Solid-State Elecmnics Vol. 30, No. 1, pp. 43-51, 1987 0038-I 101/87 $3.00 + 0.00 Printed in Great Britain. All rights reserved Copyright 0 1987 Pergamon Journals Ltd

PHYSICS AND APPLICATIONS OF OPTICAL BISTABILITY IN SEMICONDUCTOR

LASER AMPLIFIERS?

M. J. ADAMS

British Telecom Research Laboratories, Martlesham Heath, Ipswich IP5 7RE, England

(Received 11 April 1986; in revised form 27 June 1986)

Abstract-This contribution is intended as a review of the use of semiconductor laser amplifiers as non-linear and bistable elements, and their potential for applications in optical logic and signal processing. The basic physics of the optical non-linearity occurring in these devices is discussed both intuitively and in a more rigorous theoretical manner, and a survey is given of the experimental results reported to date. Bistable amplifiers are found to switch at input powers of order 1 PW and in times as short as a few nanoseconds. The resulting optical energy requirement of order femtojoules is a prime feature which, when combined with the ready availability of lasers, their inherent optical gain, and the wavelength compatibility with existing optical transmission systems, make amplifiers extremely attractive for applications where limited amounts of signal processing are required. Potential applications for these devices are discussed.

1. INTRODUCTION

Whilst there has been considerable interest recently in the subject of optical bistability (OB) occurring in semiconductor etalons[ 11, the closely related phenom- enon of OB in semiconductor laser amplifiers has received relatively little attention. The present con- tribution is concerned with a review of progress to date in the understanding and exploitation of amplifier OB for applications in optical logic and signal processing. In the next section the basic physics of the bistability is discussed in an intuitive and, hopefully, easily accessible fashion. The following section fills in the mathematical details of the theory and gives calculated predictions for InGaAsP amplifiers. Next we review the experimental data which has appeared in the literature thus far, and comment on the degree to which the theoretical predictions have been confirmed. The potential appli- cations of amplifier OB are discussed in Section 5, and our overall conclusions are summarised in the final section. The treatment throughout is intended to be at a fairly elementary level and to be of interest to the non-specialist reader.

2. OPTICAL NON-LINEARITY AND FEEDBACK

The physical origin of OB in laser amplifiers arises from changes in the refractive index due to free carriers and temperature. For the former, the effect of an input optical signal undergoing amplification is to reduce the optical gain per unit length and hence the free-carrier concentrations in the active region of the device. Gain (or stimulated emission) is related to the refractive index via the Kramers-Kronig relation,

TThis is an invited paper.

and hence there is an associated change of index in

the presence of a sufficiently strong optical input. However, the refractive index is also a function of temperature and this, in turn, is dependent on the drive conditions and on the optical input. The precise details of the interaction of gain, index, current and optical input are therefore rather complicated and difficult to specify for a given device. However, a convenient simplification which is often justified in practice[2] is to assume that the index N varies linearly with the average optical intensity I,, in the amplifier, so that an increase of Z, produces a corresponding decrease of N.

Consider now the effects arising from feedback at the facets of the laser cavity. For a Fabry-Perot cavity with gain, in the presence of a weak input signal, the spectral response is as shown in Fig. 1. In this figure the normalised average intensity I,,/Z, (where Z, is a scaling intensity to be defined later) is plotted as a function of single-pass phase change q% = 27rLN/1 for cavity length L and wavelength A. Two modes positioned near the gain peak (with respect to wavelength) are shown for a laser amplifier operated at about 95% of threshold. Let us examine the effect of increasing the optical input and hence the average internal intensity I,,, to values where the change of index N and phase q~ become significant. For a given initial phase &, determined by the input wavelength with respect to the peak of a Fabry-Perot resonance, the change of 4 will be linearly dependent on I,,. Thus values of I., close to the peak of the resonance will induce larger phase shifts than those further away from the peak. At the same time the extra amplification experienced by these high values

of Z,, will reduce the material optical gain per unit length rather more than for values of Z, further from

