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Measurements to date of the wavelength dependency of gain recovery time in semiconductor optical amplifiers (SOAs) have mostly used pump-probe techniques with a pump and probe operated on distinct wavelengths. Choice of pump wavelength, and its relative proximity to the probe wavelength, could influence measurements and impede unambiguous observation of wavelength dependence on recovery dynamics. We use a single-color pump-probe measurement technique to directly access the wavelength dependence of the gain recovery time in bulk InGaAsP SOAs. We used ultrashort pulses from a single mode locked laser to measure unambiguously the spectral dependency and temporal behavior of SOAs. Simulation results using a model that takes into account intra-band and inter-band contributions to SOA saturation, as well as experimental results for the SOA tested, show recovery rate dependency similar to gain spectrum.
©2008 Optical Society of America
1. Introduction
Semiconductor optical amplifiers (SOAs) are promising components for access networks and much work has been done to develop efficient numerical simulation tools [1]. These algorithms solve differential equations to obtain the behavior of the carrier density through time. They rely on an empirical description of the carrier recovery time, which is presumed to depend only on the carrier density. We experimentally investigate the carrier recovery time dependence on wavelength using a single color, all-fiber, simple experimental setup capable of measuring accurately this time constant for a specific wavelength. We use a pump-probe technique, previously reported in the literature in both free-space [2–10] and fiber [11–16] embodiments. Typically different wavelengths are used for pump and probe, although some exceptions exist. We begin by reviewing these previous carrier recovery time characterization methods to highlight their differences as compared with the method we propose.
Free-space experiments to characterize gain recovery are usually complex and require sensitive alignment using lenses for coupling the pump and probe beams. In [2, 3] the authors used single-wavelength, sub-picosecond lasers. They separated the pump and probe beams by cross-polarizing them. Although pump and probe are at the same wavelength, the gain recovery will depend on the probe polarization, as demonstrated in [7]. Note that some polarization conversion could occur because of the strain on the waveguide.
In [4], a free-space, two-color pump probe technique used spectrally slicing of a supercontinuum source. For this setup, the carrier recovery depends on the wavelength separation of the pump and probe [5]. This is useful to understand carrier dynamics in wavelength conversion experiments, however, does not permit measurement of the carrier recovery at the pump wavelength. In [2], a more sophisticated co-polarized pump-probe method using heterodyne techniques was demonstrated. The wavelength dependency of the gain recovery above transparency was not investigated and the experimental setup was complex. In an interesting work by Philippe, et al. [7], polarization dependency of the recovery time was investigated in free-space. They demonstrated a co-polarized pump-probe technique where the beams were separated by counter-propagating them through the device under test. They showed that the TM mode recovers faster than the TE mode, possibly due to light holes dynamics as well as strain. The counter propagation configuration was used to separate pump and probe at the same polarization. Wavelength dependency was not investigated. In [8, 10], the pump and probe were orthogonally polarized. Results for different wavelengths above and below transparency were presented, but the authors focused only on the fast dynamics near the zero delay for InGaAsP and AlGaAs waveguides respectively. Note that in our work hereafter we focus on the wavelength dependence of the long-lived changes of the gain (above transparency).
The second set of experiments use all-fiber setups that are simpler, more flexible and can exploit common fiber components such as WDM couplers and filters. However, we will see that these experiments were usually: 1) complex, and 2) only interested in pump and probe at distinct wavelengths.
Dynamics for continuous wave probe signals were tested in [11, 12] where it was demonstrated that a continuous-wave probe signal results in a lower gain recovery time due to shorter stimulated lifetimes. A CW probe will saturate the SOA to some extent [11]. To avoid saturation the probe power needs to be low. Probe recovery can then be smeared by the electronic noise, specially when using a wideband photoreceiver. Pulsed probe signals also allow measuring the recovery time due to spontaneous emission, Auger effect and amplified spontaneous emission (ASE) [12]. Hence, our method adopts the pulsed probe.
