# Detailed Theoretical Model for Adjustable Gain-Clamped Semiconductor Optical Amplifier

Authors: Lin Liu; Craig Michie; Anthony E. Kelly; Ivan Andonovic
Journal: International Journal of Optics
 (2012)

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## Abstract

The adjustable gain-clamped semiconductor optical amplifier (AGC-SOA) uses two SOAs in a ring-cavity topology: one to amplify the signal and the other to control the gain. The device was designed to maximize the output saturated power while adjusting gain to regulate power differences between packets without loss of linearity. This type of subsystem can be used for power equalisation and linear amplification in packet-based dynamic systems such as passive optical networks (PONs). A detailed theoretical model is presented in this paper to simulate the operation of the AGC-SOA, which gives a better understanding of the underlying gain clamping mechanics. Simulations and comparisons with steady-state and dynamic gain modulation experimental performance are given which validate the model.


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## Body

## 1. Introduction

Semiconductor optical amplifiers (SOAs) have attracted considerable attention during the last two decades, for use in evolving optical communication networks. SOAs can be used as not only optical amplifiers, but also signal processing devices such as wavelength converters [1], optical switches [2], and electro-optical mixers [3]. In terms of optical amplification, the key issue of operating SOAs is the management of the input optical signal power, which must be maintained within the linear regime of operation; otherwise the device would be driven into saturation causing unwanted intersymbol interference (ISI) or patterning. In order to solve this implementation problem, many different types of gain-clamped semiconductor optical amplifiers (GC-SOAs) have been proposed [4, 5]. Recently, an adjustable gain-clamped semiconductor optical amplifier (AGC-SOA) designed to maximize the output saturated power at a clamped gain which can be adjusted was reported [6].


## 2. AGC-SOA

The AGC-SOA is a semiconductor optical amplifier topology which has the unique capability to provide variable gain and maintain linear operation through gain clamping over a wide (40 dB) dynamic range, without compromising the saturable output power of the device [6]. A key advantage of this approach is that there are no mechanical tuning elements, and hence the gain can be adjusted via direct electrical control at ns timescales. While the operation of this device has been presented previously for the static gain case [6], and its behaviour under dynamic gain modulation conditions [7], the underlying mechanics is not well understood. Here, a theoretical model for an AGC-SOA has been established, based on the wideband steady-state numerical model of a SOA [8]. The travelling amplified spontaneous emission (ASE) power and spectrum within a ring cavity, steady-state, and dynamic gain modulation have been studied. Simulations are in broad agreement with experiment results.Figure1 illustrates conceptually the design of the adjustable gain clamped SOA (AGC-SOA). The architecture comprises two active (gain) regions defining a data path through the signal SOA (SOA1) and a laser cavity containing SOA1 and a control SOA (SOA2). SOA1 amplifies light in the signal path. The lasing mode derives gain from both SOA1 and SOA2. The composite gain provided by both SOAs regulates the condition for the onset of lasing. This in turn defines the carrier concentration (gain) of the signal SOA. Hence, by controlling the drive to SOA2, the gain imparted by SOA1 can be adjusted. SOA1 is continually operated at full current, and therefore, the AGC-SOA allows signals to be amplified by SOA1 at a clamped gain which is varied by SOA2. This maximises the saturation output power thereby maintaining an extended linear regime [6].Figure 1
Counterpropagating ring laser adjustable gain-clamped SOA (AGC-SOA) implementation.The key advantage that the AGC-SOA offers over other optical amplifiers is that it enables the gain to be adjusted directly through the drive current to the clamping SOA without the dramatic loss ofPsat. Hence, linear operation is maintained over a wider range of input signals. In standard SOAs, it is possible to adjust the gain by altering the drive current however, as is demonstrated in the experimental measurement shown in Figure 2, and this leads to a dramatic loss in Psat.Figure 2
Psat (dBm) variation as a function of SOA gain (dB).At high gains, where the SOA is highly inverted, thePsat value is at its highest. However, in this region, adjusting the small signal gain through bias current has a dramatic effect on the Psat value. In the example depicted in Figure 2, at high gains the Psat changes with gain at a rate of ~3 dBm/dB i.e., for every dB that the gain is reduced, the Psat value drops by 3 dBm. As the drive current is further reduced, the drop in Psat with gain is weaker at ~0.4 dBm/dB. However, by the time that this point has been reached, the Psat value is already significantly compromised (5 dBm compared to the high gain value of 10 dBm). The AGC-SOA enables gain modulation to be achieved without this dramatic loss of Psat value.Figure3 depicts the gain of AGC-SOA as a function of output power for a set of different clamping currents ranging from 0 mA to 200 mA. The Psat values are constant over the range of clamping currents despite significant gain reduction (>20 dB), demonstrated in Figure 4.Figure 3
AGC-SOA gain as a function of output power at different clamping currents. Legend: bias current of SOA2.Figure 4
Psat (dBm) variation as a function of AGC-SOA gain (dB).Additional steady-state experimental results such as gain, Noise Figure (NF), andPsat value were demonstrated in [6]. The dynamic gain modulation performance of AGC-SOA was further studied in [7]. In a dynamic packet equalisation scenario, the AGC-SOA is able to adjust and stabilise its gain in less than 2 ns, within the period of the guard band of the passive optical network (PON) transmission at 1.25 Gbit/s on the upstream direction, 32 bit periodsis equates to 26 ns. Similarly for 10-Gigabit-capable, PON system, the guard time is 64 bits at 2.5 Gbit/s on the upstream direction [9], this equates to 26 ns [9].


