1. Introduction

For semiconductor diode lasers emitting in optical and infrared wavelengths, the two-section coupled-cavity [1] geometry that is obtained by separating a single Fabry-Pérot (FP) cavity into two sections using semiconductor etching techniques has been widely used for achieving stable single longitudinal mode operation by employing the strong mode selection (loss modulation) mechanism [2–4], or for obtaining mode-locking to generate ultra-short pulses [5]. Regarding mode-locking of coupled-cavity diode lasers, the RF modulation can be intentionally applied only onto the short-section of the coupled-cavity rather than the entire FP cavity, and therefore, the modulation efficiency is higher because of the reduced device capacitance compared to the FP laser cavity. Then, the mode-locked pulses can be formed in the coupled-cavity diode lasers. To further achieve passive mode-locking of lasers, a saturable absorber [6,7] is normally needed to reshape the optical pulses. In couple-cavity diode lasers, this saturable absorber can be easily obtained by applying reversed bias voltage on the short section of the laser. Passive and hybrid mode-locking have been successfully demonstrated in coupled-cavity diode lasers [8–11].

In the terahertz regime [12], the frequency of which is roughly defined between 0.1 and 10 THz, the mode-locked and electrically-pumped semiconductor lasers are much in demand for potential applications in high-resolution metrology [13,14], non-destructive imaging [15,16] and communications [17]. The semiconductor-based terahertz quantum cascade laser (QCL) [18] with high output power [19,20], small far-field beam divergence [21,22], and broad frequency coverage [23], is an ideal candidate for generating mode-locked pulses. The active mode-locking of FP cavity terahertz QCLs with both single plasmon and double-metal waveguides has been demonstrated and pulse widths in picoseconds level have been obtained [24–27]. As it is learnt from the mode-locked diode lasers [5,8,9] and mid-infrared QCLs [28], the coupled-cavity geometry is supposed to improve the RF modulation efficiency and then further shorten the optical pulse width generated from terahertz QCLs. However, introducing the coupled-cavity configuration into terahertz QCLs for achieving active mode-locking is not a trivial work. Unlike the couple-cavity laser diodes and QCLs emitting in optical, near-infrared, and mid-infrared wavelengths, the terahertz QCLs with coupled-cavity configuration always demonstrate single longitudinal mode operation because of the strong mode selection and narrow gain bandwidth [29–31]. In continuation to the work presented in [30], we did the RF modulation onto the short section of that coupled-cavity laser. However, even under strong RF modulation, the coupled-cavity laser always demonstrated single mode operation and no sideband generation or mode-locking was observed.

Different from the work in [30], here we employ a hybrid QCL active region (bound-to-continuum + resonant phonon design) to evaluate the effect of microwave modulation on coupled-cavity lasers. With this hybrid active region, we recently demonstrated that the single plasmon FP lasers can be efficiently modulated to achieve homogeneous spectral spanning over 330 GHz with a central frequency of 4.2 THz [32]. The lasing bandwidth of 330 GHz is almost the twice of that obtained from the laser in [30]. Because of the broad lasing bandwidth and the high efficiency microwave modulation in the QCL with the hybrid active region design, we expect the laser with a coupled-cavity geometry to emit with few multi-longitudinal modes. Once we can obtain the modes, we should be able to modulate the laser and generate more sidebands because of the advantages of the coupled-cavity in microwave modulations. However, due to the strong mode selection, the fabricated coupled-cavity lasers demonstrate quasi-single mode operation and meanwhile the higher order transverse mode is excited. The interesting point is that under this situation of coexistence of fundamental and higher order transverse modes, we demonstrate, to the best of our knowledge, the first successful active RF modulation of couple-cavity terahertz semiconductor lasers for generating sidebands.

The rest of the paper is organized as follows: we first characterize the performance of the fabricated coupled-cavity terahertz QCL, such as the light-current-voltage characteristics and the emission spectra of the laser at different drive currents. Then, we show the inter-mode beat note measurement, from which we assume the higher order transverse mode is excited. To further prove that, we perform the far-field analysis. We also give a full explanation of the generation of the beat note signals observed in the experiment. Finally, we do the microwave modulation at the inter-mode beat note frequencies and an analysis of the sideband generations by the external amplitude modulation is given in detail.

