1. Introduction

Because quantum cascade lasers (QCLs) are the only solid-state sources of coherent THz radiation able to output many milliwatts of average power at frequencies > 2 THz, there is currently great interest in adopting QCLs for use in a variety of applications seeking to exploit the unique aspects of the THz radiation [1]. However, while power may be a necessary performance criterion, it is not sufficient for many popular application concepts. Precise frequency definition and excellent stability from a THz source are required in compact local oscillators for heterodyne receiver systems, range-resolving radars, and chemical vapor assaying via high-resolution spectroscopy. The frequency of a free-running THz QCL is subject to significant phase noise attributable to fluctuations and drift of both the bias and temperature that couple to the index of the QCL gain cavity. As a result of such phase noise, free-running intrinsic spectral linewidths depend on measurement integration time and have been reported to range from < 50 kHz [2–4] for instantaneous linewidths (typically measured with < 100 ms integration time) up to a several MHz at integration times of several seconds [2, 5, 6].

To obtain superior frequency definition, stability, and control, there has been much recent work on locking QCLs to a known frequency reference using active feedback. A widely used approach has been to phase lock a QCL to a conventional external THz source such as an optically pumped molecular gas laser or a microwave driven multiplier. A downconverted microwave difference frequency signal, generated by an external mixer such as a diode or hot-electron bolometer, between a QCL and a reference source is used as the error signal. Betz et al. [7] first used this technique to phase lock a 3 THz QCL to the 3.106 THz methanol line of a molecular gas laser and reported a locked QCL linewidth of 65 kHz stable over ∼1 min. Danylov, et al. [5] used a lower noise analog feedback loop and reported 3 to 4 kHz linewidth in a 2.4 THz QCL locked to the 2.409 THz deuterated methanol line of a molecular gas laser. Rabanus, et al. [6] employed a 1.5 THz microwave driven solid-state multiplier source as a reference to lock a QCL and achieved a locked linewidth of ≤100 Hz. Khosropanah, et al. [8] extended the upper frequency range reachable using a multiplier source reference to 2.7 THz and found a locked QCL linewidth of ≤1 Hz, stable indefinitely. These measurements required a reference source with a carrier frequency nearly identical to the frequency of the QCL, but there are not many sources available that are themselves frequency stable and also generate enough power to enable phase locking. More recently Barbieri, et. al. [9] used the frequency comb of a mode-locked near-infrared femtosecond laser to phase-lock the absolute frequency of the QCL at 2.7 THz. A more compact locking scheme was demonstrated by Baryshev, et al. [10]. Rather than locking to a separate THz reference source, they locked the difference frequency between two internal lateral modes of a multimode QCL and to a microwave reference. They reported a difference frequency locked linewidth of ≤10 Hz with negligible drift. Barbieri, et. al. [11], more recently showed that the difference frequency between modes can be injection locked by driving the laser bias with microwave power close to the intermode frequency difference. In all these locking schemes the difference frequency signal between QCL and reference have been shown to be excellent. In Ref. 10, the claim was made that locking the difference frequency between two lateral modes led to locking the absolute frequency (i.e. common mode definition) emitted by the QCL, but this was not demonstrated.

In this work, we report on phase locking the difference frequencies of the internal Fabry-Perot (F-P) longitudinal modes of a QCL and show for the first time, to our knowledge, the effect of such internal mode phase locking on the common mode stability of the QCLs F-P emission frequencies. We find that the phase noise bandwidth of the QCLs used is ∼0.5 MHz and that ∼40% of the total difference frequency (DF) power can be captured in the phase locked signal using a feedback loop with bandwidth of 10 kHz. The phase locked DF has ≤ 1 Hz linewidth and does not drift measurably on time scales of ∼30 min. However, mixing internally locked QCLs against each other or against a molecular gas laser line shows that phase locking of the internal DFs does not improve the common mode stability of the QCL F-P modes. Evidence suggests that a major source of common mode drift in internally locked QCLs is sensitivity to temperature fluctuations.

2. Sample and experiment description

The QCLs used in this work are monolithically integrated THz transceivers, described in detail elsewhere, where a Schottky diode is integrated into the top of a QCLs ridge waveguide cavity. The integrated nature of the transceiver obviates the need for a discrete external mixer component as used in Refs. 2–9. The cathode of the diode shares the same n+ doped GaAs layer that forms the QCLs top contact. The QCL is run in continuous wave mode and is purposely run multi-moded, with a comb of up to ten longitudinal F-P modes spaced at nearly 13 GHz intervals across a center frequency of 2.81 THz. Because the internal THz fields of the QCL modes permeate the GaAs layer making up the diodes cathode [12], the diode couples to and mixes the QCL fields to generate a downconverted DF signal at ∼13 GHz F-P mode spacing. These microwave DF signals are taken from a co-planar waveguide fed by the diode anode contact, amplified with a 20 GHz bandwidth low-noise amplification chain, and measured on a spectrum analyzer.

