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We investigate the dependence of the speed of recovery of optically excited semiconductor optical amplifiers (SOAs) on the active region dimensions. We use a picosecond pump-probe arrangement to experimentally measure and compare the gain and phase dynamics of four SOAs with varying active region dimensions. A sophisticated time domain SOA model incorporating amplified spontaneous emission (ASE) agrees well with the measurements and shows that, in the absence of a continuous wave (CW) beam, the ASE plays a similar role to such a holding beam. The experimental results are shown to be consistent with a recovery rate which is inversely proportional to the optical area. A significant speed increase is predicted for an appropriate choice of active region dimensions.
©2007 Optical Society of America
1. Introduction
Semiconductor optical amplifiers (SOAs) continue to attract much research interest for their applications in all-optical logic and signal processing [1]. Their compactness, potential for photonic integration and large nonlinearities make them excellent candidates for high-speed operations such as wavelength conversion [2,3,4], demultiplexing [5], regeneration [6] and optical logic [7,8]. However, at bit-rates ≥ 10Gbit/s, an SOA’s operation becomes limited by the relatively slow carrier recovery time (of the order of 100ps) and so the device must be incorporated in interferometric or other sophisticated arrangements to enable its use in optical switching. Such methods have allowed SOA-based all-optical wavelength converters to operate at speeds as high as 170Gbit/s [3] and even 320Gbit/s [9]. However, they do not directly deal with the fundamental issue of slow recovery times in SOAs, which are responsible for non-linear pattern effects and low phase shifts at high bit-rates, and ultimately limit the performance of the devices.
In this work, we experimentally measure the speed of recovery of optically excited SOAs of differing active region dimensions and compare their performances. Measurements are carried out using a pump-probe arrangement where both pump and probe are 3ps pulses, and have different wavelengths. It is important to note that this differs from other studies on this subject where the SOA under test was run in constant saturation with a CW probe [10,11]. A high gain SOA will always be saturated to some degree by a CW probe beam resulting in reduction of both the ASE power level and the effective lifetime. With a pulsed probe we are able to measure the unperturbed recovery dynamics of the device as well as assess the role played by the ASE in the recovery process. It is the unsaturated recovery speed of the SOA that ultimately determines the device’s performance capabilities, and our approach allows us to measure this.
We compare the experimental results with a numerical model [12], which takes as input experimentally measured SOA characteristics such as small signal gain, ASE spectra and gain saturation curves. We also use the model to examine further variations of active region dimensions and show that it is possible to significantly increase the SOA’s recovery speed by appropriate choice of device width and depth.
2. Pump-probe measurements
Fig. 1. Experimental pump-probe arrangement. TMLL: tunable mode-locked laser; EDFA: erbium doped fibre amplifier; BPF: band pass filter; VOA: variable optical attenuator; PC: polarization controller; R: reflected signal from the TOAD; T: transmitted signal.
Pump-probe measurements of the gain and phase dynamics of the SOAs were carried out using the setup in Fig. 1. Two tunable mode-locked lasers (TMLLs), driven by a 10.645GHz RF synthesizer, provided the 3ps pump (1544nm) and probe (1560nm) pulses. Using optical modulators, the repetition rates of these pulse trains were reduced to 665MHz, which ensured that the SOA under test could recover fully between successive pulses. A small frequency shift, Δf, was applied to the RF drive to the probe laser so that the probe pulses could scan temporally through the gain response of the SOA to the pump pulse. The output from the pump laser was amplified with an EDFA to increase its power to roughly 25dB greater than that of the probe.
The probe beam was input to the 50:50 base coupler of a terahertz optical asymmetric demultiplexer (TOAD) [13], which consisted of a loop of fibre with an SOA offset from the loop centre by several nanoseconds. Here the probe pulses were divided into two counter-propagating components, one of which entered the SOA before the other (the counterclockwise traveling component in Fig. 1). The polarization of the incoming probe signal was adjusted with a polarization controller so that it aligned with the principal axis of the SOA. The polarization of the TOAD loop was biased for full reflection of the probe in the absence of a pump pulse.
A pump pulse incident on the SOA, and timed to arrive before the counter-clockwise probe, caused gain and phase modulation in this probe component. The SOA then recovered before the arrival of the clockwise traveling pulse and so net phase and amplitude differences existed between the probe components recombining at the base coupler. Due to the frequency shift between the input signals, the constantly changing delay between the pump and probe pulses lead to time dependent reflection (R) and transmission (T) coefficients that were detected on photodiodes and observed in real time on a MHz bandwidth electronic oscilloscope, triggered at the frequency Δf. Pump pulses and ASE exiting the TOAD from the base coupler were optically filtered out from the signal incident on the photodiodes. The gain (G) and phase (ϕ) dynamics of the optically excited SOA were derived directly from the R and T coefficients, and the coupling ratio of the TOAD’s base coupler, d2:k2, using equations (1) and (2) [14].
