Modelling of semiconductor laser amplifier for the terahertz optical asymmetric demultiplexer

G. Swift Z. G hassemlooy A.K. Ray J . R . Travis

Abstract: A semiconductor laser amplifier (SLA) may be used as a nonlinear element in ultrafast optical asymmetric demultiplexers. For demultiplexing to take place in the optical domain it is necessary to create a switching window by placing the SLA asymmetrically in an optical loop and saturating it with a short duration control pulse. The exact size of this window, for selecting the required pulse at the output port, depends mainly on the precise location of the SLA within the loop. In the paper a finite length model of an SLA, used as a switching gate within the loop, is presented and results for the carrier density, gain and phase time responses together with transmission (switching) windows are also given. The result obtained for the latter is compared with practical data.

1 Introduction

There is an ever increasing demand for broadband, high speed communication services which in turn demand telecommunication networks having line and switching capacities exceeding those currently available. Optical time-division multiplexed communication systems may be one alternative where high-speed demultiplexing is the major requirement. The use of all optical switching is currently a focus of attention and is an active area of research. To perform any type of switching some kind of nonlinearity must be included in the device. In optical demultiplexers the nonlinearity ensures interference between two signals to give switching. This effect is exploited in optical time- division demultiplexers (OTDM) where the inherent nonlinearity due to the Kerr effect in optical fibres provides a nonlinear refractive index [I]. Problems arise with this type of architecture because the long lengths of fibre required result in walk off and polarisation.

0 IEE, 19% IEE Proceeding~s online no. 19981256 Paper received 3rd January 1997 G. Swift was with Sheffield Hallam University and is now with thc Opto- electronic Material & Devices Research Group, Department of Physics, McMaster University, Hamilton, Ontario, Canada Z. Ghassemlooy, A.K. Ray and J.R. Travis are with the Physical Elec- tronics & Fibre-optics Research Laboratories, School of Engineering, Sheffield Hallam University, Pond Street, Sheffield SI IWB, UK

Also, relatively high power control pulses are required. An alternative system has been developed which uses a SLA to give the required nonlinearity. This is smaller in size in comparison with the fibre loop demultiplexer, requires less power and is suitable for integration on a single chip. Although the nonlinearity associated with SLAs has a slow relaxation time compared with optical fibres, this can be overcome by placing the SLA asymmetrically with respect to the loop.

\ fibre

loop control coupler

,,/ ' e n t - 1 pulse

ccw

coupler da; out

data in ,/)& wJ\ ,/' port 1 port 2

Teruherrz opticcil clsymmetric demultiplexer Fig. 1

A particular form of the SLA loop mirror system i s the terahertz optical asymmetric demultiplexer (TOAD) [2]. For demultiplexing to take place it is essential that the demultiplexing switch samples the appropriate time slots in each received data frame. The essential compo- nents of the TOAD are a small optical loop mirror, a SLA and a 2 x 2 coupler to introduce the control sig- nal, as illustrated in Fig. 1. Here, the incoming optical time-division multiplexed pulse train, having a given data frame length and entering port 1, is split into clockwise (CW) and counter-clockwise (CCW) signals which propagate around the loop and reach the SLA at different times determined by the asymmetry in the loop. A short duration control pulse of sufficient energy is injected into the loop and induces a nonline- arity by saturating the SLA. With correct timing the CW and CCW signals undergo different gain and phase shifts. The signals interfere destructively on returning to the input coupler and a pulse emerges from the output port (port 2). Switching of the next frame can be performed after the device recombination time, but this does not have to be less than the channel bit period.

61 IEE Proc -Crcui ts Devk.e.s Syst., Vu/. 145, Nu . 2. April 1998

2 SLAmodel

The interaction between light and carrier density at a particular point within the amplifier can best be described by a single rate equation if spontaneous emis- sion effects are ignored [3]:

I d (1) d n j rgmXc FgmXd

- - R(n) - - I , - - - -- d t ed E E

where n is the carrier density, j is the current density, e is the unit electric charge, d is the active layer thickness, r is the mode confinement factor, E is the photon energy and I, is the optical input intensity of the control signals. Id is the longitudinally averaged data signal given by:

(2) E d B d exp(ra(n - no)L) - 1

I d = - A r a (n -

where Ed is the pulse energy, and A is the active area of the device.

