)

with 6 the Bragg frequency deviation and ero the net field gain. The amplitudes R(z) =E, exp(j~,8z) and S(z) = Eb exp(- j ~,8z) of the forward respectively backward propa­gating waves are varying slowly so the second order derivative can be neglected. Insertingequation 16 in equation 15 and 13 gives the coupled wave equations for R(z) and S(z)

- dR + [ero - j6]R _ jKexp(-jf2)Sdz

~~ + [ero - jc5]S jKexp(jf2)R

9

(18)

(19)

2.6.2 Solution to coupled wave equations

- The solution to the coupled wave equations 18 and 19 are of the form.

R(z) = T1e')'z + T2e-')'z

S(z) = S1e')'z + S2e-')'z

with the complex propagation constant I obeying the dispersion relation

(20)

(21)

(22)

For a given coupling coefficient x:, , solutions of the coupled waves are only possible fordiscrete pairs of the gain constant ao and the Bragg frequency deviation 8.

If there is no reflection at the facets, the boundary conditions for the waves are R( - ~L) =S(!L) = O. Together with equation 20 and 21 this gives a relation between the coefficientsT1,2 and S1,2'

T1 82 ')'L- = - =-eT2 S1

(23)

If the device is symmetrical in the longitudinal direction the coefficients T1,2 and 81,2 arerelated by T1 = ±82 and T2 = ±S1. Combining these results gives the solution for thelongitudinal field distribution of the modi of a DFB laser.

R(z) - sinh(r(z + ~L»)

S(z) = ± sinh(r(z - ~L»

(24)

(25)

The forward R(z) and backward S(z) propagating functions are drawn in figure 7 for apropagation constant I that is real.

2.6.3 Facet reflections

The above analysis of the field distribution is done without implementing facet reflections,i.e. they were assumed to be Anti-Reflection coated. In practice it is (almost) impossibleto coat the facets perfectly A.R. A coated facet causes not only an amplitude degeneration,but also a phase shift. A phase shift at the facets causes the laser to deviate from thetheoretical laser wavelength. Including the facet phase makes the analysis difficult becausethe phase is defined by cleaving the laser which is a random process. With a theoreticalanalysis of the facet reflectivity a prediction of the yield is possible [8].

2.7 DFB laser spectrum

An evaluation of the DFB spectrum is possible with the solution of the coupled waveequation in section 2.6 and the dispersion relation, equation 22. To determine the eigen­values of the dispersion constant I the solution is inserted into the coupled wave equation.

10

Assuming that the grating phase is zero, n = 0, this leads to the following characteristicequation [6]

or

±j,,//\, = -~-'---:-

sinh( ,,/L)

00 - j6 = ,,/cothbL)

(26)

(27)

Solutions for the characteristic equation can be found by a numerical method. This is donefor different values of 6L and ooL. Multiplication with L gives the results independent ofthe cavity length. The possible results are given in figure 8, with /\,L as a parameter.

1C1". ~""

••••0.5

10 o

2

1

10 &.

Figure 8: Solutions to the characteristic equations for a symmetrical DFB laser.

Each solid line represents a different longitudinal mode, starting with the lowest modeclose to the Bragg wavelength, 6L = O. For a given KL product, each mode has itscharacteristic field distribution, threshold gain and resonant frequency.

In figure 8 no solutions are around 6L = 0, meaning that there is a region withoutany mode. This empty region is called the stopband and lies between the lowest possiblesolutions for 6L, on each side of the Bragg wavelength. Therefore the resulting propagationconstant f3 = f30 + 6 + joo will always deviate from the Bragg propagation constant f30.

The minimum width of the stopband is determined by the lowest value of 0, and is 26because of symmetry around 6£ = O. In case of a strong coupling K » 00 and seeking forthe lowest order mode, the following equations are found

(28)

This implicates that the stopband width in a strongly coupled DFB laser is equal to 2K.

For a symmetrical DFB laser the solution of the characteristic equation in figure 8 showsthat two wavelengths are propagated, one at each side of the stopband and close to theBragg wavelength. The laser is double mode.

To comprehend the existence of the stopband in a DFB laser a rectangular grating struc­ture is regarded, see figure 9a.

11

a)

wavelength _

b)

(32)

wavelengtb ---.

Figure 9: Schematic view of grating structure and spectrum of a) uniform DFB-laser b)>../4 phase shifted DFB-Iaser.

The waves propagating through the grating are reflected with an alternating sign every halfgrating period A/2. If the waves precisely fit half a wavelength between these alternatingreflections then the total phase shift is 271" and the waves will add up. If the total round-tripis considered, there is a discrepancy because the distance is not a multiple of the gratingperiod, but half a period longer. Therefore the wavelength of the mode will deviate fromthe Bragg wavelength, implicating two modi, conform the characteristic equation.

These multiple modi are a problem for practical implementations, as for instance coherentcommunication. A solution would be to start of with a cavity equal to the grating period,see figure 9b. The resulting round-trip phase will then be a multiple of 27T. To realizethis grating structure a phase shift in the middle of the laser is suggested. This phaseshift should extend the propagation distance with half a grating period, A/2 = >../4. Thespectrum of this laser, called a >../4 DFB laser, is single mode.

In section 2.4 the mode distance for a Fabry-Perot laser was calculated. The feedbackof a DFB laser not only results from the facets, but mainly from the grating. In thetheoretical analysis the feedback of the grating was implemented in the refractive index,see equation 11. The real part of the propagation constant for two arbitrary modi with01,2 the Bragg frequency deviation can be written as

27Tneff/3T\ = /30 + 01 =~ (29)

27Tneff/3r2 = /30 + 02 =~ (30)

with /30 the Bragg propagation and >"1,2 the wavelength for modi 1 and 2. The expressionfor both the wavelengths becomes

>"1 = 27Tneff ::::: 27Tneff (1 - ~) (31)/30 + 81 /30 Po

>"2 = 271"neff ::::: 27Tneff (1 _ 02 )

/30 + 82 /30 Poand the mode distance

(33)

12

with >'Bragg = 27rneff/f30 the Bragg wavelength. In section 2.7 it was found that 8 ~ ±K

for modi with the lowest threshold gain. The mode distance now becomes

2 K>.2A \ _ \ ....!!:.. _ Bragg~A - ABragg -

f30 1l"neff(34)

For a laser with KL = 1.59, L = 250 J-Lm, >'Bragg = 1.5576 J.Lm and neff = 3.245 - thesevalues were also used in the simulation - the mode spacing becomes A>' ~ 1.2nm. TheBragg wavelength is calculated from >'Bragg = 2Aneff with A = 0.24 J-Lm the grating period.

2.8 Spatial and spectral hole burning

Spatial and spectral hole burning have a negative effect on the laser performance [11. Itis important to analyze the cause of spatial and spectral hole burning and to see if theirnegative effects can be reduced by optimizing the grating design.

2.8.1 Spatial hole burning

Spatial hole burning in a laser can be looked at from three different angles, the transverse,lateral and longitudinal direction. This report discusses only longitudinal spatial holeburning. Transverse and lateral spatial hole burning are neglected because they have aminor effect in strongly index-guided lasers.

The distribution of the field intensity in a DFB-Iaser is discussed in section 2.6. The totalfield intensity 1(z) is the sum of the forward R(z) and backward 5(z) field amplitude

1(z) = IR(z)12 + 15(z)12 (35)

The total field intensity, drawn in figure 10 for a real I' is non-uniform in the longitudinaldirection of the laser. Its minimum in the center means a relatively low generation ofphotons in that area. Since the generation of photons requires the recombination ofcarriers, the non-uniform photon generation results in a non-uniform depletion of carriers.The non-uniform depletion of carriers in the longitudinal direction of the active layer iscalled longitudinal spatial hole burning.

The flatness of the field intensity distribution can be expressed in a value, called theflatness index [9]

ri. =1cavity

(1(z) _1)2 dL z (36)

with L the cavity length and 1(z) the normalized field intensity

( 1(z) dz = 1}cavity L

(37)

Because the spatial hole burning effect is caused by the field intensity distribution, theflatness index represents the amount of spatial hole burning.

13

rfield intensity

z_

carrier density

z-

1refrective index

z-

Figure 10: Longitudinal spatial hole burning.

A flatness index of zero means a perfectly flat field intensity distribution and no spatialhole burning for a non-modulated laser. Modulation of the laser can however induce spatialhole burning, e.g. because of asymmetry of the laser.

The non-uniform field distribution has several negative effects on the laser performance.An important issue regarding optical communication systems is the single mode operationof lasers. The single mode operation can be measured by the Side-Mode SuppressionRatio (SMSR). This is the ratio between the amplitude of the main mode and the mostintense side mode. Especially for high output powers, when the carrier density reachesits maximum, leading to gain saturation, the SMSR of the laser decreases and at a givenpoint the laser becomes multi-mode. The non-uniform carrier density also deterioratesthe dynamic behavior of the laser. For those reasons it is necessary to improve the carrierdensity throughout the laser.

2.8.2 Spectral hole burning

Spectral hole burning is the saturation of gain at a specific wavelength. At another wave­length the gain still increases with bias current. This leads to a decrease of the SMSR.

Spectral hole burning can be neglected as long as the gain does not saturate. A uniformfield distribution can delay the saturation point. To what extent spectral hole burning isaffected by the carrier distribution, is difficult to determine, and is not within the scopeof this work.

14

2.9 FM response and FM efficiency

The communication over glassfiber can be done with either modulating the light intensityor the light frequency. For both options the laser current has to be modulated. In case ofintensity modulation (1M) or frequency modulation (FM) the light intensity respectivelylight frequency should be current dependent. The optimum for each of these possibilitiesis to exclude the other, meaning that 1M does not influence the frequency and FM doesnot influence the light intensity.

One way of deciding which application is best for a designed laser, is to calculate thelight intensity variation and frequency variation as function of the modulation current.Comparing these absolute values, known as the 1M or FM efficiency, will help to decideon which application is best. The modulation current should however be examined over awide frequency range, known as the 1M or FM response.

When the laser is frequency modulated the modulation current should be kept smallcompared to the bias current, to avoid intensity modulation.

As already mentioned in section 2.8.1 the FM response depends on the carrier distribution.

v = ciA = c. neff(N)AO

(38)

Altering the carrier density N changes the refractive index neff, The refractive index thenchanges the optical frequency 1/.

