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Picosecond-pulse-generation dynamics and pulse-width limiting factors via spectral filtering from intensely pulse-excited gain-switched 1.55-μm distributed-feedback laser diodes were studied. The spectral and temporal characteristics of the spectrally filtered pulses indicated that the short-wavelength component stems from the initial part of the gain-switched main pulse and has a nearly linear down-chirp of 5.2 ps/nm, whereas long-wavelength components include chirped pulse-lasing components and steady-state-lasing components. Rate-equation calculations with a model of linear change in refractive index with carrier density explained the major features of the experimental results. The analysis of the expected pulse widths with optimum spectral widths was also consistent with the experimental data.
©2013 Optical Society of America
1. Introduction
Gain switching is a very attractive method of generating rate-tunable or arbitrary-timing short pulses from simple and low-cost semiconductor laser diodes (LDs), and it has potential applications in, for example, optical communications [1,2], optical storage [3], multi-photon imaging [4], and time-resolved spectroscopy [5]. However, due to its operation principle, gain switching must include abrupt changes in carrier density and hence in refractive index in a cavity during pulse generation, and it is inevitably accompanied by strong frequency chirping [6–8] and additional pedestal or steady-state-lasing components [9]. As a result, typical gain-switched pulses significantly deviate from the Fourier-transform limit. Up to now, a lot of research has been performed using dispersion-compensation fibers [10,11], chirped fiber gratings [12,13], spectral filters [9, 14–18], etc., to generate Fourier-transform limited short optical pulses from gain-switched lasers. Herein, spectral filtering is indispensable for extracting high-speed short pulses with a simple pulse shape from a complicated gain-switched optical pulse. Very recently, short wavelength components were extracted using spectral filtering from a gain-switched 1.55-μm distributed feedback laser diode (DFB-LD) with intense nanosecond electric pulse excitations, nearly transform-limited short pulses with pulse widths below 5 ps were obtained [9]. Since the nanosecond electric pulse excitation is very general, this method is expected to significantly reduce the cost of short pulse generation, furthermore, with the help of Er-doped fiber amplifiers, periodically poled lithium niobate, and other powerful tools to increase the output-pulse power, such short pulses are highly useful for many real applications [4,5]. Therefore, getting a basic understanding of the short-pulse-generation mechanism and determining the limitations of spectrally filtered gain-switched pulses would be of great interest.
On the other hand, as mentioned above, the abrupt changes in carrier density and subsequent relaxation oscillation and steady-state-lasing during gain switching inevitably make the waveform and chirping of gain-switched pulses complicated, and it is difficult to analyze the whole pulse directly using a general method such as frequency-resolved optical gating (FROG), while as a simple and inexpensive method, spectral filtering in combination with an oscilloscope and autocorrelator has been proved to be useful in studying the chirp dynamics [18–21]. Although chirp measurement of gain-switched DFB-LD has been previously reported [21], investigation of the chirp dynamics at the condition of intense long-pulse excitation is still lacking.
In this paper, we studied the generation dynamics and pulse-width limiting factors of optical pulses via spectral filtering from an intensely excited gain-switched 1.55-μm DFB-LD experimentally and theoretically. In the experiment, we extracted a series of optical pulses at various wavelengths from the DFB-LD by using a tunable optical filter and measured the pulse widths and delay times of each pulse after spectral filtering. The results showed that short-wavelength component extended by the increased excitation amplitude stems from the initial part of the gain-switched main pulse and has a nearly linear down-chirp of 5.2 ps/nm, while long-wavelength components include chirped pulse-lasing components and steady-state-lasing components. Assuming a linear relationship between refractive index and carrier density during gain switching, these results were qualitatively explained by rate-equation simulations. An analysis of the expected pulse widths with optimum spectral widths revealed the reason for the 5.4-ps nearly Fourier-transform-limited short pulses extracted from the short wavelength side via spectral filtering, and this study can be used as a guideline to generate even shorter pulses.
