1. Introduction

Broad spectral spanning in the terahertz frequency range is much in demand for spectroscopic applications due to the unique terahertz absorption lines of various molecules. Although the time-domain spectroscopy system with photoconductive antennas or nonlinear crystals can cover a wide frequency range from 0.1 to a few THz (note that the frequency coverage is subjected to the use of different antennas or nonlinear crystals) [1, 2], the terahertz power generated from the time-domain system is weak which strongly prevents the spectrometer from diverse applications. Different from the optically-pumped terahertz radiation sources used in the time-domain system, the electrically-pumped terahertz quantum cascade laser (QCL) employing the cascade periodic structure is able to output high power in pulsed and continuous wave (cw) modes [3–5]. And in the frequency regime between 1 and 5 THz, the terahertz QCL has been proved to be the most efficient radiation source based on semiconductors and electrical pumping scheme.

It is an important work to broaden the lasing spectra of terahertz QCLs for spectroscopic applications. From the point of view of QCL active region design, different approaches, such as continuum-to-continuum transition [6], multi-stack active regions [7] and step-well design [8] have been exploited to overcome the narrow band property of QCLs and then to achieve broadband emission. Besides the internal active region innovations, another external technique, i.e., radio frequency (RF) modulation, can significantly broaden the laser spectrum by stimulating more longitudinal modes beyond the threshold and then to lase. In addition, the RF modulation is technically convenient to be implemented on lasers to maximize the utilization of the laser gain bandwidth given that the impedance matching is fulfilled. Actually, the RF modulation has been widely used for diode lasers to obtain mode-locked short optical pulses [9, 10]. In the mode-locking applications, the diode laser working in cw mode is injection mode-locked by using an external RF synthesizer. Consequently, in frequency domain the emission spectra are broadened, and meanwhile in time domain the optical pulses can be shortened. Via the efficient RF modulation, the cw laser can generate stable ultrashort optical pulses. The RF injection technique has been also adopted for modulation and mode-locking of QCLs emitting in mid-infrared and terahertz regimes [11–13]. In the previous experiments, the RF modulation was applied onto QCLs that are working in cw mode. However, for some QCL gain media, because of the imperfections in active region design, fabrication, and operation temperature limited by the cooling system, the cw operation is challenging. Therefore, the RF modulation of pulsed lasers provides a solution to broaden the emission spectra of pulsed lasers for broadband applications.

Here in this work, we at the first time demonstrate the RF modulation of terahertz QCLs working in pulsed mode. Inter-mode beat note and terahertz emission spectra of long cavity terahertz QCLs with single plasmon and double-metal waveguide geometries are experimentally investigated. Although the mode locking and ultrashort optical pulses cannot be obtained for the pulsed laser, we do observe strong spectral broadening under RF modulation.

2. Experiment and basic characterizations

Aiming at the RF modulation of pulsed terahertz QCLs, we employ a resonant phonon QCL active region which is similar to the one reported in [14]. The GaAs/Al_0.15Ga_0.85As active region with 183 periods, sandwiched between the bottom (doped to 3 × 10¹⁸ cm⁻³) and upper (doped to 5×10¹⁸ cm⁻³) GaAs contact layers, is grown by a molecular beam epitaxy system on a semi-insulating GaAs (100) substrate. To facilitate the following double-metal waveguide process, in the QCL wafer we add a 200-nm thick Al_0.55Ga_0.45 As etch-stop layer between the substrate and the bottom GaAs contact layer.

After the growth, the QCL wafer is processed into both single plasmon and double-metal waveguide structures. For single plasmon devices with ridge widths ranging from 100 to 400 µm, the upper electrode is made of Ti/Au (10/300 nm) schottky contact and the lateral electrode is made of Ge/Au/Ni/Au (13/33/30/300 nm) which is then thermally annealed for 40 s at 370 °C to form the ohmic contact. The detailed fabrication process can be found in [16]. For double-metal devices, we first bond the QCL wafer onto a n⁺ GaAs substrate by using an Au-Au thermocompression bonding technique. Then the lapping and wet-etching are employed to remove the GaAs semi-insulating substrate, which is followed by the AlGaAs etch-stop layer removal. Afterwards, the top electrode Ti/Au (10/300 nm) is fabricated by using the optical lithography, e-beam evaporation and lift-off processes. Finally, the ridge structures are realized by inductively coupled plasma (ICP) dry etching. To improve the device thermal management, the GaAs substrates are lapped down to 150 µm. The processed single plasmon and double-metal ridges are cleaved into different cavity lengths from 2 to 6 mm. The cleaved laser bar is then indium-soldered onto a copper heat sink for wire bonding.