2.10 Uniform intensity distribution

Until now the intensity distribution and its influence on the laser performance has beenanalyzed. Evidently, a uniform intensity distribution can prevent spatial hole burning. Toobtain a uniform intensity distribution we must satisfy

I(z) = IR(z)12 + IS(z)12 == constant (39)

and the forward and backward field intensities have to fulfill the coupled wave equations[10]. The solution can be straightforward if only real values for amplitude and phase of thefield intensities are considered. Assuming the solution for the forward and backward fieldintensities to be R(z) = VIfr(z)exp(jtPr(z)) respectively S(z) = ..fifs(z)exp(jtPs(z)),with tPr,s(z) the field phase and fr,s(z) the normalized field amplitude fulfilling fr(Z)2 +fs(z)2 == 1. The boundary conditions are, assuming no facet reflections, R(-~L) =S(~L) = o.Inserting the field solutions in the coupled wave equations gives an equation for the cou­pling coefficient /'i., the net field gain 0'0 and the Bragg frequency deviation 8

1 d(40)/'i.(z) = cos[~(z)] . dz [jr(z)fs(z)]

20'0(z) d 2 2] (41)= dz lJr (z) - fs (z)

26(z),,;(z). a~(z)

(42)= fr(z)fs(z) sm[~(z)]- ---a;-

15

with ~ = cPr(Z) - cPs(z) + n.There are several theoretical solutions to achieve a uniform field distribution, but in thisreport our interest lies primarily in the shape of the grating. Assume therefore thatthe Bragg frequency deviation and net field gain are constant. Using Q'o(z) == constantand the boundary conditions the normalized field amplitudes become fr(z) = .jZfL andfs(z) = Jl - z/L. The coupling constant leading to a uniform intensity distribution thenbecomes

1K.(z) --~

- cos(~)

-2z/L(43)

Excluding the phase component by assuming that the field and the grating phases arezero, ~ = 0, gives a coupling coefficient that is positive for -~L to 0 and negative for 0 to!L. A negative coupling coefficient is not physically realizable, but if the grating is shifted7r radians at Z = 0 then the coupling coefficient becomes positive for the whole cavity. Infigure 11 the coupling coefficient is drawn (broken line) in the longitudinal z direction.

J

-Ln

Figure 11: Variation of the coupling coefficient to achieve a uniform field distribution.

The phase shift of 7r in the center of the cavity leads to a >./4 DFB laser, discussedin section 2.7, with a uniform field distribution. At the facets the coupling coefficientbecomes infinite. It is however practically impossible to realize such a coupling coefficientin a DFB laser. Nevertheless, with a good approximation of the coupling coefficient thefield intensity distribution of real lasers can be made nearly uniform. An approximationof the coupling coefficient suggested by Morthier et al. [2J is given in figure 11 (solid line).

16

3 Simulation with CLADISS

A short introduction to CLADISS is given in appendix A. At first the results calculatedwith CLADISS showed a gain curve with its peak at the short wavelength side of the lasingmode, which is opposite from practical devices. Therefore the gain curve was shifted to alonger wavelength. The parameter file containing the material and structure parametersused in the simulations is given in appendix B. The parameter file was set for a calculationincluding the effects of spectral hole burning.

The laser structure used by CLADISS and defined in the parameter file is that of a bulkactive layer laser. With practical data and an analysis of MQW lasers, a for quantumwells representative layer could be implemented, but the specific quantum well effects willnot be analyzed as such by CLADISS.

The total coupling coefficient calculated by CLADISS and used in this report is definedas follows:

KL = E Ki' L isections

(44)

where a section is a user defined part of the laser grating structure.

The facet phases were well defined by using the length of the laser cavity to make it aperfect fit for the grating. The phase difference of the grating at the facets is 7r, whichmakes the field intensity distribution symmetric in the laser cavity.

The number of modi investigated is one, because the convergence of a simulation withCLADISS and the amount of CPU time depends strongly on the number of the modi usedin the calculation. A prediction, whether the laser will be single-or multi-mode, can bemade with the threshold gain difference calculated by CLADISS. This is however not acertainty and thus the laser has to be checked upon the mode behavior for higher biascurrents. It should be noted that special care is taken to make sure that the main moderemains dominant for the higher bias currents. This is possible using for instance thewavelength or output power diagram.

The choice for a facet reflectivity of 1% was made, because it is closer to reality than aperfect AR (0%) coating, although the latter would simplify the results. The calculationof the yield for lasers with different facet phases has been investigated and publishedpreviously by P.I. Kuindersma et al. [11). A calculation of the yield for the simulatedlasers in this report has not been performed.

17

4 Threshold simulation of various DFB lasers

In this section a report is given of the various grating structures that were simulatedwith CLADISS. Most of the structures found in publications have all sorts of materialand structure parameters, which makes them unsuitable for mutual comparison. For thecurrent simulations, the material and structure parameters were not altered, except forthe grating configuration.

4.1 Uniform DFB laser

A uniform DFB laser has a grating with a constant periodicity A and a constant couplingcoefficient K. A schematic view of the uniform DFB laser and grating structure was givenin figure 6. The front and rear facet are simulated to be cleaved with a phase difference ofexactly 1r. If also the amplitude of both facet reflections is equal, the laser is symmetricalin the longitudinal direction. The symmetry of the laser simplifies the analysis of thesimulation results. Not only the effect of a variable grating parameter on the result isstraightforward, but also the comparison of the results is simplified. The spectrum of asymmetric uniform DFB lasers consists of two, equally strong, main modi, see figure 9. Infigure 12a the round-trip gain at threshold is given for a uniform DFB laser with a facetreflectivity of 1% at both sides for a KL = 2.08.

IIlftolooW .....

ROUNDTRIP GAIN VS WAVELENGTH__ ~ ....... 1

FIELD INTENSITY ALONG CAVITY

0.•.

:/. ..; -i :: •

_... _ ....._~ .... _ •. . ...l_._.•. _.~.......o-..----""-- __ --.:..U4I 1.5$ 10M2 I,"" I~ 1.~

IIAVELL~GTH [pm]

a

II.

,..

.5O

:: -100

\,~".~.. ,

. ,,,\ ,,,

\ ,,,\'"

_-....0":" -60~-'-IDO-- '»0---'--:$0­

Z-COORDINATE [11m]

b

Figure 12: a) Round-trip amplitude (solid line) and phase (broken line) and field intensitydistribution (solid line) of a uniform DFB laser 1%-1% coated and KL = 2.08. The arrowsindicate the lasing modi, at an amplitude of the round-trip gain of 1 and a phase of O.The field intensity distribution is the addition of the forward and backward wave power.

The simulation program CLADISS puts the lasing wavelength in the center of the pic-

18

ture. The gain versus wavelength curve of a DFB laser, as shown in figure 5 causes theasymmetry of the round-trip gain. As discussed in section 2.2, the round-trip conditionis satisfied for a round-trip amplitude of 1 and a round-trip phase of O. The positionswhere the uniform DFB laser satisfies the round-trip condition are given by the arrowsin figure 12, showing two modi, one on each side of the stopband. A uniform DFB laserhas in the symmetric theoretical case two equal modi, but in practice the cleaving andadditional coating process can favor one of both. The backward wave power is at theleft facet always 1 . 1O-3W conform the fixed reference power at threshold. Variation ofthe coupling coefficient alters the field intensity distribution of the laser. Searching fora minimum flatness index for a 1%-1% coated DFB laser, a ",L of 2.08 was found. Thefield intensity distribution of a symmetric uniform DFB laser with 1% reflection at bothfacets and a ",L of 2.08 is given (solid line) in figure 12b. As expected, the field intensitydistribution is symmetric. The in section 2.6 extracted amplitude of the forward R(z) andbackward S(z) propagating wave, equation 24 and 25, are drawn in figure 12b with brokenlines and depend on the coupling coefficient "'.

The flatness index for the uniform DFB laser with 1%-1% coating is 0.0078618. Theflatness indices for all analyzed lasers are given in table 2 on page 31.

Asymmetrically coated DFB laser A uniform DFB laser as previously analyzed isnot single-mode and therefore not important for optical communication systems. Coatingthe laser asymmetrically can lead to a single mode uniform DFB laser [8]. For a DFBlaser that is coated 5%-30%, front to rear, the simulations show a single-mode laser, seefigure 13.

lIlnIOoJi 2:l ...

ROUNDTRIP GAIN VS WAVELENGTHWu Z3 IDA. IDCI4r I

FIELD INTENSITY ALONG CAVITY

~~1Do 1~-'--"iOo"'-'-'Z-COOHDINATE [/lm)

.......

.,;e 02

'"

loa

; 0;

"10 ~"~

• '"~xc.

.5O

;-.oa

'.j: /: i./ -'10

/ : ; ;~-;-tr----;,~.M2. 1.664 ~.658 Iw-----rie-

WAVELENGTH [sun1

••

••

...

....'

u .'

~ ..~ .'1-'-;--'--;-':""'-'-f---;.---e-..,-+--+-\-""",-f--.lrl

a b

Figure 13: a) Round-trip amplitude (solid line) and phase (broken line) and field intensitydistribution (solid line) of a uniform DFB laser 5%-30% coated and KL = 1.75. The arrowsindicate the lasing modi, at an amplitude of the round-trip gain of 1 and a phase of O.The field intensity distribution is the addition of the forward and backward wave power.

19

The flatness of the field intensity distribution reaches an optimum for a coupling coefficientof 1.75. The flatness index of the uniform DFB laser with 5%-30% coating is 0.0525809,see also table 2 on page 31.

4.2 >../4 DFB laser

A theoretical description of the A/4 DFB laser was given in section 2.7.

left facetphase shift

right facet

Figure 14: Grating structure of a >'/4 DFB laser.

The grating structure for a >../4 DFB laser is given in figure 14. According to the analysisof Soda et al. [9], the minimum flatness index for an AR coated A/4 DFB laser is foundfor KL = 1.25, a value which was also found in our simulations. Using a A/4 DFB lasercoated 1%-1% for our simulations, a minimum flatness index was found for KL = 1.59, seefigure 15b.

ROUNDTRIP GAIN VS WAVELENGTHt..,. WM 31 ..... 1

FIELD INTENSITY ALONG CAVITY

04 :

02

: ; ; ~ jI·MI~'-~"" I.W"'::""-I.Mt use loW

'fAVELENC1ll (pm]

a

.10

'GO

-,GO

-'10

eo0-

~ o.:~U 0.4

:i

to~ 0.2

".'

-'~'::':io---~- --------»o----iOo­

Z-COORDINATE Il'm]

b

Figure 15: a) Round-trip amplitude (solid line) and phase (broken line) and b) fieldintensity distribution (solid line) of a A/4 uniform DFB laser with KL = 1.59 and 1%-1%coated. The arrows indicate the main mode, at an amplitude of the round-trip gain of1 and a phase of O. The field intensity distribution is the addition of the forward andbackward wave power.

20

In figure 15a the round-trip gain is drawn as function of wavelength for a ),/4 DFB laserwith a facet reflectivity of 1% at each facet. The ),/4 DFB laser has only one mode situatedin the center of the stopband. Because there is no competition between modi, the laser isless dependent on the facet reflection.

The flatness index for a ),/4 DFB laser with AR-AR coating and "'£ = 1.59 is 0.0116710and for a ),/4 DFB laser with 10/0-1% coating and "'£ = 1.59 the flatness index is 0.0207269,see also table 2 on page 31. The amplitude of the facet reflection is evidently a factor thathas influence on the flatness of field intensity distribution. In figure 15b the forward andbackward wave power have an offset caused by the facet reflection. In this case the offsetis 1% of the counter-running wave power at that facet. The additional feedback from thefacets and interference with the Bragg reflections causes a change in the field intensitydistribution.

