Optical rise time and frequency chirpingpredictions for (forward-biased) optical

absorption modulatorsL.D. Westbrook, B.Eng., Ph.D.

Indexing terms: Semiconductor lasers, Modulation

Abstract: The modulation characteristics of the (forward-biased) semiconductor travelling-wave absorptionmodulator, a prime contender for monolithic-integration with an injection laser, is analysed. It is found that, asa consequence of the distribution of charge carriers along the length of the device, the modulator output rise/falltimes are limited for practical devices to greater than ^ 500 ps, corresponding to a maximum bit-rate of theorder of 2 Gbits/s. Moreover, phase modulation in the device resulting from fluctuations in the refractive index(linked to the change in absorption) results in unwanted frequency modulation (chirping) of the order of severalGHz. These figures suggest that, although easy to fabricate, this device offers little performance advantage overdirect modulation of the laser itself.

1 Introduction

It is well known that the high-frequency modulationresponse of semiconductor injection lasers is limited by therelaxation oscillations [1] — typically in the range1-5 GHz for conventional long wavelength lasers biased atthe threshold. Moreover, these oscillations limit not onlythe maximum modulation rate, but also the (bit-rate) x (length) product in optical fibre communicationsystems where fibre dispersion is present [2]. This isbecause excursions in the electron population level duringthe relaxation oscillations cause the operating wavelengthto vary due to the dependence of the laser refractive indexon electron level. It would seem, therefore, that if the infor-mation carrying capacity of optical fibre systems is to befurther increased, either the laser relaxation oscillation fre-quency must be increased or, alternatively, the laser lightoutput must be modulated by means of some 'external'intensity modulator.

One of the many designs of 'external' intensity modula-tor which have been proposed is the (forward-biased)travelling-wave absorption modulator shown in Fig. 1[3-6]. This device is essentially a laser diode withoutreflecting facets. Amplitude modulation of the outputsignal results from the dependence of the absorption in theactive layer (shaded region in Fig. 1) on the injectedcurrent. The absorption modulator is particularly attrac-tive because: (i) its construction is essentially the same asthat of the laser (but without end reflectors), thus it isreadily integrated with the laser to form a monolithictransmitter chip [5], and (ii) it is possible to obtain opticalgain during the 'ON' state by injecting more current thanis required to make the medium transparent, thus themodulator output can be larger than its input.

Recently, Koyama and Iga [6] have postulated that theemission spectrum from absorption modulators isbroadened as a result of unwanted phase modulation, asituation which is clearly undesirable in dispersive trans-mission systems. They also predicted that, in order toachieve minimal spectral broadening, the transition (rise/fall) times of the optical waveform must be as short as pos-sible compared with the bit period. This implies, therefore,that the modulator optical rise time should be of the orderof a hundred picoseconds or better.

Intuitively, one might expect the absorption modulator

Paper 4754J (El3), received 17th April 1986

The author is with British Telecom Research Laboratories, Martlesham Heath,Ipswich IP5 7RE, United Kingdom

doubleheterostructure

antireflection coated

Fig. 1. Schematic diagram of the forward-biased absorption modulatorshowing modulator only (top) and integrated laser-modulator IC (bottom)

of Fig. 1 to be capable of high switching speeds, as thelarge number of photons being injected into one end of thedevice should result in rapid carrier recombination viastimulated emission. However, the results presented in thispaper show that, as a result of the nonuniform distribu-tions of electrons and photons along the modulator length,optical rise and fall times considerably shorter than theelectron spontaneous emission lifetime (typically a few ns)are difficult to achieve while, at the same time, maintaininga good extinction ratio.

2 Calculation of optical rise time

The equations which govern the operation of the forward-biased absorption modulator are the same as those for thetravelling wave laser amplifier [7, 8] as these are just dif-ferent modes of operation of the same device. A rate orcontinuity equation is used for the injected carrier densityN

dt e- d

where J is the injected current density, xsp the carrier life-

IEE PROCEEDINGS, Vol. 133, Pt. J, No. 4, AUGUST 1986 273

time, G the net gain, d the thickness of the active material,vg the group velocity of light in the modulator and e theelectronic charge. Diffusion of carriers along the modula-tor has been assumed to be negligible.