The gain, as calculated from equation (1), was compared with the amplitude modulation of the probe traversing the optically excited SOA, measured directly after the device, as in Fig. 1. This ensured the accuracy of the gain calculations, and hence the phase calculations.
The SOAs measured in this way were commercially available buried heterostructure bulk GaInAs devices from KamelianTM. They each had an active region of width 1μm and the (length, depth) pairs were (1mm, 0.1μm), (1mm, 0.2μm), (1.9mm, 0.1μm) and (1.8mm, 0.2μm) respectively. The confinement factors for the 0.1μm and 0.2μm deep SOAs were ~0.2 and ~0.4 respectively [15]. The 0.1μm deep devices incorporated a separate confinement heterostructure (SCH) layer to increase the confinement to the value quoted here. Each SOA was operated at currents of between 100mA and 400mA and the dynamic curves recorded.
3. Measurement results and analysis
Typical transmission, reflection and amplitude modulation curves are shown in Fig. 2. These measurements were made using the 1mm long, 0.1 μm deep active region SOA, operating at 200mA with pump and probe pulse energies of ~25fJ and 0.1fJ respectively at wavelengths 1544nm and 1560nm.
Fig. 2. (a) Typical normalized R (heavy line) and T (light line) co-efficients from pump-probe measurements; (b) typical normalized gain measured from amplitude modulation monitor.
Fig. 3. (a) Normalised gain dynamics calculation (open squares) and fit (line); (b) phase dynamics calculation (open squares) and fit (line).
Figure 2(b) reveals the breakdown of the gain recovery into two separate stages: an ultrafast recovery stage, due mainly to carrier heating and subsequent cooling; and a relatively slow stage due to band filling by current injection [16]. The gain and phase dynamics, calculated from the curves in Fig. 2(a), using equations (1) and (2) are shown in Fig. 3, along with fits from a two-part impulse response numerical model [17].
The impulse response formulae, as given in equations (3) and (4), assume different recovery time constants for the ultrafast (τch) and the band filling (τbf) processes. τch is fixed at a value of 1ps [18], while τbf is used as a variable parameter to achieve the best fit to the measured dynamic curves. Equations (3) and (4) also assume different linewidth enhancement factors (αch and αbf) for the separate recovery processes [16]. a and b are the amplitude coefficients for band filling and carrier heating respectively and τdelay is the time delay between the arrival of the pulse and the onset of carrier heating (fixed at 0.12ps [19]). Figure 4 indicates τbf of each SOA as a function of injection current, with the SOA active region length and depth indicated in the legend. It is this band filling recovery time that determines the SOA’s capabilities in terms of bit rate capacity.
Various values of the probe wavelength between 1530nm and 1575nm were used, but no wavelength dependence of the recovery rates was observed, in contrast to [20], where a CW beam was used as a probe. It is clear from Fig. 4 that, to within experimental error, for a constant operating current the SOA recovery time is independent of active region length and depth. This observation is further explored with a numerical model in section 4.
Fig. 5. (a) Phase shift obtained from 1mm long, 0.1μm deep SOA as a function of pump pulse energy for different values of bias current (indicated in legend); (b) phase shift obtained from 1.8mm and 1mm long SOAs, both of cross-sectional area 0.2μm2 as a function of bias current.
Figure 5(a) shows the dependence of the phase shift obtained from the 1mm long, 0.1μm deep SOA on the input pump pulse energy for different values of the bias current between 100mA and 348mA. Similar trends are observed for the three other SOAs. At low pump pulse energies the phase shift increases linearly with energy but begins to saturate at about 70fJ/pulse. Figure 5(b) compares the phase shifts obtained from two SOAs of equal cross-sectional areas (0.2μm2) but different lengths (1mm and 1.8mm respectively), for a fixed pump energy of ~6fJ. Saturation with increasing bias current is observed and, as expected [17], the longer SOA exhibits larger phase shifts.
4. SOA model
A detailed description of the SOA model used to analyze the experimental results can be found in [12]. The model accounts for the saturation caused by the bidirectional ASE propagation in the device, which is an important phenomenon to understand the carrier recovery in SOAs.
In the model, the ASE is described by its total power, neglecting its spectral dependence. By using effective parameters for the spontaneous emission (SE) coupled into the waveguide, βeff, and for the modal gain of the ASE, gASE, we account for the spectral dependence of the ASE. In this way, the information on the ASE spectrum is lost, but on the other hand the equations for the propagation of the ASE are reduced to only two, one for each direction of propagation. The computational complexity, which is a key factor in time domain simulations, is thus reduced considerably compared with models where the whole ASE spectrum is propagated.
