Millimeter-wave generation with a room-temperature nonlinear quantum cascade laser Open Access

The frequency range spanning from sub-terahertz (THz) to THz has garnered considerable interest due to its potential utility in a variety of applications, including but not limited to communication, imaging, and spectroscopy.^1,2 To expeditiously enable the extensive commercial adoption of THz technology, there is a growing demand for a diminutive and reproducible coherent semiconductor source. On the low-frequency side of the THz frequency, many electronic devices such as the resonant tunneling diode,^3,4 uni-traveling carrier photodiode,^5,6 and complementary metal–oxide–semiconductor transistor^7–9 have been developed as THz emitters. Simultaneously, different technologies have been documented on the higher frequency side so far.^10–13 THz quantum cascade lasers (THz-QCLs) are significant semiconductor-based emitters with high power output capabilities. Nevertheless, the lasers exhibit significant constraints when operating within the lower frequency spectrum. Furthermore, THz-QCLs operating in the sub-terahertz (sub-THz) frequency range have been reported but can only be realized under rigorous conditions in which there is both a strong external magnetic field and cooling to liquid-helium temperature.^14,15 A promising approach to generating sub-THz radiation from a QCL is based on intracavity difference frequency generation (DFG)^16–19 in a QCL active region that has giant intersubband optical nonlinearities.²⁰ In our recent work, nonlinear DFG mixing in mid-infrared (MIR) QCLs operating at frequencies down to 420 GHz was demonstrated at room temperature²¹ by adopting a dual-upper-state (DAU) active region,^22–24 which realized high pump power (>1 W) at a long wavelength (>13 μm).^21,25 In addition, millimeter-wave radiation below 300 GHz^26,27 has been achieved by adopting second-order nonlinearity in THz-QCLs. However, these achievements were attained only in cryogenic temperatures.

Here, we demonstrate 231-GHz DFG emission at room temperature from a dual-wavelength (λ₁ ∼ 13.53 μm and λ₂ ∼ 13.39 μm) MIR QCL adopting the DAU active region, where two sections of distributed feedback grating (DFB) are fabricated for the efficient allocation of mid-infrared pumps. Furthermore, we discuss the efficiency of nonlinear DFG employing MIR QCLs in the sub-THz spectral range.

The growth of layer structures was done by the metal-organic vapor phase epitaxy technique on a semi-insulating InP substrate. The active region of our devices is designed with a uniform DAU structure consisting of 70 stages, featuring a wide gain bandwidth and optimized for a long wavelength (∼13.7 μm). Additional information regarding this active region is elaborated upon in Ref. 18. A ridge waveguide was fabricated to provide dielectric confinement for the MIR modes. Figures 1(a) and 1(b) show a schematic of the device and the cross section of the device on the x–z plane. As a lower cladding layer, 5-μm-thick n-InP (Si, 1.0 × 10¹⁶ cm⁻³) was grown on top of an InGaAs current spreading layer that was 200 nm thick (Si, 1.0 × 10¹⁸ cm⁻³). The active region of the device consisted of a lattice-matched In_0.53Ga_0.47As/In_0.52Al_0.48As between a 200-nm-thick n-In_0.53Ga_0.47As layer (doped with Si at a concentration of 1.5 × 10¹⁶ cm⁻³) at the bottom and a 450-nm-thick n-In_0.53Ga_0.47As layer (also doped with Si at a concentration of 1.5 × 10¹⁶ cm⁻³) at the top. The upper n-In_0.53Ga_0.47As guide layers were patterned using nanoimprint lithography to establish the two buried grating sections^28,29 for DFG through a two-color MIR nonlinear mixing process. This is depicted in the cross-sectional view of the device along the y–z plane in Fig. 1(c). To create two grating periods with a difference frequency of approximately 240 GHz, a long wavelength (λ₁ = 739 cm⁻¹) and a short wavelength (λ₂ = 747 cm⁻¹) were selected. The two grating coupling coefficients in this instance were comparable (∼7 cm⁻¹). A semi-insulating InP (Fe-doped) layer was applied to the wafer after it had been etched to create waveguides with ridges that were 14 μm wide. Subsequently, the process involved depositing a 15-nm-thick n-type indium phosphide (Si-doped, approximately 1.0 × 10¹⁸ cm⁻³) cap layer, followed by a 5-μm-thick n-type indium phosphide (Si-doped, 1.5 × 10¹⁶ cm⁻³) upper cladding layer. The top contacts of Ti/Au were fabricated using the process of evaporation deposition. The device was ultimately mounted in an epilayer-up configuration onto a copper heat sink.