43

44 M. .I. ADAMS

Ii I I I

” PI/2 PI 3 PI/2

9 Fig. 1. Scaled average intensity in the cavity of a laser amplifier vs phase, at about 95% of threshold. The input signal intensity is assumed to be sufficiently low that no

non-linear effects can occur.

the resonance. The net effect is illustrated in Fig. 2 where t,,/Z, is plotted vs initial phase & for three values of input intensity. With increasing input the spectral peak of a resonance shifts to smaller phases and develops a marked asymmetry.

The spectral response plotted in Fig. 2 for average internal optical intensity is also manifested in the spectrum of the transmitted signal. Figure 3 shows the corresponding plot of normalised output I,,,,/Z, vs &, for the same input intensities as Fig. 2. With the aid of Fig. 3 we can anticipate the forms of output vs input optical characteristics which may be ob- tained for various values of initial phase (i.e. of input wavelength detuning form a Fabry-Perot resonance). Consider, for example, an initial value of & = -0.037~ as marked on the figure. This gives the points A and B on the curves corresponding to normalised input (Z,,,/Z,) of 2 x 10es and 10e4, re- spectively. Clearly, for values of input between these values we expect the output to rise steeply and then level off somewhat, so that further increase of input will produce relatively small increases of output. That this is indeed the case is demonstrated by Fig. 4 where

normalised output I,,,/I, is plotted vs normalised

-PI/4 PI/4

Fig. 2. Scaled average intensity in the amplifier cavity phase, at about 95% of threshold for the three values

normalised input intensity shown

VS

of

E

\

D

c

/ ih a -PI/4

0.02

L,‘I,

Fig. 3. Normalised output vs phase for the same conditions as Fig. 2.

input I,/I,. The points A and B are again marked on the output-input curve corresponding to q$, = - 0.0371; this curve demonstrates the non-linear characteristic anticipated from the discussion given above.

Figure 3 can also be used to illustrate how optical bistability occurs for certain values of phase 4,,. For example, the vertical line shown on the figure corre- sponding to &, = -0.1x intersects the curve for Ii,,/Z,Y = 5 x 10m4 in three points C, D, E. Hence for an input wavelength corresponding to q& = -0.1~ we anticipate the possibility of up to three values of output intensity for the same value of input intensity. Turning to Fig. 4, we see that this is indeed the case, since the curve for 4” = -0.ln takes a characteristic “S’‘-shape so that a normalised input of 5 x 10e4 gives three possible outputs corresponding to the points C, D and E. However, it is relatively easy to show[3] that the branch of the output-input curve with a negative slope is unstable and would therefore not be observed experimentally. Instead the “S”-characteristic leads to hysteresis with abrupt jumps of output intensity at input values correspond- ing to the extremities of the “S”. Thus points C and E correspond to stable states in OB, whereas point D is not normally accessible in practice.

003 -

ooz-

,”

I

Fig. 4. Normalised output vs normalised input for two values of initial phase &,. All other conditions are the same

as those for Figs 2 and 3.

Physics and applications of optical bistability in semiconductor laser amplifiers 45

3. THEORY

In this section I will set out the mathematical details behind the intuitive physical picture given above. The laser amplifier is characterised by two plane parallel mirrors of reflectivities R,,R,, sepa- rated by a distance L. The net optical (intensity) gain per unit length is denoted by g, and the single-pass phase change is 4. The ratio of output intensity to input intensity is then given by[4]:

I ou, _ (1 - R,)(l - R,) egL

I, - (1 - & tiL)’ + 4a e%in2q5 ’ (1)

The corresponding result for reflected intensity Z,Cf is[5]:

I d _ (JR, - fi e”L)2 + 4&Xj egLsin24

z- (1 -@@L)2+4JRRz@Lsin2f$’

(2)