2. Experimental setup
Figure 1 shows the experiment setup. The high-speed 1.55-μm InGaAsP multi-quantum-well DFB buried-heterostructure LD (NTT Electronics, NLK5C5EBKA, 18-GHz modulation bandwidth) was maintained at 25°C with a thermoelectric cooler (TEC). Electric pulses with durations from 0.3 to 0.6 ns were used to excite the DFB-LD. An erbium-doped-fiber amplifier (EDFA) was used to amplify the output power of the DFB-LD to a proper level for the measurements. Lasing spectra, pulse waveforms, and pulse widths were measured by an optical spectrum analyzer (OSA) (Advantest Q8384), a 40-GHz sampling oscilloscope (Agilent 86100C Infiniium DCA-J) with a 28-GHz optical detector, and a high-sensitivity autocorrelator with photon-counting detection, respectively. The experiment setup was the same as the one used in reference [9], except that the short pass filter was removed and only a tunable 1-nm bandwidth optical filter was used to perform the spectral filtering.
Fig. 1 Schematic diagram of the experiment setup of short pulse generation via spectral filtering from an electrically excited gain-switched 1.55-μm DFB laser diode.
3. Experimental results and discussion
Before the spectral filtering experiments, the excitation amplitude dependence of the spectral characteristics of the DFB-LD was investigated. We characterized the pulse-lasing spectra of the DFB-LD driven at various electric amplitudes (2.0, 2.5, 3.1, 4.0 and 5.0 V) with a long duration of 0.6 ns; the lasing threshold was around 1.8 V. The results are shown in Fig. 2(a) . We can see that each spectrum consists of a sharp peak on long wavelength side and a broad shoulder on short wavelength side. The shoulder significantly broadens with increasing electric amplitude applied to the DFB-LD, while the spectral height remains almost unchanged. It is already known that the sharp peak at long wavelengths is due to the quasi-steady-state lasing component, which occupies about 80% of the total pulse [9]. Indeed, by using a short pass filter to cut off the long quasi-steady-state lasing component and using a band-pass filter to extract short wavelength components, short pulses with pulse widths of 4.7 ps were obtained in our previous experiment which was similar to the current one [9]. The short wavelength side in the spectra seemed essential for the short pulse generation. In the following, in order to increase the ratio of the short wavelength components by reducing the quasi-steady-state lasing component, we reduced the electric pulse duration to 0.3 ns and investigated the lasing spectra of the DFB-LD driven at different electric amplitudes (3.5, 4.0 and 4.5 V) with a threshold of 2.7 V. The results are shown in Fig. 2(b), it can be seen that the spectral broadening with increasing electric amplitude at short wavelengths is similar to that of Fig. 2(a), but the sharp peak at long wavelengths is significantly reduced. Since reducing the quasi-steady-state lasing component is very helpful for measuring the chirp characteristics of the pulse components, we decided to use a 4.5-V electric amplitude with a 0.3-ns duration to excite the DFB-LD and use only the band-pass filter (BPF) for spectral filtering.
Fig. 2 Pulse lasing spectra of the 1.55-μm DFB laser diode driven at various electric amplitudes with pulse duration of (a) 0.6 ns and (b) 0.3 ns.
Figure 3(a) shows the lasing spectrum after the amplification of the EDFA without spectral filtering of the DFB-LD driven by 4.5-V amplitude 0.3-ns pulses. It can be seen that the shape of the spectrum after amplification is almost unchanged from the one (Fig. 2(b), 4.5 V) before amplification; this demonstrates the linear amplification of the EDFA. In the following, we performed spectral filtering of this spectrum. By gradually changing the central wavelengths of the band-pass filter from 1546.4 to 1550.4 nm, we got a series of pulses with different spectral shapes (Fig. 3(b)). Figure 3(b) also shows a linear plot of the spectrum after spectral filtering on the short wavelength side, where the spectral width is known to be 0.5 nm. The pulse width was measured from the autocorrelation trace (Fig. 3(c)) to be 5.4 ps, much shorter than the 11.0-ps total pulse width without spectral filtering. The time-bandwidth product of the pulse on the short wavelength side was 0.34, which is very close to the value of 0.32 for a sech2 shaped pulse. This means nearly Fourier-transform-limited short pulses were obtained on the short wavelength side. The oscilloscope waveforms of the pulses corresponding to each spectrum in Fig. 3(b) are shown in Fig. 3(d), together with the pulse widths measured from the autocorrelation traces of each pulse.