As the Cherenkov phase matching scheme³⁰ was applied to induce DFG in the device easily. This was achieved through the polishing of the front facet of the device substrate at an angle of approximately 10°, as shown in Figs. 1(a) and 1(c). The results of a three-dimensional comsol simulation of the sub-THz nonlinear QCL with Cherenkov emission are shown in Fig. 1(d). Two MIR pumps (739 and 747 cm⁻¹) propagated in the active region and the model describes the nonlinear polarization waves generating the difference frequencies. The simulation was performed with a cavity length of 3 mm, a substrate width of 1 mm, and a thickness of 350 μm, assuming measured device dimensions. The simulation results clearly show that THz radiation was emitted as a Gaussian-like beam by the device in free space.

Figure 2(a) presents the current–voltage–light output characterization of the QCL device having a width of 14 μm and a cavity length of 3 mm without a grating formed on a semi-insulating InP substrate and operating in pulsed mode (pulse width of 200 ns and repetition frequency of 50 kHz). Two off-axis parabolic mirrors were used to collect the MIR output power, which was then measured with a calibrated thermopile detector. The spectral measurements were performed using a Fourier transform infrared spectrometer. The laser spectra at various currents are shown in Fig. 2(b). A Febry–Perot device produced a threshold current density of 3.5 kA/cm² at 293 K and a maximum peak power of 1.1 W (from a single facet) with a slope efficiency of 0.95 W/A; this is one of the highest peak powers reported to date for a long-wavelength (>13 μm) QCL.

Figure 3(a) shows the current–voltage–light output characteristics of a device with two sections of DFB designed for THz and MIR frequencies. The device operates in pulsed mode with a 1% duty cycle under room temperature conditions. At a temperature of 293 K, the QCL exhibited a peak power emission of around 0.6 W in the MIR region. Owing to the lasing suppression enabled by the DFB configuration, the peak power of the MIR was comparatively lower than that of the Fabry–Perot device.

In order to enhance the efficiency of DFG outcoupling, a silicon lens was positioned near the polished substrate of the QCL device in the measurement of the THz output characteristics. A silicon bolometer cooled by liquid helium was positioned approximately 5 mm in front of the silicon lens. THz emission was readily detected subsequent to reaching the MIR threshold current. The THz spectra were acquired at current values of 2.25 and 2.14 A utilizing a Fourier transform infrared spectrometer in step-scan mode, as depicted in Fig. 3(b). Two peaks were observed at frequencies of 231 GHz (7.7 cm⁻¹) and 465 GHz (15.5 cm⁻¹) for both currents.

The MIR emissions at the wavenumbers ω₁ = 746.9 cm⁻¹, ω₂ = 739.2 cm⁻¹, and ω₃ = 731.4 cm⁻¹ exhibited frequency spacings of 231 GHz (7.7 cm⁻¹) and 465 GHz (15.5 cm⁻¹), as illustrated at the bottom of Fig. 3(c). The individual frequencies ω₁ and ω₂ are associated with the DFBs, while ω₃ represents a mode that remains unsuppressed due to the Fabry–Perot device. The spacings observed in the MIR pump spectra exhibit strong correspondence with the frequencies present in the THz spectrum.