The internal parameters, such as modal gain, waveguide losses, injection efficiency and SE spectral density coupled into the waveguide, are extracted from the CW characterization of the device’s small signal gain and gain saturation. A simple quadratic function is used to approximate the modal gain of the device. The modal gain and SE spectral density are then used to derive βeff, and gASE. As highlighted in [12] the variation of βeff with the carrier concentration is small and thus in the model it is approximated by a constant. Similarly the gASE is approximated by a linear function of the carrier concentration with good accuracy.
In contrast to [12], the total carrier recombination rate is modeled using a two-term expression accounting both for bi-molecular and Auger recombination. Both the introduction of the Auger term and the ASE-induced saturation are crucial to obtain good agreement between the experiments and the modeling over a wide range of SOA bias currents. Details of parameter values used in the numerical model for one of the SOAs are given in Table 1. Any other parameter values are extracted by the model from the afore-mentioned inputs.
Table 1. Set of parameters used in model calculations
The logarithmic plot of the data in Fig. 4 is indicated in Fig. 6, along with the fits from the numerical model. It is clear from Fig. 6 that the numerical model accurately predicts the recovery time constants for each SOA. The discrepancy in the fit to the 1mm long, 0.1μm deep active region device at high currents is attributed to a breakdown at high current densities of the blocking layer in the device structure, which leads to current leakage.
Fig. 6. Logarithmic plot of recovery time constant versus SOA current data (points) and numerical model fit (solid line) for each SOA. Length and depth parameters of the SOA are indicated in the upper and lower portions of each legend respectively.
The slope of the logarithmic data set describes the dependence of the recovery time on the bias current. For an Auger dominated process, the predicted slope is -2/3 [21]. However, the mean slope of the data set in Fig. 6 is -1.37. Using a numerical model which does not include ASE yields the aforementioned predicted slope of -2/3. It is the inclusion of ASE into the model which allows the accurate predictions of the slopes of Fig. 6, so we conclude that ASE is also playing a crucial role in the recovery dynamics. In fact, in the absence of a CW beam, it appears that ASE is the dominant contributor to the speed of the gain recovery. The ASE acts in a similar way to a holding beam [22]: reducing the equilibrium carrier density to which the device must recover and thus reducing the time constant of this recovery. Equation (5) details the dependence of τbf on the Auger recombination lifetime (τAuger) and the ASE lifetime (τASE) [22].
As stated from examination of the dependence of τbf on the current, the ASE lifetime is the dominant term here, and its expansion is provided in equation (6), where PASE is the ASE power, ESAT is the SOA saturation energy, Γ is the confinement factor, A is the cross sectional area of the active region, g is the material gain coefficient and hν is the photon energy [22].
For an SOA of specified material composition, the ASE lifetime, and therefore τbf, is dependent on the ratio Γ/A (the inverse of the optical area) and clearly, this ratio should be maximized for fastest device recovery speeds, as described in [10] for a CW probe beam. Although not considered here, optimization of the recovery speed by increasing the material gain coefficient is discussed in [23]. The dependence of the recovery rate on the optical area is reflected in our observations and numerical modelling, which show that for a given bias current the recovery time constant is approximately independent of the active region depth, since the optical areas of all the devices are very similar. We note that it is difficult to predict an analytical expression for the dependence of the ASE dominated lifetime on the bias current, because of the complex interdependence of the number density and the ASE power.
In assessing the length dependence of the speed of recovery of the SOA gain, it is important to note that the parameter to be fixed for comparison between devices of different length is the bias current and not the current density [24,25], or transmission gain [20]. The current determines the electrical power consumed by SOAs as they are implemented in all-optical switching schemes. By increasing the device length but maintaining the current density, the current and therefore the electrical power consumption must increase. The advantage gained by such an increase in length, in terms of higher ASE powers or faster recovery speeds, is counterbalanced by an increase in power consumption. In fact, as large a benefit to the SOA speed is to be gained by simply applying the same increase in bias current to a shorter device. This is in evidence in Fig. 4, where recovery speeds for amplifiers of length 1mm, 1.8mm and 1.9mm are approximately equal. Similar results are reported in [20]. However, while increasing the device length does not appear to offer an advantage in terms of speed of recovery for the same current, longer devices do offer greater phase shifts (as is evidenced in Fig. 5(b)), which are important in optical switching, and in particular in all-optical regeneration where a π radians phase shift is key to the device operation. Hence, comparing the two devices of Fig. 5(b), the 1.8mm long device will, in principle, be capable of operating at a higher switching rate than the 1mm long device, since a π radians recovery at the bit rate is the switching requirement [1].