2. Coupled-cavity laser

The coupled-cavity QCL used in this work is fabricated based on a single plasmon FP QCL. The active region with a hybrid structure is based on an Al_0.25Ga_0.75As/GaAs material system [33] grown through a molecular beam epitaxy (MBE) on semi-insulating GaAs substrates. The emission frequency of the QCL is designed to be around 4.2 THz. The MBE-grown wafer is processed into single plasmon FP ridges using the traditional semiconductor laser processing technology. The fabricated ridges with a substrate thickness of 200 μm and a ridge width of 200 μm is cleaved into a FP cavity with a length of 2.5 mm. Then, the cleaved laser bar is mounted onto a copper heat sink, which is followed by the gold wire bonding for the QCL electrical pumping. Finally, the fully packaged FP QCL is sent to a FIB chamber for air gap etching to construct a coupled-cavity geometry with a gap width of 4 μm. Note that for the coupled-cavity laser, in order to achieve high efficient RF modulation, a microwave transmission line is mounted close to the short section cavity. In the experiment, both the DC pump and RF modulation are applied onto the short cavity. However, the long cavity is only electrically pumped with the direct current (DC).

Figure 1 shows the device geometry and the performance of the coupled-cavity terahertz laser. The air gap with a width of 4 μm and a depth of >12 μm penetrating the entire active region of the laser gain medium is fabricated by using a focused ion-beam (FIB) etching [34] as shown in Fig. 1(a). The short cavity with a length of L₁ = 300 μm [see the inset of Fig. 1(a)] is electrically connected to a microwave transmission line for RF modulation as well as for the DC pumping for the laser operation, while the long section with a length of L₂ = 2.2 mm is only pumped with the DC and without RF modulation. Note that the short section length of 300 µm is chosen due to the tradeoff between electrical and microwave implementations, i.e., a sufficient larger area is needed for wire boding and simultaneously a small short section is expected for efficient microwave modulations. For all the measurements demonstrated in this work, both cavities are electrically switched on. In principle, we use only one continuous wave (cw) power generator which is working in a constant voltage mode. The voltage from the power supply is sent to the both cavities simultaneously. The short section with reduced area is supposed to improve modulation efficiency to generate sidebands. In Fig. 1(b), we plot the calculated loss of the coupled-cavity laser using a transfer matrix method [30] for two cases, i.e., without material loss (black) and with a constant material loss of 4 cm⁻¹ (green). The scatters represent the calculated eigen frequencies which are the results of the resonance of the long cavity. The slow modulation with a period of 125 GHz is due to the short section resonance which follows the relation of c/2L₁n where c is the speed of light and n is the refractive index of the laser. Note that, the value of refractive index is derived from the inter-mode beat note measurement of a FP laser processed from an identical wafer. In [32], we reported an inter-mode beat note frequency of 6.2 GHz measured from a 6 mm long FP laser. And therefore, the refractive index can be calculated to be n = c/2Lf_b≈4 where L = 6 mm is the cavity length of the FP laser and f_b = 6.2 GHz is the measured beat note frequency. Because of the slow modulation, eigen modes show different losses. Therefore, the mode selection can take effect. Only the modes with minimum losses can finally go to lase because of the gain clamping effect in lasers. The red stars shown in Fig. 1(b) are the measured two frequencies shown in Fig. 1(d). As can be seen that the two frequencies are very close to the loss minima of the green curve (the two vertical grey lines indicate two loss minima positions of the coupled-cavity laser).

 

Fig. 1 (a) Schematic of the coupled-cavity terahertz QCL. The inset is a scanning electron microscope image of the fabricated short cavity and air gap of the laser. (b) Calculated total propagation losses as a function of eigen mode frequency of the coupled-cavity with material loss (green) and without material loss (black). The scatters are the calculated results and the solid lines are for the guide of eyes. The red stars are the measured lasing frequencies obtained from (d). (c) Measured light-current-voltage (L-I-V) characteristic of the coupled-cavity laser in continuous wave (cw) mode at 20 K. (d) Normalized terahertz emission spectra as a function of drive current without RF modulation at 20 K. Each spectrum is shifted vertically for clarity. The insets of (d) are magnified spectra to clear show the spectral degeneracy.

