Gain-switched pulses of InGaAs double-quantum-well lasers fabricated from identical epitaxial laser wafers were measured under both current injection and optical pumping conditions. The shortest output pulse widths were nearly identical (about 40 ps) both for current injection and optical pumping; this result attributed the dominant pulse-width limitation factor to the intrinsic gain properties of the lasers. We quantitatively compared the experimental results with theoretical calculations based on rate equations incorporating gain nonlinearities. Close consistency between the experimental data and the calculations was obtained only when we assumed a dynamically suppressed gain value deviated from the steady-state gain value supported by standard microscopic theories.
© 2013 OSA
Short optical pulses with high response speeds and large peak power are in demand in many fields such as high-speed optical communication, medical/biotechnology applications, and so on [1–3]. Because of their simplicity of fabrication and low manufacturing costs, gain-switched semiconductor laser diodes are considered very attractive for use in potential applications such as compact tunable optical pulse sources. Thus far, optical pulses with durations ranging from several picoseconds to one nanosecond have been observed experimentally from gain-switched semiconductor lasers [4–6]. However, the understanding of the limiting factors of the output pulse width has not been comprehensive, and quantitative predictions or simulations of short-pulse generation from gain-switched semiconductor lasers have not been attempted thus far.
The primary difficulty lies in the complicated intrinsic gain nonlinearities (deviations from a simple linear gain with a constant differential gain g0), which include gain compression  and steady-state gain saturation [8–10]. A gain compression factor ε was introduced to account for relaxation-oscillation damping in the device during gain switching  and fast dynamical gain suppression in the presence of intense light fields . The steady-state saturated gain (gs) stems from state filling in a finite density of states, which increase in strength in low-dimensional semiconductors . Prior to the present analysis of experimental data, we theoretically investigated gain-switching dynamics including the abovementioned gain-nonlinearity effects (ε and gs) . An additional difficulty originates from the uncontrollable parasitic capacitance or electrical driving bandwidth in laser diodes, which makes quantitative analysis very difficult. Such complexity could be resolved by performing additional optical-pumping experiments.
In this study, we performed optical pumping and current injection into Fabry–Perot-type ridge-waveguide InGaAs double-quantum-well (QW) lasers with identical structures to investigate the characteristics of gain-switched optical short pulses. Almost identical values of the shortest output pulse-width (about 40 ps) were obtained at high excitation intensity under conditions of both optical pumping and current injection. This result demonstrates that the 40-ps pulse width was not limited by the electrical driving bandwidth of the device. The pulse width of 40 ps is considerably longer than the lifetime of photons in the cavity (cavity lifetime), and it is most probably limited by the intrinsic gain properties and photon-carrier dynamics occurring during gain switching. Introducing a nonlinear-gain model including the parameters ε and gs, we performed quantitative rate-equation simulations of the experimental results. We found that the experimental results and quantitative rate-equation simulations disagreed for any choice of ε when we used g0 and gs as determined by steady-state gain curves supported by standard microscopic gain theories [13–15]; however, the results and simulations agreed well when we assumed a considerably smaller value of gs. This indicates that an intrinsic dynamical gain suppression effect existed in addition to the gain compression (ε), which limited the gain-switched pulse width.
2. Experimental setup
Two devices fabricated from the same wafer grown on a GaAs substrate by molecular beam epitaxy were used for current injection and optical pumping. The devices were fabricated into ridge-waveguide lasers with a ridge width (w) of 2.5 μm and a cavity length (L) of 500 μm. The sample structure is shown in Fig. 1(a) . The active layer that consists of two 5.5-nm InGaAs QWs is sandwiched between two 1.4-μm AlGaAs cladding layers. For optical pumping, a Ti-sapphire pulse laser with 730-nm wavelength (photon energy hν = 1.7 eV), 2-ps duration, and 80-MHz repetition was used. The schematic of the optical pumping method is shown in Fig. 1(b). A laser beam was uniformly focused on the ridge via a cylindrical lens. The optical spectra of the output pulses from the InGaAs double-QW laser were measured using a monochromator with a liquid-nitrogen-cooled charge-coupled-device (CCD) camera, and the waveforms were measured using a high-speed oscilloscope (50 GHz) with a high-speed photodetector (40 GHz). The schematic of the current injection method is shown in Fig. 1(c). Electrical pulses with amplitude of 4.0 V, duration of 0.6 ns, and a repetition frequency of 100 MHz generated by an electrical pulsar were applied to the device with a bias direct current (DC). The working temperature of the laser diode (LD) was maintained at 25 °C by means of a thermoelectric cooler (TEC). The waveforms of the output pulse were characterized by an oscilloscope (28 GHz) with a high-speed photodiode (25 GHz), and the spectra were measured by an optical spectrum analyzer (OSA).
