1. Introduction

One of the most important applications of semiconductor laser diodes (LDs) is reading and recording data in optical disks. The increasing requirements for higher density optical storage have promoted the shortening of wavelengths from 780 nm for AlGaAs LDs for CDs to 650 nm for AlGaInP LDs for DVDs, and then to 405 nm for InGaN LDs for Blu-ray discs. The next generation of 3D optical storage [1–3] is expected to have much higher density and capacity. However, its introduction necessarily needs optical-pulse light sources with short pulse widths for reading and recording [2–4]. Therefore, gain-switched short wavelength semiconductor lasers [5, 6] might be possible candidates because of three advantages of being simple, low cost, and compactable. Consequently, studying the generation of short pulses from gain-switched GaN based semiconductor lasers is of great interest.

Although the high reflectivity of distributed-Bragg reflectors (DBRs) may dramatically increase the photon lifetime of nitride-based blue VCSELs [6–8], the intrinsic short length of cavities can still produce short photon lifetimes that are very useful for generating short pulses if there are appropriate designs for cavities. In fact, we previously demonstrated optical pulses as short as 6.0 ps from a gain-switched InGaN VCSEL [6], indicating that nitride-based blue VCSELs are indeed very good prospects for generating short pulses. However, lasing only occurred in multi-modes, which made it very difficult to quantitatively and theoretically analyze it. Consequently, generation dynamics of the 6 ps pulses was not clarified. A quantitative study of gain-switching dynamics is crucial to understand or design nitride-based gain-switched VCSELs that generate short output pulses. For this purpose, single-mode gain-switched pulses that are convenient for physical analysis are on demand.

In this paper, we obtained single-mode gain-switched short pulses from an InGaN VCSEL under impulsive optical pumping. We studied the lasing characteristics of the single-mode pulses through detailed measurements of pulse widths and delay times as functions of pump power. Single-mode rate-equation calculations with a nonlinear-gain model were undertaken to quantitatively analyze and also predict gain-switching dynamics. Quantitative simulations indicated that subpicosecond pulses could be generated in nitride-based VCSELs through structural improvements of the devices.

2. Experimental setup

The sample used in this study was the same as that in previous studies [6, 7], which consisted of two (top and bottom) Ta₂O₅/SiO₂ distributed Bragg reflector (DBR) layers and an optical cavity with a length of 2.3 μm. The active region consisted of three sets of In_0.2Ga_0.8N asymmetric quantum wells (with thicknesses of 2.5, 3.0 and 3.5 nm) and 5-nm GaN spacer layers. There is a schematic of the experiment setup in Fig. 1. The sample was optically pumped with a 1-kHz pulse laser beam of 400 nm at 300 fs that was focused on the sample’s surface with a beam size of ~50 μm with an optical lens. The 400-nm laser beam was the second harmonic generation (SHG) of an 800-nm laser beam with a duration of 120 fs from a regenerative amplifier. The time-integrated emission spectra were measured with a spectrometer system with a liquid-nitrogen-cooled charge-coupled device (CCD). The time-resolved emission spectra were measured with a streak camera with a system resolution of 5.2 ps. Since the system resolution of the streak camera may not have been sufficient to measure pulse width, a system of supplementary up-conversion measurements with a time resolution of 0.12 ps (limited by the 800-nm gate pulse width) was used to measure the pulse width with elevated pump powers.

 

Fig. 1 Schematic of experimental setup for gain-switching dynamics of InGaN VCSELs. BS: Beam splitter, SF: Sum frequency, BBO: Beta-Ba₂BO₄ (Beta-Barium Borate) crystal, and PMT: Photonmultiplier tube.

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3. Experimental results and discussion

The time-integrated emission spectra with various pump powers are plotted in Fig. 2(a). Single-mode lasing at 444.5 nm started at 20.8 μW (average power and subsequently the following power) and continued the single mode even at elevated pump powers. Multiple-mode lasing was observed in a previous study with an excitation beam size of ~500 μm. The single mode lasing observed in the present study demonstrated that reducing the excitation beam size was indeed helpful to obtain single-mode lasing [9]. We know from the log plot of input-power vs. output-power in Fig. 2(b) that the spontaneous emission coupling factor of the VCSEL is ~3.0 × 10⁻², which is in good agreement with the previous results [7].

 

Fig. 2 (a) Time-integrated spectra of gain-switched VCSEL with various pump powers. (b) Plot of output power vs. input power of VCSEL. (c) Waveforms of gain-switched pulses with various pump powers. Dashed line plots simulation results for waveform with pump power of 200 μW.

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Figure 2(c) plots the time-resolved waveforms of the single-mode output pulses of the VCSEL with pump powers of 38, 52 and 200 μW. These results indicate that gain-switched pulses have a long pulse width of 18 ps and a long delay time of 48 ps with pump powers at around the threshold, while they have a short pulse width of 6.0 ps (full width at half maximum) and a delay time of 16 ps with a pump power of 200 μW. The spectral width of the time-integrated spectrum of the 6.0-ps short pulses is around 0.2 nm (resolution ~0.15 nm). The time-bandwidth product of the pulse is around 1.9, which is much larger than the Fourier-transform-limited value of 0.44 (Gaussian) or 0.31 (Sech²), indicating that the single-mode 6.0-ps pulses we obtained are strongly chirped. This was also in good agreement with the results obtained from previous Kerr-gate experiments [6].