## 3. Model of AGC-SOA

Several numerical models have been developed to investigate the characteristics of both conventional SOAs [8] and gain-clamped SOAs using either an external [10, 11] or internal [12, 13] lasing mode. However, the underlying mechanism of gain clamping achieved by adjusting wideband amplified spontaneous emission (ASE) power still remains largely unknown. In this study, the wideband steady-state SOA model [8] is adapted to form a ring cavity; the evolution of travelling ASE power and spectrum within the ring cavity, important for gain clamping, is then characterised. The gain, Noise Figure (NF), and maximum output power at gain saturation (Psat) of an AGC-SOA under different clamping currents are also studied. Based on this model, the timescale for adjusting and stabilising the gain, crucial for dynamic packet equalisation, is evaluated.As shown in Figure5, ASE circulating within the AGC-SOA travels in clockwise and counterclockwise directions, however, the isolator in the ring cavity ensures that ASE travelling in the clockwise direction is not amplified. Thus, the counterclockwise ASE generated by both SOAs accounts for gain clamping. In this model, the two SOAs are simulated as independent modules using different sets of material parameters summarised in Table 1. (Typical bulk SOA parameters from [8, 14, 15]). Both SOAs generate ASE in the forward and backward directions in the active regions. In each SOA, the ASE profile extends over 1300 nm ~1650 nm and is partitioned into discrete frequency bands.Table 1
Device parameters used in AGC-SOA simulation.
SymbolParametersSOA1SOA2LcCentral active region length400μm840μmLtTapered active region length200μm160μmdActive region thickness0.4μm0.1μmWActive region width0.4μm1.1μmyMolar fraction of arsenide0.8920.816ΓConfinement factor0.150.15R1Input facet reflectivity5×10-51×10-5R2Output facet reflectivity5×10-51×10-5ηinInput coupling loss3 dB2 dBηoutOutput coupling loss3 dB2 dBK0Carrier-independent absorption loss coefficient6200m-13000m-1K1Carrier-dependent absorption loss coefficient7.5×10-21m26.83×10-21m2n1Active region refractive index3.223.56C1Recombination coefficients3.7×108s-1C25.6×10-16 m3/sC33×10-41 m6/sαcouplerWDM coupler pass band insertion loss0.5 dBFigure 5
Schematic of the simulation model for an AGC-SOA.In order to simulate the wideband ASE profile for a single SOA, the material gain coefficient of the SOA active region in an InGaAsP direct bandgap bulk material is given by [8, 16]
(1)gm(ν,n)=c242π3/2n12τν2(2memhhħ(me+mhh))3/2×∫0∞(ν′-Egh)1/2×(fc(ν′)-fν(ν′))×(2T01+(ν′-ν)2(2πT0)2)dν′=c242π3/2n12τν2(2memhhħ(me+mhh))3/2×(ν-Egh)1/2×(fc(ν)-fν(ν)),