The material gain g,ax = a(n-no) at data and control signal wavelengths, ~1~ is the carrier density required for transparency and a is the material gain coefficient.

In eqn. 1 the second term on the right-hand side is the Auger recombination term and is necessary for high bias currents. It is given by:

R(n) = An + Bn2 + Cn3 (3) where A , B and C are Auger recombination coefficients.

For wave propagation in a laser amplifier with gain g,, the optical fields obey the following differential equation [4]:

- - dE dz _ - - j k E ( z ) + E(z)g (4)

with the solution given as: E = Eo exp(g - j k ) z (5)

where Eo is the initial condition imposed at z = 0, and k is the propagation constant equal to:

27rN k = - x with N being the refractive index of the material.

When modelling SLAs consideration should be given to the modulation time in relation to the carrier dynamics of the device, and to whether the amplifier is in the saturation region or not. When the amplifier is unsaturated, its carrier density is constant and signals, of any shape, are amplified undistorted. When satu- rated, the carrier varies according to the light intensity and consequently signal gain and phase are signifi- cantly affected. At saturation the following conditions must be met when modelling SLA: (i) the temporal response of the input signals must be slower than the carrier lifetime, (ii) the change in the light intensity must be sufficiently faster than the recombination time and (iii) the control pulse rate should be of the same order as the carrier lifetime. Here, we are mainly inter- ested in the last condition, where the leading edge of the pulse receives high amplification due to the high carrier density. If saturation is regarded as instantane- ous the carrier density quickly approaches saturation and pulse distortion occurs because of a different gain over the pulse width. The SLA can be modelled as a point element and as a finite length element. In the former model the finite length of the amplifier is

62

ignored and it is treated as a single point placed sym- metrically within the loop. This method results in sim- ple analyses since the carrier density is assumed to be constant over the entire device length [5]. For more accurate analysis the finite length model is best used. This is the subject of the study.

2.1 For large asymmetry and low resolution the NLE may be approximated by a single point element [5] , since the loop asymmetry is large compared to the length of the SLA. However, in a loop mirror, with small asymme- try, this approximation is not valid. In this situation the minimum duration of the sampling window is determined, in principle, by the rise time of the nonlin- earity as the SLA can be placed arbitrarily close to the loop centre. In practice the finite length of the SLA places a limit on the switch time resolution such that the minimum sampling window is twice the propaga- tion time of the device with a full width at half maxi- mum (FWHM) approximately equal to the propagation time [6]. For a typical device of length 5 0 0 p the FWHM is = 5ps.

Eqns. 1, 3 and 4, solved numerically, are used to model the SLA as a finite length element. Initially the SLA is split into sections of equal length AL = LIL,, where L is the device length and L, is the number of segments, and the carrier density in each segment is being stored as a matrix. The incoming pulse enters the SLA at z = 0 at interval of Allspeed of light in the amplifier c,, with the leading edge element of the pulse matrix lining up with the first element of the carrier density matrix. The rate equation is in matrix form as:

Finite length model for SLA

r a - _ E

where 7, is the spontaneous recombination life time. Eqn. 7 is solved for the carrier density at each point along the amplifier length. To model small loop asym- metries, information about the carrier density is calcu- lated at a particular point and time within the amplifier. A carrier density matrix is generated with data in rows and columns representing the discrete positions and discrete time intervals within the ampli- fier, respectively. The rate equation is solved numerically in matrix form to calculate the carrier density matrix using the follow- ing difference equations:

3 ed

n ( k ) = - - n(k)[7-]p1 - [ r a { n ( k ) - n o } ~ ( k ) ] ( E ) - l

(9)

n(k + 1) = n(k) + Atn(k) (10)

IEE Proc-Circuits Devices SyAt., Vol. 145, No 2, April 1998

A

2.2 Initial conditions for control signal: The SLA receives an input consisting of two signals with different modulation rates, a high bit rate data signal and a low bit rate control signal. If the data signal has a bit length equal to Bd and if lIBd << recombination time, then the system can be modelled as a continuous wave low power data signal superposed by a high power control signal at time intervals much larger than the period of the data.