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The light-current-voltage (L-I-V) curve of the coupled-cavity laser measured in cw mode at 20 K is plotted in Fig. 1(c). We can see that in cw the coupled-cavity laser can emit 1.8 mW power measured using a terahertz power meter (Ophir 3A-p THz). Note that the cw power value shown in Fig. 1(c) is the detected power from one facet of the laser without considering any collection efficiency and losses in the optical beam. In order to reduce the water absorption as much as possible, the optical path is purged with dry air. Figure 1(d) shows the terahertz emission spectra in the entire current dynamic range of the laser without RF modulation. The emission spectra are measured using a vacuum FTIR spectrometer (Bruker v80). Similar with the power measurement, to reduce the water absorption, the FTIR chamber is pumped down to 2 mbar and the beam path outside the FTIR is purged with dry air. The spectral resolution used in this measurement is 0.1 cm⁻¹ (3 GHz). In the low current range from 450 to 550 mA, the coupled-cavity laser demonstrates quasi-single mode operation and the lasing frequency is measured to be around 4.17 THz. With increasing the drive current, we observe bi-mode operation with the dominant mode moving to 4.28 THz as shown in Fig. 1(d). The two modes at 4.17 and 4.28 THz are corresponding to the two loss minima shown in Fig. 1(b). At low currents, because the gain curve is narrow and only the mode at 4.17 THz lies in the laser gain or lasing bandwidth, we only observe the first mode. However, the gain curve should be blue-shifted and broadened partially due to the hole-burning effect with increasing drive current. Therefore, we see bi-mode lasing. The two lasing frequencies are separated by 110 GHz which shows good agreement with the calculation (125 GHz). The small difference between the calculation and the experiment is resulted from the uncertainties of the refractive index values and the cavity length measurements. It is worth noting that, as shown in the insets of Fig. 1(d), around 4.17 THz the spectral degeneracy is clearly observed when the laser is driven at 550, 650, or 700 mA. The two modes around 4.17 THz is separated by ~4.3 GHz that is far below the free spectral range of the laser cavity, which infers that the higher order transverse mode could be activated. In the next section, we perform the inter-mode beat note and far-field analysis to investigate the mode structure of the coupled-cavity laser.

3. Inter-mode beat note and far-field analysis

Although the coupled-cavity laser shows quasi-single mode operation as shown in Fig. 1(d), the fine mode structure of the laser can be incorrectly evaluated due to the spectral resolution and detection limits of the terahertz spectrometer. However, the indirect method, i.e., electrical inter-mode beat note measurement, is sensitive to the weak signal mixing/beating and can be used to investigate the mode structure of lasers. Once there are two modes in the laser cavity with a frequency difference smaller than the bandwidth of the testing system (Bias-T, RF cable, transmission line, etc.), the inter-mode beat note measurement makes it possible to sensitively see the down-converted signal using a spectrum analyser (bandwidth of 26 GHz) with the assistance of a Bias-T (bandwidth of 40 GHz) and a low noise amplifier (gain of 30 dB). The detailed experimental setup can be found in [24].

For the coupled-cavity terahertz laser, if the two modes at 4.17 and 4.28 THz are pure single-frequency, we wouldn’t find any signal in the inter-mode beat note spectra. However, as shown in Fig. 2(a), in the current range from 450 to 700 mA we always observe two frequencies around 4 and 8 GHz. As already elaborated previously, the short cavity L₁ and long cavity L₂ give the calculated round-trip frequencies of 125 GHz and 17 GHz, respectively. The bandwidth of the spectrum analyser is up to 26 GHz, if multiple longitudinal modes of a same transverse/spatial mode are oscillating simultaneously in the cavity, we should be able to see the inter-mode beat note signal around 17 GHz. However, we cannot see a signal at 17 GHz, which means the coupled-cavity laser is almost working in single-longitudinal mode. What we observe in the inter-mode beat note spectra are the two dominant down-converted frequencies at 4 and 8 GHz. Obviously, these two inter-mode beat note frequencies are not from the beating of the longitudinal modes of a same transverse mode. Therefore, we assume that the coupled-cavity activates higher order transverse mode and the frequency of the higher order transverse mode is very close to that of the fundamental transverse mode. The fundamental and higher order transverse modes can beat/mix and then generate the inter-mode beat note frequency around 4 GHz. Indeed, as clearly shown in the insets of Fig. 1(d), at currents of 550, 650, 700 mA, we can see two terahertz modes around 4.17 THz and the two modes have a frequency difference of ~4 GHz. Concerning the generation of the 8-GHz signal, it would be more complicated and will be elaborated later. It is worth noting that we only observe fundamental inter-mode beat note signal for FP QCLs with similar ridge widths fabricated from the same wafer. This indicates that the higher order transverse mode is excited mainly due to the implementation of the coupled-cavity geometry, which can be also confirmed by a 2-D finite difference frequency domain simulation [30].