Fig. 3 (a) Pulse lasing spectrum without spectral filtering after the amplification by an EDFA from DFB-LD driven by 0.3-ns pulses with an amplitude at 4.5 V. (b) A series of pulse lasing spectra with different spectral shapes after spectral filtering. The top plot also shows a linear plot (dotted plot) of one of the lasing spectra on the short wavelength side after spectral filtering; the spectral width is 0.5 nm. (c) Autocorrelation traces of the total pulse without spectral filtering and the filtered pulse corresponding to the spectrum at the top of (b). From the sech2 fittings, the pulse widths are shown to be 11.0 and 5.4 ps, respectively. (d) waveforms of each pulses after spectral filtering corresponding to the lasing spectra in (c). The pulse widths measured from the autocorrelation traces are also shown. (e) Pulse widths and relative delay times of the pulses after spectral filtering plotted against the corresponding central pass wavelength of the band-pass filter.
Figure 3(e) plots the relative delay times (red triangles) of the oscilloscope waveforms and the pulse widths (blue squares) of each corresponding pulse. The pulse width was short and nearly constant at around 6 ps in the short wavelength region below 1547.5 nm, whereas it was long in the wavelength region from 1549 to 1550 nm. On the other hand, the delay time of the pulses on the short wavelength side was short (in other words, pulses on the short wavelength side were generated faster than the others), and a nearly linear increase in the relative delay time versus increased wavelength (a nearly linear down-chirp) was measured on the short wavelength side in the region from 1546.4 to 1549 nm. The magnitude (slope) of this down-chirp was found to be 5.2 ps/nm. On the other hand, up-chirping was measured in the longest wavelength region above 1549 nm. These results indicate that the short wavelength region below 1547.5 nm consists solely of the fast component generated at the beginning of the short main pulse during gain switching, whereas the long wavelength region above 1547.5 nm is a mixture of chirped pulse-lasing components and steady-state-lasing components with longer delay times and durations after the fast components.
To help us understand these experimental results, theoretical calculations were performed using rate-equation simulations with a linear relationship between the refractive-index shift and the carrier density [6, 8, 18]:
Here, the parameter N(t) denotes carrier density, S(t) denotes photon density, P(t) denotes the transient pumping intensity with a pulse duration of 0.3 ns, vg denotes group velocity, g0 denotes differential gain, Г denotes confinement factor, Nt denotes transparent carrier density, τr denotes carrier lifetime, τp denotes photon lifetime, βsp is the spontaneous emission coupling factor, Δf denotes the transient frequency shift, α denotes line enhancement factor, u(t) denotes optical pulse amplitude (electric field) including phase, the power spectrum can be obtained from the square of the Fourier-transform of u(t). A Gaussian function was used to simulate the spectral filtering.The simulation results are shown in Fig. 4 . Figure 4(a) shows the time evolutions of the transient frequency shift during pulse lasing at various excitation intensities. The corresponding time evolutions of the photon density were shown in Fig. 4(b). We can see that the transient frequency in Fig. 4(a) is enlarged and then falls rapidly during the first intense pulse generation, as noted by the sharp photon-density peak in Fig. 4(b). We then calculated the excitation-intensity-dependent lasing spectra shown in Fig. 5(a) , by applying the Fourier transform of the electric fields including the frequency shift in Fig. 4(a) for various excitation intensities. The results are very similar to the experiment results in Fig. 2, especially the characteristic spectral broadening on the short wavelength side with increasing excitation intensity. Using Gaussian spectral-filtering functions at various wavelengths, we also calculated spectrally filtered pulse waveforms, from which we evaluated the wavelength-dependent pulse widths and delay times, shown in Fig. 5(b). The simulated wavelength dependence of the pulse widths and delay times are close to the experimental results in Fig. 3(e): i.e., short pulses on the short wavelength side and long pulses on the long wavelength side with a rapid increase in pulse width in the middle wavelength region. The simulations also show that chirping increases (or the slope of the delay time decreases) with increasing pumping intensity.
Fig. 4 Simulated time evolutions of the excitation intensity dependent transient frequency shift (a) and the corresponding photon density (b).
Fig. 5 Simulated excitation intensity dependent spectra (a) and wavelength dependent pulse width and pulse delay time (b) calculated from rate equations with a linear chirp model.
These simulation results demonstrate that the experimental results are qualitatively explained by introducing refractive-index change with linear dependence on carrier density. Thus, the chirp dynamics is understood as follows: At the beginning of the short pulse generation by gain switching, lasing starts at the shortest wavelength because of the temporarily high carrier density. At the end, however, lasing occurs at the longer wavelengths because of the temporarily low carrier density. The longest delay region near 1549 nm reflects the steady-state-lasing component of the pulse, and the up-chirp with wavelengths above 1549 nm reflects a recovery process from the undershoot to the steady state in carrier density after the large initial short pulse.
