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Abstract
The picosecond carrier dynamics observed in quantum cascade lasers (QCLs) poses a fundamental obstacle for the formation of intracavity pulses. On the other hand, the ultrafast gain response makes the QCL ideally suited for high frequency modulation of its pump current. In this work, we leverage this property and use short electrical excitations to generate 33 ps optical pulses with up to Watt level peak power. We ensure lasing on a single resonator mode via optical injection seeding. The resulting pulses are characterized in both time and frequency domains using an optical sampling method in combination with a spectrometer. We interpret the obtained results using laser rate equations. The results presented in this work open new pathways for the generation of highly tunable, high power mid-infrared pulses from a monolithic source.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
In recent years, a lot of effort has been put into the generation of short and ultrashort pulses from quantum cascade lasers (QCLs) [1,2]. These efforts were driven from both fundamental and application perspectives. From an application viewpoint, such sources are, for instance, useful for optical ranging [3], non-linear and time-resolved spectroscopy [4], coherent control [5], or free space optical communication [6,7]. For these applications, typical emission spectra of QCLs, ranging from the mid- to far-infrared, are particularly suited. First, it is in this frequency band where the highly transparent atmospheric windows are located and therefore allow for long distance free space signal propagation. Second, many light molecules exhibit their fundamental roto-vibrational resonances in this frequency range, which highlights its importance for spectroscopy and sensing applications.
On the other hand, the fundamental interest in generating QCL pulses is owed to the rich physics found in these devices, governed by ultrashort gain response times [8] and huge Kerr non-linearities [9]. These properties make it particularly challenging to implement conventional mode-locking schemes as often used in diode lasers [10–12]. However, it was found that QCLs can naturally enter a mode-locked state through the cascaded effect of four-wave mixing [13]. From that, ultrashort pulses can be generated externally via phase compensation [14]. Similarly, the subtle interplay between laser dispersion and Kerr non-linearity also allows the generation of QCL ultrashort pulses in the form of dissipative Kerr solitons [15,16]. Such solutions were previously mainly known from optically pumped passive microresonators [17].
While the abovementioned techniques provide the means to generate coherent ultrashort pulses, they usually require sophisticated alignment or precise tuning of laser parameters. At the same time, the obtained peak powers could so far not considerably exceed those of QCLs operated in continuous wave [18]. This raises the question of whether approaches based on direct modulation of the QCL bias current could yield comparable results, in particular for applications where the pulse-to-pulse coherence is of subordinate relevance. For this reason, we revisit earlier gain-switching experiments [19] using state-of-the-art QCLs optimized for high frequency modulation.
In this approach, short electrical pulses are used to bring the QCL above lasing threshold for a transient time window leading to the emission of optical pulses. Apart from the inherent simplicity of this approach and the high degree of tunability that comes with it, QCLs are uniquely suited for high frequency modulation given their picosecond carrier dynamics. For comparison, conventional interband diode lasers exhibit intrinsic carrier lifetimes of the order of a few nanoseconds. For most other laser systems, even larger relaxation time constants are observed [20].
2. METHODS
In this work, we use a step recovery diode (SRD) to produce short electrical pulses. The SRD is driven by the amplified (AMP) sinusoidal output of a radio-frequency synthesizer (SYN), as shown in Fig. 1. Before being applied to the QCL, the negative electrical pulses are superimposed with a constant current offset. The QCL used in this work is packaged for high frequency modulation and contacted with a coplanar microwave probe.
Fig. 1. Experimental setup. Short negative electrical pulses are generated in a step recovery diode (SRD), which is pumped by the amplified (AMP) output of an RF synthesizer (SYN). A bias tee is used to superimpose the electrical pulses with a constant bias current. The combined current is then applied to the radio-frequency optimized QCL using a coplanar probe. We use an FTIR and ASUPS for the spectral and temporal characterization of the emitted optical pulses, respectively. A single-mode QCL is used as a seed laser to initiate lasing on a single Fabry–Perot mode of the gain-switched laser.
Fig. 2. Electrical pulse and QCL frequency response. (a) The time-domain output of the SRD across a $50\;\Omega$ output is shown. We observe a peak amplitude of ${\sim}13\;{\rm V}$ and pulse duration of ${\sim}100\;{\rm ps}$. (b) In frequency space, the SRD generates a microwave frequency comb with a 3 dB bandwidth of ${\sim}3\;{\rm GHz}$ and mode spacing of 105 MHz. (c) Modulation response of the QCL used in this work as measured by ASUPS. We identify a 3 dB modulation bandwidth of ${\sim}7.5\;{\rm GHz}$.
