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Abstract
The dynamics of second-quantized-state laser oscillation were investigated for semiconductor laser diodes with quantum-well structures inside. We found that the second-quantized state often dominates laser oscillation instead of the first-quantized state under intensive pulse excitation, while the DC bias superposition tends to suppress the second-quantized-state oscillation. The operation characteristics were studied in detail through experimental studies and numerical calculations.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Gain-switched semiconductor laser diodes (GS-LDs) have been extensively studied because they are useful for high-speed optical communication applications [1–5]. In recent years, GS-LD technologies have extended the fields of pulsed laser micromachining [6,7] and multiphoton biomedical imaging [8–14]. Aside from their successful applications, in view of the physical and engineering sciences, there are still many unknown features for the generation of short and high-peak-power optical pulses from GS-LDs [15–17]. In this study, we focus on second-quantized-state (SQS) laser oscillation in LDs with quantum-well (QW) structures inside under GS operations. Although SQS oscillations have been studied in recent years [18–22], technological application perspectives were unclear at the time, and it appeared that extensive studies were not continued. However, we found that SQS laser oscillations frequently occur under intensive GS operation of QW-LDs, and they can generate high-peak-power picosecond optical pulses.
In our initial stage study, we unintentionally observed SQS laser oscillation in InGaAs-GaAs single-quantum-well (SQW) LDs; the layer structure is shown in Fig. 1(a). These devices were designed and fabricated for generating 1030 nm optical pulses by GS operation and consisted of a strained QW separate-confinement-heterostructure (SCH) with a QW of approximately 8 nm thickness. We found that a 170µm-long ridge-waveguide structure Fabry-Perot LD (FP-LD) having a pair of cleaved facets indicated laser oscillation around the 960 nm wavelength region, instead of the 1030 nm wavelength regions, as shown in the optical spectrum of Fig. 1(b). This laser oscillation can be due to the SQS optical transition because the SQS can provide a higher laser gain reflecting the higher density of states in comparison with the first-quantized-state (FQS) transition under a strong excitation, and thus at a high carrier density. Therefore, to generate 1030 nm optical pulses, we changed thereafter the SQW layer to a double-quantum-well (DQW) or triple-quantum-well (TQW) layer, which structure can provide a sufficient FQS gain for laser oscillation at a desired wavelength [9,23].
Fig. 1. (a) SQW-LD layer structure for which we observed SQS laser oscillation under a GS operation, and (b) optical spectrum indicating the SQS laser oscillation.
However, we also found that SQS laser oscillation often occurs in strong GS operation experiments for commercially available LDs in wavelength regions shorter than 1030 nm. Currently, it is very common to fabricate LD devices incorporating QW structures to control the laser wavelength and to improve the operation properties such as lower threshold current and higher response speed. All of these provided LD devices are intended for use with FQS laser oscillation and do not assume SQS laser action. However, as illustrated below, once the SQS laser oscillation appears, it seems to dominate the main GS operation features instead of the FQS laser oscillation. In other words, SQS laser oscillation may indicate novel properties for various types of LD devices under GS operation. In this article, we describe some notable features of SQS oscillations in GS-LDs, which may result in attractive applications.
2. Experimental results
To carry out the experiment in a very similar circumstance for different LD devices, we employed the experimental setup schematically shown in Fig. 2, using the same instruments for electric excitation and measurements. The LDs used were mostly in butterfly module packages, and some were laboratory-made. The instruments used were an electric pulse generator (Avtech Electrosystems, model AVM-2-C), variable microwave attenuator (Hewlett-Packard, model 8494B and 8495B), optical spectrum analyzer (Ando Electric, model AQ6317), and high-speed sampling oscilloscope (Keysight Technologies, model DCA-X 86100D with 34 GHz optical sampling head 86105D). Several optical band-pass filters (BPFs) were used depending on the LD device, the necessary central wavelength, and bandwidth; BPFs were installed in a fiber-coupled cartridge module combined with an optical variable attenuator (Optoquest Co. 12H56 and PCC-A). Although not shown in Fig. 2, we also used an optical power meter (ADC Corp. model ADCMT 8230 with an 82323 B sensor head) to adjust the optical power for the necessary measurements. The average optical power coupled to the oscilloscope optical input port was limited to a few microwatts (depending on the optical pulse peak power) to avoid damage to the photodiode inside the oscilloscope. When the DC bias was superimposed, we used a bias tee (Picosecond Pulse Labs, model 5541A) and a DC electric power supply (ADC Corp. model ADCMT 8230).