Although the simulation results are in good qualitative agreement with the experimental results, they still show some deviations. For example, the simulation result in Fig. 5(b) shows that the pulse width is constant at around 5 ps on the short wavelength side, while the experiment results in Fig. 3(e) shows that there is a small slope of the pulse width in the wavelength region from 1547.5 to 1546.4 nm. This small slope may imply that there exist some additional (possibly nonlinear) mechanisms affecting pulse width in the short wavelength region during gain switching. Further study may avoid or utilize such mechanisms to generate even shorter pulses than obtained in our present and previous work.
Finally, we investigated the limitations of the pulse width. Figure 6 plots the estimated pulse widths as functions of spectral width for the case of 5.2 ps/nm chirping and for the case of the Fourier-transform limit without chirping. The pulse width for the chirped case (the solid curve) was calculated as the square root of the squared sum of the 5.2 ps/nm linear chirping shown by the dash-dotted line and the Fourier-transform-limited width shown by the dashed curve. The plot shows that Fourier-transform limit dominates the pulse width of the pulses with narrow spectral widths, and increasing the spectral width makes the Fourier-transform limited pulse width shorter, but the contribution of linear chirping larger. Thus, the minimum pulse width with the 5.2 ps/nm chirping occurs at the spectral width of 0.7 nm. The 5.4-ps short pulse on the short wavelength side obtained in the experiment has a spectral width of 0.5 nm, which is below, but close to the critical 0.7-nm spectral width, and therefore, it is almost the nearly Fourier-transform-limited shortest pulse.
Fig. 6 Plots of chirping-limited (dash-dot line) and Fourier-transform-limited (dashed curve) minimum pulse widths versus spectral width. The solid curve is a convolution of the chirp and the Fourier-transform limit.
The pulse spectrum and chirping depend on the excitation amplitude, as can be seen from the excitation intensity dependent slopes of the decreasing parts of the peaks in Fig. 4(a). Increasing the excitation amplitude should extend the short wavelength component, as shown in Fig. 2 and Fig. 5(a), which makes extraction of the short wavelength component easier by spectral filtering. It will also increase the chirping (decrease the slope of the dash-doted blue line in Fig. 6), and assist shortening of the output pulses following the present model until neglected nonlinear effects become important.
From Fig. 6, we can also expect that if the chirp can be completely compressed, the Fourier-transform limited pulse width could be shorter than 2 ps. In this case however, according to the rate equation [22], the saturation gain [22, 23] and the photon lifetime in cavity may limit the pulse width to 3 or 4 ps, and this should be another limitation of the pulse width. Therefore, semiconductor lasers with high saturation gain and shorter photon lifetime (for example, vertical-cavity surface-emitting lasers (VCSELs) [24]) are also very important in the generation of even shorter optical pulses. In addition, new single-mode laser structures (DFB-LDs or VCSELs) with larger separations between side modes may allow further extension of the short wavelength component under strong excitation and generation of even shorter pulses.
7. Conclusions
In summary, through an investigation of the spectral and temporal characteristics of the output pulses from a gain-switched single-mode 1.55-μm DFB-LD using spectral filtering, we characterized the wavelength chirping of the pulses and found that picosecond-short pulses were generated by a short wavelength component consisting solely of the component generated at the beginning of the short main pulse during gain switching. The long pulses, on the other hand, were generated in the long-wavelength region where the chirped components were mixed with steady-state-lasing components with longer durations. Moreover, a nearly linear chirp of 5.2 ps/nm was measured on the short wavelength side, and the major features of the experiment results were qualitatively simulated very well using rate equations with a model of the linear change in refractive index with carrier density. The analysis of the expected pulse widths with optimum spectral widths was consistent with the experimental data. These experimental and theoretical investigations of the chirp dynamics have revealed the mechanism of the short pulse generation via spectral filtering, which should be applicable not only to DFB-LDs but also other single-mode lasers such as vertical-cavity surface-emitting lasers. These results will be helpful in the design of short pulse generation schemes based on gain switching by spectral filtering with and without chirp compensation. Our present model analysis suggested that further increase of excitation amplitude should extend the short wavelength component with increased chirping and help generation of still shorter pulses by spectral filtering until neglected nonlinearity causes new limitations.
Acknowledgments
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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