The emitted optical pulses are then characterized in both time and frequency domains. In time domain, we employ asynchronous upconversion sampling (ASUPS) [14,21]. This non-linear optical sampling method employs near-infrared femtosecond sampling pulses and allows for a full intensity reconstruction of the emitted QCL field. We have previously evaluated the root-mean-square temporal resolution of this technique to be ${\sim}200\,{\rm fs}$ [21]. To measure the spectrum of the emitted QCL pulses, we use a Fourier-transform infrared spectrometer (FTIR) with a spectral resolution of $0.0125\;{{\rm cm}^{- 1}}$ (375 MHz).
In the configuration shown in Fig. 1, the driving frequency of the SRD determines the repetition rate of the emitted optical pulses and can be easily adjusted by the choice of electronic driver. The optical pulse repetition rate is therefore independent of the laser resonator setup, as opposed to mode-locked lasers where the repetition time is fully determined by the resonator round trip time. As each gain-switched pulse is newly generated from spontaneous emission, subsequent pulses are not expected to be mutually coherent.
Prior to the experiment, we characterized the electrical pulses emitted from the SRD across a $50\;\Omega$ load using a high bandwidth (18 GHz) sampling oscilloscope. The result is shown in Fig. 2(a). At the onset of each negative half cycle of the sinusoidal pump, the charge stored during the preceding positive half cycle is released in a short ${\sim}100\;{\rm ps} $ pulse with a peak amplitude of ${\sim}13\;{\rm V}$. Here, we used a pump frequency of 105 MHz.
The spectrum of the emitted electrical pulses, as measured with an electronic spectrum analyzer, is shown in Fig. 2(b). We observe a microwave frequency comb that extends up to a 3 dB bandwidth of ${\sim}3\;{\rm GHz} $, with the comb mode spacing given by the SRD pump frequency of 105 MHz. For gain-switching, it is crucial that these comb modes are efficiently injected into the QCL, as otherwise the effective pulse duration arriving on the gain medium would be increased.
For this reason, we measured the small-signal modulation response of the 1.7 mm long QCL. The employed device is high reflection coated at the rear facet and features a microstrip-like line waveguide geometry, which makes it microwave compatible while minimizing the optical waveguide losses [22]. By direct comparison of the emitted optical modulation depth to the injected microwave amplitude, we obtain the results shown in Fig. 2(c). We observe a 3 dB cut-off frequency of ${\sim}7.5\;{\rm GHz} $ and an almost flat frequency response within the spectral bandwidth of the electrical pulse. These results are in good agreement with measurements previously conducted using a microwave rectification technique [22].
3. RESULTS
In the experiment, the electrical pulses from the SRD are superimposed with a constant current bias of ${\sim}10\;{\rm mA} $. The emitted optical pulses from the QCL are subsequently characterized using ASUPS. The measurement results, as obtained at a laser temperature of ${-}30^\circ {\rm C}$, are shown in Figs. 3(a) and 3(b). We observe a train of isolated pulses with a repetition time of ${\sim}9.5\;{\rm ns} $, which is commensurate with the repetition time of the SYN. The pulses are subject to considerable intensity fluctuations, as the analysis of different ASUPS time traces shows (see Supplement 1 Section 2 for details). The full width at half maximum (FWHM) pulse duration is evaluated to be ${\sim}47\;{\rm ps} $, and the corresponding pulse spectrum extends over almost $50\;{{\rm cm}^{- 1}}$, as shown in Fig. 3(c).
Fig. 3. Gain-switched pulses in time and frequency domains. (a) Using ASUPS, we observe a train of isolated pulses with a repetition time of ${\sim}9.5\;{\rm ns} $ and peak power of ${\sim}900\;{\rm mW}$. (b) The FWHM pulse duration is evaluated to be ${\sim}47\;{\rm ps} $, and we identify an irregularly fluctuating intensity distribution on the peak of the pulse. (c) The emission spectrum of the gain-switched QCL, as measured using an FTIR, is shown in blue. By optical injection of a single-mode seed laser, we achieve gain-switched operation on a single Fabry–Perot (FP) mode (red), as shown in detail in the figure inset. (d) Emitted gain-switched pulse after injection seeding as measured by ASUPS. We observe a smooth pulse profile with a pulse duration of ${\sim}33\;{\rm ps} $ and peak power of ${\sim}970\;{\rm mW} $.