5. SOA device optimisation
To further test the claim that the SOA recovery speed is ASE dependent, we performed a theoretical optimisation of the dimensions of the device and compared the findings to the results predicted by the numerical model. Our hypothesis that the ASE contributes to the speed up of the SOA gain recovery time in much the same way as a CW holding beam suggests that, to achieve the fastest recovery, the ratio Γ/A must be maximised, as per equation (6). This ratio is plotted as a function of active region width for a device of fixed depth (0.1μm) in Fig. 7. The confinement factors are calculated using the effective index method [26], and assuming a waveguide structure without SCH layers.
Figure 7 suggests that a width of approximately 0.6μm will yield the maximum ratio of confinement factor to active region area. The proposal that this optimum width should correspond to the fastest gain recovery speed was tested using the numerical model. With the length, depth and operating current parameters fixed at 1mm, 0.1μm and 200mA respectively, the recovery speeds for various active region widths were calculated. To achieve this, the modal gain and ASE of the device in the model was adjusted according to the new dimensions and confinement factor of the active region for each width. The model results are indicated in Fig. 8, with the ratio A/Γ (the optical area) overlaid for comparison.
Fig. 8. Modelled recovery time constant as a function of active region width (points) and modelled area to confinement factor ratio (solid line) overlaid for comparison.
It is clear from Fig. 8 that an optimum width for fastest SOA recovery exists, and that it corresponds closely to that predicted from the simple theory. By reducing the active region width from 1μm (which is the width of the real devices characterised) to 0.6μm, a reduction of the recovery time constant by roughly 20% is possible. Also evident from Fig. 8 is the close agreement between the recovery time variation predicted from the numerical model and the A/Γ ratio, which supports the argument that the ASE is indeed contributing greatly to the gain recovery mechanism.
Further modelling of the SOA confinement factor for varying widths as well as depths was carried out to determine whether an overall optimum dimension set exists for fast recovery speeds. The Γ/A ratio for depths ranging between 0.05μm and 0.5μm, and for varying widths, are plotted in Fig. 9, with the dimensions of the active region for each curve indicated in the legend.
Figure 9 predicts a maximum Γ/A ratio for a square active region of side 0.3μm. It is important to note that in this modelling there is a discrepancy between the Γ/A values for the 0.1μm and 0.2μm deep curves at 1μm width (i.e. the cross-sectional areas of the real devices measured). The real devices of 0.1μm depth had a separate confinement heterostructure design to increase their confinement factors, as described previously, which is not taken into account in the simple waveguide model used here. Thus the actual Γ/A ratios for the real devices had much more similar values than Fig. 9 would suggest, and this accounted for the near equality of their recovery rates, as previously discussed.
For an SOA with a 0.3μm square active region cross-section, the numerical model predicts a recovery time constant of less than 10ps for an operating current of 200mA, compared to the 50ps measured for the real device. As well as the obvious advantage of the much faster recovery speeds offered by this optimum dimension set, the gain of the device should be polarisation insensitive due to the square nature of its cross-section [27]. Such a design optimisation of the active region would result in significant improvement in the speed response and performance of the SOA. This is technologically challenging, but has been demonstrated by the authors of [27].
6. Conclusion
We have measured the dependence of the recovery time constant of semiconductor optical amplifiers on the dimensions of the active region. Each of the devices measured showed a very similar dependence of recovery rate on bias current. These observations were consistent with an ASE dominated recovery rate, and the near equality of the optical areas of the devices studied. A sophisticated numerical model incorporating ASE corroborated these observations.
A theoretical study of the speed dependence on the SOA width revealed an optimum value of 0.6 μm for fastest recovery for a depth of 0.1μm, which closely agreed with the width predicted to optimize the Γ/A ratio for the device. This optimized width yielded a speed up of roughly 20% in the gain recovery of the SOA. Further investigation suggested that an overall optimized dimension set exists for the realization of fast recovering SOAs, corresponding to a square active region of side 0.3μm. Such an active region design is expected to result in a polarization insensitive gain as well as a much-improved speed of recovery.
Acknowledgments
This work is supported by Science Foundation Ireland under grant number 03/IN.1/1340 and also by the Irish Research Council for Science Engineering and Technology scholarship scheme. We would like to acknowledge Dr. T. Kelly and Dr. C. Tombling of Amphotonix Ltd. for useful discussions. We are indebted to Zarlink Semiconductor for provision of the frequency dividers used in this work.
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