4.3 Coupling coefficient modulated DFB laser

A coupling coefficient modulated (CeM) DFB laser [12] is a laser with a ),/4 phase shift,a constant grating periodicity and a variable coupling constant. The used coupling coef­ficient modulation is remotely related to the theoretical analysis and proposed structureof Morthier et a1., see section 2.10. The coupling coefficient varies in eight equal stepsfrom a maximum to a minimum, see figure 16, and the step size in longitudinal directionis constant. This approximation of the coupling coefficient is used to rather "simply"approach the theoretical optimum in an advanced production process [13].

A laser with a '" from 100/em down to 60/cm, according to [12], was simulated for a cavitylength of 250 pm. The coupling coefficient, round-trip gain and field intensity distributionare shown in figure 16.

- ...........m:1.D INn:NSITY ALONG CAVITY

,,,

"·.!---'--;r--oli"..-Hi..- .._~--J

'-COOIlDlmE (pm)

C

....

~ ..

e··~,.

t;.. I

, 0

IlVllDlCTll 110-1

b

- ............ROUNDTRIP GAIN VS WAV~:I.t:NGTII

••f------..---oli",.--;:;;..-_..__-----''-_11110-1

a

COUPlJNC COEmCIOO BACKlfARD TO FORWARD

Figure 16: a) Coupling coefficient, b) round-trip amplitude (solid line) and phase (brokenline) and c) field intensity distribution of a CCM DFB laser with total "'£ = 1.95 andflatness index 0.0792860. The coupling coefficient '" has a multiplication-factor of 10-2 .

The arrows indicate the main mode, at an amplitude of the round-trip gain of 1 and aphase of o. The field intensity distribution is the addition of the forward and backwardwave power.

21

The coupling coefficient K in figure 16a has a multiplication-factor of 10-2, which is thesame for all coupling coefficient diagrams. From figure 16 it is obvious that such a gratingdoes not yield a fiat -field intensity distr-ibution. A rather simple improvement can bemade, to realize the fact that a high coupling coefficient is needed at the facets, accordingto the theoretical analysis in section 2.10. Furthermore, the coupling coefficient at thephase shift should not be too low, in order to assure the effect of the phase shift. Withthese primary conditions the coupling coefficient was optimized for a flat field intensitydistribution. The coupling coefficient, round-trip gain and field intensity distribution areshown in figure 17.

COUPUNC co£mCl£~'T BACKlJARD TO fORWARD- .....,.. ....

ROUNDTRIP GAIN VS WAVELENGTH FiELD INn:NSITY ALONG CAVITy'

,,'

1

"r-----a--....-..--------;:r-----'• -COOImICAlI u...)

a

u:

,n""""'lI=l

b

...l-COOIlI)!?<ATE (pm)

C

Figure 17: a) Coupling coefficient, b) round-trip amplitude (solid line) and phase (brokenline) and c) field intensity distribution of a CCM DFB laser with total KL = 1.28 andflatness index 0.0019790. The arrows indicate the main mode, at an amplitude of theround-trip gain of 1 and a phase of O. The coupling coefficient K has a multiplication­factor of 10-2• The field intensity distribution is the addition of the forward and backwardwave power.

Comparing with the original CCM DFB grating structure this grating seems rather simple.The maximum coupling coefficient used for optimization of the flatness index is 235/cm.This theoretical value is far beyond the practical application. Therefore an optimum fieldintensity distribution was searched for a coupling coefficient from 100/cm, to a possiblelowest value of 10/cm. To obtain a better field intensity distribution also the length of theouter sections were varied. The coupling coefficient, round-trip gain and field intensitydistribution are shown in figure 18. The flatness index for the CCM DFB laser is 0.0792860in figure 16, 0.0019790 in figure 17 and 0.0036342 in figure 18, see also table 2 on page 31.The flatness of the field intensity distribution can be improved substantially compared toa >./4 DFB laser, without the use of a large coupling coefficient modulation.

4.4 Partially corrugated DFB laser

A partially corrugated (PC) DFB laser [14] is a combination of a Fabry-Perot laser witha DFB laser, see figure 19.

22

COUPUNG COElTlcrENT BACK'fARD TO FORfAllll

....or-~r------r---"

.. -z-_tll.al

a

- ~" ..ROUNDTRIP GAIN VS WAVELENGTIt

.. I~--+-'--'--L.---+-'--\----+---l' ~..

• I

Un2JXC1II l.aJ

b

FiELD INTENSITY ALONG CAVITY'

Z-COORlllllln: IIaoJ

C

Figure 18: a) Coupling coefficient, b) round-trip amplitude (solid line) and phase (brokenline) and c) field intensity distribution of a CeM DFB laser with total /'i,L = 1.34 andflatness index 0.0036342. The arrows indicate the main mode, at an amplitude of theround-trip gain of 1 and a phase of O. The coupling coefficient /'i, has a multiplication­factor of 10-2 • The field intensity distribution is the addition of the forward and backwardwave power.

p

active layerA-R facet

corrugation

H-R facet

Figure 19: Schematic view of grating structure inside a PC DFB laser.

The grating has a constant periodicity, a constant coupling coefficient and contains nophase shifts. According to [14] , the analysis was based on a laser length of 300 /Lmwith an optimum corrugation length of 100 Jlm. To compare the lasers simulated in thisreport, the cavity length used for the PC DFB laser is 250 /Lm. For this cavity lengththe corrugation length and coupling coefficient were analyzed, in order to approach a flatfield intensity distribution. In table 1 the optimum flatness indices of a PC DFB laser areshown as function of the corrugated length L and with a total cavity length of 250 Jlm. Fordifferent corrugated lengths, keeping the total cavity length constant, the flatness indexwas minimized by changing the coupling coefficient. From table 1 a minimum flatnessindex is found for a corrugation length of 100.08 pm 1, the same value found by [14] fora 300 /Lm PC DFB laser. Notice that the minimum flatness indices were found for a /'i,Lproduct of 0.60±0.02.

lFor reason of comparison of the different PC DFB lasers and other analyzed lasers the corrugatedcavity length was a multiple plus a half times the grating period, A = 0.24.

23

h.. h d'ffi£ PC DFB I. d'e : 'ptIma atness III Ices or aser WIt 1 erent corru~ation lengtL (JLmJ K{10-3/JLm] KL flatness index lthreshold (rnAJ79.92 7.30 .58 .0039011 22.710783.32 7.00 .58 .0037040 22.778790.00 6.45 .58 .0034207 22.9468100.08 5.90 .59 .0030611 23.0342109.92 5.60 .62 .0035621 21.0214120.00 5.10 .61 .0031928 23.2093130.08 4.55 .59 .0048040 23.7350

Tabl 1 0 . I fl

In figure 20 the simulation results for a flatness index optimized PC DFB laser with agrating part of 100.08 JLm and a coupling coefficient of K = 5.9 . 10-3 / Il-m are given.

l.c.1C tUfthoid n mA

ROUNDTRIP GAIN VS WAVELENGTH1,-...: MM a ml. .... 1

FIELD INTENSITY ALONG CAVITY

~--'-'-orolli;c---iio 'roll 20Il

Z-COORDINATl: lJ<m]

Eo.•ert~ u:8o.'"'"•~ orf:

. -IDO

. ·10

;': 1M

.. tOO

: .

,

.'

:/ -150

~----'~I.~S i~ ~1.M.-"':"'-l$51 I~ 1.51

WAVElENGTH !J.m]

I':

0.' :

0.• :

o.

...~ 0.1 ~~ f;-'--;----;---;;-:--+t--'-I't-:--+I--t-+~_,__:j. 0 ~

0.8 . . xc..

a b

Figure 20: a) Round-trip amplitude (solid line) and phase (broken line) and b) the fieldintensity distribution of a PC DFB laser with KL of 0.59. The arrows indicate the mainmode, at an amplitude of the round-trip gain of 1 and a phase of O. The field intensitydistribution is the addition of the forward and backward wave power.

The reduction of the grating section has a negative effect on the mode stability of a PCDFB laser, because several modi approach the round-trip gain condition. Note that themain mode is found at about 1552nm. This was also the lasing wavelength of the >./4DFB laser at the center of the stopband, defined by the two highest sub modi. Theuncertainty about the stopband of a PC DFB laser is caused by the complexity of theemission spectra. Definition of the emission spectra can help to define some laser aspects,e.g. the KL product, and analyze the influence of the partially corrugated grating structure.

24

In the corrugated part of the laser, gain is supported by Bragg reflections. The differencein gain between both cavity parts leads to a higher field intensity at their intersection, seealso the forward and backward propagating waves (broken lines) and the resulting fieldintensity distribution (solid line) in figure 20b. Therefore the junction between the cavitywith and without grating acts as a phase shift in a >./4 DFB laser, regarding the fieldintensity. The field intensity at the High Reflection (HR) facet is increased with a 75%reflection coating, which also increases the total output power at the AR facet.

The optimum flatness index found for a PC laser diode with a grating section of 100 /-Lmis 0.0030530, see also table 2 on page 31.

4.5 Multiple phase shifted DFB laser

A laser with one phase shift at the center of the grating is the >./4 DFB laser. A multiplephase shifted (MPS) DFB laser has a grating structure with an even number of phaseshifts added to the >./4 DFB laser. These phase shifts are placed symmetrically in thelongitudinal direction of the laser, see figure 21.

phase shift

left facet right facet

Figure 21: Grating structure of aMPS DFB laser.

This way the field intensity distribution is kept symmetrical. For a >./4 DFB laser thephase shift is 1r radians. The phase shifts can however be varied from 0 to 21r, but the bestsingle mode performance can be expected from waves that fit the grating with a multipleof their wavelength as depicted in section 2.7. To obtain a minimum flatness index thecoupling coefficient is varied along the cavity. In figure 22 the coupling coefficient for three­the first MPS DFB laser has a constant coupling coefficient - analyzed lasers is given. Firsttwo phase shifts were added, dividing the laser into four sections, with an equal length foreach section. The coupling coefficient, kept equal for each section, was optimized for a flatfield intensity distribution. A KL product of 1.43 was found. Then the coupling coefficientwas optimized separately for each section, keeping the laser symmetrical, see figure 22a.From that point on both the coupling coefficient and length were varied to flatten the fieldintensity distribution. Again the laser was kept symmetrical, see figure 22b. The wholecycle was repeated for a grating with five phase shifts, see figure 22c.

25

COUPUNC COEITICIElIT BACKWARD TO FORWARD

!. .

COUPUHC COEITlCIM BACKWARD TO rORIARD

....<r-------,------.-----"1

1- I

~. .

COUPUNC COEll1ClE.\T BACK1IARD TO FORWARD

'.~----.r---;,r-----;Ii",-_~

'-""""""''''(,om)a

'.

Figure 22: Coupling coefficient of MPS DFB lasers with a) three phase shifts, equal sectionlength and total f'i,L of 1.36, b) three phase shifts and total f'i,L of 1.34, c) five phase shiftsand total f'i,L of 1.32. The coupling coefficient f'i, has a multiplication-factor of 10-2•

The round-trip gain diagram for lasers with more than a single phase shift is given infigure 23 on page 27.