Measurements with a pulsed probe signal using two mode-locked lasers (MLLs) at different wavelengths were reported in [13]. This requires tunable pump and probe optical pulses with short duration. Frequency dividers are also required. Moreover, the timing jitter and synchronization between the pump and probe pulses are delicate [4]. In [6] a spectrogram technique was used with a mode locked laser for the pump and a CW laser followed by an electro-absorption modulator for the probe. Note that the measured gain recovery time is in this case a function of the spectral separation between the two lasers [14]. This could provide insight to gain recovery during wavelength conversion experiments. It also allows characterization of the recovery at the pump wavelength. Our method uses a single mode locked laser, greatly reducing complexity and can give recovery time at a arbitrary pump wavelength.
In [13, 15, 16] the pump-probe technique is used to measure the gain of the probe pulse as a function of the wavelength difference and the time delay between the pump and probe pulses. The pump and probe wavelengths are necessarily distinct so they can be separated via proper filtering. Since different wavelengths have different gain and saturation, this will result in recovery times depending on wavelength separation.
Results on wavelength dependency of SOA gain recovery have been contradictory. In [17], although using pulsed signals, no change was observed in the recovery rate while varying the probe wavelength and keeping the pump wavelength fixed. In contrast, [16, 14, 15, 5] observe wavelength dependency; however, tunable CW probe signals were used at distinct wavelengths from the pump which was placed at the shorter wavelengths than the peak gain wavelength. In such a configuration, moving the probe toward the peak gain increases the saturation. This may be the reason why they observe decreasing recovery time, in contradiction with results we present here. Clearly pump-probe techniques on separate wavelengths give ambiguous results for SOA gain recovery dependence on wavelength, possibly due to the choice of the pump wavelength relative to that of the probe. In order to investigate the wavelength dependency, we chose an experimental approach similar to [7]. Since we used an all-fiber experimental setup we could separate counter propagating pump and probe signals using a circulator even though they were at the same polarization and wavelength. This approach has three advantages:
Fig. 1. Schematic diagram of the experimental setup. ODL: Optical Delay Line, MLL: Mode-locked Laser, PD: Photodiode, SOA: Semiconductor Optical Amplifier, VOA: Variable Optical Attenuator, PC: Polarization Controller, BPF: Bandpass Filter.
• It uses the common pump-probe strategy with a strong pulsed pump signal depleting the amplifier, followed by a low power pulsed signal that probes the gain recovery from its saturated value to its small signal value. A single femtosecond MLL generates two counter-propagating pulses that: 1) deplete carriers and thus the gain of the SOA (pump signal) and 2) probe the gain after a certain time delay (probe signal). Note that generating the pump and probe pulses with a single laser was reported previously using free space transmission, however, no wavelength dependency was explored [7].
• Since only one wavelength ever enters the SOA, this approach yields unambiguous results on wavelength dependency.
• It is a simple, efficient and robust measurement technique requiring less test equipment. Our setup requires only one low repetition rate MLL without any external modulators.
In order to explain the observed experimental results and investigate the recovery rate dependency for a wider wavelength range than permitted experimentally, we performed numerical simulations. Since the wavelength dependency of the gain dynamics using short pulses is investigated, it is important that the model include intra-band phenomena (spectral hole burning (SBH) and then carrier heating (CH)) as they contribute to the gain dynamics, as well as saturation effects that influence the stimulated carrier recovery [18]. Models used in [14, 15, 16] neglected such contributions. The model used by [8] took into account ultrafast phenomena, however saturation effects were not included. Finally, in [17], authors assumed an impulse response function consisting of the sum of exponential decays. They choose the decay rates so to fit experimental data. Although good for fitting single wavelength results, this rather empirical model is not suited to explore wavelength dependency. We use a model developed in [18], and shown to have good agreement with the experimental results in [3].
The remainder of the paper is organized as follows. First, the experimental setup is detailed. Then the experimental results are presented and discussed in section 3. Being limited by the tunability of the mode-lock laser, we simulate the gain dynamics for a wider range and present simulation results in section 4. Finally, the main findings of this work are summarized and conclusions are drawn.