To achieve stable gain-switched pulses, lasing operation must be achieved on only one axial mode. On other laser platforms, several approaches have been employed to achieve such operation, including choosing a sufficiently small laser resonator, using specifically designed laser feedback structures, or via injection seeding [23]. In the latter case, a single-mode optical signal provides an initial excitation of one cavity mode well above its spontaneous emission noise level. As a result, the gain-switched laser starts oscillating only on this axial mode.
In this work, we use a single-mode QCL as a seed laser, which we inject into the gain-switched QCL using a beam combiner (BC) as shown in Fig. 1. An isolator (ISO) is used to mitigate optical feedback to the seed laser. By tuning the seed laser’s temperature and current, we alter its emission wavelength such that it overlaps with one of the longitudinal modes of the gain-switched QCL.
The emission spectrum of the gain-switched QCL after injection seeding is also depicted in Fig. 3(c). We observe lasing on only one longitudinal mode. As can be seen in the inset of Fig. 3(c), the emission spectrum of the gain-switched laser is considerably broader than the linewidth of the seed laser. For further details, please refer to Supplement 1 Section 1.
In Fig. 3(d), the gain-switched pulse after injection seeding is shown. As compared to the unseeded pulse in Fig. 3(b), we observe a decreased pulse length of ${\sim}33\;{\rm ps} $. Moreover, we can no longer identify the pulse intensity noise present in Fig. 3(b), but observe a smooth pulse profile.
4. DISCUSSION
To interpret the obtained results, we use a semi-classical approach based on non-linear rate equations [24]. These equations describe the dynamic interplay between population inversion and laser field, in response to a change in pumping conditions. The QCL active region is represented by three energy levels $i \in \{1,2,3\}$, each populated with a sheet carrier density ${n_i}$. A schematic diagram of all relevant transitions between these states is shown in Fig. 4(a).
Fig. 4. Rate equation analysis of gain-switched pulses. (a) The QCL active region is described by three energy states with respective sheet carrier densities ${n_{i \in 1,2,3}}$. The upper laser level is pumped at a rate $J/e$. From there, electrons either scatter to levels 2 and 1 with rates $\tau _{32}^{- 1}$ and $\tau _{31}^{- 1}$, respectively, or participate in the process of stimulated emission with the rate ${g_c}S({n_3} - {n_2})$. The lifetime of the carriers in the lower laser level is given by ${\tau _2}$. (b) For the parameters given in Table 1 and the experimentally measured electrical pulse [Fig. 2(a)], we numerically solve the non-linear rate equations. The solution is in close agreement with the measured optical pulse. (c) For the same parameters, we calculate the light-current characteristic, which is commensurate with a measurement performed in pulsed operation at low duty cycle.
The upper laser level ($i = 3$) is pumped at a rate $J(t)/e$, where $J(t)$ is the time dependent current density. In the present case, $J(t)$ is composed of a constant contribution ${J_0}$, which is overlayed with short electrical pulses ${J_p}(t)$. From the upper laser level, electrons may non-radiatively scatter to the lower laser level ($i = 2$) or ground level ($i = 1$). The lifetimes of the corresponding transitions are given by ${\tau _{32}}$ and ${\tau _{31}}$, respectively. The third important transition occurring at a rate ${g_c}S({n_3} - {n_2})$ corresponds to the stimulated emission or absorption of photons. Here, ${g_c}$ stands for the gain cross section, and $S$ is the photon flux per QCL period and unit active region width.
The lower laser level ($i = 2$) can be populated by electrons coming from level $i = 3$, but can also be filled by thermally excited electrons from the injector level of the following QCL period. This thermally activated population will be accounted for by the sheet carrier density $n_2^{\rm{th}}$. The lifetime of the carriers in the lower laser level is given by ${\tau _2}$.
Last, the rate of change of photons inside the resonator is given by the laser gain due to stimulated emission, the laser loss ${\alpha _{\rm{tot}}}$, and spontaneously emitted photons with a lifetime ${\tau _{\textit{sp}}}$. Only a fraction $\beta$ of the spontaneously emitted photons couples to the considered optical mode.
The full set of rate equations then reads
Table 1. Parameters Used for Rate Equation Analysis
We observe a pulse that closely follows the gain-switched pulse measured experimentally [Fig. 3(d)]. Moreover, the calculated light-current characteristic [Fig. 4(c)] is commensurate with a measurement conducted in pulsed operation at low duty cycle (100 ns pulse width, 100 kHz repetition rate) at the same temperature at which the gain-switched experiment was performed (${-}30^\circ {\rm C}$).