For the device characterization, a continuous-flow liquid-helium cryostat equipped with a 3-mm thick high density polyethylene (HDPE) window is used to provide the cryogenic working environment and terahertz light out-coupling window for QCLs. The lasers are driven in pulsed mode with a repetition rate of 2 kHz and a pulse width of 5 µs (1% duty cycle). The inter-mode beat note spectra of free running lasers are measured using a spectrum analyser with an assistance of a Bias-T with a bandwidth of 18 GHz. A RF synthesizer with the frequency up to 30 GHz and maximum power of 30 dBm is used for RF modulation. The output power is detected by a terahertz thermopile detector and the power value is read using a calibrated laser power meter (Ophir). The terahertz emission spectra are measured using a Fourier transform infrared (FTIR) spectrometer (Bruker v80) with a spectral resolution of 0.1 cm⁻¹ (3 GHz).

In Fig. 1 we show the light-current-voltage (L – I – V) characteristics of single plasmon [Figs. 1(a) and 1(b)] and double-metal [Fig. 1(c)] terahertz QCLs with different device dimensions recorded in pulsed mode. For the power calibration, we consider two factors, i.e., the terahertz light transmission of the 3-mm HDPE window and the double-emission of front and rear laser facets. The transmission of the 3-mm thick HDPE is measured to be 66% at 4.3 THz using a FTIR spectrometer. Any other factors, such as collection efficiency, water absorption, and mirror reflection are not taken into account for the power calibration. In this work, for the RF modulation experiments, we use 6-mm long laser cavity which results in smaller round-trip frequency around 6 GHz. As elaborated in [12],15], for the effective QCL RF modulation, we normally inject the RF signal at the laser round-trip frequency. If we can elongate the laser cavity and then lower the round-trip frequency, in principle the RF injection efficiency can be significantly improved due to the smaller signal attenuation of the RF cable. For the 6 mm devices, we can see from Fig. 1 that the single plasmon laser can work up to 100 K and the double-metal laser lases up to 120 K. However, the double-metal laser demonstrates much lower peak power than the single plasmon QCL due to the poor optical coupling efficiency caused by impedance mismatch of the subwavelength mode in double-metal waveguide and the fabrication imperfection. Another clear difference is that at low temperatures from 10 to 60 K, the L – I curves of the double-metal QCL show unexpected behaviour, i.e., as we increase the drive current from 4 to 7 A, the power decreases. Since the both I – V curves of the single plasmon and double-metal devices show good agreement with each other and the single plasmon lasers behave regularly with temperature which infers that the active region structure and electrical property of the QCL are free of defects, the unexpected power degradation of the double-metal laser at low temperatures is solely due to the poor optical waveguide resulted from the fabrication imperfections, e.g., wafer bonding, ridge etching, cleaving, device mounting and so on. As the temperature is higher than 60 K, the L – I curves of the double-metal device shown in Fig. 1(c) return to the normal. Actually, it is hard to explain the temperature behaviour. One possible reason is that this unexpected temperature performance is related to the unreliable wafer bonding that affects the optical performance at low temperatures and the adverse effect becomes weak with increasing temperature. For reference, in Fig. 1(b), the performance of a broad ridge laser with a ridge width of 400 µm and a cavity length of 4 mm processed from a same wafer is presented. We can see that at 10 K the peak power of the broad laser can reach 1.2 W which indicates that the design and the growth of QCL are excellent for high pulsed power output.

 

Fig. 1 Measured L – I – V characteristics of single plasmon [(a) and (b)] and double-metal (c) terahertz QCLs with different device dimensions in pulsed mode (2 kHz repetition rate and 5 µs pulse width) at different heat-sink temperatures ranging from 10 K to 120 K.