2. Single color pump-probe setup
Femtosecond pulses, generated by a single tunable mode-locked laser (Pritel) with a repetition rate of 20 MHz, are used to probe the gain recovery of a bulk SOA. The tuneable range of the laser is from 1530 nm up to 1560 nm. Thus, the experimental results were limited to this wavelength range. To ensure perfect timing and exact wavelength match between probe and pump, a pulse emitted by the MLL is split by a 3 dB coupler. The pump pulse, traveling counter-clockwise in Fig. 1, passes through an optical circulator then through a polarization controller (PC) and enters the SOA under test. The clockwise-traveling probe pulse exits the 3 dB coupler and passes through an optical delay line (ODL), a variable optical attenuator (VOA) and a PC. The clockwise probe pulse then enters the device under test, an Optospeed SOA model 1550 MRI X1500, a bulk InP/InGaAsP amplifier with a peak gain wavelength at 1560 nm when biased at 500 mA. After passing through the SOA, the probe pulse enters the circulator at port 2, exits at port 3, and then enters an optical tunable bandpass filter (BPF); the BPF is centered at the maximum laser wavelength to reduce the amplified spontaneous emission (ASE) generated by the SOA. The spectrum of the laser inside the loop was measured using an ANDO optical spectrum analyzer with a resolution of 0:01 nm. Based on the measured spectrum, the pump and probe pulse widths were estimated to be 2 ps (due to dispersion in the fiber). The temporal resolution of the ODL is 3:3 ps.
Although the spectrum of the pulsed laser is larger than the 3 dB bandwidth of the BPF (1:25 nm), the frequency content of the received signal is ultimately limited by the electrical bandwidth of the photodetector (PD) rather than by the optical BPF. The PD used is an Agilent 86116A with a 3 dB bandwidth of 50 GHz. Using the ODL, we can vary the relative delay between the probe and pump pulses. At each temporal step, the BPF is re-centered to maximize the peak voltage of the electrical output pulse. The recovery curve is then built point by point for each pump-probe delay value. Hence, experimental results will not depend on the impulse response of the electronic circuitry. The temporal resolution is rather fixed by the minimal pump-probe time delay. Note that the SOA induced chirp will not affect the measured recovery since the BPF is readjusted at each point. The probe polarization is set to maximize probe pulse gain when the pump is not present at the amplifier (large delay between the pulses). The pump polarization is adjusted to minimize the gain of the probe signal when both signals are present in the SOA. Thus, both probe and pump signals are aligned on the maximum SOA gain polarization. We set mean probe power to -32 dBm and mean pump power to -13 dBm.
The time domain interpretation of our experiment is the following: the pump pulse has energy of approximately 1:7 pJ (assuming a Gaussian pulse shape) and completely saturates the SOA as it passes through it and does not observe any significant gain. The counter-propagating probe pulse has a much smaller energy than the pump, around 20:5 fJ, and is amplified as it passes through the SOA. The gain the probe observes depends both on the time of its passage (relative to that of the pump pulse) and its power. As the pulse has a FWHM (full width half maximum) of roughly 2 ps, it can sample the gain recovery with a high resolution in the time domain, limited by the precision of the delay line used (3:3 ps).
3. Experimental results
The gain recovery behavior of the SOA is sampled at five wavelengths in the tunable range of the MLL; detailed results are provided for 1530, 1542 and 1555 nm. The amplifier injection current is set at 500 mA. We sweep the time delay between the arrival of the pump and the probe signal at the SOA, with negative relative delay indicating the probe arriving before the pump. At the receiver, the gain of the probe signal is measured for the given relative time delay. As gain typically varies from wavelength to wavelength, we plot for each wavelength examined the normalized gain defined by the following
At each wavelength, GSAT is the saturated gain, GSS is the small signal gain. These gain values are inferred from the measured photodetected voltages as indicated in (1) and explained in the following. The peak voltage of the probe pulse is recorded for each relative delay. The minimum peak voltage,Vmin, and the maximum peak voltage,Vmax, determine the saturated gain and small signal gain, respectively, for that wavelength. The gain recovery time (τ), defined as τ≜=t(G̃=90%)-t(G̃=10%) is then computed from our normalized gain curves.
Fig. 2. (a) Measured change in the normalized probe gain versus pump-probe delay for different wavelengths, GSS is the small signal gain, while GSAT is the saturated gain; time resolution is 3:3 ps; (b) measured gain recovery time as a function of wavelength (squares) and SOA fiber-to-fiber gain spectrum (circles), continuous curves are a fit of the experimental points. Bias current is 500 mA and average pump power -13 dBm.