3. Experimental results and discussion
Figure 2(a) shows the spectra and the corresponding waveforms of the optical pulses from the current injection device for two different bias currents. Although the cavity lifetime of this device is around 3.7 ps, it can be observed that the pulse width is significantly limited at around 40 ps, independent of the excitation intensity.
Figure 2(b) shows the obtained pumping-power-dependent pulse-lasing spectra (left panel) and the corresponding waveforms (right panel) in the pulsed optical pumping experiment. The waveform data show that the pulse width decreased from 70 to 40 ps with increasing pumping power, and subsequently, it remained unchanged at around 40 ps (The temporal resolution of the detection system is around 13 ps). When the pulse width reached a value of 40 ps, the delay time also did not decrease anymore.
The 40-ps pulse width obtained for both optical pumping and current injection indicated that the pulse width was not limited by the electrical bandwidth or the parasitic capacitance of the devices, but by the intrinsic gain properties and photon-carrier dynamics occurring during gain switching. When compared with the cavity lifetime, the lengthy duration of these pulse widths indicates that strong gain nonlinearity occurred during gain switching in these samples.
The pulse-lasing spectra in Fig. 2(b) show that the lasing modes shift to the low-energy region, and the lasing spectra exhibit broadening with increasing pumping power. This phenomenon could be due to the band-gap renormalization effect and carrier thermalization effects caused by the optically generated high-density carriers. Figure 2(b) also shows that all the multi-mode lasing spectra have envelopes of an approximately Gaussian shape with a similar width, and that the wavelength separation between the modes is far smaller than it. There seems to be no mode competition, selection or coupling. These features allow our single-mode rate-equation analysis shown below for the present lasers operated in multiple modes. It should be commented that the pulse waveforms in Fig. 2(b) have a tail longer than the cavity photon lifetime after the dominant part of the output pulses. We suspect that the tail is caused by intra-band relaxation dynamics inherent to electron and hole bands in semiconductor materials. Such an intra-band relaxation effect will be neglected in the two-level rate-equation analysis shown below to explain the dominant part of the output pulses.
Figure 3(a) shows the plots of the relative delay time (squares), rise time (triangles), and pulse width (circles) obtained from the experimental data shown in Fig. 2(b). The solid curve in Fig. 3(b) shows the experimental data of the output power as a function of the input power.
The dashed curves in Figs. 3(a) and 3(b) show the quantitative simulation results. The simulation was performed with two-dimensional (2D) rate equations obtained using a nonlinear-gain model [11, 12]:7]. The terms g0 and gs in Eq. (3) denote the differential gain and the saturated gain , respectively. The dashed curve in Fig. 4(a) shows the gain curve calculated for the present InGaAs-double-QW laser using standard microscopic calculations based on the k•p effective-mass theory [13–15], which includes mixing of heavy-hole and light-hole bands via the k•p effective-mass theory and Coulomb effects via two-band semiconductor Bloch equations with static screening under a single-plasmon-pole approximation. The calculated gain curve is fitted well by the solid red gain curve given by Eq. (3) with g0 = 1.0 × 10−9 cm and gs = 3700 cm−1. It is known that the gain curves calculated using standard microscopic calculations agree well with the experimental carrier-density-dependent gain curves for steady-state operation of the QW and double-heterostructure lasers . The solid green straight line in Fig. 4(a) shows the curve for the linear gain model g = g0 × (n2D – n02D), or infinitely large values of gs; this model is often used in conventional qualitative simulations of gain-switched lasers.