The average intensity in the amplifier is given by a straight-forward longitudinal average of the forward and backward travelling-wave intensities, with the result[4]:

I m - (tiL)(l - R,)(l + R, @L)

I, - gL [( 1 - m ePL)2 + 4m egL sin241 ’ (3)

Equations (I)-(3) give the relationships between the various optical intensities in terms of the net gain g and phase C#J. To evaluate these relations, it is neces- sary to use the appropriate equations for g and C$ in terms of other laser parameters including the optical non-linearity. For the case of a non-linearity de- pending only on the free-carrier concentration, the necessary equations are given by[6]:

gL = r&J + (80 - 4); - a (4)

(5)

where the new parameters are given as follows: r = optical confinement factor (ratio of intensity confined in the active laser cross-section to the total intensity), g, = unsaturated material gain per unit length (i.e. gain in the absence of an input signal), b = ratio of real to imaginary index changes (= -4n/(La) dN/dn, where 1 = wavelength, N = effective index, n = electron concentration, a = gain coefficient = dg,/dn). Note that b is identical to the linewidth broadening factor ‘a’[7].

c( = effective loss per unit length (including scatter- ing and absorption losses both inside and outside the active region), 5 = electron lifetime (assumed con- stant), t = time, I, = scaling intensity = E/(Taz), where E = photon energy.

Equation (5) is a rate equation for single-pass phase in the cavity, which is equivalent to the more familiar rate equation for the electron

concentration[6]. The final term in equation (5) takes account of the optical non-linearity by including the change of refractive index with carrier concentration. Similarly, equation (4) relates the net optical gain to the unsaturated material gain and the single-pass phase, again including the dependence of index on carrier concentration. Whilst equations (4) and (5) are appropriate for transient analysis of non-linear laser amplifier characteristics, the steady-state results may be found by setting d4/dt = 0. In this case, equation (4) reduces to the form:

In this form the effect of gain saturation at high input intensities is clearly seen.

It is pertinent at this point to review the main assumptions made in the derivation of the equations given above. In the first place, spontaneous emission has been ignored since it has been assumed that the input signal is always sufficiently large to swamp any effects of spontaneous emission in determining the non-linear properties of the amplifier. Secondly, it has been assumed that the input signal is mono- chromatic with a characteristic photon energy E. The analysis has been simplified by describing the non- linearity in terms of a single average optical intensity in the amplifier. Thus the spatial dependence of carrier concentration has been neglected and replaced by a single mean value; this simplification has been shown to be a good approximation for amplifier analysis[S]. Finally, since the electron lifetime 7 is about three orders of magnitude larger than the cavity round-trip time, it is reasonable to assume that the transient evolution of the optical fields follows that of the carriers. This adiabatic approximation has been used to avoid the need for transient equations describing the time-dependence of the optical fields.

Equations (I), (3), (5) (with d4/dt = 0) and (6) were used to calculate the plots shown in Figs I-4. The value of unsaturated gain g0 assumed is quoted as a proportion of the gain at threshold. The latter is given by the condition for the denominator of equation (1) to be zero on resonance, i.e. 2(gL),h = -In(R, R,). Other parameters are given in Table 1. In order to illustrate the dependence of the results on g, (and hence on current), Fig. 5 gives plots of I,,JIs vs I,,/I, for a fixed value of & = -0.1 T[ and for various values of g,. As g, is reduced from the threshold value, the width of the hysteresis loop decreases and eventually the curve reduces to a non-linear gain characteristic. Thus Fig. 5 represents

Table 1. Parameter values used in the calculations

4 0.3 RI 0.3 r 0.5 aL 0.5 b 5

46 M. J. ADAMS

0 0.0005 0.0010 0.00 15 0.0020 0.0025

I,“‘4 Fig. 5. Nonnalised output vs nortnalised input for an initial phase &, = -O.ln, for four values of unsaturated gain

relative to the threshold value (i.e. g,,/(g&,).