Figure 2(a) shows probe normalized gain versus relative pump-probe delay at 1530, 1542 and 1555 nm. Note, that this experimental technique yields not only the time constant τ, but also the complete gain recovery dynamics. These curves exhibit the typical time evolution of semiconductor amplifier gain: fast depletion (caused by the pump’s arrival when the probe is already at the SOA), followed by fast (first few ps) and slower recoveries (caused by the probe arriving after the pump has depleted the carriers) [7]. As can be seen in this figure, we did not detect any significant wavelength dependence in the fast recovery, within the 3:3 ps resolution of our measurements, as is also reported by others [4]. In [8], et al., however, a variation of this fast recovery with the wavelength was observed. Our work here focuses on the slow component of the recovery for wavelengths above transparency. Unlike the initial fast recovery, the slow recovery due to injection, radiative and non-radiative recombination is clearly wavelength dependent. In Fig. 2(b), the solid line shows the gain recovery time, τ, as a function of wavelength. Note that the solid line represents a spline fit to the experimental points showed on the same figure. The fiber-to-fiber gain spectrum of our SOA is the dashed line in Fig. 2(b), with the scale given to the right. We see that the gain recovery time as a function of wavelength has a similar shape as the gain spectrum. Results show a variation of the gain recovery constant ranging from 193 to 230 ps. This is because recovering from a saturated value (which varies slightly with wavelength [19]) to a lower steady state value is faster than recovering to a higher steady state value. This suggests that the gain recovery dependency on wavelength is determined by both saturation and gain for different wavelengths. Although the carriers are replenished more quickly near the bandgap, the steady state gain is also higher [19, 4], resulting in a net increase of the gain recovery. In order to assess the validity of the technique used, we also measured recoveries for different bias currents and saturation levels.
Fig. 3. Measured change in normalized probe gain versus pump-probe delay at 1530 nm for (a) bias current 500 mA and average pump power Pavg=-13 dBm (squares), I=410 mA and Pavg=-13 dBm (circles) and I=410 mA and Pavg=-8 dBm (triangles); (b) simulation fit at I=410 mA and Pavg=-13 dBm using two exponential impulse response. Resolution is 3:3 ps.
Figure 3(a) shows, as reported in several works (Ex [3, 11]), that higher bias as well as deeper saturation results in faster recovery. Furthermore, Fig. 3(b) shows a good fit of the experimental transmission at 410 mA using the impulse response function consisting of two exponential decays [17].
4. Modeling
We use the SOA model reported in [21, 18, 20], shown to have good agreement with pumpprobe experimental results in [3]. This model extends the definition of the integrated modal gain, introduced in [22], to take into account the ultrafast contributions. Even though the focus of our work is on the long-lived recovery, the ultrafast contributions are left for the sake of completeness. Note that this model has some simplifications when compared to more complex ones. It does not take into account the carrier distribution along the propagation direction since the material gain is integrated. Hence, no difference is made between co-propagating and counter-propagating cases. This results in errors in the time scale of the same order as the SOA transit time. For the SOA we used, the simulations error bar is estimated around 5 ps. This blurs the ultrafast simulated recovery, but not the long gain response. In spite of these simplifications the model remains accurate enough for the long gain recovery [1, 20]. Accuracy could further be increased by cascading few sections. Note that ASE has been neglected during the simulations hereafter. ASE could be added proceeding as in [1, 20]. The material gain can then be written as a sum of three contributions: carrier density pulsation (CDP), spectral hole burning (SHB) and carrier heating (CH). The integrated modal gain is
where Γ is the mode confinement factor, L is the length of the gain medium, hi, i ∊ CDP;SHB;CH, are the contribution of each process to the total integrated gain [18]. The time behavior of each contribution to the total integrated modal gain is governed by an ordinary differential equation (ODE) as follows [18]
Fig. 4. SOA gain as a function of the input coupled power for several wavelengths. Bias current is 500 mA.