 

Fig. 2 (a) Electrical inter-mode beat note mapping of the couple-cavity laser in free running mode at 20 K. (b) Magnified inter-mode beat note evolutions around 4 GHz and 8 GHz. The resolution bandwidth used in this measurement is 100 kHz and each trace is averaged for 20 times.

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In Figs. 2(b) and 2(c), we plot the inter-mode beat note evolutions with drive current for the 4-GHz and 8-GHz signals, respectively. For both cases, as the current is increased, the beat note frequencies show a clear blue shift which is entirely different from FP terahertz QCLs in which the red shift of the inter-mode beat note with current is observed [32,35]. This could be another proof that the higher order transverse mode is activated in the coupled-cavity laser. As the drive current is increased, the fundamental and higher order transverse modes could shift toward the opposite directions or the high frequency mode shows faster blue shift than the lower frequency mode, and therefore, we observe the blue shift of the beat note signal.

To further investigate the transverse mode profile of the coupled-cavity laser, we perform the far-field measurements at various drive currents. Figure 3(a) shows the device and experimental configurations for the far-field measurements. The far-field beam patterns of the coupled-cavity laser are recorded using a Golay cell detector which is mounted on a LabView-controlled rotating stage. The Golay cell detector is 10 cm away from the laser output facet and during the measurement it moves on a spherical surface. To improve the far-field angle resolution, a pinhole with a diameter of 1 mm is placed in front of the Golay cell aperture. Note that in the far-field measurement, the laser is working in pulsed mode with additional slow modulation of 10 Hz to match the slow detection of Golay cell. In Fig. 3a, the horizontal and vertical directions are denoted as α and β. Three typical beam profiles measured at 500, 600, and 700 mA are depicted in Figs. 3(b)-3(d), respectively. If the higher order transverse mode shows strong competition with the fundamental mode, in principle we should be able to see two lobes in the far-field beam patterns along the horizontal direction α. However, it can be seen from Fig. 3 that only one lobe is observed, which indicates that the fundamental transverse mode always dominates in the entire current dynamic range. Note that in the far-field measurement, the detection sensitivity is limited by the terahertz detector and the experiment is carried out in the open air which can result in strong water absorption for the terahertz radiation. Both above mentioned factors could make the weak higher order transverse mode invisible in the far-field beam profiles. However, from the measurement shown in Fig. 3, we cannot firmly say that the higher order transverse mode appears.

 

Fig. 3 (a) Laser geometry and definitions of α and β directions for the far-field measurements of the coupled-cavity terahertz laser. (b), (c) and (d) are the measured far-field beam profiles at 500, 600, and 700 mA, respectively.

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To further investigate the far-field of the coupled-cavity laser, we perform the simulation analysis using the finite-element modeling. The modes are first excited in the laser cavity, and then we calculate the near-field electric field distributions on the laser facet for the fundamental and higher order transverse modes as shown in Fig. 4(a) and 4(b), respectively. Employing the Fourier transform, the far-field patterns as shown in Fig. 4(c) and 4(d) for the fundamental and higher order modes, respectively, can be calculated from the near-field distributions. If we assume there is only either the fundamental or the higher order transverse mode in the coupled-cavity laser, the simulated far-field patterns don’t show agreement with the experimental data in Fig. 3. In view of this, we think that in the current coupled-cavity laser the fundamental and higher order modes coexist. In Fig. 4(e), 4(f), and 4(g), we superimpose the far-field intensities of the two modes using different mode power ratios R which is defined as the power ratio of the higher order mode to the fundamental mode. From Fig. 4(e) to 4(g), the higher order mode contribution to the far-field increases, the corresponding values of R are 0.5, 0.8, and 1, respectively. It can be clearly seen that when R is small ~0.5 (higher order mode contribution is less), the far-field pattern is characterized by a single lobe. However, when the higher order mode contribution is increased to be equivalent to the fundamental mode (R = 1), the two lobes in far-field dominate as shown in Fig. 4(g). From this analysis, we can deduce that in our coupled-cavity laser, the higher order mode is excited but its power is weaker than the fundamental mode. Therefore, we only observe one far-field lobe in Fig. 3. Furthermore, from the simulation shown in Fig. 4, we can also see that once the higher order mode contributes to the far-field, the divergence along α direction increases. In Figs. 4(e)-4(g), from left edge to the right edge, the calculated divergent angle is around 30 degrees which agrees well with the experimental results shown in Fig. 3. This could be another proof that the higher order mode does exist in the coupled–cavity laser.