Initially, the rate equation is solved in the steady state as:

I d j rgrnxa 0 = - - R(n) - ~

ed E Solving eqns. 2, 3 and 11 gives the initial conditions

for eqns. 8, 9 and 10 which in turn are solved with a control signal input.

2.3 Amplifier gain and phase modulation: The CW and CCW data signals experience gain and phase modulation when the amplifier has received a control pulse. The data modulation is calculated at discrete time intervals by integrating over the carrier density matrix at the speed of propagation. This is performed in one direction for the clockwise signal and in the other direction for the CCW signal. Any discrepancy in propagation speed due to the index change is ignored and all three signals are assumed to move at the same speed. It is also assumed that no losses are introduced at the intraloop coupler. The gain and phase modula- tion at discrete time k are calculated from the following expressions. Phase modulation:

1=0

for CCW

where ku,,y = t,,,/At is the discrete asymmetry, and the remaining parameters are defined as before.

IEE Pruc.-CircuiIy Deviws Sysr., Vol. 145. No. 2, A p d 1998

length/device length propagation time 10 0

Fig.2 Currier dmsity against device length and simulation time

1 2 3 time/device propagation time

Fig.3 Gain modulation

17 -

1 6 b b 4 6 b 1'0 1'2 1'4 16 time, ps

Fig. 4 Phase modulution

3 Results

Fig. 2 shows carrier density plotted against SLA length and simulation time using eqn. 11, when a control pulse of energy 8OOfJ and FWHM of Ips is input to the SLA. A background pulse train of lOfJ, Ips FWHM and 25OGHz has also been used, which sets the carrier density initial conditions prior to control input. The plot shows a pictorial representation of the carrier density with rows and columns representing the length and time axes, respectively. As can be seen, the plot has three distinct regions: region A with a constant

63

carrier density indicating the situation where the control pulse is about to enter the SLA, region C, again with flat carrier density characteristics, where the

1.0-

0.8

c - U) .-

.E 0.6-

E!

% 3 0.4- E b

ul

c -

.-

0.2

0 2 4 6 8 10 12 16 16 time, ps

Loop mirror transmission window, S L A placed at the centre point Fig. 5

-

-

time, ps

Looo nzivor transmission window. S L A close to the centre noint hg.6

2At

pulse has just left the SLA and region B, which is the intermediate stage with changing carrier density characteristics, where the pulse is propagating along the SLA. Before the control pulse enters the SLA the carrier density is assumed to have a value determined by the data signal. After the control pulse leaves the SLA the carrier density is assumed to remain saturated for a time equal to the period between data pulses (= 4ps) which is small compared to the recombination time of around Ins. With the SLA positioned at the centre of the loop the gain and phase responses are shown in Figs. 3 and 4. Fig. 3 shows the gainltime response for CW and CCW data signal components calculated from eqn. 15. The gain value, in dB, is relative to the steady-state value and represents data signal amplification. Fig. 4 is the corresponding phase1 time plot calculated from eqn. 6 and gives the difference in phase relative to the value before the control pulse is applied. The gain and phase response have identical profiles due to the summations being equal in eqns. 13 and 15. However, the major difference is in the fall time between the CW and CCW signals. The CW has a fast response time similar to the medium with large asymmetry loops, whereas the CCW has a slower response which spans a time interval of