From the round-trip diagram of the >-./4 DFB laser the center of the stopband of the MPSDFB laser is assumed to be 1552nm. This is possible because the material and structuralparameters, except for the grating structure, of the MPS DFB laser and >"14 DFB laserare the same. The number of competitive modi increases with the number phase shifts.The competition between these modi reduces the single mode stability and leads to modehopping for higher bias currents. With increasing bias current, mode hopping becomesvisible by abrupt wavelength shifts and/or output power changes, called kinks.

Because the maximum of the material gain curve lies at approximately 1.56 J-Lm for thethreshold carrier density, the longer wavelength modi are amplified more. Assuming thelatter are the main modi the laser will have a longer wavelength for every additional setof phase shifts.

The field intensity distributions are drawn in figure 24 on page 28, with a flatness im­provement from laser a to d.

The laser flatness indices of the MPS DFB lasers in figure 24 respectively are a) 0.0054551,b) 0.0037231, c) 0.0025131 and d) 0.0004775, see also table 2 on page 31.

26

_ 2ImA

ROUNDTRIP GAIN VS WAVELENGTHI'mUft l1I.taho1d 28 ....

ROUNDTRIP GAIN VS WAVELENGTH

0.1

.. ,:....

'"§ 0.1

0..

::!

o.c:

0.2

..

:OJ'.,

60.,...GO.,

:E....,:

~a.

-60

.' -'DO..

I .i,.

"0.1

.... '.

..,

~ 0.1Co.

::!

O.C

0.2

.'

..

I.M 1.552

WAVELENGTH [;un]

...'00

-10

-'00

-III

a b

ROUNDTRIP GAIN VS WAVELENGTH ROUNDTRIP GAIN VS WAVELENGTH

-'00

'DO

'11

-'50

OJ'.,60 ~

GO..3

. 0

. -10

1.512

.10

.00OJ'.,

10.,

<.:I ...Q GO

§.,

:E.."- 0 ..,::! ~

a.oc -10

-'0002

-'10

c d

Figure 23: Round-trip amplitude (solid line) and phase (broken line) of multiple phaseshifted DFB lasers with a) three phase shifts, equal section length and ",L of 1.43, b) threephase shifts, equal section length and total ",L of 1.36, c) three phase shifts and total KLof 1.34, d) five phase shifts and total ",L of 1.32. The arrows indicate the main mode, atan :amplitude of the round-trip gain of 1 and a phase of O.

27

1ftDa« bw 28 mA. mod:t 1

FIELD INTENSITY ALONG CAVITY.. Um&.lDlIlh.

FIELD INTENSITY ALONG CAVITY

~ 08 E 0.8

0:: 0:: .'

~ ~0 0C. 0..

~0.8

~08

lI= ~

!:\ ~'-' 04 u U-< <"" c:l

+ +

tIC ..0:: 0.2 0:: 020 0.... r..

100 150 200 250 100 150 200 250

Z-COORDINATE (pm] Z-COORDINATE [}Lm]

a b

biu28I1l.1, ..... 1

FIELD INTENSITY ALONG CAVITY..... 28 ......... 1

FIELD INTENSITY ALONG CAVITY

E 0.80::

""lI=oC.CIJ 0_1

:!:\~ 0.•

""+IOi~ 02

E 08

~o0..

'"' 0.8

~

~~ 0.4

+;0;e0.2

100 150 200

Z-COORDINATE [/lm)50 100 tSO 200

Z-COORDINATE [/lm)

c d

Figure 24: Field intensity distribution of MPS DFB lasers with a) three phase shifts, equalsection length and ",L of 1.43, b) three phase shifts, equal section length and total ",L of1.36, c) three phase shifts and total ",L of 1.34, d) five phase shifts and total ",L of 1.32.The field intensity distribution is the addition of the forward and backward wave power.

28

4.6 Corrugated pitch modulated DFB laser

A corrugated pitch modulated (CPM) DFB laser is a laser containing a grating withvariable periodicity, a constant coupling coefficient and no phase shifts [5]. If only a smallpart has a different grating pitch, this part will act as a phase shift. The CPM DFB laserhas a great resemblance to the >./4 DFB laser. A schematic view of the grating of a CPMDFB laser and a >./4 DFB laser are given in figure 25.

;------L------:-A- -A.-

a)

b)

phase-arrangingregion

-A-

Figure 25: Schematic view of the grating for a) CPM DFB laser with modulated pitchand b) >./4 DFB laser.

The single mode effect of a >./4 phase shift can also be achieved with a CPM DFB laser.The modulated pitch has to resemble a >./4 = A/2 = 1r phase shift. If the length of thephase-shifting region is L, the pitch of the grating is A and the pitch of the phase-shiftingregion is AI. then the phase difference accomplished with a larger pitch is 21r[L/A-L/A I ]

which has to be equal to 7r. Using A « L, the condition for the grating pitch of the CPMDFB laser in the phase-arranging region becomes

(45)

with A the grating pitch outside the phase-arranging region. A flat field intensity distri­bution reduces the spatial hole burning and improves the mode gain difference. The fieldintensity distribution becomes flatter when the phase shift is distributed more along thecavity, but because a difference in grating pitches has a negative effect on the main modeit also decreases the single mode stability. This means a compromise has to be foundbetween the single mode stability and the flatness of the field intensity distribution. Ac­cording to [5] the optimum relative length for the modulated pitch region is Lcavity / L = 4for /\,L = 2.0 considering single mode stability. Simulation of a CPM DFB laser for the op­timum relative length of 4 the minimum flatness index was found for /\,L = 1.77. Althougha search for the optimum normalized power gain difference for a /\,L product of 1.77 wasnot performed, the criterion for single mode operation [8] is still met. In figure 26a theround-trip gain is given for a laser with a relative length of 4 and a /\,L product of 1.77.

29

tbrenec lhrnUN a au

ROUNDTRIP GAIN VS WAVELENGTH

WAVELENGTH lJunJ

a

~ .... 21 ...... '

FIELD INTENSITY ALONG CAVITY

~~ 0.•

'"+,;e0.2

................

~-"""----llCI~-~IIlO-----,llCl~-200--

Z-COORDINATE (jlm]

b

Figure 26: a) Round-trip amplitude (solid line) and phase (broken line) and b) the fieldintensity distribution for a CPM DFB laser with Lcavity/L = 4 and ",L = 1.77. Thearrows indicate the main mode, at an amplitude of the round-trip gain of 1 and a phaseof O. The field intensity distribution is the addition of the forward and backward wavepower.

The >./4 DFB laser mode is situated at the center of the stopband. In figure 15a this isat 1552 nm. Comparing with figure 26a the main mode is slightly moved from the centerof the stopband. In figure 26b the field intensity distribution is given for a laser with arelative length of 4 and a ",L product of 1.77. The phase shift covers a quarter of the laserlength, distributing the field intensity over a wider range of the cavity. The flatness indexof the CPM DFB laser is 0.0142938 and is improved compared to the optimum for a >./4DFB laser, 0.0207269, see also table 2 on page 31.

30

5 Field intensity distribution at and above threshold

At threshold the field intensity distribution of the simulated lasers has been optimizedwith the grating parameters. For an above threshold analysis it is important to know ifthe field intensity distribution changes when the current is increased. The field intensitydistribution was obtained at the threshold current Ith and at a bias current of 80 rnA (~

2.5Ith).

Before comparing the shape of the field intensity distribution, the field intensity distribu­tions were normalized. In figure 27 the normalized field intensity distributions at thresholdand at 80 rnA are given for several lasers.

d DFB If. d·fl tT bl 2 0 t"a e : 'pllmum a ness In Ices 0 ana ze asers.laser KL Ith flatness index

[rnA] at lth at 80 rnA

MPS DFB laser d 1.32 26 0.00047 0.00045MPS DFB laser c 1.34 28 0.00251 0.00229PC DFB laser, 100 J.Lm 0.59 20 0.00305 0.00314simplified CCM DFB laser 1.34 27 0.00363 0.00342MPS DFB laser b 1.36 28 0.00372 0.00347MPS DFB laser a 1.43 28 0.00545 0.00509uniform DFB laser, 1%-1% 2.08 28 0.00786 0.00599CPM DFB laser 1.77 30 0.01429 0.01349>./4 DFB laser 1.59 31 0.02072 0.02068uniform DFB laser, 5%-30% 1.75 23 0.05258 0.04268CCM DFB laser 1.95 25 0.07928 0.06974

For the uniform DFB laser, coated 5%-30%, the bias current was 60 rnA.

The shape of the field distribution is unchanged the same for higher bias currents, whichcan also be seen from the flatness indices in table 2, where the flatness indices of theanalyzed lasers are collected. Only the flatness index of the PC DFB laser increases, Le.becomes less satisfactory, for a higher bias current; the >./4 DFB laser is the most constantover the analyzed bias current range.

In table 2 the MPS DFB laser gives the best results and can hardly be improved. Formore than three phase shifts these lasers became multimode. Further analysis of the MPSDFB laser can be done to determine the optimum place and phase, besides >"/4, of eachphase shift [15, 16]. The PC DFB laser is interesting for its simple grating structure andyet relatively low flatness index. Next to the MPS DFB lasers and the PC DFB laser,the simplified CCM DFB laser seems most promising. This latter DFB laser reduces thespatial hole burning compared with a >./4 DFB laser, but its round-trip gain diagram,figure 18 on page 18 seems worse with regard to the side mode suppression ratio.

31

NORMAUZED FIELD INTENSITY ALONG CAVITY NORMAUZEO FIELD INTENSITY ALONG CAVITY

0.9 / 0.9

\~~ 0.8 ~ 0.81Jl 1Jlz ffiw

0.7 0.7 'l~ ~

\",::?/0 0-' ulw

0.6 0.8li: ii:

0.5 'un5-lhres' 0.5 'kw·thres' -'un5-tlOrnA' ... - '1<w·60mA' _._.

0.4 0.40 50 100 150 200 250 0 50 100 150 200 250

Z·COORDINATE [mum) Z-eOORDINATE [mumj

a b

NORMAUZEO FIELD INTENSITY ALONG CAVITY NORMAUZED FIELD INTENSITY ALONG CAVITY

.~

0.9 0.9 ~~-.-

~ 0.6 ~ 0.8(JJ inffi z

0.7w

0.7~ ~0 0iil

0.6iil 0.6ii: Ii:

0.5 'ccs-thres' - 0.5 ·pc·thres' -'ccs·80mA' -_. 'pc-llOmA' -'-'

0.4 0.40 50 100 150 200 250 0 50 100 150 200 250

Z-eOOROINATE {mum) Z-eOORDINATE [mum)

C d

NORMAUZEO FIELD INTENSITY ALONG CAVITY NORMAUZED FIELD INTENSITY ALONG CAVITY

0.9 0.9

~ 0.8 ~ 0.8 ~(JJ en ~ffi ffi~ 0.7 ~ 070

~iil0.6 0.6Ii: Ii:

0.5 'mu5-lhres' - 0.5 'cp-thres' -'mu5-6OmA' ....- 'cp-BOmA' .......

0.4 0.40 50 100 150 200 250 0 50 100 150 200 250

Z-eOOROINATE [mum) Z-eOORDINATE [mum)

e f

Figure 27: Normalized field intensity at threshold and at 80 rnA for a) uniform DFB lasercoated 5%-30%, b) >./4 DFB laser, c) simplified CCM DFB laser, d) PC DFB laser, e)MPS DFB laser with five shifts and f) CPM DFB laser.

