1. Introduction

Electrically pumped continuous-wave (EPCW) operation is one of the most demanded characteristics for semiconductor lasers. Electric pumping is the key for miniaturization, integration, and practicability, and continuous-wave (CW) operation is indispensable for ultranarrow linewidth and ultra-stable output power, which are the core of applications including optical communication, sensing, spectral analysis, metrology [1], etc. EPCW semiconductor lasers – including multi-quantum well lasers [2], quantum cascade lasers [3], and interband cascade lasers [4] – usually operate with high input power density, and the nanometer-thick multilayers of the active region imply low vertical thermal conductivity [5,6]. Therefore, the power consumption and thermal conduction are the fundamental issues that limit the laser performances such as operating temperature and output power. The situation becomes more challenging at long operation wavelength because the device size and thus the heat accumulation increases dramatically with the wavelength [7–9].

Up to now, THz QC lasers generate coherent radiation with the longest available wavelengths in the context of semiconductor lasers [10–13]. Innovations of the active region and the laser resonator have witnessed substantial progresses of THz QCLs, including near room temperature operation in pulsed mode [14–16], high output power and high beam quality [17–21]. Nevertheless, the maximum CW operating temperature (T_cw) has been stuck at cryogenic temperature for many years [12,22,23], mainly because of the high input power density and the poor thermal conductivity of the active region. Recent advances to improve T_cw focus on the wire lasers, where the ridge width is much less than the wavelength [23–28]. The wire lasers enable small pumping area but relatively large specific surface area, which reduces the power consumption and facilitates the lateral heat dissipation. Novel resonators based on the wire laser have been developed to realize high CW output power and tight beam pattern. Successful examples include third-order distributed feedback (DFB) THz QC lasers [23,24], phased array of antenna coupled third-order DFB lasers [25], unidirectional DFB lasers [26], wire lasers hybridizing a DFB grating with an emission grating [27], metasurface-based vertical-external-cavity surface-emitting lasers [28], etc. Nevertheless, there is still huge room for the development in terms of the T_cw, the output power, and the beam quality.

Recently, optical bound states in the continuum (BICs) or quasi-BICs have attracted substantial attention as versatile tools to manipulate the photon behaviors [29–32], and have greatly boosted the research of ultra-low threshold lasers [33], sensing [34], nonlinear optics [35], topological photonics [36], etc. Optical BICs refer to the special electromagnetic modes that locate inside the continuum and coexist with extended waves, but they remain perfectly confined without any radiation. BICs are thus spatially bound and spectrally discrete with an infinite quality factor (Q-factor). True BICs exist only in an infinite periodic structure due to either symmetric incompatibility (symmetry-protected BICs) or destructive interference (non-symmetry-protected BICs). In a finite system and by symmetry breaking, BICs can be converted into quasi-BICs with controllable radiation quality factor (Q_rad) [29–33].

Symmetry-protected BICs were also regarded as the non-radiative band-edge modes and used in surface-emitting semiconductor lasers, including DFB or photonic crystal (PhC) lasers [37–39]. Recent efforts intentionally break the inversion symmetry to excite the quasi-BICs with controllable Q_rad, which leads to high output power, high beam quality, and still relatively low threshold [40–42]. However, all these efforts were conducted in multi-periods lasers where the resonator (grating or PhC) contains many periods. By minimizing the laser resonator – which is important for EPCW operation – the quasi-BICs inevitably suffer from severe in-plane leakage [43]. Although super-BICs or accident-BICs have recently been proposed that enable high Q_rad in few-periods or subwavelength resonators [31,44], they were only demonstrated in passive devices or optically pumped lasers [45].

In this work, we demonstrate the CW operation of 1D THz QC microlaser arrays that work on various BIC states. First, in a multi-periods microlaser array, we prove that symmetry breaking can activate a quasi-BIC as the laser mode, leading to high output power with a tight beam under the CW condition. To further increase T_cw, we hybridize the quasi-BIC generated in a biased few-periods microlaser array with a high Q-factor spoof surface plasmon polariton (SPP) mode formed in another unbiased array. The so-called hybrid-BIC greatly reduces the pumping area while keeping the in-plane leakage substantially low. Moreover, the discretely distributed microlasers considerably reduce the device thermal resistance. The resultant microlaser array exhibits single-mode emission with significantly improved T_cw, high beam quality, and moderate output power under the CW condition.

2. Device concept, design, and results

We first investigate the quasi-BIC in the multi-periods THz QC microlaser arrays, and then the hybrid-BIC in the few-periods (biased) microlaser arrays. For simplicity, we name them as the quasi-BIC and hybrid-BIC microlaser arrays, respectively.