To phase lock the difference frequency between internal F-P modes, we follow a phase-locked loop set-up similar to that reported in Ref. 10, but adapted to our integrated transceiver configuration. The amplified microwave DF signal originating from the diode is split by a directional coupler so that 1/4 of the signal power is monitored by a spectrum analyzer, and the rest of the signal is input into a microwave frequency counter (EIP 578B) with error correction. The frequency counter generates a phase error signal proportional to the difference between the DF input and a set point microwave frequency. This error signal is fed back to a voltage-controlled power supply (ILX LDX-3232) that biases the QCL. The bandwidth of this feedback loop is 10 kHz, limited by the bandwidth of the frequency counter.

3. Demonstration of phase lock

Figure 1(a)–1(c) presents evidence that the DF signal is phase locked. Shown is the DF peak, offset from its 12.9287 GHz central value, with the feedback loop closed, taken using spectrum analyzer instrumental resolution bandwidths (RBWs) of 1 MHz, 10 kHz, and 1 Hz, all at constant video bandwidth of 30 Hz. At 1 Hz RBW the DF signal linewidth is still instrumentally limited, so the intrinsic linewidth of the locked signal is ≤1 Hz. This very narrow linewidth indicates that, upon locking, the frequency spacing between all F-P modes is the same to very high precision. This implies that the modes are coupled and maintain a fixed phase relationship. While this implies that the laser output fluctuates periodically in time, our measurements cannot show whether there is any point in the period when all the modes have the same phase, the required condition for mode-locking. The amplitude of the locked signal is constant for RBWs ≤100 Hz, but rises by 2 dBm at RBW = 10 kHz, consistent with 10 kHz being the bandwidth of the feedback loop. At RBW = 1 MHz the locked DF signal amplitude is about 4 dBm higher than at 1 Hz, a result of signal contributions from outside the 10 kHz feedback bandwidth that are not captured by the locking. Figure 1(d) shows the DF signal amplitude as a function of RBW. The amplitude is constant for RBWs << 10 kHz, demonstrating phase locking of all signal contributions within 10 kHz of the center frequency. The amplitude rises with increasing RBW in the range 10 kHz to 0.5 MHz as unlocked signals outside the 10 kHz feedback bandwidth contribute, then saturates at RBW > 0.5 MHz. Our interpretation of this is that the intrinsic phase noise bandwidth of the QCL is less than 0.5 MHz. This saturation at large RBW indicates that the phase noise bandwidth of our QCL is approximately ± 0.5 MHz about the center frequency. By comparing signal powers at 1 Hz and 1 MHz [13], we estimate that approximately 40% of the total DF signal power is phase locked at the center frequency.

 

Fig. 1 Internal F-P mode difference frequency spectra of one phased locked QCL transceiver taken with spectrum analyzer RBWs of (a) 1 MHz, (b) 10 kHz, and (c) 1 Hz, and a constant 30 Hz VBW. Frequency scale is shown as an offset from the 12.9287 GHz center frequency. At 1 Hz the −3dB linewidth of the peak signal is instrumentally limited by the RBW. (d) F-P difference frequency peak power plotted against the RBW of a phase locked QCL. The phase locked loop has a feedback bandwidth of 10 kHz. The open circles were taken as as the RBW was increased, and the closed circles correspond to repeating the measurement but starting from high RBW and decreasing.

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4. Common mode frequency stability

To study the common mode frequency characteristics of internally DF phase locked QCLs, two separate transceivers are individually locked in the manner described above. The beam of one transceiver (acting as transmitter, with locked F-P DF of 12.8797 GHz) is edge coupled into the facet of the other (acting as receiver, with locked F-P DF of 12.8897 GHz). The external DF spectrum, consisting of the difference frequencies between the transmitters and receivers F-P modes generated by the receivers integrated diode, is measured. In contrast to the internal locked DF spectra of Fig. 1, the external DF spectrum is sensitive to absolute or common mode frequency variations that might occur in one or both QCLs. Because the F-P mode frequency spacing in the two QCLs are incommensurate, the external DF spectrum between the QCLs is a comb of signals separated by the difference between the two locked F-P frequencies as shown in Fig. 2(a). This external DF spectrum is shown as a function of time in Fig. 2(b). For direct comparison, the internal DF signal from one locked QCL is shown as a function of time in Fig. 2(c) but with a much higher resolution frequency scale. Over a 5 min time scale, the external DF spectrum peaks are clearly seen to drift within ±5 MHz of the mean peak positions. By contrast, the internal DF signal peak does not move measurably on the scale of 1 Hz over 8 minutes, and we have recorded stability to within ±1 Hz over 30 min. The drift of the external DF spectrum is direct evidence that one or both internally locked QCLs is still subject to large common mode frequency variations. The common mode drift represented in Fig. 2(a) is comparable to an unlocked QCL.