Fig. 2. Experimental setup configuration for the operation and the measurement of GS-LD optical outputs.
It should be noted that, for taking the experimental data shown in the following, the optical power was regulated by an optical attenuator. Therefore, we cannot give the quantitative intensity value for the data shown in the figures. Instead, the average optical output power obtained from the LD device is shown in each figure.
One example is a 920 nm band distributed-feedback (DFB) LD (Eagleyard Photonics, model EYP-DFB-923-00100-1500-CMT02-000). Figure 3 indicates a set of optical spectra and oscilloscope temporal waveforms for this device under a strongly excited GS operation (electric pulse duration: 1.8 ns, pulse amplitude: 8.7 V). Figure 3(a) shows two different types of laser oscillation spectral components: one is the sharp-line DFB laser mode at 923 nm and the other is the broad spectral component that peaks at approximately 880 nm, corresponding to multimode Fabry-Perot (FP) laser oscillation. For the FP laser oscillation, we observed multimode structures corresponding to the 1.5mm-long LD. An InGaAs-AlGaAs strained QW layer is typically used for this wavelength LD. The optical spectrum in Fig. 3(a) shows that the DFB laser mode was due to the FQS transition, whereas the FP laser modes were attributed to the SQS transition. The temporal waveform in Fig. 3(b) consists of an initial sharp pulse and nanosecond pulse component. When the spectral component around 880 nm was extracted by a 10nm-bandwidth BPF (Edmund Optics, #65-668), only the initial sharp pulse component with a 50 ps duration appeared in the oscilloscope waveform, as shown in Fig. 3(c) and (d). Therefore, it is reasonable to consider that SQS laser oscillation contributes to the formation of the preceding picosecond optical pulses.
Fig. 3. Optical spectra (a), (c), and oscilloscope temporal waveforms (b), (d) for a gain-switched 920 nm DFB-LD without and with spectral filtering by a BPF. The DFB-LD was excited by electric pulses of 1.8 ns duration, and 8.7 V amplitude at 10 MHz. The average optical power was 1.1 mW without the BPF, while it was 20 µW after the BPF.
Next, we describe a series of experimental results that examined the spectral and temporal behaviors by changing the pulse excitation conditions for a 905 nm band FP-LD module (Wavespectrum Laser, Model WSLX-905-002m-4-H14-T-PD). Figure 4 shows the changes in the optical spectrum and corresponding oscilloscope temporal waveform for the LD. As shown in the optical spectra (upper figures), the shorter-wavelength SQS components (peaked at 880 nm) increased more intensively than the FQS components (peaked at 905 nm) by increasing the excitation pulse voltage. The wavelength difference between the FQS and SQS transitions observed is similar to that previously reported for InGaAs QW-LDs [19]. In the corresponding oscilloscope temporal waveforms (lower figures), by increasing the excitation pulse voltage, an initial sharp peak grew, followed by a gentle trailing decay pulse. In Fig. 5, we show the filtered spectral components and corresponding oscilloscope temporal waveforms for the highest pulse excitation case for this LD. In the experiment, we used a 10nm-bandwidth BPF (Edmund Optics, #65-669) to filter out the 880 nm wavelength components. When the SQS spectral components were extracted, we found that they formed an initial sharp optical pulse with a duration (FWHM) of approximately 30 ps. We also found that this optical pulse had 130 pJ pulse energy, and thus the pulse peak power was more than 0.4 W. On the other hand, the FQS components bear the sub-nanosecond pulse, which has a peak power several times lower than the initial sharp pulse.