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It has been known that the subwavelength aperture of double-metal QCL waveguides can cause non-directional far-field beam patterns that seriously affect the practical applications of terahertz QCLs. Many photonic engineering methods such as third-order DFB [18], graded photonic heterostructures [19], antenna feedback scheme [20], and meta-surface QCLs [21] have been exploited to achieve low-divergence narrow beams. However, these methods, meanwhile, result in single longitudinal mode operation due to the strong mode selection mechanism besides the narrow beam profile. Therefore, they are obviously not suitable for broadband emission. Because of this, in this work to not do harm on the laser’s spectrum, we use a hemispherical Silicon lens [22] which is mounted just in front of the laser facet to improve the far-field beam quality of double-metal terahertz QCLs. The Silicon lens technique is practically broadband depending on the anti-reflection coating. Furthermore, it, independence on fabrication process, is generally applicable for any terahertz QCL to reshape the laser beam. Figure 2(a) shows the schematic of the double-metal QCL with a Silicon lens coupler. Note that the pulsed electrical pump is applied onto the QCL chip through a contact pad which is located beside the laser. A 50-Ω microwave transmission line mounted behind the laser cavity is only used for RF signal, either for monitoring the inter-mode beat note signal or for external RF modulation. Figures 2(b)–2(f) show the measured far-field patterns at different drive currents. The α and β axes shown in Figs. 2(b)–2(f) are corresponding to the directions sketched out in Fig. 2(a). We can clearly see that in the entire current dynamic range the double-metal terahertz QCL with the Silicon lens coupler always demonstrates single-lobe narrow beam patterns without any interference fringes. The measured full widths at half maximum of the beam patterns are not larger than 2.8° in the vertical direction and 2.5° in the horizontal direction. The best values obtained from the measurement are 2.6° (vertical) and 2.4° (horizontal) at a drive current of 5 A. To the best of our knowledge the divergence angles presented in this work are the smallest among the experimental results reported in literatures for terahertz QCLs. However, it should be noted that the mounting of Silicon lens coupler is a delicate work. The far-field beam pattern is strongly dependent on the relative position of the lens coupler to the laser facet. Even a small misalignment could result in unexpected divergent beams.

 

Fig. 2 (a) Schematic of the double-metal terahertz QCL with a Silicon lens coupler. Measured far-field patterns of a 6-mm long double-metal laser at drive current of 4 A (b), 5 A (c), 7 A (d), 8 A (e), and 9 A (f). For the far-field measurement, a Golay-cell detector with a small pinhole mounted in front of the detection element is used. The Golay-cell is placed 10-cm away from the laser emitting facet and moves in the vertical and horizontal directions on a 10-cm-radius sphere during the far-field measurement. To satisfy the slow response of the detector, we apply additional slow modulation of 10 Hz onto the terahertz laser for the lock-in detection. The measurement is performed when the laser is temperature-stabilized at 10 K.

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3. Inter-mode beat note and RF modulation induced spectral broadening

As demonstrated in [16], we have succeeded in modulating a long cavity terahertz QCL operating in cw mode at the laser round-trip frequency to broaden the terahertz spectra for homogeneous spanning over 330 GHz. For cw lasers, we can use a Bias-T for electrical pump and RF signal monitoring or modulation simultaneously. Since the electrical pulses with a repetition rate of kHz level cannot go through the Bias-T, we therefore separate the electrical pump and RF modulation in this work for pulsed QCLs. As shown in Fig. 2(a), we mounted a contact pad beside the laser chip for pulsed electrical pump and a microwave transmission line for RF monitoring and modulation. Different from the RF modulation of cw QCLs [11, 12, 16] where the terahertz light emission is continuous and the RF modulation takes effect continuously too, the RF modulation of pulsed QCLs only takes effect when the laser is switched on for 5 µs for each electrical cycle in this work. The frequent switching of the electrical pumping signal for the QCLs would bring about large electrical noise which then prevents the laser from active mode-locking operation with RF injection due to the large-scale frequency instability. Although the RF-assisted active mode-locking is difficult to achieve for pulsed QCLs, the RF modulation technique can be used to generate side bands and then to broaden the terahertz spectra.