 

Fig. 2 (a) Schematic of the two combs of lines emitted by two QCLs indicating the Fabry-Perot difference frequency for each QCL (DF_F-P,i) and the set of difference frequencies between the two combs (DF_i). (b) Time dependence of the difference frequency comb (DF_i), generated by mixing the F-P modes of two separately locked QCLs. Frequency scale is shown as an offset from 18.6497 GHz. The peaks wander by approximately ±5 MHz over an 8 minute time interval. The scale bar units are dBm. (c) Time dependence of the internal F-P difference frequency peak of one of the locked QCLs. Frequency scale is shown as an offset from 12.9287 GHz. The peaks are fixed to within 1 Hz over a 5 minute time interval.

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A possible major source of common mode frequency instability in internally locked QCLs is temperature fluctuation. Evidence for this is shown in Fig. 3. Here, the known 2.841143 THz gas line from a CO2-pumped molecular gas laser is edge-coupled into one internally locked transceiver. The diode of the transceiver then generates a signal at the DF between the gas line and one (or more) of the QCLs F-P modes. Since the molecular gas line frequency is stable (to within 5 MHz, which is small compared to the QCL frequency shifts with temperature), changes in the absolute frequency of the QCLs F-P mode by more than a few 5 MHz can be measured. The inset to Fig. 3, shows the mixer response when the molecular gas laser is incident on the QCL with the QCL heatsink temperature held at 20 K. The taller peak corresponds to the internal F-P DF of the QCL modes which are locked at 12.8897 GHz and are stable to ±1 Hz. The shorter peak corresponds to the difference frequency between the molecular gas laser line and the QCL mode that is roughly 13.5 GHz lower in absolute frequency than the gas laser frequency. The main part of Fig. 3 plots the extracted absolute frequency of this QCL mode as a function of QCL operating temperature, as read from a thermometer buried in the QCL heat sink. Relative to the fixed molecular gas laser frequency, the absolute frequency of the QCL F-P mode has a significant temperature dependence even though the difference frequency between the QCL modes is internally locked. By contrast, the internal F-P DF peak of this locked QCL is temperature independent, by definition, over the same temperature range. In our experimental set-up, the operating temperature recorded on the heat-sink thermometer typically fluctuates by ±1 K (at a heat sink temperature of 10 K). Using the slope of the data of Fig. 3, we estimate that a 1 K temperature fluctuation corresponds to roughly a 5 MHz change in frequency, which is in agreement with the fluctuation observed in Fig. 2(a). Thus temperature fluctuations can be expected to generate common mode fluctuations of the absolute QCL F-P frequencies, even while the locked internal F-P DF is undisturbed.

 

Fig. 3 Temperature dependence of the QCL frequency. obtained by measuring the difference frequency between a molecular gas laser line (ν_FIRL = 2.841143 THz) and one of the modes of a locked QCL. This difference frequency decreases by approximately 1 GHz as the operating temperature of the locked QCL is increased from 15 K to 45 K. The inset shows the RF spectrum of the mixer at 20K. The taller peak at 12.8897 GHz corresponds to the stable difference frequency between the QCL modes (locked to within ±1 Hz). The shorter peak is the difference frequency between the calculated QCL mode and the molecular gas laser line.

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5. Conclusion

In summary, we have demonstrated that 40% of the difference frequency power can be phase-locked with a linewidth of less than 1 Hz, using a phase-lock loop bandwidth of 10 KHz. The power in the phase locked line saturates for resolution bandwidths above 500 kHz, suggesting that increasing the feedback bandwidth to 1 MHz would allow one to phase lock nearly 100% of the difference frequency. The drift of the absolute laser frequency is independent of whether the difference frequency between longitudinal modes is phase-locked. By changing the heat sink temperature while keeping the difference frequency at a fixed value, the independence of the absolute frequency and difference frequency between modes is clearly shown. Therefore a calibrated frequency reference near the THz QCL frequency is still required for absolute frequency locking of THz QCLs.