the type of hysteresis curves which would be observed if the input signal wavelength were fixed at a constant offset from a Fabry-Perot resonance for each value of current, i.e. at each current the wavelength would have to be tuned to a specific value in the limit of very low signal input. In practice, a simpler experimental approach is to fix the input signal wavelength for a given input power and simply vary the amplifier bias current[9]. In this case the initial detuning phase I& will also be a function of current and we need a different relationship for 4. If we (arbitrarily) decide

to relate 4 to & at Zusing threshold, then the steady- state equivalent of equation (5) becomes:

where (g&, is the threshold value of g,. Note that if (g& were replaced by g, in equation (7), then the steady-state form of equation (5) would be recovered. Solving equation (7) self-consistently with equations (6) and (3) yields results for transmitter intensity as a function of g&g&, or, equivalently, of bias current relative to threshold. Figure 6 gives plots of this type using & = -0.17~ and other appropriate values for InGaAsP amplifiers at 1.55 pm (see Table 1). Reso- nance effects are clearly seen at about 60% of thresh- old, together with a general tendency of the output to increase as threshold is approached.

Time-dependent results for amplifier bistability can be calculated with the aid of equation (5) using

0.0 5 1

“? T

% ,” 0.010

0.005

0 0.5 0.6 0.7 0.8 0.9 1.0

%‘(%‘,h Fig. 6. Normalised output vs normalised gain g&g,),,,, for

t/r Fig. 7. Scaled output intensity vs time in response to a rectangular input pulse (also shown, magnified 10 times) for initial phase I#+, = -0.1~ and relative gain gO/(gO),,, = 0.95. The time axis is normalised to the carrier recombination

time 5.

equations (3) and (4) to calculate Z,,/I, and gL, respectively, at each time increment. The response to a rectangular input pulse is plotted as a function of time in Fig. 7. After an initial fast increase of output, there is a slow rise with time towards a sharp spike, followed by a return to the equilibrium “on” state. The transient spike is associated with the Fabry-Perot resonance as the system passes from the low to the high transmission state. At the peak of the spike the single-pass phase 4 passes through zero (or an integral multiple of 27~) and this gives rise to the sharp increase in output. Note that if the input signal length were shorter than the delay to the spike, then the device would not achieve the high transmission state. Once the “on” state is achieved, however, the amplifier can be held in that condition by means of a holding input beam whose intensity lies within the steady-state hysteresis loop. After the removal of the holding beam the output drops rapidly. However, the phase 4 takes some time to return to its previous value, since C#J is related to the carrier concentration whose response time is determined by the re- combination lifetime 5.

From a practical point of view the time limitation on switch-up in amplifier bistability is determined by the delay between the leading edge of the input signal

8 -.

7-

6-

t 5-

- 4-

3-

2-

l-

0 0.001 0.002 0.003 0.004 0.005

I,“‘L

Fig. 8. Time to the peak of the output spike (scaled to the recombination time T) vs normalised input intensity for

an initial phase do of -0.1~ (relative to lasing threshold). three values of initial phase &, and for gO/(gO),h = 0.95.

Physics and applications of optical b&ability in semiconductor laser amplifiers 47

and the output spike. The delay (normalised to r) is plotted in Fig. 8 as a function of the normalised input intensity for three values of initial phase detuning &,. The delay shows a strong dependence on input intensity for each &,-value. Use of the detuning to reduce the delay only gives a significant reduction for cases where the contrast between “on” and “off state output intensities is considerably degraded. The long delays seen for input intensities close to the minimum required for switching are an example of “critical slowing down”[lO].