The CW and CCW will have different refractive indi- ces after traversing through the loop. If the index change is sufficient to cause a phase change of 180" between the CW and CCW pulses then interference will occur at the coupler, thus resulting in transmission not reflection and a pulse should emerge from port 2. Zero phase shift between CW and CCW components means the data leaves via port 1. Therefore, the difference between the CW and CCW responses results in an opening of a transmission window. As previously men- tioned the window cannot be smaller than twice the propagation time of the SLA so in theory the smallest pulse period that can be demultiplexed is equal to twice the propagation time of the SLA. The normalised transmission plot using the power transmission matrix given in [7] is shown in Figs. 5-7. With the SLA posi- tioned at the centre of the loop, k,, = 0, the transmis- sion plot has generated a two-pulse shape due to the finite rise times of the CW response resulting in the central dip, see Fig. 5. A single pulse shape is only achievable with an SLA having a zero nonlinearity rise time. The transmission rise and fall times are related to the relative position of CW and CCW responses. With the loop's time asymmetry At = Axlv,oop = 500 x x 3.513 x lo8 = 6ps and device response time of 2At, the normalised transmission response is shown in Fig. 6. The rising edge is -12ps and the trailing edge is the SLA nonlinearity rise time. With the SLA positioned further away from the centre, loop time asymmetry will increase and the normalised transmission becomes more asymmetrical, see Fig. 7 . The long trailing edge of the CCW is introducing the fundamental limit on the width of the switching window.

-10ps.

Table 1: Comparison of practical and simulated results

Parameters Experimental [61 Simulation 4 '

I I I I I 14 15 Pulse width (ps)

9 8

b-

01 0 5 10 15 20 25 FWHM (ps)

time, ps Fig.7 Loop mirror trammission window, S L A away fvom the centre Rise time (ps) -1 1 -12

point Fall t ime (ps) 4 3.5

IEE ProcCircuits Devices Syst., Vol. 145. No. 2, April 1998 64

Finally, the simulation results are compared with the practical data [6], showing good agreement as given in Table 1.

4 Conclusions

Semiconductor laser amplifier analysis and simulation for the TOAD has been presented. The SLA finite length model is analysed numerically both in space and time. The result for the carrier density is presented when a high power input control signal is applied to the SLA at intervals close to the recombination time. The CW and CCW gain and phase time responses show the effect of the finite length of the SLA. Switching (sampling) windows are also shown when the SLA is placed at different locations within the TOAD demonstrating the switch resolution relative to the device propagation time.

5 Acknowledgments

G. Swift is grateful for the studentship received from Sheffield Hallam University. Thanks are also due to

IEE Pvoc.-C‘ircuilr D r v ~ e a Sy.\f., Vol 145. No. 2, Aprrl 1998

Professor M.J. Adams (formerly at British Telecom, now at the University of Essex) for his valuable sugges- tions and comments.

References

BLOW, K.J.. DORAN, N.J., and NELSON, B.P.: ‘Demonstra- tion of the non-linear fibre loop mirror as an ultrafast all optical demultiplexer’, Ekctron. Lett., 1990, 26, (14), pp. 962-964 SOKOLOFF, J.P., GLESK, I., PRUCNAL, R., and BONCEK, R.K.: ‘Performance of a 50 gbit/s optical time division multi- plexed system using a terahertz optical asymmetric demultiplexer’, IEEE Photonic.v Technol. Lett , 1994, 6, ( I ) , pp. 98-100 MANNING, R.J.: ‘Three wavelength device for all optical signal processing’, Opt. Lett., 1994, 19, (12), pp. 1140-1142 MARCUSE, D.: ‘Computer model of an injection laser ampli- fier’, IEEE J. Quantum Ekwrvon., 1983, QG19, (l), pp. 63-73 SWIFT, G., RAY, A.K., GHASSEMLOOY, Z., and TRAVIS, J.R.: ‘Modelling of semiconductor laser amplifier for optical time division demultiplexing’. The Manchester Metropoli- tan University third Communication networks symposium, 1996 KANE, M.G., GLESK, I., SOKOLOFF, J.P., and PRUC- NAL, P.R.: ‘Asymmetric optical loop mirror: analysis of an all optical switch’, AppL Opt., 1994, 33, (29), pp. 6833-6842 SWIFT, G.: ‘Modelling of an optical time division demultiplexer’. PhD thesis, Sheffield Hallam University, 1997