2.1 Quasi-BIC microlaser arrays

Figures 1(a) and (b) respectively show the schematic of a quasi-BIC microlaser array, and the 2D cross-section of one period. The device is based on a metal-metal waveguide, where the active region is sandwiched between the bottom and top metallic layers. The device consists of N periods with a periodicity of Λ. A single unit contains two microlasers, each of which is deep-subwavelength in thickness (t_AR, z-direction) and in width (x-direction) but is elongated in length (L_y, y-direction). The widths of the two microlasers in each unit are respectively w + δw and w-δw, where δw<<w, hence breaking the in-plane inversion symmetry. For current injection, each microlaser is linked to the electric pads via two tapered waveguides along the y-direction. In the region of the electric pads and the tapered waveguides, there is a SiO₂ isolating layer underneath the top metallization, and therefore the current injection occurs only in the microlasers.

 

Fig. 1. Operation principle of a quasi-BIC microlaser array. (a) 3D schematic of the quasi-BIC array. (b) 2D cross-section of one period. The array contains N periods with the periodicity of Λ. Each period contains two microlasers with slightly different widths (w + δw and w-δw). Each microlaser is t_AR in thickness, L_y in length, and Λ/2 (center-to-center) from the neighbor. The red and blue regions refer to the biased and unbiased active regions, respectively. (c) Calculated photonic band structure of the array (Λ=60.0µm, w = 12.1µm, δw = 0.3µm), where the quasi-BIC is marked as the red point. (d) Electric fields (E_z and E_x) of the quasi-BIC in one periodic unit. (e) Dependence of Q_cav on the asymmetric factor (δw/w) for the quasi-BIC state in an infinite-periods array, a multi-periods (N = 22) array, and a few-periods (N = 3) array. Note that logarithmic axes are used for both horizontal and vertical axes. (f) The calculated α_rad, g_th, and α_rad/α_tot as a function of δw/w for a multi-periods quasi-BIC array (N = 22, Λ=60.0µm, w = 12.1µm).

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In the quasi-BIC array, w is chosen so that the microlaser supports a dipole mode oscillating in x-direction. The unbiased tapered waveguides act as absorbing boundaries and eliminate high-order modes in y-direction. Here, we use tapered waveguide since – compared to the straight waveguide – it slightly improves the mode confinement along the y-direction, mainly due to the impedance mismatch between the microlaser and the tapered waveguide. As such, each microlaser acts as a dipole antenna and delivers significant radiation in the vertical direction, and because of the fringing effect, the electric field extends considerably out of the microlaser and contributes to the coupling between the adjacent microlasers. On the other hand, Λ is chosen to make the device operate on the Γ-point of the band structure, as shown in Fig. 1(c). Figure 1(d) presents the electric field of the quasi-BIC [marked by the red point in Fig. 1(c)] in one unit. The numerical calculations were conducted by means of full-wave finite element method (see the Method section). Evidently, the broken symmetry makes the electric field (E_x, the dominant radiation field) of the quasi-BIC not perfectly odd symmetric and thus couple to the free space in a controllable manner. Figure 1(e) plots the relationship between the cavity quality factor (Q_cav) and the asymmetric factor (δw/w) for an infinite-periods array, a multi-periods (N = 22) array and a few-periods (N = 3) array, respectively. Here, ${({{Q_{cav}}} )^{ - 1}} = {({{Q_\parallel }} )^{ - 1}} + {({{Q_{rad}}} )^{ - 1}}$, where Q_// is the in-plane Q-factor. For the infinite-periods array (${Q_{cav}} = {Q_{rad}}$), the relationship between Q_rad and δw/w perfectly consists with the perturbation theory [32]:

In a practical THz QC microlaser array, the waveguide loss (α_w), the in-plane loss (α_//), and the radiation loss (α_rad) must be judiciously designed to balance the threshold and the power efficiency. Because a significant part of the electromagnetic (EM) field extends out of the microlasers, an accurate estimation of the effective index of the microlaser array is difficult. For this reason, a simple relationship between the loss components and the quality factors is not available. In the Supplement 1, we detail the method to numerically calculate the relevant quantities of the quasi-BIC array. For a quasi-BIC array (N = 22) with designed operation frequency of 3.2 THz, Fig. 1(f) illustrates the influence of δw/w on the α_rad, the threshold gain (g_th), and the ratio α_rad/α_tot (α_tot is the total loss, ${\alpha _{tot}} = {\alpha _w} + {\alpha _\parallel } + {\alpha _{rad}}$, and α_rad/α_tot is proportional to the slope efficiency of the output power). When δw increases from 0 to 0.4 µm, α_rad increases significantly from 0.05 cm⁻¹ to 5.24 cm⁻¹, confirming that the symmetry breaking is a powerful tool to tailor the power extraction. However, due to the relatively low optical confinement factor Γ (∼21%), g_th also increases from 20.1 cm⁻¹ to 44.5 cm⁻¹. Figure 1(f) also indicates that the increase of α_rad/α_tot is not as significant as that of α_rad, because of the small and constant α_w. Table S1 in the Supplement 1 lists the structure parameters and the calculated physical quantities of an optimized quasi-BIC array, aiming at the high CW output power.