 

Fig. 4 Near- and far-field simulations for the fundamental and higher order modes. (a) and (b) are the calculated electric field (real part) distributions of the fundamental and higher order modes on the laser facet, respectively. (c) and (d) are the simulated normalized far-field intensity patterns of the fundamental and higher order modes, respectively. (e), (f), and (g) are the composed far-field patterns by superimposing the fundamental and higher order mode patterns with different values of R that is defined as the power ratio of the higher order mode to the fundamental mode.

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In Fig. 2, the inter-mode beat note measurement shows that besides the 4-GHz signal we also observe its second harmonic at ~8 GHz. In Fig. 5, we schematically show the generation processes for the two signals. As already stated previously, the 4-GHz signal in Fig. 2 is generated from the beating of the fundamental and the higher order transverse modes, the process of which is label as 1 in Fig. 5. The two terahertz modes (ν₀ and ν₀ + △) are spaced by ~4 GHz denoted as △. Then, the frequency △ can beat with the fundamental terahertz mode ν₀ and generate a sideband at ν₀-△. Finally, shown as the process labeled 3, the sideband ν₀-△ can mix with the higher order transverse mode ν₀ + △ and produce a beat note frequency 2△. Concerning the generation of 2△, the direct second harmonic generation (SHG) from △ labeled 4 is also possible. Due to the strong nonlinearity (χ⁽²⁾) of the QCL active region, the SHG process can be more efficient than the process labeled 3. The beating processes labeled as 1, 2, 3, and 4 can fully explain the results obtained in Fig. 2. Due to the measurement uncertainty and the perturbations of the external mechanical and electrical noises, the 2△ and △ signals shown in Fig. 2 do not follow exactly the same pattern with increasing the drive current. The whole process shown in Fig. 5 is based on the strong nonlinearity of the gain medium. Furthermore, the four-wave mixing effect can result in more sidebands generation which, nevertheless, is not shown in Fig. 5. It is worth noting that among the three experimental techniques, i.e., terahertz spectrum, inter-mode beat note, and far-field beam pattern, the inter-mode beat note technique is the most sensitive method to analyse the mode structure of terahertz semiconductor lasers.

 

Fig. 5 Schematic of the generation of the two-beat note frequencies observed in Fig. 2. The first beating labeled 1 generates the beat note frequency △, the second beating labeled 2 produces additional sideband at frequency ν₀-△, and the third beating labeled 3 and the SHG process labeled 4 produce the beat note frequency 2△. SHG: second harmonic generation.

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Here, we have to realize that the fundamental and higher order transverse modes are, in principle, orthogonal with each other. This results in very weak coupling between these two modes. However, due to the imperfect cavity quality resulted from the growth and fabrication processes, we are still able to see the beating or mixing between the fundamental and higher order modes. Indeed, this beating signal is quite weak. In this work, to measure the inter-mode beat note signal, a low noise amplifier with a gain of 30 dB is used to significantly amplify the weak signal. Even with the amplification, the measured power of the beat note signal is around −38 dBm. As for comparison, for the beat note signal resulted from the beating of cavity eigen modes, the power without amplification is measured to be between −40 and −50 dBm (see [32]). Therefore, for a fair comparison, the beat note signal measured from the beating of the fundamental and higher order modes is around 23 dB weaker than the signal generated from the beating of cavity eigen modes of a FP laser.

Since the beating signal △ is already weak, the 2△ signal that is resulted from △ should be even weaker. However, from Fig. 2 one can clearly see that when the drive current is larger than 600 mA, the 2△ signal is even stronger than the signal at △. We attribute this unusual phenomenon to the possibility that in some situations the current system is more favorable for the transmission of the 2△ signal. Actually, this could happen because the whole system including the microwave cable, strip line, RF feedthroughs, and so on, are not specifically optimized. In Fig. 7, we show the microwave rectifications for the coupled-cavity laser. One can see that at high currents of 600 and 700 mA, the 2△ modulations give higher responses than the modulation at the frequency △, which partially explains the reason that in some situations the 2△ signal is even stronger than the signal at △.