The other parameters of the lasers in our study include the transparent carrier density n02D = 0.7 × 1012 cm−2, carrier lifetime τr = 1.0 ns, photon lifetime τp = 3.66 ps, quantum well number m = 2, cavity length L = 0.05 cm, ridge width w = 2.5 × 10−4 cm, confinement factor Г = 0.049, group velocity vg = 8.57 × 10−3 cm/ps, spontaneous emission coupling factor β = 0.5 × 10−4, and power absorption rate η = 0.25. The differential gain is fixed as g0 = 1.0 × 10−9 cm.
A close consistency was obtained between the experimental and simulation results, (Figs. 3(a) and 3(b)) for a very low saturated gain of gs = 1100 cm−1 and a weak gain compression factor of ε = 0.16 × 10−12 cm−2. In contrast, when we assumed the steady-state values of g0 = 1.0 × 10−9 cm and gs = 3700 cm−1 as supported by the standard microscopic theories [13–15], such a consistency was not obtained for any choice of ε. This implied that an additional dynamical gain-suppression effect reducing gs from 3700 cm−1 to 1100 cm−1 occurred during gain switching, which could not be represented by the gain compression factor ε. We believe that this additional effect is the main reason for the increased pulse widths. Since during gain switching, carriers with high densities are excited in ultra-short time intervals, the strong carrier–carrier scattering and carrier–phonon interactions in the non-equilibrium system can possibly result in a very high transient carrier temperature, and carrier heating [18–20] could be a possible reason for the observed low saturated gain.
The necessity of the present rate-equation model should be remarked: It is important to note first that the gain compression is not effective while light intensity (or photon density) is low. The gain compression effects appear only when emission intensity is strong enough. This is true not only in the present model using the phenomenological parameter ε, but also in other gain compression models . In the present experiments, delay times and rise times of gain switched pulses after short impulsive excitation must at least be explained with gain physics without gain compression effects, because light intensity is still weak in such an early stage of gain switching. To account for the small gain values consistent with the measured delay times and rise times, it was necessary to introduce at least one parameter like gs in Eq. (3). We emphasize here again that the small gain values under low light intensities can never be explained by light-intensity-dependent gain compression effects, but by the carrier-dependent gain saturation effects caused for example by the state filling and the many-body carrier-carrier interactions [8, 12–17]. Therefore, satisfactory quantitative simulations of our present experiment results cannot be achieved without including a gain saturation effect or a parameter like gs.
Figure 4 (b) shows the calculated dependence of pulse width on the saturation gain gs. This shows that increase of the saturation gain from 1100 to 3700 cm−1 causes the pulse width significantly reduced from 40 ps to 10 ps. Therefore, enough attentions should be paid on the saturation gain in sample design for short pulse generation by gain switching, and in order to get much shorter pulses, it is of great importance to improve the saturation modal gain by, for example, optimizing device structure and increasing quantum well numbers.
In summary, 40-ps optical pulses that are considerably longer than photon lifetimes were obtained from gain-switched InGaAs QW lasers under both current injection and optical pumping conditions, which demonstrated that the output pulse widths were limited not by the bandwidth of the device but by the intrinsic gain properties occurring during gain switching. Further investigations indicated that the experimental results cannot be quantitatively explained by the general gain compression factor, while by introducing a saturated gain into the rate equation, good agreement of the quantitative simulation results with the experimental results was achieved. The simulation results revealed that although the saturated gain of the samples is high at steady-state, it becomes very low during gain switching, and the low value of the dynamically suppressed gain of the samples was demonstrated to be the most important limitation of the output pulse width during gain switching. An understanding of the dynamically suppressed gain is essential to understand or predict the dynamics of gain switching and the characteristics of gain-switched optical pulses.
This work was partly supported by KAKENHI grant no. 20104004 from MEXT, no. 23360135 from JSPS, and the Photon Frontier Network Program of MEXT in Japan.
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