32

Conclusively, the field intensity distribution hardly changes over the regarded currentrange. This suggests the spatial hole burning is independent of the bias current.

The uniform DFB laser, coated 1%-1%, is taken along only for comparison, for it is multi­mode.

33

6 Above threshold simulations for several ""L products

Comparison of the field intensity distribution of a DFB laser for a number of KL productsin addition to the one for an optimum field intensity distribution, gives an indication aboutthe influence of the field intensity flatness.

For several lasers the linewidth, FM response, output power and differential efficiencywere investigated as a function of the KL product. Because the simulation results behavedsimilar for all lasers with respect to the KL product, only two lasers are presented fully.These lasers are the simplified CCM DFB laser and the PC DFB laser. The simulationresults for these and the other analyzed lasers are collected in table 3 on page 40.

The indices used in the diagrams are a combination of the first letters of the simulatedlaser followed by 'kl', which denotes the KL product and finally the KL product itself.

6.1 Simplified coupling coefficient modulated DFB laser

For the simplified CCM DFB laser the KL variation was achieved changing the centercoupling coefficient, see section 4.3. The coupling coefficient of the outer sections is de­termined by a manufacturing limit, Kmax./Kmin = 10. A total of three KL products areanalyzed, i.e. the optimum, with flattest field intensity distribution, one above and onebelow the optimum product.

The field intensity distributions at 80 rnA for a simplified CCM DFB laser are given infigure 28.

FIELD INTENSity ALONG CAVITY0.0115 ,-------....---~--~--~--__,

0.Q11

~ 0.0105

t 0.010;~ 0.0095~

9 0.009Ul

ii: 0.0085

0.008

/\ ·ccsldl.25' ­·ccsld1.34· ..._..·ccsld1.5O'

2SO200100 ISOZ·COORDINATE (mum)

so0.0075 '--------~--.........--~--~----'

o

Figure 28: Field intensity versus cavity length at 80 rnA of simplified CCM DFB laser forseveral KL products.

The optimum field intensity distribution was found for a KL product of 1.34. Increasingthe KL product and therefore the coupling between the forward and backward propagatingwaves, gives an increased field intensity in the center of the laser.

The linewidth for each simplified CCM DFB laser is given in figure 29.

34

UNE~OTHVERSUSINVERSEPOWER8

7

'N 6:I:!. 5

~~

4

z::J 3

2

10

'ccsJdl.25' ­·ccsJdl.34' ­'ccsJdl.5O' ..._.

50 100 150 200 250 300 350 400INVERSE ( P • PIll) [11W)

Figure 29: Linewidth versus bias current for simplified CCM DFB lasers with several KLproducts.

The linewidth decreases rapidly for increasing power. According to [17] , the linewidthcan increase again for higher power values caused by the onset of side modi affecting themain-mode linewidth through spatial hole burning. However, the single mode CLADISSsimulations of the linewidth do not include the effects of the side modi on the linewidth,

The FM response at 80 rnA for a simplified CCM DFB laser is given in figure 30.

FM RESPONSE0.15

0.1

~ 0.05...:I:

0\;!.g -0.05UI

'" -0.1z0Q. -0.15'"UIII: -0.2::Iiu.

-0.25

-0.35

·ccsld1.25' ­·ccskl1.34' ­·ccskl1.50········

5.5 6 6.5 7 7.5 8 6.5 8 9.5 10MODULATION FREQUENCY [\og(Hz))

Figure 30: FM response versus modulation frequency at 80 rnA of simplified CCM DFBlasers for several KL products.

The curves in figure 30 show that an optimum field intensity distribution is not an optimumfor the FM response. It should be noted that the CLADISS version used does not includethermal effects. The thermal effect causes a dip in the lower frequency region of theFM response and is theoretically analyzed in [18]. The influence of the thermal effectreaches a frequency of about lOMHz, At high frequencies (several GHz) the FM responseis dominated by the relaxation oscillations which can cause a peak in the FM response.The FM response simulated at a bias current of 80 rnA, did not show such a peak for anyof the analyzed lasers.

In [19J a dynamic model is presented for analyzing the FM response. For the influence ofthe spatial hole burning it was found that it is only dominant at a low bias current. There­fore the plots of FM response at 80 rnA are most likely not dependent on the spatial hole

35

burning, At the higher bias currents the dominant factor is amongst others the spectralhole burning. Simulation results for the FM response without taking spectral hole burninginto account show a much lower FM response and a dominant relaxation- oscillation, seefigure 31. This makes the spectral hole burning an important factor concerning the FMresponse of DFB lasers.

-1.5

·1 'ccskl1.34' -·ccskll.34·s' -'-

or-----------~

-0.5

/-2 •__-/

·2.5~-~-~~-~-~~-~~-~---'5 5.5 8 6.5 7 7.5 8 85 9 9.5 10

MODULATION FREQUENCY [log(H<J]

Figure 31: FM response at 80 rnA with and without (-s) spectral hole burning of simplifiedCCM DFB laser for several /'l,L products.

The influence of the spatial hole burning is expected to be similar for other bias currents,because the field intensity distribution is only slightly current dependent, see chapter 5.

The output power for a simplified CCM DFB laser is given in figure 32.

'ccskll.25' ­'ccsldl.34' ..-.­'ccsld1.5O'

0.003

0.006

0.006

0.004

i[ 0.008

IX: 0.007

~~§

0.002

0.001 '------=-_~~_~~~~_~~_~___i0.03 0.035 0.04 0.045 0.05 0.055 0.08 0.085 0.07 0.075 0.08

BIAS CURRENT [AI

OUTPUT POWER (lett facet) VERSUS BIAS CURRENT0.01 ,----~~-_~'"-~-~~-~__,

0.009

Figure 32: Output power versus bias current of simplified CCM DFB lasers for several ",Lproducts.

Because the coupling coefficient difference between the lasers is small, a clear view is notpossible in this case for the effect of the increasing ",L product. However, simulation ofthe output power for wider spaced ",L products showed a decrease of the slope for anincreasing ",L product, see also the differential efficiency for a simplified CCM DFB laser,given in figure 33.

36

0.19DIFFERENTIAL EFFICIENCY (left 'acet) VERSUS BIAS CURRENT

'ccsld125' ­'ccsld1.34' ­'ccsld1.5C7 ...

0.174 '----'--.-....-~-~~~~-.-....-~-~--'0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08

BIAS CURRENT [AI

Figure 33: Differential efficiency versus bias current for simplified CCM DFB lasers withdifferent KL products.

The differential efficiency is decreasing at higher currents for lasers with a high, but alsowith a low KL product. Therefore the linearity is not improved for a flat field intensitydistribution.

6.2 Partially corrugated DFB laser

The field intensity distribution at 80 rnA for a PC DFB laser is given in figure 34.

FIELD INTENSITY ALONG CAVITY

2SO

·pcklO.SC7 ­'pckIO.59' ... _..'pckJ1.0C7

200100 ISOZ-COORDINATE [mum]

.I..'

.,/

so

!£'''-''''...._--::::=--;.! _.-......--.....-._-_....._.__......

0.018

0.016

~ 0.014~iiiz 0.012w~

9 0.01wIi:

0.008-..,....•.

0.0060

Figure 34: Field intensity versus cavity length at 80 mA of PC DFB lasers for several KLproducts.

The ,optimum field intensity distribution was found for a KL product of 0.59. Simulationswith a KL product lower than 0.50 were interrupted, because CLADISS found several modiat threshold. This can be explained by the small corrugated part and coupling coefficient,which makes this laser almost like a Fabry-Perot.

The linewidth for a PC DFB laser is given in figure 35.

37

'pddO.50' ­'pcklO.59' -'pckll.00' .

llNEWIDTIi VERSUS INVERSE POWER5.5 ,------.-~-~-~-~-~-~~

5

4.5

4

3.5

3

2.5

2

1.5

0.5 L-_~----,_~_~_~_~_~--Jo 50 100 150 200 250 300 350 400

INVERSE ( P • Plh ) "1W)

Figure 35: Linewidth versus bias current for PC DFB lasers with different ",L products.

The linewidth of the PC DFB laser is smaller than for all other simulated lasers, see table 3on page 40. In fact the lasers with the smallest Iinewidth, i.e. the PC DFB laser, CCMDFB laser and MPS DFB laser a, have the flattest field intensity distribution, see table 2on page 31. The FM response at 80 rnA for a PC DFB laser is given in figure 36.

0.2 ---_.._..__...---.._.--_.._._.--_._---_..._--.....0.1

o

-D.l 'pckIO.50' ­'pckIO.59''pckJ1.00' .. .

-D.2

-D.3 '-----~_~~_~~_~~_~~____J5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10

MODULATION FREQUENCY [Iog(Hz)]

Figure 36: FM response versus modulation frequency at 80 rnA of PC DFB lasers forseveral /'i.L products.

The FM response for the PC DFB laser is higher than for all other simulated lasers, seetable 3 on page 40, In combination with the grating structure the laser has a high reflectionfacet. This latter seems to influence the improvements made for the FM efficiency. Thisis verified by the uniform DFB laser with a facet coating of 5%-30%. Both lasers have thehighest FM efficiency.

An optimum for linewidth and FM response were not found for the optimized field intensitydistribution in a PC DFB laser, but instead for the largest /'i.L product.

The output power for a PC DFB laser is given in figure 37.

38

0.016

0.014

~ 0.012a:

~0.01

~0.008

a 0.008

0.004

OVTPUT POWER (Ie/I faall) VERSUS BIAS CURRENT

'pcldo.5O' ­'pcIdO.59' -'pckl1.00' .

0.002 L-~_~_~_~~_~_~_~----'0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08

BIAS CURRENT [AI

Figure 37: Output power versus bias current of PC DFB lasers for several KL products.

Compared with other simulated lasers the output power of the PC DFB laser is muchhigher for a small KL product and can be subscribed to the combination of a partiallycorrugated grating structure with a high reflection facet coating.

The differential efficiency for a PC DFB laser is given in figure 38.

DIFFERENTiAl EFFICIENCY (left racel) VERSUS BIAS CURRENT028

g0.26

~

~ 0.24UI

~ 0.22"-III~ 0.2

~0.18UI

a:

~ 0.18l5

~-_.~----------------

'pcklO.5O' ­'pcIdO.59' ..-­'pcldl.OO' ......

0.14 '--~-~-~-~~~~-~-~-'0.035 0.04 0.045 0.05 0.055 0.08 0.065 om 0.075 0.08

BIAS CURRENT [AI

Figure 38: Differential efficiency versus bias current for PC DFB lasers with different KLproducts.

The differential efficiency shows that the LI-curve, i.e. output power versus bias currentcurve, of the most non uniform field intensity distributed laser is most linear for thesimulated range. This linearity is of interest for analog intensity modulation transmissionsystems.

6.3 Overall conclusion of K,L variations

Changing the KL product has the same effect on all analyzed lasers, which means that forincreasing coupling coefficient the laser has a decreasing linewidth and an increasing FMefficiency. Lasers with a high KL product have initially, Le. for low bias currents, a higheroutput power. For higher bias currents their power is less rapidly increasing, see 77eff intable 3 on page 40.

