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Circuit model for traveling wave semiconductor laser

ampliersWeiyou Chen *, Aijun Wang, Yejin Zhang, Caixia Liu, Shiyong Liu

Department of Electronic Engineering, Jilin University, Changchun 130023, People's Republic of China

Received 2 December 1999

Abstract

A circuit model of a traveling wave semiconductor laser amplier is presented for the circuit level simulation of

single device or Optoelectronics Integrated Circuit (OEIC) included ampliers. To verify the model, the simulated

results are compared with the experimental results. 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Traveling wave amplier; Circuit model; Computer-aided analysis

1. Introduction

A semiconductor laser is capable of amplifying lin-

early coherent light, below the threshold. Linear semi-conductor laser ampliers (SLA) are of two types: one is

the traveling wave (TW) amplier [1,2], and the other is

the FabryPerot (FP) amplier. The principle of

TW-SLA and FP-SLA is identical, i.e. intrinsic stimu-

lated light amplication. The dierence is reectivity of

facets. FP-SLA is of a higher reectivity; light propa-

gates reciprocally in cavities, resulting in resonance

amplication. TW-SLA is of a lower reectivity; the

incident light is amplied in a single pass. TW-SLA is of

greater interest than FP-SLA. This article mainly studies

the circuit model of TW-SLA.

2. Model description

Traveling wave-semiconductor laser amplier oper-

ates in a multi-longitudinal mode, so it is necessary to

construct a circuit model by means of multi-longitudinal

mode rate equations. However, it is very complex to do

so, because the mode number is an uncertainty and a

large value. In our previous works [3], we adopted the

assumption [3] that the emission spectra of the amplier,

as a function of wave-length is of Gausss shape. This

assumption is also used in this article. For the conve-

nience of derivation, we suppose that the output of theamplier is the linear superimposition of amplied

spontaneous emission and signal so that the spontane-

ous emission and signal can be processed separately.

2.1. Signal propagation behavior in a cavity

Fig. 1(a) schematically shows the propagation be-

havior of signal in a cavity. Here, we assume that the

incident light is illuminated on the left facet. The signal

photon density distributions are shown schematically in

Fig. 1(b), sf stands for the propagation in +z, and sb

stands for the propagation in)

z. Under the assumptionof uniform gain along the cavity, sf and sb can be written

as

sf sf0 expgmzY 1

sb sbL exp gmL zY 2

where, gm is the average net gain,

gm CgnY ki aintY 3

C is the optical connement factor, aint is the cavity

absorption coecient, ki is the signal light wavelength, g

is the gain function. Because TW-SLA operates under

Solid-State Electronics 44 (2000) 10091012

*Corresponding author.

0038-1101/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 3 8 - 1 1 0 1 ( 0 0 ) 0 0 0 1 5 - 0

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a threshold, gain saturation eect can be neglected, gas a

function of carrier density and wavelength can be rep-

resented as

gnY k g0n ntrf1 2k kp2aDk2ggY 4

where, g0 is the gain constant, n is the carrier density in

an active region, ntr is the transparency carrier density,

Dkg is the FWHM of this function, kp is the center

wavelength.

At the left and right facets, the boundary conditions

are

sf0 sin RLsb0Y 5a

sbL RRsfLY 5b

where, sf0 and sb0 are the forward and backward prop-

agation photon densities at the left facet, respectively,

whereas sfL and sbL are the photon density at the right

facet. RL and RR are the re ectivity of left and right

facets. sin is the incident photon density at left the facet,

as a function of incident light power can be expressed as

sin giPin

hmWDcHY 6

where, Pin is the incident light power, gi is the incident

eciency, hm is the signal photon energy, W and D are

the width and thickness of the cavity. cH is the light speed

in the medium.

From Eqs. (1) and (2), we can get

sfL sf0 expgmLY 7a

sb0 sbL exp gmLY 7b

where L is the cavity length.

Solving the equation set of Eqs. (5) and (7),

sf0

sin

1 RLRR exp2gmL X 8

The average signal photon density is

ss 1

L

L0

sf sbdz

sin1 RR expgmL exp gmL 1

gmL1 RRRL exp2gmLX

9

The signal output powers from the left and right facets

are

PoutL hmWDcH1 RLRRsf0 exp 2gmLY 10a

PoutR hmWDcH1 RRsf0 exp gmLX 10b

2.2. Model derivation

According to Eqs. (10a) and (10b), if gm is known, it

is easy to get the signal output. However, it is very dif-

cult to get gm, because gm is determined with the carrier

density, and the carrier density is relative to spontaneous

emission recombination, nonradiative recombination,

and stimulated emission recombination. Therefore, we

must solve the carrier and photon rate equations. Due tocontinuous spectrum operation of TW-SLA, we adopt

multi-longitudinal mode rate equations,

dn

dt

Ij

Q Rnn Rrn

I0

CcHgnY ksk dk

CcHgnY kissY 11

dsk

dt CcHgnY ksk

sk

sph bspkRrnY 12

where Ij is the injection current, Q qVact, q is theelectron charge, Vact WDL. Rn(n) and Rr(n) are thenonradiative and radiative recombination rates, respec-

tively [3].

According to the assumption of the Gaussian func-

tion of spontaneous emission spectra, the spontaneous

emission photon density as a function of wavelength can

be expressed as [3]

sk sp expf4 ln2k kp2aDkp

2gY 13

where s(k) is the total photon density inside and outside

the active region per unit wavelength, dening as the

total photon number inside and outside the active region

divided by active region volume. This is equivalent to

compressing the photon outside the active region into

Fig. 1. (a) Schematic propagation of the signal, and (b) sche-

matic of the photon density distribution.