Fig. 4. Changes in the optical spectrum (upper figures) and the corresponding oscilloscope temporal waveforms (lower figures) for a 905 nm FP-LD with varying the excitation electric pulse amplitude (no DC bias). The electric pulse duration was 0.83 ns, and the repetition rate was 10 MHz. The electric pulse amplitude and the average optical output power was 2.7 V, 2 µW for (a), (b), 4.3 V, 96 µW for (c), (d), 4.9 V, 130 µW for (e), (f), and 5.5 V, 170 µW for (g), (h).
Fig. 5. Optical spectra and oscilloscope traces for the 905 nm FP-LD when the device was excited by electric pulses of 0.83 ns, and 6.5 V amplitude at 10 MHz repetition rate (no DC bias). An optical spectrum without any BPFs is shown in (a), and the corresponding oscilloscope waveform is shown in (b). The average optical output power for (a) and (b) was 260 µW. (c) and (d) indicate the optical spectrum extracted by a 880 nm BPF (10nm-bandwidth) and the corresponding oscilloscope waveform; for these the average optical output power was 130 µW, which is half of the entire optical output power. (e) and (f) represent the optical spectrum extracted by a 905 nm BPF (10nm-bandwidth) and the corresponding oscilloscope waveform.
Based on the measurement of the laser oscillation mode spacing, the LD device length was estimated to be 330 µm. We found that a periodic modulation structure always appears in the FQS oscillation modes, whereas we did not observe a clear periodic structure for the SQS oscillation modes. The origin of this phenomenon is currently unclear.
Because we need a rather high electric pulse voltage to observe a clear SQS laser oscillation, we expected to decrease this voltage by superposing a DC electric bias, which has been widely used for GS-LD in the past years. However, the SQS laser oscillation feature was weakened by increasing the DC current, in contrast to expectations. Although the average optical output power is nearly the same as in Fig. 5, the SQS laser oscillation completely disappears for this operation condition, as shown in Fig. 6(a), and a conventional GS-LD relaxation oscillation feature is observed in the oscilloscope waveform. This result is quite unexpected, and we have tried to understand mechanisms for this with the aid of numerical calculation analyses described in the next chapter.
Fig. 6. An optical spectrum and an oscilloscope trace for the 905 nm FP-LD when the device is excited by electric pulses of 0.83 ns, and 5.0 V amplitude at 10 MHz repetition rate with the superposition of 10 mA DC current. The average optical output power was 250 µW for this condition.
It should be noted that the DC superposition commonly results in a weakening of the SQS laser oscillation for all the LD devices we examined.
3. Numerical calculation analyses
To understand the observed operational characteristics, we attempted numerical calculation analyses using a set of two-mode rate equations. The rate equations used are as follows:
Equations (1) and (2) represent the excited carrier density N and photon density Si for laser mode i, respectively. These densities are uniformly averaged within the laser oscillation mode volume. The parameters in the above equations are, P: pumping rate (excited carrier generation rate), N: total excited carrier density, N0i: transparent carrier density for laser mode i (i = 1, 2), Si: photon density for laser mode i, Ri: stimulated emission coefficient for laser mode i, γN: relaxation rate of excited carriers (inverse of the carrier lifetime), γS: photon decay rate (inverse of the cavity photon lifetime), C: coupling factor of spontaneous emission for a laser oscillation mode.
It should be noted that we have simplified the model and the equations as much as possible [24], adopting these for a two-mode semiconductor laser to understand some essential points for the features observed in the experiments. In this simplified model, the two different quantized states are not explicitly described by different energy notations. Instead, SQS is characterized by a larger transparent carrier density and a higher differential gain compared to FQS. Furthermore, a set of SQS (or FQS) laser oscillation modes was represented by a single laser oscillation mode. Because the carrier density is distributed continuously in the energy states in a quantum well structure (not likely in a quantum dot structure), we did not separate the carrier density for the SQS and FQS modes. This implies that the single carrier density provides gains for both modes, with different transparent carrier densities and different differential gains.