39

Table 3: Above threshold simulation results for several ,!,L products.

DFB laser KL Ith All 7JFM P 7Jeff[rnA] [MHz] [GHz/mA] [mW] [W/A]

1.50 25 17.6 1.32 8.65 .236uniform 1.75 23 13.7 1.38 8.40 .226

2.00 23 11.1 1.44 8.11 .2161.25 39 94.3 0.94 9.64 .211

>./4 1.59 31 25.5 1.14 9.77 .1942.00 26 9.6 1.41 9.26 .1741.25 38 5.5 1.22 9.79 .182

simp\. CCM 1.34 27 5.0 1.23 9.74 .1801.50 27 4.4 1.30 9.61 .1760.50 20 4.0 1.43 14.69 .250

PC 0.59 20 2.3 1.51 13.76 .2331.00 20 1.2 1.91 9.18 .1551.25 30 9.0 1.19 9.73 .187

MPS a 1.43 29 6.7 1.23 9.64 .1812.00 26 3.4 1.39 9.08 .1631.25 38 73.7 0.99 9.58 .211

CPM 1.77 30 20.8 1.19 9.78 .1902.00 28 12.6 1.28 9.61 .182

.::lll is at P-Pth = 5 mW. 77FM is at 100 MHz and 80 rnA. P and 77eff are at 80 rnA. For the uniformDFB laser coated 5%-30% the reference bias current was 60 rnA.

If spectral hole burning is not included in the simulations, the FM response at a highbias current is much lower. Elimination of the spectral hole burning makes the relaxationoscillation a dominant factor at high frequencies and bias currents.

According to the simulations the effect of the grating design on the linewidth and FMresponse mainly results from the magnitude of the ",L product, rather than from theparticular type of grating used. Increasing the coupling coefficient for a >./4 DFB laser[20, 21] will improve its characteristics, such as the FM response and linewidth, but oftenthese lasers become multi-mode already at low power levels. This is attributed to thenon uniform field intensity distribution. Having a flat field intensity distribution shouldprevent the laser from becoming multi-mode. However, a flat field intensity distributioncould not be obtained for higher coupling coefficients, e.g. to flatten the field intensitydistribution of the MPS DFB laser the total ",L product had to be decreased.

40

7 Measurement results

The lasers used for measurements are the CCM DFB laser and the PC DFB laser. Tobetter compare the simulations with the manufactured lasers, new simulations were madewith adjusted structure parameters.

7.1 CCM DFB laser measurements

The cavity length of the simulated and measured CCM DFB laser was 400 JLm. Thecoupling coefficient varies in eight steps from 100/cm at each facet down to l6/cm at thecenter. This makes the total K,L product 2.32. Simultaneously with the CCM DFB laser,a number of >../4 DFB lasers from the same wafer were processed for comparison. Effortwas made to give all measured lasers the same K,L product. Therefore the cavity length ofthe >../4 DFB lasers is only 250 p,m. With a coupling coefficient of 100/cm this amountsto a KL product of 2.50.

Even so, precision of the production process next to other factors, such as cleaving/coatingthe facets, will have its influence on the comparison. Only when the process and resultscan be reproduced on a large scale, improvements become worthwhile.

The measured DFB lasers are selected to be single mode and to have no kinks in the LI­curve. In table 4 the static values are given for the simulated and measured lasers, withIth the threshold current, Pmax the maximum output power at 200 rnA, 7'/eff the differentialefficiency, >.. the wavelength at 80 rnA, 7'/FM the FM efficiency for a modulation frequencyof 100 MHz at 80 rnA, and 6.v the linewidth of the main mode at 80 rnA.

lt should be noted that the CCM DFB laser and >./4 DFB laser where designed for anarray of different wavelengths, see>" in table 4, which is less convenient for our comparison.

For the measured lasers the FM efficiency has the same order of magnitude. This con­firms the simulation results, where the various grating structures did not improve the FMresponse. In figure 39 the FM response of the simulated and measured lasers is given.

FM RESPONSE0.2 .---~----,.---.---~---.--_-~------,

ob---------------__

-0.2 CCM CFB sim. -CCMCFBII04 .

-0.4 1ambda/4 CFB 117 ..

::;;~/~CC===C'=::, '=::.1V·

9.596.5 7 7.5 8 8.5MOCULATION FREQUENCY [1og(Hz))

.1.2 L...-_-'-_--'-__-'-_---'-__-'----_--'-_-----'

6

Figure 39: FM response of the simulated and measured lasers.

The simulation result is a factor four higher than the measured data and has no low

41

Table 4: Static values of measured lasers.

MOQT2782-3 LD1626 - GGM DFB laserno. Ith Pmax 71eff -\ 71FM ~v

[rnA] [mW] [W/A] [nm] [MHz/rnA] [MHz]#04 19.2 17.58 0.120 1534.4 309.76 5#12 16.7 18.02 0.122 1543.1 311.83 6#15 20.3 25.52 0.222 1543.1 307.38 14#20 25.5 26.02 0.240 1548.0 302.66 22#49 22.8 23.74 0.179 1549.7 260.13 16

MOQT2782-3 LD1625 - -\/4 DFB laserno. Ith Pmax 71eff -\ 71FM ~v

[rnA] [mW] [W/A] [nm] [MHz/rnA] [MHz]

#01 34.8 2.09 0.137 1547.8 297.83 479#03 28.7 7.93 0.212 1552.8 370.45 171#15 30.7 4.37 0.106 1534.6 291.21 186#17 26.8 7.40 0.179 1550.3 282.59 192

#19 24.8 12.52 0.246 1553.8 104.64 103

Simulated GGM DFB laserno. Ith Pmax 71eff -\ 71FM ~v

[rnA] [mW] [W/A] [nm] [MHz/rnA] [MHz]

81m. ~ 31.8 _1_6_.5_0---1.__0._10_3---,[ 1552.3 [ 1079.21 4

Measurements were made for a device temperature of 20 degrees centigrade. Pmax was measured at200 rnA. T/eff, >., T/FM and ~/I were measured at 80 rnA.

42

frequency dip because CLADISS does not implement the thermal FM response. Thethermal FM response contribution is dominating up to a frequency of about 10 MHz. Forthe measured lasers the relaxation oscillation becomes dominant, i.e. the FM responseincreases, at a frequency of several GHz. As depicted earlier, the relaxation oscillation inFM response simulations were only dominant for the lower bias currents. A reason forthe difference in FM response between the simulated and measured is contributed to theparameters used to define the laser, e.g. the active layer dimension in transversal andlateral direction.

Notable is the difference in linewidth between the CCM DFB laser and >"14 DFB laser andis on the average a factor 18 smaller for the CCM DFB laser. If the difference in lengthof the lasers is compensated, according to [22], only a factor (400/250 =) 1.6 is accountedfor. Most likely an improvement is made using a modulated grating structure.

The LI-curve of a simulated CCM DFB laser, a measured CCM DFB laser and a measured>..j4 DFB laser is given in figure 40.

OUTPUT POWER (left lacet) VERSUS BIAS CURRENT0.01

0.009

0.008

~ 0.007II:

~0.006

0.005

~0.004

0.0030

0.002

0.001

00

CCM DFB 61m. ­CCM OFB jj()4 -­

tambda/4 OFB '17

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1BIAS CURRENT [AJ

Figure 40: Output power of the simulated and measured lasers.

For higher currents (about 100 rnA) the output power of the measured >../4 DFB lasersdecreases rapidly, which explains the difference in output power at 200 rnA, see table 4.The better field distribution of the CCM DFB laser seems to postpone the saturation ofthe output power, which also improves the linearity of the LI-curve.

7.2 PC DFB laser measurements

The PC DFB laser in chapter 4.4, had a wavelength around 1.55 J.Lm. Because the man­ufactured PC DFB laser has a wavelength around 1.3 J.Lm, the simulation was repeatedfor this smaller wavelength. The material parameters used for the 1.3 J.Lm DFB laser aregiven in appendix C.

Along with the PC DFB lasers, a number of DFB lasers with an uniform grating structureare measured. The coating of the PC DFB laser and uniform DFB laser is AR-77%respectively AR-30%. Their production process was also different, Le. they came ofseparate wafers. In table 4 the static values are given for the simulated and measured

43

Table 5: Static values of measured lasers.

CQF94 LX13513 - PC DFB laserno. Ith Imax 1Jeff .x 1JFM Llv

[rnA] [mW] [W/A] [nm] [MHz/rnA] [MHz]

#02 20.6 49.32 0.336 1309.6 173.86 14#61 27.7 74.22 0.211 1306.0 370.22 32#64 27.2 74.95 0.201 1307.0 265.94 14#81 25.2 52.25 0.382 1308.6 198.06 15#101 19.5 47.97 0.339 1307.9 264.19 11

TLQR0964 LD13377 - uniform DFB laserno. Ith I max 1Jeff .x 1JFM Llv

[rnA] [mW] [W/A] [nm] [MHz/mAl [MHz]

#05 21.4 49.68 0.344 1309.3 174.67 10#07 24.5 51.64 0.362 1309.2 207.29 16#20 24.3 56.72 0.288 1308.6 162.07 10#28 20.7 53.22 0.297 1307.7 154.42 8#35 20.7 50.66 0.326 1308.0 161.89 12

Simulated PC DFB laser diodeno. Ith I max 1Jeff .x 1JFM Llv

[rnA] [mWI I [W/Aj [nm] [MHz/rnA] [MHz] _

_s_lm_.--'~ 25.9 Q9_.2_0_L--_O._28_O_[ 130n=] 1705.62 4

Measurements were made for a device temperature of 20 degrees centigrade. [max was measured foran output power of 10 mW. l1eff' >., I1FM and D.v were measured at 80 rnA.

lasers, with Ith the threshold current, Imax the maximum current at 10 mW, 1Jeff thedifferential efficiency, .x the wavelength at 80 rnA, 1JFM the FM efficiency for a modulationfrequency of 100MHz at 80 rnA, and Llv the linewidth of the main mode at 80 rnA.

As it turns out, almost identical FM responses can be found amongst PC DFB lasersand uniform DFB lasers. An example is given in figure 41. This figure shows, next tothe simulation, the almost identical FM response of a PC DFB laser and a uniform DFBlaser. The fact that it is possible to find lasers with identical FM response suggests thereis no significant difference accomplished with this partially corrugated grating structure.This confirms the simulation results, where the various grating structures did not improvethe FM response.

The simulated FM response is more than four times the largest measurement, a valuefound earlier for the difference between simulated and measured CCM DFB lasers. Alsoin this case it is assumed that the parameters used for simulation do not exactly representthe produced laser.

The linewidth improvement established with a CCM DFB laser is not accomplished forthe PC DFB laser. For an adequate statement about the similar linewidth, the /'i,L product

44

FM RESPONSE0.4 r--~--"-------'---"""----'---~---,

0.21:----------------

o·0.2

-0.4

PCDFBsim. ­PCDFB'64 _•..••un. DFB 107 .

..=-~...........~ ..'-.~.~.,~

...