From these results, several conclusions can be drawn. From Figs. 2(a) and 3(d), it becomes apparent that the emitted gain-switched pulses are considerably shorter than the original electrical excitation. This can be understood by the fact the constant current bias ${J_0}$ was chosen considerably smaller than the laser threshold, leading to a shorter effective electrical pulse length above the lasing threshold. Moreover, a finite time is required for stimulated emission to build up after the initial formation of population inversion. As a result, the rise time of the optical pulse is shortened as compared to the electrical pulse.
On the contrary, the falling edges of the optical and electrical pulses are in close agreement, except for a short temporal delay in photon emission. This is a direct consequence of the unique carrier dynamics in QCLs where relaxation oscillations are overdamped [25]. The absence of relaxation oscillations is also indicated by the inexistence of resonances in the transient response shown in Fig. 2(c). For conventional diode lasers, the situation is vastly different, as typical carrier lifetimes lie in the range of nanoseconds. In that case, gain-switching corresponds to the excitation of the first relaxation oscillation, which means that the optical fall time is shorter than the one of the electrical pulse.
From Fig. 3(c), it becomes evident that multiple resonator modes reach the lasing threshold under gain-switched operation. We attribute this observation to the momentary overshoot of the population inversion in response to each electrical pulse arriving on the laser. The observed optical modes are spectrally broadened to ${\sim}10\;{\rm GHz} $ as compared to a QCL driven in continuous wave with typical linewidths of the order of hundreds of kilohertz [26]. This broadening can be ascribed to the formation of modulation sidebands spaced by integer multiples of the driving frequency of the SRD. Due to the limited frequency resolution of the FTIR used in this work, these sidebands could not be spectrally resolved.
By injecting an optical frequency close to a resonator mode of the gain-switched laser, the corresponding optical mode builds up from this initial excitation and not from spontaneous emission. As a result, it starts oscillating before any other cavity mode. As long as the electrical pump pulse is short enough to prevent higher gain modes from catching up and taking over, this seeded mode dominates the emission spectrum [23]. This explains the results shown in Fig. 3(c), where we observe single-axial-mode emission in gain-switched operation after injection seeding.
Prior to injection seeding, we observed a temporally fluctuating structure in the emitted pulses [Fig. 3(b)]. We attribute this intensity noise to spectral beating, as for every laser pulse, multiple resonator modes reach the lasing threshold, which are not mutually phase coherent [27]. In accordance with this interpretation, the irregularly fluctuating intensity distribution disappears after injection seeding [Fig. 3(d)]. Please refer to Supplement 1 Section 2 for further details about axial mode beating.
5. CONCLUSION
In conclusion, we have demonstrated the generation of high power 33 ps pulses from a gain-switched QCL. Short electrical pulses are used to modulate the gain of the laser, which is packaged for high frequency modulation. Using an external single-mode seed laser, we obtained gain-switched operation on only one resonator mode. The emitted optical pulses were characterized using ASUPS, whose high temporal resolution (${\sim}200\;{\rm fs}$) for the first time allowed precise study of the laser dynamics in response to fast pump current variations. The results obtained in the experiment are in excellent agreement with simulations based on laser rate equations.
Our work exemplifies a simple approach for the generation of powerful, highly tunable, short pulses in the mid-infrared frequency range. Further steps towards higher peak powers could include the design of high gain quantum cascade structures and specifically tailored current pulse generators. Moreover, there have been reports where gain-switched laser pulses were externally compressed [28]. Such phase compensation could further increase achievable peak powers while decreasing pulse durations. For improved pulse coherence, the laser gain medium can be modulated close to the cavity round trip frequency, which leads to the emission of mode-locked pulses [14].
It should be noted that also injection seeded gain-switched lasers can possess a high degree of temporal coherence and thus exhibit characteristics similar to frequency combs [29,30]. In the near-infrared, such sources have been used for frequency synthesis [31], optical telecommunication [32], and dual-comb spectroscopy [33]. Our study’s results may facilitate the implementation of such applications within the mid-infrared frequency range, which is optimally suited for these purposes.
Funding
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (176584).
Acknowledgment
The authors gratefully thank Barbara Schneider for providing the laser housing used in this work. Moreover, we acknowledge the help of Mathieu Bertrand in the implementation of the rate equation model.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this work are available from the corresponding author upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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