4. Microwave modulation and rectification

Since we observe two inter-mode beat note lines when the coupled-cavity laser is working in free running, we try to modulate the laser at various beat note frequencies. The AC port of the Bias-T is for extracting the inter-mode beat note signal as well as for injecting the external RF signal. The RF modulation is achieved by using a RF synthesizer which can output 25 dBm microwave power in the frequency range between 1 MHz to 30 GHz. In Fig. 6 we show the terahertz and RF spectra obtained at 20 K in cw when the laser is modulated at frequencies △ (a,b) and 2△ (c,d). For clear comparison, the bottom panel of each column shows the case without RF modulation (RF off). We can see that, for the RF modulation at △ = 4.274 GHz, as we increase the RF power up to 10 dBm, the first sideband appears. Even when the RF power reaches 25 dBm, there is still only one sideband [see Fig. 6(a)]. While, the situation for the modulation at 2△ is different. As shown in Fig. 6(c), with increasing the RF power, the terahertz spectra show tremendous change from single mode to multimode operation. At 2△ with 25 dBm, we can observe 6 sidebands. In Figs. 6(a) and 6(c), the dashed lines are used to accurately locate the peak positions of different modes. Once we get the sidebands, the spacing of neighbouring modes is firmly locked to the injected RF frequency, which is the sign of active mode-locking. Here, note that the generated sidebands or the proliferation of modes under RF modulation shown in Fig. 6(c) are not the eigen modes of the laser cavity. It is different from the RF-modulation induced mode proliferation in a FP laser where all the generated sidebands are (or very close to) the eigen modes of the cavity. However, we can clearly see from Fig. 6(c) that even the coupled-cavity laser is not modulated at the cavity round-trip frequency, the sidebands can be excited. As the laser is modulated by the RF, actually we achieve the amplitude modulation of the drive current, which results in the amplitude modulation in the terahertz field. Simply due to the strong amplitude modulation introduced by the external RF, we finally observe the sideband generation. Since the mode spacing, △ or 2△, cannot be derived from the calculations shown in Fig. 1(b), the generated sidebands are not longitudinal modes. In principle, we can say that these modes are attached to the fundamental or higher order transverse modes. But it is difficult to distinguish what exact mode they are. Similar results were also reported in [36] where the modulation frequency was swept from 2 GHz to the laser round-trip frequency and sidebands were successfully generated even when the modulation frequency was far below the round-trip frequency. It is true that sidebands can be generated by modulating FP laser at frequencies other than the cavity round trip frequency. However, a “seed” frequency (Δ or 2Δ) obtained from the two-section coupled-cavity can help for generating uniform and more sidebands. For example, as shown in Fig. 6(a), as we modulate the laser at the fundamental inter-mode beat note frequency Δ with a power of 20 or 25 dBm, the generated sideband has almost same power as the carrier mode. The number of sidebands is less than the case at 2Δ modulation, which can be explained by the imperfect RF circuit as shown in Fig. 7 and Appendix Fig. 11.

 

Fig. 6 Terahertz emission spectra (a,c) and RF spectra (b,d) of the coupled-cavity terahertz laser under RF modulation on the short section with various RF power measured at a drive current of 500 mA. In (a) and (b), the modulation frequency is set as △ = 4.274 GHz; and in (c) and (d), the modulation frequency is 2△. In each subfigure, the bottom panel shows the results without RF modulation (RF off). The dashed lines in (a) and (c) are used to locate the mode positions.

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Fig. 7 Microwave rectifications measured at QCL drive currents of 500 mA (a), 600 mA (b) and 700 mA (c). The RF power is fixed at 10 dBm and the frequency is swept from 1 to 15 GHz. The dashed and solid vertical lines show the inter-mode beat note frequencies around △ and 2△, respectively.

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In Figs. 6(b) and 6(d), the corresponding RF spectra are plotted for RF modulations at △ and 2△ with various RF powers, respectively. Within the bandwidth of the spectrum analyser, it is obvious that we can observe several harmonics of the injected RF signal for both △ and 2△ modulations. As we inject the 2△ RF signal, the line at frequency △ which is observed in free running mode is significantly suppressed [see Fig. 6(d)]. This, in principle, can explain that when the laser is modulated at 2△, the terahertz modes are equally spaced by 2△ rather than △. Note that this is not the case for modulating FP cavity lasers where even the RF modulation is performed at harmonics of the cavity round-trip frequency, the terahertz spectra show a mode spacing of fundamental round-trip frequency.