9.596.5 7 7.5 8 8.5MODUlATION FREQUENCY [log(Hz)1

•1.2 "--_.........__-'---_---L.__-'--_---'-__---'----_---l

6

Figure 41: FM response of the simulated and measured lasers.

of the lasers is of importance. The KL product can only be determined after synthesis ofthe emission spectra of the measured laser [23J, and is not within the scope of this work.

The LI-curve of a simulated PC DFB laser, a measured PC DFB laser and a measureduniform DFB laser is given in figure 42.

OUTPUT POWER (left facet) VERSUS BIAS CURRENT0.03 .-----....-~....__~..----:__.-:.........,-__.-~-~-----,

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1BIAS CURRENT {AI

PCDFBslm. ­PC DFB Il64 --un. DFB 107 .

......................

.......­.........-..

....,..-.._-_._--_._--_......-..__...

OL---.........~'------''------'----'----'----'----'------'0.01

0.01

0.025

0.015

0.005

~cr: 0.02

~

i

Figure 42: Output power of the simulated and measured lasers.

Because the LI-curve is still linear up to high output powers, the PC DFB laser is mostsuitable for intensity modulation.

45

8 Conclusions

Simulations of identical lasers, except for their grating structure, gives an opportunity toextract knowledge about grating structures, their effect on the field intensity distributionand the effect of spatial hole burning on the DFB laser characteristics. Several gratingstructures were designed to achieve a fiat field intensity distribution. It was found that theflatness of the field intensity is not a critical design parameter for the linewidth and FMresponse. According to the simulations an increase of the coupling coefficient will improvethe linewidth and FM response.

The measurements confirm that an improvement of the field intensity distribution has noeffect on the FM response for the mid frequencies, Le. between 100 MHz and 1 GHz.

Because the thermal contribution at lower frequencies is not implemented in the simula­tion package this effect can not be evaluated. In the measurements, no improvement inthe thermal FM-dip, Le. a shift towards lower frequencies, was found in lasers with animproved (flatter) field intensity distribution, as compared to uniform-grating DFB lasers.

A combination of a fiat field intensity distribution, to prevent the laser from becomingmulti-mode, and a high KL product (> 2), for improved linewidth and FM response, couldnot be obtained.

The parameter files used by CLADISS enable us to design an almost endless variety ofgrating structures. The simulation of these structures above threshold is however notan easy task, because these calculations performed by CLADISS need parameters withinnarrow ranges.

46

References

[1] J.E.A. Whiteaway, B. Garrett, G.H.B. Thompson, A.J. Collar, C.J. Armis­tead, and M.J. Fice, The static and dynamic characteristics of single and mul­tiple phase-shifted DFB laser structures, IEEE Journal of Quantum Electronics,28(5):1277-1293, May 1992

[2] G. Morthier, K. David, P. Vankwikelberge, and R. Baets, A new DFB-laser diodewith reduced spatial hole burning, IEEE Photonics Technology Letters, 2(6):388­390, June 1990

[3] G.P. Agrawal and N.K. Dutta, Long-wavelength semiconductor lasers, AT&TBell Laboratories, Murray Hill, New Jersey, 1986

[4] J. BullS, Single frequency semiconductor lasers, Plessey Research Caswell Ltd,June 1989

[5] M. Okai, Spectral characteristics of distributed feedback semiconductor lasers andtheir improvements by corrugation-pitch-modulated structure, Journal of AppliedPhysics, 75(1):1-29, Januari 1994

[6] H. Kogelnik and C.V. Shank, Coupled-wave theory of distributed feedback lasers,Journal of Applied Physics, 43(5):2327-2335, May 1972

[7] W. Streifer, R.D. Burnham, and D.R. Scifres, Effect of external reflectors onlongitudinal modes of distributed feedback lasers, IEEE Journal of QuantumElectronics, 11(4):154-161, April 1975

[8] P.P.G. Mols, P.L Kuindersma, W. van Es-Spiekman, and LA.F. Baele, Yield anddevice characteristics of DFB lasers: statistics and novel coating design in theoryand experiment, IEEE Journal of Quantum Electronics, 25(6):1303-1313, June1989

[9] H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, Stability insingle longitudinal mode operation in GalnAsP/InP phase-adjusted DFB lasers,IEEE Journal of Quantum Electronics, 23(6):804-813, June 1987

[10] T. Schrans and A. Yariv, Semiconductor lasers with uniform longitudinal intensitydistribution, Applied Physics Letter, 56(16):1526-1528, April 1990

[11] P.I. Kuindersma, P.P.G. Mols, W. van Es-Spiekman, and LA.F. Baele, 50.000different DFB devices, Proc.14th Eur.Conf.Optical Commun. ECOC'88, No. 292,Part 1:384-387, 1988

[12] H.R.J.R. van Helleputte, M.J. Verheijen, and J.J.M. Binsma, Coupling CoefficientModulated Distributed Feedback gratings with E-beam lithography, Microelec­tronic Engineering 23:473-476, 1994

[13] J.P. Weterings, Cladiss berekeningen voor DFB's met gereduceerde spatial holeburning, Philips Research Eindhoven, Nat. Lab., June 1993

47

[14] T. Okuda, H. Yamada, T. Torikai, and T. Uji, Novel partially corrugated wave­guide laser diode with low modulation distortion characteristics for subcarriermultiplexing, Electronic Letters, 30(11):862-863, May 1994

[15] H. Ghafouri-Shiraz, B.S.K. Lo, and C.Y.J. Chu, Structural dependence of three­phase-shift distributed feedback semiconductor laser diodes at threshold using thetransfer matrix method, Semiconductor Science and Technology, 9(5):1126-1132,May 1994

[16] M. Matsuda, S. Ogita, and Y. Kotaki, Phase-shifted gratings for DFB lasers,Fujitsu Scientific and Technical Journal, 26(1):78-85, April 1990

[17] P. Vankwikelberge, G. Morthier, and R. Baets, Cladiss - A longitudinal multi­mode model for the analysis of the static, dynamic, and stochastic behavior ofdiode lasers with distributed feedback, IEEE Journal of Quantum Electronics,26(10):1728-1741, October 1990

[181 G. Soundra Pandian and S. Dilwali, Om the Thermal FM Response of a Semicon­ductor Laser Diode, IEEE Photonics Technology Letters, 4(2):130-133, February1992

[19] P. Vankwikelberge, F. Buytaert, A. Franchois, R. Baets, PJ. Kuindersma, andC.W. Fredriksz, Analysis of the carrier-induced FM response of DFB lasers: The­oretical and experimental case studies, IEEE Journal of Quantum Electronics,25(11):2239-2253, November 1989

[20] H. Hillmer, S. Hansmann, and H. Burkhard, Realization of high coupling co­eflicients in 1.53 mm InGaAsP/lnP first order quarter wave shifted distributedfeedback lasers, Applied Physics Letter, 57:534-536, 1990

[211 A. Mecozzi, A. Sapia, P. Spano, H. Burkhard, S. Hansmann, and H. Hillmer Non­linearities in high-index-coupled >.j4-shifted distributed-feedback semiconductorlasers, lEE Proc.-Optoelectron., 141(1):8-12, February 1994

[22J T. Kimura and A. Sugimura, Linewidth reduction by coupled phase-shiftdistributed-feedback lasers, Electronic Letters, 23(19):1014-1015, September 1987

[23J P.J. de Waard, Synthesis of the spectra of distributed feedback lasers, PhilipsResearch Eindhoven, Nat. Lab. Report NL-R 6775, April 1994

[24] H.J.M. Vos, Cladiss, Philips Research Eindhoven, updated manual, December1991

[25] H.J.M. Vos and J.P. Weterings, Cladiss under unix, Philips Research Eindhoven,Nat. Lab. Technical Note NL-TN 104/92, April 1992

[26] C.H. Henry, Theory of the linewidth of semiconductor lasers, IEEE Journal ofQuantum Electronics, 18(2):259-264, February 1982

48

A Introduction to the CLADISS simulation package

CLADISS, short for Compound Cavity LAser DIode Simulation Software, handles a widevariety of compound cavity laser diodes. Use [24, 25J for detailed information about thelaser modelling software. Included are the static, the dynamic and the stochastic modelsand the main features of the models are described. The strength of CLADISS derives fromthe fact that it takes into account non-linear gain suppression, longitudinal spatial holeburning and more than one longitudinal mode.

CLADISS has the possibility to define for each laser section different parameters. Ap­pendix C and B give an example of the material and structural parameters for eachsection used by CLADISS.

Each laser section is defined as a waveguide with a rectangular cavity. The injected carrierdensity in the section is then assumed to affect only the carrier concentrations of this cavity.For the description of the electrical field inside the laser cavity, only the lowest TE-modeis assumed to carry power.

Types of analysis CLADISS offers five types of analyses, i.e. a static threshold analysis,a self-consistent static DC analysis, a dynamic small-signal AC analysis, a small-signalnoise or linewidth analysis and a supplementary analysis. These analyses are preceded bythe initialization procedure needed by the threshold analysis. The analysis sequence to befollowed is shown in figure 43.

The initialization procedure asks for an initial estimate at threshold of the optical power,the wavelength and the current for each section. The threshold analysis precedes the DCanalysis, but can be omitted if a good initial estimate can be predicted. Because the lastthree analyses are based on the linear representation of the laser equations around a givenbias point, they always should be preceded by the DC analysis.

Figure 43: Diagram of interrelationship between the different types of analyses.

Thr.eshold analysis The threshold analysis determines the current that must be in­jected, such that some laser mode would reach its threshold. This current is then called

49

the threshold current of the considered mode. The mode with the lowest threshold cur­rent, Le. the main mode, determines the laser threshold. Simultaneously, the thresholdwavelength of each mode is calculated. If the analyzed number of modi is more than one,the gain difference between the main mode and the mode with the 2-nd lowest thresholdcurrent is determined as well. The obtained gain difference is a measure, never a guarantee,for the single mode behavior of the laser.

DC analysis The DC analysis determines the LI characteristic of the laser. The laserequations are solved self-consistently and the longitudinal dimension is taken into accountby dividing each section in many small segments. Therefore longitudinal spatial hole burn­ing is included accurately. Moreover, also non-linear gain suppression can be considered.In a multi-mode analysis the spontaneous emission that couples into a mode must beincluded in order to model the mode competition correctly.

AC analysis With the small-signal AC analysis of CLADISS the dynamic propertiesof the laser structure can be investigated. More particular, the AM response and FMresponse of the device can be studied at a given bias current for a specified range ofmodulation frequencies. The bias current used for the AC analysis is a bias point definedby the user prior to the DC analysis.

The AC analysis considers non-linear gain suppression, longitudinal spatial hole burningand several longitudinal modi simultaneously.

Noise or linewidth analysis Similar to the AC analysis, the linewidth analysis is basedon a small signal approximation which allows a linear representation of the laser equationsaround some bias point.

The linewidth analysis takes into account non-linear gain suppression and longitudinalspatial hole burning.

It must be noted that the linewidth now can be calculated in three different ways. Firstis the calculation that belongs to the DC analysis, using the simple analytic formuladerived by Henry [26). The other possibilities are given with the linewidth analysis. Thelinewidth can be calculated immediately from the low frequency FM noise, or by takingthe half width of the calculated power spectral density.