Current–light output characteristic measurements were performed with a bandpass filter (BPF) having transmission around 300 GHz, as shown in Fig. 3(a), to separate the frequencies. The output power measured with the BPF was 14% of that measured without the BPF. This result is in good agreement with the transmittance of the BPF being 11% at 231 GHz as shown in Fig. 3(b) and indicates that the radiation at a frequency of 231 GHz is attributable to DFG. This frequency is the lowest reported operating frequency for QCL sources at room temperature.

Figure 4(a) presents the MIR and THz current–voltage–light output characteristics of the device operating in pulsed mode at a temperature of 250 K. The MIR peak power increased and was approximately ∼1.7 W at 250 K. There was a more pronounced increase in THz power with decreasing temperature, with the THz power at 250 K being 63.8 times that at 293 K. Figures 4(b) and 4(c) show the MIR and THz spectra of the device measured at a temperature of 250 K. The MIR emissions were observed at the wavenumbers ω₁ = 748.5 cm⁻¹, ω₂ = 740.8 cm⁻¹, and ω₃ ∼ 726.0 cm⁻¹. Both THz peaks at 231 GHz (7.7 cm⁻¹) and around 675 GHz (22.5 cm⁻¹), which correspond to ω₁−ω₂ and ω₁−ω₃, respectively, were observed. The frequency peak of around 675 GHz is dominant in the device at a temperature of 250 K. On the other hand, the peak at a frequency of 231 GHz is observed to be negligibly small.

The MIR-to-THz power conversion efficiency, which is defined as the ratio of the THz peak power to the product of the MIR pump powers, is directly proportional to the square of the generated frequency ω_DFG, the intersubband optical nonlinearity χ⁽²⁾, and the coherent length l_coh.¹⁶ The coherent length exhibits a decline at lower frequencies due to increasing THz absorption caused by free carrier in the waveguide.³¹ Thus, the MIR-to-THz power conversion efficiency dramatically decreases as the difference frequency becomes low. From the experimental results in Fig. 3, the conversion efficiency of the device is estimated to be ∼2 μW/W² for the DFG at 231 GHz. This is significantly lower compared to the results reported for millimeter-wave generation in GaAs-based THz QCLs,^26,27 in which higher χ⁽²⁾ can be obtained due to larger quantum wells for THz lasing. Furthermore, based on the results shown in Fig. 4, we analyze the MIR to THz conversion efficiency of ∼80 μW/W² for the DFG at 675 GHz, which is almost comparable with the previous result.²⁵ Despite the enhanced MIR peak power at 250 K, an MIR pump power of ω₃ is estimated to be much lower compared to the main peaks at ω₁ and ω₂. Thus, the dramatic increase in the THz output powers at 250 K is attributable to the higher MIR to THz conversion efficiency for THz emission at a higher frequency of 675 GHz. As a result, the significant degradation of the MIR-to-THz conversion efficiency was experimentally observed in the lower frequency range.

We demonstrated sub-THz sources using a powerful MIR QCL with two DFB sections, producing an emission frequency of 231 GHz at room temperature, which is the lowest reported frequency among single monolithic semiconductor laser sources at this temperature. Moreover, we discussed the MIR-to-THz power conversion efficiency and obtained the value of ∼2 μW/W² for the DFG at 231 GHz from experimental results.

This work was supported by MIC/SCOPE (No. JP235006003). The authors express their gratitude to K. Kuroyanagi for the technical support in the THz measurements.

The authors have no conflicts to disclose.

Shohei Hayashi: Data curation (lead); Formal analysis (lead); Visualization (lead); Writing – original draft (lead). Akio Ito: Investigation (supporting); Methodology (supporting); Validation (supporting). Tatsuo Dougakiuchi: Data curation (supporting); Investigation (supporting); Methodology (supporting); Validation (supporting); Writing – review & editing (supporting). Masahiro Hitaka: Investigation (supporting); Methodology (supporting); Writing – review & editing (supporting). Kazuue Fujita: Conceptualization (lead); Data curation (supporting); Formal analysis (supporting); Funding acquisition (lead); Investigation (supporting); Methodology (supporting); Project administration (lead); Supervision (lead); Writing – original draft (supporting); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.