where Pin(t) is the input power, τCDP, τSHB and τCH are the carrier lifetime, carrier-carrier scattering time and temperature relaxation time respectively. The nonlinear compression factors due to spectral hole burning and carrier heating are eSHB and εCH, respectively. Note that the wavelength dependency of the gain recovery is introduced through the saturation power Psat (λ) as well as the small-signal modal gain ho(λ)=ln(Go(λ)) in (3). The total gain is
5. Simulation results
Numerical simulations based on the model detailed in section 4 are used to calculate the recovery time for a range of wavelengths wider than we could achieve experimentally, in particular, wavelengths longer than the peak gain. First, we measure the amplifier gain as a function of the input power for several wavelengths from 1540 nm up to 1580 nm. This allows us to set numerical values for ho(λ) and Psat (λ). Results are presented in Fig. 4. We can see in this figure that the steady-state gain drops quickly for the longer wavelengths. However the 3 dB output saturation power is larger for longer wavelengths. This is due to the gain peak shift due to the band-filling effect [19].
Table 1. Values of model parameters used in the calculation of the wavelength dependency of the gain recovery time.
Having experimentally estimated Psat (λ) and ho(λ), we run numerical simulations as follows: A 2 ps, 1:7 pJ gaussian pulse is injected into the SOA, and the time-response of the gain is numerically observed, from which the gain recovery time t is extracted in the same way as in section 3. First, the model parameters were set in order to fit the effective recovery time τ for only the peak gain (1560 nm). Hence, for the following simulations, we use numerical values of the different parameters provided in [20], Table I. With these parameters fixed, we calculate the probe gain for each wavelength. The time-varying solution of the coupled differential equations (3)–(5) is found by using the Runge-Kutta method of the 4th order. Steady-state solutions are used as an initial condition for the subsequent time evolution. The same normalization as in (1) is used to extract τ for several wavelengths. Figure 5(a) depicts the contribution of each mechanism to total gain recovery at 1560 nm. These single wavelength results are in accordance with what has already been reported in [2, 8, 18, 21]. Figure 5(b) shows the simulated gain recovery versus pump-probe delay time for the same wavelengths as in Fig. 2(a). The calculated results are seen to agree qualitatively with the measurements: the long-lived recovery is slower for wavelengths closer to the gain peak.
Fig. 5. (a) Simulation of the contributions of CH, SHB and CDP to the total gain recovery at 1560 nm. (b) Calculated normalized probe gain versus delay for various wavelengths.
Fig. 6. Gain recovery time vs. wavelength: measured (circles); solid curve represents simulation results. Bias current is 500 mA and average pump power -13 dBm.
Finally, Fig. 6 shows the simulation results of the gain recovery time for the same conditions as in the experiment, but as a function of a wider range of wavelengths. Optical filter shape and photodiode impulse response are not included in the simulations since we numerically have access to the amplifier gain dynamics. Hence, some discrepancies can be seen between simulations and experiment; however this will not affect the trend of the wavelength dependency of the recovery time. The solid line on this figure represents the simulation results of the recovery time while the dashed line is a fit of the experimental SOA gain. This Fig. also shows the previously obtained experimental points. From the simulation solid curve, we observe a variation of the gain recovery constant ranging from 190 to 230 ps. As observed in the experiment, recovery from GSAT toward higher Gss necessitates longer time. This explains the higher recovery time observed at the peak gain.
6. Conclusion
In this paper, we measure the gain recovery dynamics of a SOA using a single mode-locked laser. The pump and probe pulses are at the same wavelength and polarization, and they are separated by a circulator. Although similar experimental setups were employed to study SOAs gain dynamics, no wavelength dependency was investigated using a single color pulsed pumpprobe experiment. This could be the reason for the varying (and sometimes conflicting) results in the literature on wavelength dependence of recovery dynamics. Our experimental results show significant variation of the slow relaxation recovery over the range 1530 nm to 1555 nm. Numerical simulations of the gain dynamics showed a increase of the recovery time for wavelengths around the gain peak. The wavelength dependency is introduced to the simulation via the saturation powers and the gain spectrum. These results need to be expanded to SOA devices other than bulk.
Acknowledgment
The authors would like to acknowledge Dr. José Rosas Fernández for several helpful dicussions.
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