Supplementary analysis The supplementary unit calculates several properties relatedto the carrier and optical distribution. Some of these are also generated in previousanalyses. Additional are however the average Bragg deviation, the distribution of theeffective carrier lifetime and average carrier lifetime for each mode. Similar to the AC andlinewidth analysis, these properties are calculated in a bias point, i.e. a user defined pointon the LI characteristic.

50

B Example of parameter file for 1.5 J..Lrn DFB lasers

This parameter file contains the material and structure parameters of the 1.5 p.rn uniformDFB laser, coated 1%-1%.

onesec1150.E-41.E-6100.1.E-57.5E-51..20.2400.00.1,0.00.1,0.05.0E-9.9949,0.0.9949,0.0.101.50249.965.00.0,8.3E-30.0,-8.3E-33.245,-1.3E-44.02O.1.0.4684235E-60.71074080.774253102.88450.58668564.172654.7570.0-.169E-7-0.2076E-214.2038.6-49.33.8013

one section, 1500 nm standard DFB laser, KL=1.25, coated 1%-1%SEGMENT NUMBERBRAGG ORDERINTERNAL LOSS COEFFICIENT, [1/p.mJLOCAL SPONTANEOUS EMISSION FACTORBIMOLECULAR RECOMBINATION COEFFICIENT, [p.m3 /5JMAXIMUM CURRENT STEP AT SWEEPING, [AJAUGER RECOMBINATION COEFFICIENT, [p.m6/ sJETA: INJECTION EFFICIENCYPOWER FILLING FACTOR IN ACTIVE LAYERPERlOD OF THE GRATING, [p.mJPHASE OF THE GRATINGAMPL. REFL. (1%) ON LEFT FACET 1AMPL. REFL. (1%) ON RlGHT FACET 2LIFETIME OF THE CARRIERS, [sJAMPL. TRANSM. (99%) ON LEFT FACET 1AMPL. TRANSM. (99%) ON RlGHT FACET 2ACTIVE LAYER THICKNESS, [p.m]STRlPE WIDTH, [p.mJSEGMENT LENGTH, [p.mJ'PROPAGATION' STEP, [p.mJXABO: COUPL COEF FROM WAVE B TO WAVE A, [1/p.mJXBAO: COUPL COEF FROM WAVE A TO WAVE B, [l/p.mJEFFECTIVE REFRACTIVE INDEXGROUP INDEXDIMENSIONLESS PARAMETER FOR Iff-NOISE1. OPTION "1.": USE SPECTR. HB. EXPRESSION, OPTION "2.": USE (1-E2. G1: 1ST PARAM. GAIN CALCULATION (1550nm)3. G2: 2ND4. G3: 3TH5. G4: 4TH6. G5: 5TH7. G6: 6TH8. G7: 7TH9. G8: 8TH10. R1: 1ST PARAM. REFR. INDEX CALCULATION (1550nrn)11. R2: 2ND12. R3: 3TH13. R4: 4TH14. R5: 5TH15. R6: 6TH

51

4.236E-9-0.72E-2-1. 115e-80.018847.357e-9-0.012250.60106E-20.104886£-80.79744750.6918891e-13-0.829738ge-7-0.622e-2-0.449958e-60.8005530.648947e-9-1550.-18.60.835.36E-9-68.35£-934.4E-9532.E-4-1034.E-4524.E-41.144E-4-2.646E-41.738E-4-0.025535E-40.0475E-4-0.0265E-4O.O.o.O.o.O.o.O.O.O.O.o.O.O.O.4.1.

16. R7: 7TH17. R8: 8TH18. R9:- 9TH19. RIO: 10TH20. Rll: 11TH21. R12: 12TH22. 51: 15T PARAM. 5PECTR. HB. CALCULATION23. 52: 2ND24. 53: 3TH25. 54: 4TH26. 55: 5TH27. 56: 6TH28. 57: 7TH29. 58: 8TH30. 59: 9TH31. 510: 10TH32. 511: 11TH33. 512: 12TH34. AI: 1ST PARAM. INTERVAL. BAND. AB5. CALC. (1550nm)35. A2: 2ND36. A3: 3TH37. A4: 4TH38. AS: 5TH39. A6: 6TH40. A7: 7TH41. A8: 8TH42. A9: 9TH43. AlO: 10TH44. All: 11TH45. A12: 12TH46.47.48.49. l5T PARAM. USED IN VOLTAGE CALCULATION50. 2ND51. 3TH52. 4TH53. HEAT CAPACITY OF P-LAYER54. HEAT CAPACITY OF ACTIVE-LAYER55. HEAT CAPACITY OF N-LAYER56. HEAT CONDUCTIVITY OF P-LAYER57. HEAT CONDUCTIVITY OF ACTIVE-LAYER58. HEAT CONDUCTIVITY OF N-LAYER59. THICKNESS OF P-LAYER60. THICKNESS OF N-LAYER61. E-FACTOR IN FORMULA (l-EP), IF OPTION PARAMETER 1 = "2." I62. IF "2." THEN U5E l300nm ELSE USE l550nm LA5ER

52

-0.0093225E-6-0.008485.E-37.E-6150.E-I0-342.&10200.E-1O234.8E-4306.88&41.42609E-4-3.3121E-41.9807E-41.E-1O-2.E-I01.5E-I0

63. Rl': 1ST PARAM. REFR. INDEX CALCULATION (1300nm)64. R2': 2ND65. R3': 3TH66. R4': 4TH67. AI': 1ST PAR. INTERVAL. BAND. ABS. CALC. (1300nm)68. A2': 2ND69. A3': 3TH71. A5': 5TH72. A6': 6TH73. A7': 7TH74. A8': 8TH75. A9': 9TH76. AIO': 10TH77. All'; 11TH78. AI2': 12TH

53

C Example of parameter file for 1.3 /-lm DFB lasers

This parameter file contains the material and structure parameters of the 1.3 ILIn PartiallyCorrugated DFB laser, coated 1%-77%.

twosec1150.E-41.E-4100.1.E-43E-51..300.20000.00.1,0.00.0,0.0.22E-8.9949,0.01.0,0.0.131.50100.3210.0.0,5.9E-30.0,-5.9E-33.28,-1.3E-44.02O.1..331373E-6.881605.633745681.4139.76210163.75856.730.9-.169E-7-0.2076E-214.2038.6-49.33.8013

two sections,1300 nm partially corrugated DFB laser, coated 1%-77%SEGMENT NUMBERBRAGG ORDERINTERNAL LOSS COEFFICIENT, [l/ILm]LOCAL SPONTANEOUS EMISSION FACTORBIMOLECULAR RECOMBINATION COEFFICIENT, [ILm3 / s]MAXIMUM CURRENT STEP AT SWEEPING, [A]AUGER RECOMBINATION COEFFICIENT, [ILm6/ s]ETA: INJECTION EFFICIENCYPOWER FILLING FACTOR IN ACTIVE LAYERPERIOD OF THE GRATING, [ILm]PHASE OF THE GRATINGAMPL. REFL. (1%) ON LEFT FACET 1AMPL. REFL. (0%) ON RIGHT FACET 2LIFETIME OF THE CARRIERS, [s]AMPL. TRANSM. (99%) ON LEFT FACET 1AMPL. TRANSM. (100%) ON RIGHT FACET 2ACTIVE LAYER THICKNESS, [ILm]STRIPE WIDTH, [ILm]SEGMENT LENGTH, [ILm]'PROPAGATION' STEP, [ILm]XABO: COUPL COEF FROM WAVE B TO WAVE A, [l/ILm]XBAO: COUPL COEF FROM WAVE A TO WAVE B, [l/ILm]EFFECTIVE REFRACTIVE INDEXGROUP INDEXDIMENSIONLESS PARAMETER FOR l/f-NOISE1. OPTION "1.": USE SPECTR. HB. EXPRESSION, OPTION "2.": USE (1-2. G1: 1ST PARAM. GAIN CALCULATION (1300nm)3. G2: 2ND4. G3: 3TH5. G4: 4TH6. G5: 5TH7. G6: 6TH8. G7: 7TH9. G8: 8TH10. R1: 1ST PARAM. REFR. INDEX CALCULATION (1550nm)11. R2: 2ND12. R3: 3TH13. R4: 4TH14. R5: 5TH15. R6: 6TH

54

4.236E-9-0.72E-2-1.115e-80.018847.357e-9-0.012250.45193e-20.18185e-80.94874660.4208e-13-0.65143e-7-0.821ge-2-0.11157e-40.955280.7601ge-9-1550.-18.60.9535.36E-9-68.35E-934.4E-9532.E-4-1034.E-4524.E-41.144E-4-2.646E-41.738E-4-0.025535E-4O.0475E-4-0.0265E-4O.O.O.O.O.O.O.O.O.O.O.o.O.O.O.4.2.

16. R7: 7TH17. R8: 8TH18. R9: 9TH19. RIO: 10TH20. Rll: 11TH21. R12: 12TH22. Sl: 1ST PARAM. SPECTR. HB. CALCULATION23. S2: 2ND24. S3: 3TH25. S4: 4TH26. S5: 5TH27. S6: 6TH28. S7: 7TH29. S8: 8TH30. S9: 9TH31. S10: 10TH32. S11: 11TH33. S12: 12TH34. AI: 1ST PARAM. INTERVAL. BAND. ABS. CALC. (1550nm)35. A2: 2ND36. A3: 3TH37. A4: 4TH38. A5: 5TH39. A6: 6TH40. A7: 7TH41. A8: 8TH42. A9: 9TH43. A10: 10TH44. All: 11TH45. A12: 12TH46.47.48.49. 1ST PARAM. USED IN VOLTAGE CALCULATION50. 2ND51. 3TH52. 4TH53. HEAT CAPACITY OF P-LAYER54. HEAT CAPACITY OF ACTIVE-LAYER55. HEAT CAPACITY OF N-LAYER56. HEAT CONDUCTIVITY OF P-LAYER57. HEAT CONDUCTIVITY OF ACTIVE-LAYER58. HEAT CONDUCTIVITY OF N-LAYER59. THICKNESS OF P-LAYER60. THICKNESS OF N-LAYER61. E-FACTOR IN FORMULA (l-EP), IF OPTION PARAMETER 1 = "2."62. IF "2." THEN USE 1300nm ELSE USE 1550nm LASER

55

-0.0093225E-6-0.008485.E-37.E-6150.E-10-342.E-10200.E-10234.8E-4-524.7E-4306.88E-41.42609E-4-3.3121E-41.9807E-41.E-1O-2.E-101.5E-1O

63. R1': 1ST PARAM. REFR. INDEX CALCULATION (1300nm)64. R2': 2ND65. R3': 3TH66. R4': 4TH67. AI': 1ST PAR. INTERVAL. BAND. ABS. CALC. (1300nm)68. A2': 2ND69. A3': 3TH70. A4': 4TH71. A5': 5TH72. A6': 6TH73. AT: 7TH74. A8': 8TH75. A9': 9TH76. A10': 10TH77. All': 11TH78. A12': 12TH

56