4. EXPERIMENTAL DATA

Experimental results on optical bistability in semi- conductor laser amplifiers have been reported for GaAs devices at 0.85 pm and for InGaAsP lasers at 1.3 and 1.55 pm. The main requirements for observ- ing these effects are a laser source tuneable over at least an appreciable fraction of the amplifier cavity mode separation, and means for coupling sufficient optical intensity into the active region of the amplifier. In order to study the time-dependent be- haviour it is also necessary to modulate the input optical signal to the amplifier. In practice these requirements can usually be met by the use of a semiconductor laser as the source, either using accu- rate temperature control or an external cavity with a dispersive element (e.g. a grating) to effect the tuning. Modulation can be achieved either by directly modu- lating the drive current to the laser or by the use of an external electro-optic modulator on the optical input to the amplifier. Coupling sufficient power to the amplifier relies on a suitable lens arrangement or the use of tapered and/or lens-ended optical fibres. An optical isolator is usually desirable between the source and the amplifier in order to prevent effects from optical feedback into the source laser cavity.

The amount of wavelength tuning necessary can be gauged from noting that the spacing between longi- tudinal modes of a Fabry-Perot cavity is given from equation (1) by AI#I = z, or in terms of wavelength Al:

12 AA: =-

2LN,

where N, is the group index, given by:

N,=N--d$,

For example, for a wavelength of 1.55 pm in In- GaAsP where N, u 4, and a cavity length L of 200pm, the mode spacing A1 from equation (8) is about 1.5 nm. Thus to obtain a tuning of l/10 of a mode spacing, as for the case illustrated in Figs 3-5, we need a tuning range of 0.15 nm or about 20 GHz. This range is achievable by control of the temperature of the source and amplifier lasers; good spectral

control calls for temperature stability down to about f 0.01 degree[l 11. In many ways a more convenient approach is the use of an external cavity-controlled laser source[l2] which places less stringent demands on the temperature stability of the amplifier. Another method is to use the same device as source and amplifier[9], with a length of single-mode optical fibre as a feedback delay line.

The input intensity required to observe optical bistability can be estimated from Figs 3-5, together with the definition of the scaling intensity 1, [given after equation (5)]. For a photon energy of 0.8 eV (corresponding to 1.55 pm), a confinement factor r of 0.3, a lifetime of 2 ns, and a gain coefficient dg,,/d, = 2.7 x 10-‘6cm2[13] (all appropriate to In- GaAsP lasers), the scaling intensity Z, is estimated as 7.9 x 105W/cmZ. From Figs 3-5 we may estimate a minimum scaled input intensity L,,/Z, to give bi- stability as about 10s4. It follows that the minimum input intensity necesssary will be of order 100 W/cm’, or, equivalently, 1 ~WW/~m*. Thus for a laser whose active area is about 1 pm’, we need to inject power levels of around 1 p W to stand a chance of observing optical bistability. This is well within the capability of present-day semiconductor lasers used in conjunction with good coupling optics. Turning to modulation rates for time-dependent measurements, Figs 7-8 imply that speeds on the order of the carrier lifetime (2 ns typically) are the fastest we may wish to observe, and once again this can easily be achieved by direct modulation of the laser source.

Asymmetric detuning curves of the type illustrated in Fig. 3 have been observed experimentally by a number of workers[4,11,14,15]. The first report by Nakai et a1.[14] used channeled substrate planar- stripe (CSP) lasers at 0.83 pm as both source and amplifier. A shift of resonant wavelength with input power at a rate N 0.6 b;/mW was observed, together with asymmetric tuning curve of one resonance at an input of 80 p W. Using similar lasers and temperature tuning, Otsuka and Kobayashi[ 151 observed hyster- esis in the output power/wavelength curves for injec- ted input powers in excess of - 9.2 dBm (120 pW). The frequency width of the hysteresis was 1.1 GHz for an input of -9.2 dBm and 2.3 GHz for -7.53 dBm. Tuning characteristics of 1.5 pm In- GaAsP amplifiers were reported by Kuwahara et

al.[ 1 l] who observed a wavelength shift of -0.36d;/mA with increase of current below thresh- old. Whilst this shift is mainly due to the change of free-carrier concentrations, a shift of 0.11 AjmA ob- served above threshold was attributed to thermal effects. Measured detuning effects for 1.55 pm amplifiers have been compared with theory by Adams et a1.[4] and satisfactory agreement was found based on the type of analysis given in Section 3 above.