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the active region, but those photons are not capable of

stimulating. sp is the peak value, Dkp is the FWHM.

The processing method of Eqs. (11) and (12) is sim-

ilar to that in Ref. [3].

The output powers of the spontaneous emission from

the left facet and the right facet per unit wavelength are

pLk hc2WDRL 1 ln RLRR

2ngk1 RL RLaRR

p1 RR

skY 14a

pRk hc2WDRR 1 lnRRRL

2ngk1 RR RRaRL

p1 RL

skX 14b

From integralI

0pkdk, the total output power can be

obtained. In general, if Dkp ( kp, then the k in de-nominator of Eq. (14) can be replaced by kp. The total

output powers are

PL hc2WDRL 1 ln RLRR

2ngkp1 RL RLaRR

p1 RR

stotY 15a

PR hc2WDRR 1 ln RRRL

2ngkp1 RR RRaRL

p1 RL

stotX 15b

Based on Eqs. (10)(12) and (15), we construct the

TW-SLA circuit model as shown in Fig. 2, where

Isti QCcHgnY kiss. The other meaning of the elements

in this circuit model is similar as in Ref. [3].

There are seven ends in this model, the two ends re-

lated to Ve

correspond to real electrical ends, the upper

one is for anode, the lower one is for cathode. The other

ve ends are virtual. The end marked with Pin is for the

power input; the input light source must be regarded as

the voltage source. The four ends placed at the lower

right are for signal output and spontaneous emission

output from the left and the right facets.

3. Simulation

The above model is converted to the subcircuit of

PSPICE; the simulation has been done by using

PSPICE, with the circuit shown in Fig. 3. Most of the

model parameters are mainly taken from Refs. [1,2,4], as

shown in Table 1. The parameters not shown in Table 1

are set to be zero.

To verify the model, the simulated results have been

compared with the experimental results given in Ref. [1],

as shown in Fig. 4. The solid curves are the simulated

results, the scatters are the experiment results. It can be

seen that for a smaller biased current, simulated resultsagree well with the experimental results. For high cur-

rent, the output power of the right facet is far away from

the experimental result. This has resulted the gain sat-

uration eect is not being included in this model.

As examples, the other characteristics of the

TW-SLA have been simulated (Figs. 5 and 6). Fig. 5

shows the output power versus the incident power; it can

be seen that when the incident power increases, the

spontaneous emission output power decreases, the signal

Table 1

Model parameters

Parameters

(unit)

Value Parameter

(unit)

Value

An1 (s1) 2 108 Rs (X) 1

An3 (cm6 s1) 5 1029 Vbi (V) 1.13

Ar2 (cm3 s1) 1.4 1010 W (lm) 600

Cp (pF) 10 Dkg (nm) 150

Csc0 (pF) 10 Dks (nm) 150

D (nm) 10 C 0.05

ng 4.0 aint (cm1) 3

G0 (cm3 s1) 1.9 106 bsp0

(lm1)

6 104

L (lm) 1500 g 2

ntr (cm3) 1.2 1018 gi 0.7

nr 3.4 ki (lm) 0.9

Rd (X) 1 1010 kp (lm) 0.86

RL (RR) 0.0026Fig. 2. The circuit model of TW-SLA.

Fig. 3. The circuit for simulation of TW-SLA.

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output power from right facet increases, the signal out-

put from left facet increases initially and then decreases.

The amplication ratio (dened as the right facet signal

output power/incident power) decreases with an increase

in the incident power. This is because for a xed biased

current, the increase in the incident power will result in

the increase of the photon density, the decrease of the

carrier density, and of the medium gain.

Fig. 6 gives the output power versus reectivity. As

shown in this gure, the output powers from the left and

the right facets are close to each other, with increasing

reectivity.

4. Conclusion

A circuit model of TW-SLA has been presented for

the circuit level simulation of OEIC with this type of

device. This model can be used to simulate the DC, AC

and transient characteristics of single TW-SLA or

OEIC.

References

[1] Goldberg L, Mehuys D, Hall DC. 3.3W CW diraction

limited broad area semiconductor amplier. Electron Lett1992;28(12):10824.

[2] Goldberg L, Mehuys D. 21W broad area near-diraction-

limited semiconductor amplier. Appl Phys Lett 1992;

61(6):6335.

[3] Chen W, Liu S. Circuit model for multilongitudinal-mode

semiconductor lasers. IEEE J Quant Electron 1996;32(12):

212832.

[4] Dai Z, Michalzik R, Unger P, Ebeling KJ. Numerical

simulation of broad-area high-power semiconductor laser

ampliers. IEEE J Quant Electron 1997;33(12):224053.

Fig. 4. Signal output power versus biased current. The incidentpower is 500 m W ((d) right facet output, () left facet output).

Fig. 5. The output power versus the incident power, under

dierent biased currents. The dashed curves are for spontane-

ous emission, the dotted curves are for signal output from the

left facet, the solid curves are for the signal output from the

right facet.

Fig. 6. The output power versus the re ectivity: The solidcurves are for signal output from the right facet and the dashed

curves are for signal output from the left facet.

1012 W. Chen et al. / Solid-State Electronics 44 (2000) 10091012