where c is the velocity of light in vacuum, ν is the optical frequency, n1 is the active region refractive index, τ is the radiative carrier recombination lifetime, ħ is the normalized Planck constant, me is the effective mass of an electron in conduction band (CB), mhh is the effective mass of a heavy hole in valence band (VB), Eg is the band gap energy of the material, T0 is the mean lifetime for the coherent interaction of electrons with a monochromatic field, and fc and fν are the Fermi-Dirac distributions for the conduction and valence bands, respectively.The gain coefficient can be divided into two parts: stimulated emission rateRe and stimulated absorption rate Ra,(2)gm(ν,n)=Re(ν,n)-Ra(ν,n),
where
(3)Re(ν,n)=c242π3/2n12τν2(2memhhℏ(me+mhh))3/2×(ν-Egh)1/2×fc(ν)(1-fν(ν)),Ra(ν,n)=c242π3/2n12τν2(2memhhℏ(me+mhh))3/2×(ν-Egh)1/2×fv(ν)(1-fc(ν)).The propagation of optical field in the SOA can be described as(4)dAj+dz=[-iβ+12(Γgm(ν,n)-α)]Aj+,dAj-dz=[iβ-12(Γgm(ν,n)-α)]Aj-,
where Aj+ and Aj- are the forward and backward travelling waves of the jth active region section, respectively, βis the propagation constant, Γ is the confinement factor, and α is the internal loss coefficient.The propagation of the spontaneous emission field is presented as(5)dSk+dz=[Γgm(νk,n)-α]Sk++Rsp(νk,n),dSk-dz=-[Γgm(νk,n)-α]Sk--Rsp(νk,n).Sk+and Sk- are the forward and backward amplified spontaneously emitted photon densities per unit frequency spacing centred at frequency νk. Rsp(νk,n) is the ASE noise coupled into Sk+ or Sk-, and it is expressed as Rsp(νk,n)=ΓRe(νk,n)Δν,Δν is frequency spacing.The carrier rate equation is presented by(6)dn(Z)dt=IqV-R(n(z))-∑j=1nΓgm(ν,n)Across(Aj++Aj-)-∑k=1m2Γgm(νk,n)Across(Sk++Sk-).The recombination rate termR(n(z)) is given by(7)R(n)=C1n+C2n2+C3n3,
whereC1, C2, and C3 are the nonradiative recombination, bimolecular radiative recombination, and auger recombination coefficients, respectively.The numerical model for the whole system of Figure5 is achieved using iterative circulations. In the first iteration, the ASE in both directions of SOA2 is calculated assuming no ASE power is coupled in. Then the ASE generated by SOA2 travels in both clockwise and counterclockwise order towards SOA1. Under this boundary condition, the ASE originated from SOA2 together with the one generated by SOA1 is amplified by SOA1 as it travels through; however, only the backward ASE inside the SOA1 is input to SOA2. For any successive iterations, the ASE from SOA1 couples into SOA2 before SOA2 generates ASE. When ASE travels inside the ring cavity, the facet reflectivity and coupling loss of both SOAs, the insertion loss for the isolator, and WDM couples are taken into account. The round trip time is ~1.67 ns namely, the fibre length is about 0.5 m. Therefore, fibre loss and dispersion are neglected. The iterative procedure is terminated when the maximum difference of the ASE powers at each discrete frequency band between successive iterations is less than the desired tolerance. The numerical model is implemented using Matlab.