The equation for the variation in photon density Salong the propagation direction z is (ignoring spontaneousemission coupled into the mode)

dS dS 1 dS _ x , ,7" = T + ~ ' "57 = G z ' r ' S z ' 'az dz «„ dt

(2)

The net gain (or loss) is assumed, for the sake of simplicity,to be a linear function of the injected carrier density of theform

G(z, t) j ^ • (N(z, t) - No) (3)

where g is the active region gain, F is the wave confine-ment factor — the proportion of the guided light travellingin the active layer — and No is the carrier level at whichthe material becomes transparent. Examination of the cal-culated gain curves of Stern [9] (for constant wavelength)confirms that this simple approximation is useful down toquite large loss coefficients.

In order to calculate the steady-state z-dependence ofthe carrier and photon distributions and the output powerfor the OFF-state current (t = 0), the modulator wasdivided into segments. The photon density in the firstsegment is related to the modulator input power Pin by

S(z = 0) =A • hv • v.

(4)

In our calculation, the cross-sectional area of A of themodulator active region and the photon energy hv weretaken to be 0.2 nm2 and 0.8 eV (1.55 yum), respectively.The steady state carrier density in the first segment is thusgiven by:

N(z, t = 0) =e-d dN

^ S ( z , t = O)(5)

This calculated value for N determines the gain G in thefirst segment, from which we can calculate the photondensity in the second segment from eqn. 2, and so on downthe device. Lastly, the output power is related to thephoton density in the last segment by:

Pout = S(z = L) • A • hv • vc (6)

find initial steady-state solutions N(z ,0)S(z ,0 ) from Pjn

find N(z,t*dt)from N(z.t)and S(z,t)

findG(z,t»dt)fromN(z.Udt)

find S(z>dt)and Pout

from G(z,t*dt)and Pin

= Udt

Fig. 2 Flowchart used for the calculation of the carrier N(z) and photonS(z) distributions as functions of time

The time dependent calculation for the modulator outputis illustrated in Fig. 2 in the form of a flowchart. We notethat the 'time of flight' of photons passing through themodulator is only of the order of picoseconds. This there-fore permits the use of an adiabatic approximation inwhich the photon density is assumed to respond instanta-neously to a change in the carrier distribution. Therefore,the time dependent calculation begins with the initialsteady-state carrier distribution, and a Runge-Kuttaroutine is used to integrate eqn. 1 to obtain the carrierdistribution as a function of position after a small timeinterval t = dt. The new carrier density profile N(z) deter-mines the gain G(z) which, in turn, determines the photondistribution S(z) and the output power. This process isthen repeated for time t = 2dt, and so on.

The segment length dz was typically 50 fim. The iter-ation time dt was varied over the range vg • (dt/dz) = 1-10with no significant variation in the computed results, pre-sumably because of the absence of optical feedback in thedevice.

3 Results

Before calculating the time dependence of the modulatoroutput, it is necessary to specify the device length. Fig. 3

L,mm0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-10

-20P =0.1mW

-30

Fig. 3 Zero-bias insertion loss against device length

shows the modulator transmission loss at zero bias,assuming the linear gain relationship of eqn. 3 with No =1018 cm"3 and dg/dN = 2.5 x 10"1 6 cm2 [10]. The otherparameters were: F = 0.5 and xsp = 2 ns. The absorptionloss is shown as a function of modulator length for differ-ent input power levels from 0.1 to 100 mW. Taking atypical output power from the laser of, say, 10 mW, we seethat if we wish to maintain an extinction ratio of at least20 dB, then the modulator should be approximately 1 mmlong (assuming it is modulated between zero bias andtransparency).