The resonance in output intensity as a function of current (as illustrated in Fig. 6) was first observed experimentally by Watanabe and Sakuda[9]. A single CSP GaAs laser at 825 nm was used as both source

48 M. J

and amplifier, with a 288 m length of single-mode fibre as a feedback delay line. An optical pulse of IO-25 ns width was fed back and arranged to arrive at the laser during a 500ns below-threshold bias current pulse. This technique avoids the severe tem- perature control required for separate devices. Vary- ing the amplitude of the bias current pulse produced a resonance in the optical output of the type shown in Fig. 6. The effect was shown to be in agreement with calculations based on equation (7). Resonant output dependent on bias current for a fixed input wavelength can also be seen in results reported by Webb and Devlin[l6] for a 1.5 pm amplifier pumped by a 1.523 pm HeNe laser. Resonance effects were lower than for the usual case since the amplifier facets were coated to give a reflectivity of 34%.

The first observation of optical bistability in a semiconductor laser amplifier was made by Nakai et a[.[21 using GaAs CSP lasers at 820 nm. Non-linear output-input characteristics were observed at an input of about 30 PW with the amplifier biased close to threshold. Bistabihty was seen after a slight in- crease of current. The input signal was modulated with an electro-optic modulator at frequencies lo&200 kHz. At 200 kHz the hysteresis loop ob- served was stable, but as the modulation frequency was lowered the curve became more and more unsta- ble. This instability was interpreted as a result of competition between the index change due to free carriers and that due to thermal effects. Using a 1.3 pm InGaAsP amplifier, Sharfin and Dagenais[l7] reported optical bistability at an input optical power of 3 /IW. The effect was attributed to the carrier- dependent nonlinearity mechanism, as discussed above in Sections 2 and 3. Westlake et a/.[ 181 studied bistability in 1.55 grn InGaAsP devices using an external grating-controlled laser source. The min- imum input required was about 2 /L W and a contrast ratio between “on” and “off” states of about 4: 1 was observed. Recently, Wyatt and Adams[ 191 reported optical bistability in 1.55 pm distributed feedback (DFB) laser amplifiers. Hysteresis was seen at input power levels of around 1 ptw with greater than 10: 1 change between the on and off states.

At the time of writing there are remarkably few experimental measurements of the transient behav- iour of optical bistability in laser amplifiers. Sharfin and Dagenais[20] measured the switching time of 1.3 pm bistable amplifiers to be about 0.5 ns. The first observation of the sharp spike on switch-up illus- trated in Fig. 7 was reported by Wyatt and Adams[l9] for a DFB amplifier. Good agreement with the output pulse shape predicted theoretically was achieved using an analysis based on that of Section 3 above. The theory was modified somewhat to account for the effects of distributed feedback, and thus equations (l)-(3) were replaced by equivalent formulae involving the parameters of the DFB gra- ting rather than the Fabry-Perot mirrors. The output snike as oredicted for Fabrv-Perot devices has re-

ADAMS

cently been observed by Westlake et aZ.[21] and once again good agreement with theoretical predictions has been achieved.