## 4. Simulation Results and Discussions

The characteristics of AGC-SOA were studied from the initial state when no input signal is introduced. The ASE power after every counterclockwise ASE round trip is recorded. In Figure6, the counterclockwise output ASE powers from SOA2 and SOA1 are displayed after each loop transit.Figure 6
Counterclockwise ASE power afterN loops. Cross: SOA2 output ASE power. Circle: SOA1 output ASE power.The ASE power increases rapidly within the first 3 loops and then stabilises. Since the cavity round trip time is ~1.7 ns, stabilising the travelling ASE power in the loop takes between 1.7 and 5.1 ns (several round trips). The ASE spectrum within the clamping mode was examined after every circulation. Figure7 shows the SOA2 output ASE spectrum at different loop transits. In the first loop, the output ASE power from SOA2 is relatively low, and the whole spectrum is divided into two parts falling outside the C-band due to presence of the WDM coupler in the ring cavity.Modeled SOA2 ASE spectrum (counterclockwise). (a) Loop number = 1; (b) loop number = 10; (c) loop number = 20; (d) loop number = 100.
(a)(b)(c)(d)Initially, the ASE power within the S-band is greater than that within the L-band. However, as the lasing mode becomes established, the output ASE power develops as predicted in Figure6. With the ASE power within the S-band decreasing significantly, the spectrum becomes sharp and narrow.As ASE circulations progress, ASE emission in the S-band is further restrained becoming negligible, and ASE within the L-band accounts for gain clamping. This results from the fact that the lasing threshold is lower at longer wavelengths hence once lasing action is established, the shorter wavelength energy states are depleted. The results agree well with experimental observation.Having established the steady-state conditions of model operation, an input optical signal was introduced after the ASE inside the AGC-SOA cavity stabilizes. The gain of 1550 nm CW light as a function of travelling ASE loop numbers is depicted in Figure8. An optical signal power of −20 dBm was injected into SOA1. The drive current of SOA1 was set at 200 mA, and SOA2 at 65 mA. The simulation demonstrates that the signal gain settles within the first ASE loop transit and then remains unchanged; thus, after AGC-SOA stabilizes from the initial state (shown in the evolution depicted in Figure 7), it takes <2 ns (within one loop time) for the gain to settle.Figure 8
CW light (1550 nm, −20 dBm) gain as a function of circulating ASE loops after AGC-SOA stabilisation.The variation of the gain with clamping SOA drive current was modelled over a range of clamping currents to corroborate that the model faithfully reproduced the experimental behaviour of the AGC-SOA. The model outputs (Figure9) indicate broadly that the model is predicting the trends. There is no significant loss of Psat with gain reduction, however, the exact values of gain and Psat differ slightly from experimental measurements. This difference most likely derives from small differences between the physical parameters used in the model and the real device.Figure 9
AGC-SOA gain as a function of output power at different clamping currents (modeling result).The DC parametric operation of the AGC-SOA can be estimated using the above model. CW light (1550 nm) was introduced into AGC-SOA once the steady-state operation was established. The input signal power was then increased steadily from −35 dBm to 20 dBm, and the normal performance metrics of gain, maximum output power at gain saturation (Psat), and noise figure (NF) were recorded for a given clamping current condition; the clamping current is changed from 0 mA to 200 mA. The simulation results are presented as a function of clamping current in Figure 10. The overall trends given by the models are in good agreement with previously reported experimental characterizations [6]. Gain clamping begins at a clamping bias current of greater than 0 mA. Experimentally this value was observed to be nearer 10 mA before there was sufficient gain within the clamping SOA to overcome loop losses and allow the lasing mode to stabilize. This difference is mainly due to the overestimation of ASE noise within the model [8]. Strong clamping is observed when the control SOA is operated at high gain levels; here, the AGC-SOA is driven into attenuation. As the gain is clamped, the NF increases, but in the main, the Psat value remains relatively constant when the clamping current is <100 mA.Figure 10
Experimental [6] and theoretical steady-state AGC-SOA performance comparisons. Red line: simulation results of NF. Red dot: experimental results of NF. Blue line: simulation results of gain. Blue cross: experimental results of gain. Green line: simulation results of Psat. Green star: experimental results of Psat.The theoretical model could also be used to better understand the dynamic behaviour of the AGC-SOA. In order to do this, the model was run under the following conditions. Firstly, stable operation of the AGC-SOA was ensured by running the simulation with only ASE for the first 30 loop iterations and at an SOA2 (clamping SOA) bias of 20 mA. At this point, a 0 dBm input signal was introduced, and it can be seen that the gain of the AGC-SOA is around 10 dB. The clamping SOA bias current was then increased every 10 loops, from 20 mA to 200 mA, in steps of 20 mA and the gain change observed (Figure11). It is clear from these simulations that the gain is indeed adjusted and stabilized within 1 or 2 loops of the model iteration. This implies therefore that the gain can be adjusted within nanosecond timescales which agree with experimental results [7].Figure 11
Dynamic gain variation as a function of clamping current.


## 5. Conclusion

A detailed wideband model for adjustable gain-clamped semiconductor optical amplifier (AGC-SOA) has been established, which can be used to analyse steady-state and dynamic gain modulation performance of the device. The simulations agree with the experimental results, showing the advantage of AGC-SOA not only lies in extended linear amplification regime and adjustable device gains, but also the ability of adjusting and stabilising its gain within nanosecond timescales. This feature could enable the device to work as power equalizer and linear amplifier in packet-based dynamic systems such as passive optical networks (PONs).



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