Figure 7 shows a few representative calculation results for a pulse excitation GS-LD with and without a DC bias. In the calculation, the numerical values of the equation parameters are given as follows: γS = 1011/s (photon lifetime:10ps), γN = 109/s (carrier lifetime:1 ns), N01 = 1.1 × 1017/cm3, N02 = 1.2 × 1018/cm3, R1 = 0.7 × 10−7cm3/s, R2 = 1.42 × 10−7cm3/s, C = 10−4. For the pumping, 1 ns duration quasi-rectangular pulse excitation with 100 ps rise and fall time is applied and the pumping intensity is set to be 1.2 × 1028/(s⋅cm3), and 2.8 × 1027/(s⋅cm3) for pulse and DC, respectively. When an appropriate pulse excitation is employed without a DC bias, a sharp SQS pulse precedes and a lower-height FQS relaxation oscillation follows, as shown in Fig. 7(a) and (b). On the other hand, with a DC bias superposition, the SQS pulse is almost suppressed, and the FQS dominates the entire laser oscillation process, as indicated in Fig. 7(d). Note also that, in Fig. 7(d), the FQS laser pulse generation timing becomes earlier, and the pulse duration becomes broader. These results suggest that the SQS laser oscillation is apparent, owing to a higher gain, even with a higher transparent carrier density under a strong pulsed excitation, before the FQS laser oscillation becomes dominant. However, once the FQS laser action starts at a lower gain with a lower transparent carrier density, it expends the gain (carrier), and the SQS cannot reach a sufficient gain for laser oscillation. It appears that the present model and numerical calculation qualitatively explain the laser processes for the experimental results.
Fig. 7. Numerical calculation results with the rate equations given in Eqs. (1) and (2). Calculation parameters are given in the text. Excitation pulses shown in (a) and (c) respectively indicate without and with DC bias. (b) and (d) give temporal responses for carrier, SQS and FQS laser pulses. The pulse excitation peak intensity is 7.5 times of the threshold value for FQS laser oscillation by DC excitation.
4. Summary
In this study, we describe several novel features of SQS laser oscillations with strong-pulsed GS operations. One notable point is the generation of clean single optical pulses by the spectral extraction of the SQS laser oscillation components. SQS optical pulses can provide watt-level peak power due to a higher gain under strong excitation, and this feature is advantageous for the following pulse amplification by an optical amplifier intended for kilowatt peak power for applications in micromachining and multiphoton bioimaging. Although we have not tried to generate very short optical pulses below several picoseconds duration in the present study, this feature will be enabled by spectral selections incorporating DFB structures for SQS laser transitions, whose properties have so far only been shown in FQS laser transition DFB-LDs [9,16].
Another attractive aspect of SQS laser transition is that the optical pulse spectral resource is extended for applications, especially for multiphoton excitation purposes in biomedical imaging, in which many different kinds of fluorescent proteins are used. We also expect that SQS laser oscillation may provide nano-joule-level sub-nanosecond optical pulses in visible LDs, and these properties are beneficial for stimulated-emission-depletion (STED) optical pulses that enable super-resolution microscopy of bio-specimens [12,13]. We expect that some of the features described above can be demonstrated in the next few years.
Funding
Japan Agency for Medical Research and Development (AMED) “Brain Mapping by Integrated Neurotechnologies for Disease Studies (Brain/MIND)” (JP22dm0207078); Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research(S) (KAKENHI), (JP20H05669).
Acknowledgments
The author is grateful to H. Yamada, and T. Nemoto for their fruitful discussions, K. Sato, A. Shibata, K. Misaitsu, and Y. Takada for their technical assistances.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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