5. POTENTIAL APPLICATIONS

At the time of writing very few applications for OB in laser amplifiers have been demonstrated or even discussed in detail. However, this is not the case for “passive” Fabry-Perot etalons in semiconductors which have attracted considerable interest for appli- cations in optical logic and signal processing[l]. By comparison with passive etalons, amplifiers offer some considerable advantages but also suffer from a few disadvantages, and these will be discussed below. First, however, we illustrate the use of non-linear amplifier characteristics in performing logic oper- ations. Figure 9(a) shows the output-input character- istic for a detuning of &, = -0.037~ which was origi- nally plotted in Fig. 4. Superimposed on the curve are two horizontal bands corresponding to the logic 0 and 1 states. The input signal intensities A and B are also shown for two cases in Fig. 9(a), corresponding to use of the device as an AND and an OR gate. Truth tables for these operations are shown in Fig. 9(b). Note that in this case the non-linearity occurs sufficiently close to the origin that there is no neces- sity for an optical holding beam to bias the device close to the non-linear regime. In many cases (e.g. the curve for g&g,),, = 0.85 on Fig. 5) this is not so, and an optical bias is needed. It is worth noting also that NAND and NOR gates can be notionally construc- ted in principle by using the device in reflection rather than in transmission[22] (again with appropriate val- ues of drive current and signal wavelength), but these cases will not be discussed here.

Recently an AND gate using a 1.3 pm bistable laser amplifier has been experimentally demonstrated by Sharfin and Dagenais[23]. The device showed a contrast ratio of the high output state (with both inputs) to the low state (with either input) of 5: 1. For an optimised device with appropriate detuning and realistic constraints these authors have shown[23]

(a) 0010 ---

logic 1

4 - I

L!LYY?

(b)

And

\ 00 0

5 0.005

A B Outwt

- rI

01 0

10 0

11 1

logic 0 Or

0 5x E-5 0.0001 A B Output

L’L 00 0

A --- And

rI

01 1 B -- 10 1

A ~~..- ~- Or B -___ 11 1

Fig. 9. (a) Scaled output vs input curve illustrating the use of non-linear gain in logic gates. (b) Truth tables for the AND and OR gates using the characteristic of Fig. 9(a).

Physics and applications of optical bistability in semiconductor laser amplifiers 49

that the maximum contrast that can be expected theoretically is 10: 1.

Figure 10 shows the output-input characteristic for a detuning of & = -0.11r reproduced from Fig. 4; this time the hysteresis loop has been indicated explicitly. In order to operate the device as a memory or latching switch, an optical bias could be used at the input level indicated as H on Fig. 10. Addition of a switching pulse of amplitude S would then cause the device to switch to the logic 1 state and this would be retained even when S was removed. A momentary removal of the holding intensity H could be used to effect a return to the logic 0 state, and again this would be preserved after the restoration of H.

The applications of laser amplifiers as logic gates, memory switches and for other similar functions (e.g. optical transistor, optical limiter[l]) can of course be duplicated by passive etalons. If we compare the performance of amplifiers with etalons made from identical material, the most striking advantage offered by the former is the lower optical input requirements. Typically the input power required to switch from the logic 0 to logic 1 state is about IO3 lower for the amplifier than for the etalon[4]. The combination of microwatt input powers with nano- second switching times leads to energy requirements in the order of femtojoules[20,24] and this represents the lowest value yet reported for any OB devices. Since many applications call for the output from one gate to act as input for one or more others, the inherent optical gain in the amplifier is a powerful argument in its favour by comparison with the pas- sive etalon. A further advantage is the ready avail- ability of laser diodes and the absence of any need for further processing for use as bistable amplifiers. The wavelength compatibility with existing optical trans- mission systems is another significant point of merit for amplifier OB. Against these advantages must be set the need for current supply to the amplifier with accompanying problems of heat dissipation, and the difficulty of making 2-D arrays of devices. Since the parallel processing of many signals is often cited as a prime factor in optical logic[l] the latter restriction

I I I I I 0 0.0002 0.0004 0.0006 0.0006 0.0010

I,“/4 H S

Fig. 10. Hysteresis loop in light output vs input; intensity H shows a typical optical bias, whilst S indicates a switching

pulse.

1x4 wnte 4x1 read opt~coi swtch optical swlfch

Input - BS LDS

OptlCOl hqhway

m

256 Mbps I$%j@&+

w

w

Fig. 11. Optical time division switching experiment[25] using bistable laser diodes (BS LD’s) and LiNbO, directional

coupler switches (read and write gates).

may be a serious one for the large-scale use of amplifier OB. These and other aspects have been discussed more fully in my recent review of semicon- ductor laser optical bistability[24], and the arguments will not be repeated in detail here.