Employing the geometry shown in Fig. 2(a), we can record the inter-mode beat note spectra and terahertz emission spectra of QCLs with and without RF modulation. As what we already elaborated previously, to reduce the RF signal attenuation and strengthen the RF modulation efficiency we use 6-mm long laser cavity which results in an inter-mode beat note frequency between 6.0 and 6.3 GHz. Figure 3 shows the experimental results obtained from the 6-mm long single plasmon terahertz QCL. In Fig. 3(a), from bottom to top panel we show the measured beat note signal of the laser in free-running mode at different drive currents from 4 to 8 A. The black curves are single-shot RF traces measured with a resolution bandwidth of 300 kHz, while the gray ones give the traces in Max-Hold mode recorded for a time duration of 2 minutes. It is worth mentioning that for cw terahertz QCLs with a similar cavity length the inter-mode beat note signal is stable and frequency comb operation can be obtained [16]. However, from Fig. 3(a), we can clearly see that the free-running pulsed QCL shows strong frequency instability which is characterized by the multi-line beat note spectra and broad Max-Hold traces. As the drive current is increased from 4 to 8 A, the Max-Hold linewidth increases from 38 to 350 MHz. As elaborated previously, the broad beat note is as what we expect for pulsed QCLs and the electrical noise resulted from the electrical pulsing can make the frequency unstable. The multi-line beat note is more pronounced when the laser is driven at higher currents. This is because at high drive current, the terahertz spectrum becomes broader [see Fig. 3(b)] and the frequency beating in wide frequency range leads to complex situations (index dispersion can also contribute to the broad beat note). In Fig. 3(b), we also show the RF spectra of the single plasmon laser under RF modulation at different drive currents. The bottom panel of Fig. 3(b) is the RF spectrum recorded when the laser is off and the RF modulation is on. We can see that even the laser is not pulsed the RF spectrum shows visible noise indicated by the black arrows. The noise shown here is attributed to the crosstalk between the pulser and the RF generator. Note that in this case, the pulser is just connected to the power and it doesn’t output electrical pulses to the QCL. As we switch on the QCL, it can be seen that even at low currents we observe the multi-line beat notes from the QCL. With 25-dBm RF modulation, the QCL beat note cannot be injection locked, which indirectly verify that the phase noise of the pulsed laser is too high and the modes can not be locked.

 

Fig. 3 Inter-mode beat note spectra in free running (a), microwave spectra under RF modulation (b), and terahertz emission spectra (c) of the 6-mm long single plasmon terahertz QCL measured at different drive currents from 4 to 8 A. In (a), the black curves are single-shot traces and the gray ones are the Max-Hold traces measured with a time duration of 2 minutes. The laser is working in free-running mode (without RF modulation). In (b), for the sake of clear comparison, the cental frequency around 6.2 GHz is subtracted in each panel. In (c), the black and red curves correspond to the spectra without and with RF modulation, respectively. The resolution used for the measurement is 3 GHz. All the data are recorded at a heat sink temperature of 10 K.

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Although we are not able to achieve comb operation for the current lasers operating in pulsed mode, it is worth noting that the frequency comb is indeed observed in pulsed terahertz QCLs [23] and it is even possible to do the completely computational extraction of the phase and timing signals of a multi-heterodyne spectrum for spectroscopy [24]. Back to this work, even the inter-mode beat note is not stable, the RF modulation in principle can be used for broadening the terahertz spectra. As shown in Fig. 3(c), we plot the terahertz emission spectra without (black) and with RF modulation (red) for the 6-mm long single plasmon terahertz QCL. For the RF injection, we use an external RF synthesizer and set the RF signal frequency equal to the strongest beat note frequency obtained from the free-running measurements shown in Fig. 3(a). The RF power is set as 25 dBm. However, due to the RF cable attenuation and signal reflection induced by the impedance mismatching, only small part of the RF signal finally enters the laser cavity. In Fig. 3(b) all the spectra are normalized for clarity. At some currents, e.g., 6 and 8 A, we can see that the RF modulation can broaden the terahertz spectra and make them homogeneous. Typically, at 8 A with RF modulation, we obtain continuous spectral spanning over 320 GHz from 4.18 to 4.5 THz (52 longitudinal modes). However, for the single plasmon laser, the RF modulation doesn’t make great spectra at all the drive currents. Especially, at 7 A the emission spectrum under RF modulation is almost identical to the one without RF modulation.

In comparison with the single plasmon waveguide, the double-metal waveguide geometry is more suitable for high frequency modulation due to the fact that the metal-metal films together with the QCL gain medium are similar to the configuration of microwave transmission lines [17]. In Fig. 4, we show the similar measurements for a 6-mm long double-metal terahertz QCL, the L – I – V characteristics of which are shown in Fig. 1(c). The inter-mode beat note spectra in free running, RF spectra under RF modulation, and terahertz emission spectra in the entire current dynamic range are shown in Figs. 4(a)–4(c), respectively. Similar as the single plasmon lasers, with increasing the drive current the free running beat note shows a red shift and it changes from single line to multi-line behavior as the terahertz emission becomes broader and broader. The Max-Hold linewidth increases from 40 to 400 MHz as the drive current is increased from 3 to 9 A. The RF spectra under RF modulation shown in Fig. 4(b) demonstrate similar behaviour as the single plasmon laser. Here in Figs. 3(a) and 4(a) we employ the Max-Hold measurement to characterize the long term frequency stability of free running lasers. It shows that at most of drive currents multi-line beat note signal is observed which indicates that the modes are strongly incoherent with each other. Note that to systematically analyse the long term mode stability, the Allan variance measurement, which can provide more information on frequency and amplitude oscillations, should be performed. The Allan variance measurement has been successfully used to prove that the QCL-based dual-comb setup in the mid-infrared wavelength range is an efficient spectroscopic tool with a signal to noise ratio (SNR) close to shot noise limit [25, 26].