The calculated steady-state transfer characteristic (i.e.output versus input) for a 1 mm long device, is shown inFig. 4. The curves are for different injected current den-sities ranging from zero bias (bottom) to 6 kA/cm2 (top) in500 A/cm2 steps. As previously noted, these steady-statecurves are those of the travelling-wave amplifier [7, 8], andgain compression is evident for output powers exceeding amilliwatt or so. Note also the linear transfer characteristicfor the current density corresponding to transparency(approximately 1.5 kA/cm2).

274 IEE PROCEEDINGS, Vol. 133, Pt. J, No. 4, AUGUST 1986

Fig. 5 shows the time response of the 1 mm longabsorption modulator pulsed from zero bias to twice the

Fig. 4 Steady-state input/output (in dBm) transfer characteristic. Curvesare for J varying between zero-bias (bottom) to 6 kA/cm2 (top) in 500 Afcm2 steps

1.2

1.1

1.0

0.9

0.8

0.7

3-0.6

| 0.5

- 0.4

0.3

0.2

0.1

1 103 A 5 6 7 8t,ns

Fig. 5 Light output traceJ = 2X transparency, Pin = 1 mW

transparency level with an input optical power of 1 mW.These parameters were chosen to illustrate the generalcharacteristic of the light output against time traces. Thecurve has two important periods: a delay time, definedhere as the time between the application of the modulatingcurrent pulse and the time at which the modulator outputreaches 10% of its final value, and a rise time, here definedas the time taken for the output to rise from 10% to 90%of its final value.

As one would expect, both the delay time and 10-90%rise time are dependent on the electrical pulse amplitudeand the input optical power. In Fig. 6 we can see the effectof varying these parameters on the delay time (solidcurves) and the 10-90% rise time (broken curves). Thethree sets of curves are, from top to bottom, for Pin =0.1 mW, 1 mW and 10 mW, respectively. Both the delayand 10-90% rise time are reduced as the pulse amplitudeor optical input power are increased, however, theminimum combined rise time at a current level of 6 kA/

cm2 is approximately 500 ps, which suggests that thisdevice is not really suitable for Gigabit-rate modulation.

9.0

7.0

5.0

3.0

1.00.9

0.5

0.3

0.1

10.0

0.1 3.0 5.0 7.0 9.00.3 0.5 0.7 0.91.0Jp/Jt

Fig. 6 Effect of varying Pin and J on delay time (solid curves) and10-90% rise time (broken curves)

The curves are for Pin = (top to bottom) 0.1, 1 and 10 raW, L = 0.001

This conclusion is confirmed in Section 3, where the lightoutput trace is calculated for simulated Gigabit modula-tion.

4 Turn-on delay

Turn-on delay is, of course, a well known feature of thesemiconductor injection laser, and, for the case of a con-stant carrier lifetime, the delay is given by [11]

T{delay) = xsp • In - JrJJ] (7)

where J is the current density of the applied drive pulseand Jth is the laser threshold current density. In Fig. 7 we

5r

£ 3

1 2 3 4 5 6 7 8 9JP/(Jp-Jt)

Fig. 7 Turn-on delay against J/(J — J,)

Pin = 1 mW

test the applicability of this expression to the absorptionmodulator by plotting the 0-10% delay time as a functionof J/(J — Jt), where J, is taken to mean the current densitycorresponding to transparency. The solid line in thisFigure is eqn. 7. Agreement between the numerical dataand eqn. 7 is quite good for this input power level (Pin =

IEE PROCEEDINGS, Vol. 133, Pt. J, No. 4, AUGUST 1986 275

1 mW), especially for pulse amplitudes greater than2.5 kA/cm2. By contrast, as Fig. 8 shows, if the power isincreased to 10 mW, then agreement with eqn. 7 is poor.