The terahertz and RF spectra are also recorded at other drive currents (see Appendix Figs. 8 and 9 for details) and the similar results are obtained. The above-mentioned sideband generation is achieved by modulating the short section cavity of the laser. In Appendix Fig. 10, we show the results obtained by modulating the long section of a coupled-cavity laser with identical ridge width and section lengths. In Appendix Fig. 10(b), the measured inter-mode beat note spectrum is recorded. It can be clearly seen that two inter-mode beat note frequencies around 4 GHz and 8 GHz are obtained in the new coupled-cavity laser. In Appendix Fig. 10(c), (d) and (e), we show the terahertz emission spectra measured with RF off, RF power of 25 dBm at 4 GHz, and RF power of 25 dBm at 8 GHz, respectively. We observe again the sideband generation by modulating the long cavity at 8 GHz. However, by comparing the number and power distribution of sidebands, we can conclude that as expected the modulation of the long cavity is inferior to the modulation of the short cavity as shown in Fig. 6.

 

Fig. 8 Terahertz emission spectra (a,c) and RF spectra (b,d) of the coupled-cavity terahertz laser under RF modulation on the short section with various RF power measured at a drive current of 600 mA. In (a) and (b), the modulation frequency is set as △ = 4.172 GHz; and in (c) and (d), the modulation frequency is 2△. In each subfigure, the bottom panel shows the results without RF modulation (RF off).

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Fig. 9 Terahertz emission spectra (a,c) and RF spectra (b,d) of the coupled-cavity terahertz laser under RF modulation on the short section with various RF power measured at a drive current of 750 mA. In (a) and (b), the modulation frequency is set as △ = 4.325 GHz; and in (c) and (d), the modulation frequency is 2△. In each subfigure, the bottom panel shows the results without RF modulation (RF off).

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Fig. 10 Effects of microwave modulation on the long cavity of the coupled-cavity laser. (a) Schematic demonstration of the measurement setup. The microwave modulation is applied onto the long cavity (2.2 mm) section and the both cavities are pumped with DC. (b) Inter-mode beat note signal of the laser. (c) Emission spectrum of the coupled-cavity laser without RF modulation. (d) and (e) are the emission spectra of the coupled-cavity laser measured with RF modulations at 4 GHz and 8 GHz, respectively, with a RF power of 25 dBm. For the inter-mode beat note and emission spectra measurements, the coupled-cavity laser is driven at a current of 500 mA and the heat sink temperature is set as 20 K.

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From the terahertz emission spectra, it is obvious that the modulation at the second harmonic frequency 2△ is much more efficient than the fundamental RF modulation. To clarify this difference in modulation response, we carry out the microwave rectification measurement. The microwave rectification technique is a powerful and convenient method to investigate the modulation response of semiconductor chips [37]. The RF signal swept from 1 to 15 GHz with different power values together with the DC pump current that is necessary for the laser operation is injected into the laser employing a Bias-T. The rectified voltage or current is measured directly from the DC port of the Bias-T using a lock-in amplifier. To facilitate the lock-in amplifier measurement, the injected RF signal is strongly amplitude modulated at a frequency of 50 kHz using a wave function generator. The normalized rectified signal as a function of microwave frequency measured at 500, 600, and 700 mA is plotted in Figs. 7(a)-7(c), respectively, with a RF power of 10 dBm. At most of currents, we observe stronger modulation response at 2△ than the modulation at △. In Appendix Fig. 11, we also show the results recorded with a RF power of 25 dB that is identical to the situation for the generation of 6 sidebands in Fig. 6(c). It is clearly shown that as the RF power is increased, at all drive currents the modulation at 2△ always leads to higher modulation response. This can explain why we get more sidebands under the RF modulation at ~8 GHz (2△) rather than ~4 GHz (△). On the other hand, by looking at Figs. 6, 8, and 9, it can be seen that even under the same RF modulation at 2△, the sideband generation at 600 and 750 mA is not as good as the one measured at 500 mA. Although at all drive currents, the 2△ modulation shows advantages over the modulation at △, the final outcome of the modulation is dependent on the amplitude modulation depth that is applied onto the laser. The modulation depth is determined by slope efficiencies of the L-I curve shown in Fig. 1(c). Apparently, at 500 mA the slope efficiency is higher than those obtained at 600 mA or higher currents. Therefore, the modulation at 500 mA results in higher modulation depth and then more sidebands.

 

Fig. 11 Microwave rectifications measured at QCL drive currents of 500 mA (a), 600 mA (b) and 700 mA (c). The RF power is fixed at 25 dBm and the frequency is swept from 1 to 15 GHz. The dashed and solid vertical lines show the inter-mode beat note frequencies around △ and 2△, respectively.