From the above discussion we may conclude that the first applications of amplifier OB might be ex- pected to occur in relatively small-scale optical pro- cessing requirements, such as signal regeneration, where parallel processing is not needed. One example which has actually been demonstrated, using a slightly different form of bistable laser, is that of optical time-division switching[25]. This experiment, shown schematically in Fig. 11, uses bistable laser diodes, each having an absorbing and an emitting region, rather than the conventional amplifiers dis- cussed here. Nevertheless it is relevant and worth considering since the principles of the application apply equally to both types of device. As shown in Fig. 11, LiNbO, directional coupler matrices are used as read and write gates, in conjunction with laser diodes as the memory elements. Four 64 Mb/s digi- tally encoded colour video signals are time- multiplexed in bit-interleaved form and applied to the time switch. The write gate supplies the 256 Mb/s time-multiplexed signal to each memory element in turn, and the bistable lasers store the optical signals for a frame period. The stored signals are then read out according to the required sequence, and time switching has been accomplished. In the version demonstrated the memory elements are reset elec- trically since the bistable lasers used have hysteresis loops in the output-current as well as the output-input curves[26]. However, if amplifiers were substituted as memory devices it would seem appro- priate to use optical clock signals to perform the reset function.

Recently a bistable amplifier has been used to demonstrate all-optical signal regeneration in a pre- liminary experiment at 140 Mb/s[27]. A schematic illustration of the experimental system is shown in Fig. 12. An optical clock waveform generated by a tunable laser source was arranged to have peak power just below the bistable threshold. The data stream from a DFB laser was combined with the clock and coupled into the amplifier. When the data is low a slightly amplified clock pulse appears at the output. When the data is high the output jumps to a

50 M. J. ADAMS

OptIcal regenerator experiment

Optlcal data

DFB laser stream 1526 nm /

140 Mb/s

pattern

generator

Regenerated data 1514 nm

Electrical

Ext -cavity Bistable Bandpass 200 MHz

laser (tunable) laser amp filter receiver

Optical clock

waveform 1514 nm - Fibre

Fig. 12. All-optical signal regeneration experiment[27] using a bistable amplifier as a decision gate to retime and restore the levels of an optical data stream.

higher level, which is insensitive to the data power, and reverts to low only at the end of the clock pulse. Error rates of 3 x lo-* were obtained with a 2”-1 bit NRZ pseudo-random data stream.

6. CONCLUSION

This article has been concerned with the use of semiconductor laser amplifiers as bistable elements and their potential for applications in optical logic and signal processing. The physical origin of the optical non-linearity, in common with that in passive Fabry-Perot etalons, arises from the relatively strong dependence of refractive index (and hence phase) on carrier concentration. The main advantage of amplifiers over etalons is that most of the phase change can be achieved by direct current injection so that relatively small optical signals can provide the small amount of extra phase change to cause switch- ing. Hence optical power requirements are some three

orders of magnitude lower for amplifiers than for etalons using the same material, wavelength, etc. Switching times for the two sorts of devices are broadly comparable, being limited by the carrier recombination time. Bistable amplifiers are found to require input powers on the order of 1 PW and to switch in times of a few nanoseconds. The resulting energy requirement of order femtojoules is a prime advantage which, when combined with the ready availability of lasers, their inherent optical gain, and the wavelength compatability with optical trans- mission systems, make amplifiers extremely attractive for applications where large amounts of parallel processing are not required. An example of time- division switching has been cited as pointing the way in which early applications of amplifier OB may progress. It will be interesting to see other applica- tions evolve in the future as the attractions of amplifier OB become more widely recognised.

H. J. Westlake and R. Wyatt. This work was partially supported by the Joint Optoelectronics Research Scheme. The Director of Research, British Telecom, is thanked for permission to publish.

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