The delay times and pulse widths of pulses with different pump powers are summarized in Fig. 3. It can be seen that the delay times and the pulse widths gradually decreased with increasing pump powers and then simultaneously stayed at certain values at pump powers over 100 μW. The shortest delay time was limited to 16 ps and the shortest pulse width was limited to 6.0 ps independently of the pump power. The power dependencies of the delay time and pulse width are similar to those in other gain-switched semiconductor lasers [10–13]. These typical features indicate that gain switching indeed occurred in the VCSEL.

 

Fig. 3 Delay times and pulse widths of gain-switched pulses with various pump powers. Dashed lines plot simulation results.

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The power dependencies of the delay time and pulse width of the gain-switched pulses were quantitatively simulated with a model of a single-mode-laser rate equation [10, 14] given below to clarify the gain-switching dynamics and factors in the pulse-width limitations of the VCSEL.

Differential gain g₀, gain compression factor ε, and saturated material gain g_s are the three main fitting parameters. Best agreement with the experimental results was obtained when a value for differential gain g₀ = 2.0 × 10⁻¹⁰ cm, a very small value for gain compression factor ε = 2.0 × 10⁻¹⁶ cm², and a high value for saturated material gain g_s = 4.9 × 10⁴ cm⁻¹ were used. The order of saturated material gain was in very good agreement with the theoretical calculations [15, 16], and was considerably larger than the values for (In)GaAs lasers [10], indicating that the material gain of nitrides is indeed very large. The large gain of the nitrides was considered to have resulted from the three bands in the valence band close to the band edge and the large reduced-effective mass of each valence band [16]. This reasonable value for the saturated gain of the nitrides we obtained and the good agreement between the experimental results and quantitative simulation demonstrated that the rate-equation model we used was indeed suitable to describe the gain-switching dynamics of InGaN VCSELs.

We discuss possible ways toward accomplishing even shorter pulses in what follows. According to Eq. (2), the shortest pulse width (PW) with strong excitations is approximately given by:

Since the 6.0-ps pulse width is ten times longer than the 0.6-ps photon lifetime of the VCSEL, the 6.0-ps pulse width is not limited by the photon lifetime but saturated modal gain. We also know from Eq. (4) that increasing saturated modal gain $g_s^{\mathrm{mod}al}$ by increasing the number of quantum wells or the confinement factor should be useful for generating even shorter pulses. If the number of quantum wells in the present InGaN VCSEL could be increased to 20, corresponding to an increase in modal gain to ~1500 cm⁻¹ according to the quantitative rate-equation simulations, the shortest pulse would be expected to be as short as ~0.9 ps, which is near the photon-lifetime limit. Therefore, reducing photon lifetime τ_p could help to obtain even shorter pulses. Note that while the photon lifetime decreases with decreasing cavity length, the product of ${\tau }_p{v}_g{g}_s^{\mathrm{mod}al}$does not depend on cavity length; therefore, the shortest pulse width repeatedly decreases with decreasing cavity length. The simulation indicated that if the cavity length could be decreased to 1.0 μm, the shortest pulse width could be ~400 fs. Therefore, we can obtain subpicosecond photon-lifetime-limited short pulses by decreasing the cavity length and increasing the number of quantum wells in VCSELs.

We should comment that the decay tail of the gain-switched pulses could not be simulated well while most of the experimental results were quantitatively simulated with the rate equations. We can see that the decay tail at the end of the experimentally obtained pulses is much longer than that in the simulation results by comparing the pulse shape in the experiment with that in the simulation (shown as a dashed curve in Fig. 2(c)) with a high pump power of 200 μW. The decay time of the pulse with a high pump power should theoretically be mainly limited by the photon lifetime in the cavity of the VCSEL. Although the exact origin of the long tail is still unknown, the long tail should also be suppressed or removed to obtain even shorter gain-switched pulses.

Finally, we examined the necessary output power of the InGaN VCSEL for some applications. A previous data-recording experimental results [4] have shown that data recording can be performed with a 405-nm 3-ps pulse laser with a maximum peak power of 100 W via amplification of a 3-W peak power from a mode-locked laser oscillator [17]. The maximum peak power of the pulses for present sample was 0.2 W. Assuming the beam size of the output pulses was similar to the excitation beam size of 50 μm in diameter, the peak power density was then estimated to be 10 kW/cm². To generate a peak power of 3 W for applications of data recording, we may increase the single-mode lasing area of the VCSEL to around 200 μm in diameter, or use a higher amplification.

7. Conclusion

In summary, a single-mode 6.0 ps blue pulse was generated by gain switching from an optically pumped InGaN VCSEL. Single-mode gain-switching dynamics in the VCSEL was quantitatively analyzed by both experimentally and theoretically investigating the pump-power dependencies of delay time and pulse width of gain-switched output pulses. The results from simulation demonstrated that subpicosecond short gain-switched pulses could be expected from nitride-based VCSELs by increasing the number of quantum wells and decreasing the cavity length. These results as well as the quantitative rate-equation model are expected to provide very significant reference values to future designs of samples and basic studies on nitride-based VCSELs.