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In this work, by modulating the coupled-cavity terahertz laser we achieve 6-sideband generation. The sideband number is far less than that of a RF modulated FP cavity terahertz laser. For the same gain medium, the lasing bandwidth measured from a FP cavity laser is around 300 GHz [32]. Although the generated spectra of the modulated coupled-cavity lasers are not that broad, this technique results in two benefits: first of all, by employing the coupled-cavity geometry, we are able to generate dense modes with short cavities. This could be used for some specific high resolution spectroscopic applications since the mode spacing is much smaller than the round-trip frequencies of the cavities. On the second hand, to generate terahertz sidebands equally spaced by 4 or 8 GHz in FP lasers, the cavity length should be much longer than the coupled-cavity length of 2.5 mm used in this work. The longer cavity would not only bring about the difficulty in current injection and degradation of terahertz output power (see [32]), but also require much more electrical power for laser operations.

We use the coupled-cavity geometry to excite high order transverse mode and the beating of the fundamental and higher order modes is then used as a “seed” frequency for RF modulation to generate dense sidebands. Note that that by simply broadening the laser ridge, the higher order modes can be also excited. However, as the laser ridge is broadened, the device will consume higher electrical power for lasing. Furthermore, if the second, third, and fourth order transverse modes are excited, the situation would become much more complex. All the higher order modes lase at different frequencies because for each transverse mode the effective index is different. In that situation, the RF spectra will be in a mess and it would be difficult to find a resonance frequency or a “seed” for the RF modulation. On the other hand, we have to repeat that the modulation on the short section of the coupled-cavity shows advantages in the modulation efficiency over the modulation of an entire FP cavity.

Since the laser active region shows a broad gain bandwidth [32], there is a big room to exploit the gain bandwidth and then achieve broadband spectral spanning of coupled-cavity terahertz laser utilizing RF modulation technique. There are several possibilities to improve performances of coupled-cavity lasers. (1) One option is to optimize the section length of the coupled-cavity to construct a Gires-Tournois interferometer (GTI) mirror. The short GTI mirror can strongly reduce the loss modulation and then overcome the mode selection effect, as well as achieve the dispersion compensation in QCLs for frequency comb generations [27,38,39]. In principle, the RF modulation can be combined with the GTI mirror for producing broadband frequency comb operation in terahertz QCLs. (2) Compared to the single plasmon waveguide used in this work, the metal-metal waveguide is supposed to be more favorable for supporting the microwave signal. And therefore, it can significantly improve the RF modulation efficiency for the mode proliferation in the coupled-cavity lasers. (3) The RF circuit is also critical for the further improvement. As shown in Fig. 7, for the current device the modulation response is not flat due to the impedance mismatching of the RF circuit of the system. If we can optimize the circuit and then obtain a flat response up to 10 GHz, we would gain a lot in the modulation at fundamental inter-mode beat note frequency Δ. One proof for this claim is that as shown in Fig. 6 the sideband generated by the modulation at Δ has almost a same intensity as the carrier mode due to the resonant modulation at the “seed” frequency. However, the number of the generated sidebands is limited by the RF circuit. Once the impedance adaption can be achieved, we believe that the modulation at the fundamental frequency Δ will result in significant improvement in the mode proliferation. In addition, the RF-induced mode proliferation can be used to other laser geometries, i.e., photonic lattice integrated coupled-cavities [40], Y-branched cavities [41,42], quasi-crystal resonators [43], for investigating the mode behavior under modulations.

5. Conclusion

In conclusion, we have reported the first active modulation of coupled-cavity terahertz QCLs. Due to the strong mode selection, the couple-cavity laser showed quasi-single longitudinal mode operation in free running. The inter-mode beat note measurement and far-field analysis revealed that higher order transverse mode co-existed with the fundamental mode in the coupled-cavity laser. The generation of the inter-mode beat note signal was fully analysed based on the nonlinearity of the gain medium and the four-wave mixing effect. With RF modulation at the fundamental or harmonic of the inter-mode beat note frequency, the coupled-cavity terahertz laser demonstrated 6 sidebands spanning over 50 GHz. The technique of mode proliferation induced by the microwave modulation of two-section coupled-cavity lasers shows the advantages in generating dense modes for high resolution spectroscopic applications and consuming less electrical power over the FP lasers. Further performance improvements can be obtained by optimizing the waveguide geometry and RF circuit.