000°°

1 2 3 4 5 6 7 8 9JP/(Jp-Jt)

Fig. 8 Turn-on delay against J/(J — J,)Pin = 10 mW

The reason for this difference between the two inputpowers is believed to lie in the different mean carrier levelsat zero-bias. In the 1 mW case, the mean electron concen-tration is effectively zero, whereas in the 10 mW case, theinput power raises the mean carrier density due toelectron-hole generation (absorption). This is evident inFigs. 9 and 10, which show the carrier and photon dis-tributions at various time intervals. The carrier distribu-tions for t = 0 are very different for the two cases. Thus, inthe 10 mW case, less current is required to raise the carrierdensity to its 'bleaching' level Jbl (here defined as thatwhich results in a transmission loss of 10 dB). Confirma-tion of this hypothesis can be seen in Fig. 11, where the

z,mm

z.mmFig. 9 Photon distribution (top) and carrier distribution (bottom) (attime intervals of 500 ps)for an input power of I mW

10 mW data of Fig. 8 has been replotted, this time as afunction of [J/(J — ./w)].

z, mm

Eo

Fig. 10 Photon distribution (top) and carrier distribution (bottom) (attime intervals of 500 ps)for an input power of 10 mW

1.0 1.1 1.51.2 1.3JP/(Jp-Jb1)

Fig. 11 Turn-on delay against J/(J — Jbl)

/>,. = 10 mW

The similarity between the modulator delay time andthe laser turn-on delay suggests the means for minimisingthe delay for low input power levels. The delay can bereduced by prebiasing the modulator close to the bleach-ing current density Jbl. The limit on the amount of prebiaswhich can be used will obviously be determined by thedesired extinction ratio.

5 Chirp

Variations in the instantaneous frequency (chirping) in theforward-biased absorption modulator result from varia-tions in the modulator output phase. This is because of the

276 IEE PROCEEDINGS, Vol. 133, Pt. J, No. 4, AUGUST 1986

Kramers-Kronig relation between the real and imaginaryparts of the refractive index (i.e. between refractive indexand absorption).

The modulator output power is related to the inputpower by

(8)

(9)

Thus it is possible to write the relation between theangular frequency shift ( = d(pout/dt) and the output power[6] as

by

p — p •1 out ~ l in

Likewise, the output phase may be written

2 • n _ . . . .dz

2-n-fc = d<l>outdt

a J _ dP0Ut

2 PL rout

dt(10)

The alpha parameter relates the change in the real part ofrefractive index to a change in the gain/loss and is defined

1.21.11.00.9

~ 0.8£ 0.7"5 0.6° 0.5r. 0.4•^0.3

0.20.1

0

10

3 4t.ns

cr•̂ -5

Fig. 12 Time dependence of amplitude and frequency

1 Gbits/s

1.21.11.00.9

- 0.8a. 0.7| 0.6° 0.5£0.4- 0 3

0.20.1

0t.ns

Fig. 13 Time dependence of amplitude and frequency2 Gbits/s

IEE PROCEEDINGS, Vol. 133, Pt. J, No. 4, AUGUST 1986

4 • not =

dn

dg(11)

A typical value for | a | is 5, although it has been shown tovary, depending on the difference between the photonenergy and the bandgap [10].

In Figs. 12-14 we plot the chirp resulting from modu-lating a 1 mm long device with a (... 0000)1010101 ...

1.21.11.00.9

_ 0.8£0.7^ 0 . 6o 0.5- 0 . 4O.0.3~ 0.2

0.1

10

1t,ns

-10Fig. 144 Gbits/s

Time dependence of amplitude and frequency

sequence at bit rates of 1, 2 and 4 Gbits/s. The inputpower is 10 mW, and the device current is modulated fromzero bias to 4X (transparency), which was judged to be themaximum practical current density (6 kA/cm2). Thesesimulations usefully illustrate two important points. First,the modulator is incapable of bit rates exceeding 2 Gbits/sfor the chosen value of carrier lifetime. Fig. 14 in particularshows severe patterning effects. Secondly, the accompany-ing frequency modulation (chirp) is quite severe, the peak-peak deviation being about 15-20 GHz (over anangstrom) in these examples.