 

Fig. 4 Inter-mode beat note spectra (a), microwave spectra under RF modulation (b), and terahertz emission spectra (c) of the 6-mm long double-metal terahertz QCL with a Silicon lens coupler measured at different drive currents from 3 to 9 A. In (a), the black curves are single-shot traces and the gray ones are the Max-Hold traces measured with a time duration of 2 minutes. The laser is working in free-running mode (without RF modulation). In (b), the cental frequency around 6.2 GHz is subtracted in each panel. In (c), the black and red curves correspond to the spectra without and with RF modulation, respectively. All the data are recorded at a heat sink temperature of 10 K.

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Figure 4(c) shows the RF modulation effects on emission spectra of the 6-mm long double-metal terahertz QCL. Same as what we do on the single plasmon laser, here for the double-metal laser the RF frequency is set according to the corresponding free-running beat note frequency shown in Fig. 4(a) and the RF power is 25 dBm. From Fig. 4(c) we can observe a significant spectral broadening of the double-metal terahertz QCL by employing the RF modulation technique at all drive currents. At lower currents of 3 and 4 A, the free-running terahertz spectra consist of only few modes, while with RF modulation the spectra get broadened immediately. In higher current range from 6 to 8 A, without RF modulation the terahertz spectra are inhomogeneous with spectral holes (mode missing). Once the RF signal is applied, the frequency holes can be filled and the spectra become homogeneous and broad. At 9 A, with RF modulation, we obtain broadest spectrum which is homogeneously spanning over 340 GHz from 4.28 to 4.62 THz. In the entire current dynamic range, with RF modulation the emission spectra of the double-metal QCL can continuously span over 600 GHz from 4.0 to 4.6 THz, while the single plasmon terahertz QCL covers around 400 GHz frequency range as shown in Fig. 3(c). All the data shown in Fig. 4(c) indicate that double-metal waveguide is actually favorable for RF modulation to generate broadband terahertz emission even when the laser is working in pulsed mode.

One thing should be mentioned is that although the output power of the two devices differs by 10 times, the power inside the cavities may be similar due to the differences in waveguide and mirror losses. Therefore, it is still reasonable that we observe similar SNR of the inter-mode beat note from both the single plasmon and double-metal devices as shown in Figs. 3(a) and 4(a). However, for the RF modulation the situation is different for both waveguide configurations. The double-metal waveguide is an analogue of the transmission line and the latter is widely used in the microwave technology. Therefore, the double-metal waveguide configuration inherently shows advantages over the single plasmon waveguide in the impedance matching and low loss transmission properties in the microwave frequency regime. Because of this, more RF power can be finally injected into the double-metal laser cavity for the more efficient modulation. So we observe that the double-metal waveguide is favorable for RF modulation to efficiently broaden the terahertz spectra.

4. Conclusion

We have demonstrated RF modulation for pulsed terahertz QCLs based on both single plasmon and double-metal waveguides. The Silicon lens coupler that doesn’t reshape the laser spectra was implemented on double-metal terahertz QCLs to improve the far-field beam quality. Using the Silicon out-coupler, we achieved single-lobe narrow beam patterns with a record beam divergence of 2.6° and 2.4° in vertical and horizontal directions, respectively. Although the mode locking and ultrashort optical pulses cannot be obtained for the current pulsed laser by employing the RF modulation technique, we observed strong spectral broadening of the pulsed lasers with single plasmon and double-metal waveguide configurations under RF modulation. The inter-mode beat note and terahertz emission spectra were investigated systematically in the entire current dynamic range for both lasers. As expected, we found that the double-metal terahertz QCL was more favorable for RF modulation to generate homogeneous terahertz spectra. In the entire current range, the spectra of the double-metal laser spanned over 600 GHz with RF modulation, while the single plasmon laser showed a spectral coverage of around 400 GHz in the entire current dynamic range.