6 Trade off between chirp and extinction ratio

Finally, we demonstrate that a trade off exists between themaximum frequency deviation and the optical extinctionratio using eqn. 10. For this purpose we approximate therising edge of the optical output waveform by

^out — P0ff + (^on ~ Poff)• l\ n • l

J l n ^

L2 • W

(12)

where Poff is the output power in the 'OFF' state and Pon

is the power in the 'ON' state, then the resulting chirp is

fc =

— OL( / ? - ! ) • sin

tris

! + ( / ? - ! ) • sin:(13)

where R is the extinction ratio (PoJPOff). The maximumfrequency deviation is thus

fc(max) = (14)

277

The normalised chirp | (8 • trise • fjcc) \ calculated from eqn.13 is plotted in Fig. 15 for extinction ratios between 2 :1

R=100:1

o 4

I32

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0t/Trise

Fig. 15 Dependence of normalised chirp on extinction ratio R

(3 dB) to 100 :1 (20 dB) and clearly shows the trade offbetween the extinction ratio on the one hand, and fre-quency modulation on the other. Of course, this trade offalso exists for the directly modulated laser.

7 Conclusions

The time response of the (forward-biased) absorptionmodulator has been analysed for the first time. The modu-lator output was found to compose of a turn-on delay anda rise time, both of which were found to reduce withincreasing optical input power and electrical drive current.Nevertheless, the minimum practical combined delay andrise time was found to be of the order of 500 ps for a spon-taneous lifetime of 2 ns — implying a maximum modula-tion rate of 2 GBits/s. Reducing the carrier lifetime (byusing a heavily zinc-doped active region for example)would result in a faster rise time, but at the expense of

increased operating current. Furthermore, the accompany-ing frequency modulation was shown to be severe, being ofthe order of GHz (the exact value depending on the outputextinction ratio).

It is concluded, therefore, that, although this type ofmodulator offers considerable fabricational advantages, itis unlikely to offer significant performance advantages overdirect modulation of the laser itself. Indeed, improvementsin laser design are now emerging, producing significantincreases in the laser relaxation frequency [12].

8 Acknowledgment

The author thanks the Director of Research, BritishTelecom, for permission to publish this paper.

9 References

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2 LINKE, R.A.: 'Transient chirping in single frequency lasers: lightwavesystems consequences', Electron. Lett., 1984, 20, pp. 472-474

3 SHAMS, M.K, NAMIZAKI, H., and WANG, S. 'Monolithic integra-tion of GaAs-(GaAl)As light modulators and distributed-Bragg-reflector lasers', Appl. Phys. Lett., 1978, 32, pp. 314-316

4 LEE, T.P, BURRUS, C.A, EISENSTEIN, G., SESSA, W.B., andBESOMI, P. 'Amplifier-modulator integrated with a cleaved-coupled-cavity injection laser', Electron. Lett., 1984, 20, pp. 625-627

5 YAMAGUCHI, M., EMURA, K., KITAMURA, M., MITO, I., andKOBAYASHI, K.: 'Frequency chirping suppression by a distributedfeedback laser diode with a monolithically integrated loss modulator',Proc. Optical Fibre Conference, Venice, 1985

6 KOYAMA, F., and IGA, K.: 'Frequency chirping of external modula-tion and its reduction', Electron. Lett., 1985, 21, pp. 1065-1066

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10 WESTBROOK, L.D.: 'Measurements of dg/dN and dn/dN and theirdependence on photon energy in 1.5 ^m InGaAsP laser diodes', IEEProc. J, Optoelectronics, 133, pp. 135-142

11 DIXON, R.W., and JOYCE, W.B.: 'Generalised expressions for theturn-on delay in semiconductor lasers', J. Appl. Phys., 1979, 50, pp.4591-4595

12 LIN, C, and BOWERS, J.E.: 'High-speed large signal digital modula-tion of a 1.3 /xm InGaAsP constricted mesa laser at a simulated bitrate of 16 Gb/s', Electron. Lett., 1985, 20, pp. 906-908

278 IEE PROCEEDINGS, Vol. 133, Pt. J, No. 4, AUGUST 1986