To force the device operate on the fundamental quasi-BIC mode, the number of microlasers (N), the length of the microlasers (L_y) and the length of the unbiased tapered waveguide need to be carefully optimized to make its threshold gain sufficiently lower than the high-order modes. Fig. S4 in the Supplement 1 shows the dependence of operation frequency of the fundamental quasi-BIC mode on the width (w) or the periodicity (Λ) of the array, indicating that lithographically tunable single-mode emission is expectable in the quasi-BIC devices.

In experiments, the gain of the active region covers the frequency range from 2.8 to 3.5 THz and peaks near 3.15 THz. Quasi-BIC devices with different w, δw and Λ were systematically fabricated and measured. For all the devices, the values of N and L_y are 22 and 400 µm, respectively. Details of the device fabrication and measurements are described in the Method section.

To study the mechanism of the quasi-BIC, we first measured the quasi-BIC microlaser arrays in pulsed mode, and the results are presented in Fig. 2. Figure 2(a) presents the SEM picture of a quasi-BIC microlaser array. Figures 2(b) and 2(c) show the lasing spectra and light-current-voltage (L-I-V) curves of 4 devices with different w but the same δw (0.1 µm) and Λ (60.0 µm). Single mode emission is observed in all devices in the whole laser dynamic range, and the lasing frequency varies from 3.19 THz to 3.31 THz when w decreases from 12.5 µm to 11.9 µm. The L-I-V curves of these 4 devices illustrate very close peak power around 35 mW. We also investigated the spectra and L-I-V curves of another set of quasi-BIC devices, where w and δw are respectively fixed as 12.1 µm and 0.1 µm, but Λ varies from 56.0 µm to 64.0 µm, and the results are shown in Fig. S5 of Supplement 1. Again, stable single-mode emissions and similar output powers were observed. Fig. S4 in Supplement 1 compares the calculated and measured relationship between the laser frequency and the parameters of w and Λ, confirming good agreement.

 

Fig. 2. Quasi-BIC microlaser arrays operating in pulsed mode (the pulse width is 1µs, the repeat frequency is 10 kHz) at 20 K. (a) SEM picture of a microlaser array. (b) and (c) show the measured emission spectra and L-I-V curves of 4 quasi-BIC devices with different w marked in the figure (δw = 0.1 µm, Λ=60.0 µm). Emission spectra at different injection current are given. (d) and (e) plot the measured far-field beam pattern and polarization of a quasi-BIC device (w = 12.1 µm, δw = 0.3 µm, Λ=60.0 µm). (f) Measured L-I-V curves of 5 quasi-BIC devices, where δw varies from 0 to 0.4µm with an interval of 0.1µm (w = 12.1 µm, Λ=60.0 µm). The threshold current densities of these 5 devices are 375, 395, 408, 422, 435 A cm⁻², respectively. The corresponding slope efficiencies are 27, 102, 286, 545, 511 mW A⁻¹, respectively.

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Figures 2(d) and 2(e) show the measured 2D far field beam and the polarization of a representative device (w = 12.1 µm, δw = 0.3 µm, Λ = 60.0 µm). Single-lobed vertical emission with a low divergence of 5°× 15° was observed, which is linearly polarized along the array direction. Fig. S1 in Supplement 1 presents the calculated beam pattern, as well as the definition of the scanning angles during the measurement of beam pattern. Perfect agreement between the measurement and calculation was observed. The results confirm that the devices operate on the fundamental quasi-BIC mode.

Figure 2(f) shows the pulsed L-I-V curves of 5 devices, where w is fixed as 12.1 µm and δw increases from 0 to 0.4 µm, measured at the heat-sink temperature of 20 K. With the increase of δw, the slope efficiency (dP/dI) increases from 27 mW A⁻¹ to 511 mW A⁻¹, validating the influence of symmetry breaking on the radiation efficiency. Because of the increased α_rad, the pulsed threshold current density (J_th,p) increases from 375 A cm⁻² to 435 A cm⁻², and the maximum pulsed operating temperature (T_p) decreases from 130 K to 90 K. Figure 2(f) also points out that, after the threshold, the differential resistance (dV/dI) increases with δw which shortens the laser dynamic range. The reason is that the increased α_rad decreases the photonic density in the resonator and suppresses the photon assisted electrical transition. Combining the slope efficiency and the laser dynamic range, the pulsed output power and the wall plug efficiency (WPE) reach to the maximum (120 mW and 1%) when δw is 0.3 µm, as shown in Fig. 2(f).

We systematically investigated the spectral and L-I-V characteristics of an optimized quasi-BIC array (w = 12.1 µm, δw = 0.2 µm, Λ = 60.0 µm) in pulsed and CW mode, and the results are presented in Fig. 3. Figures 3(a) and 3(b) plots the pulsed and CW emission spectrum, respectively, confirming single-mode emission with the SMSR above 22 dB. Figures 3(c) and 3(d) show the pulsed and CW L-I-V curves at different operation temperatures. In pulsed mode and at 20 K, the threshold current and threshold current density (I_th,p and J_th,p) are respectively 0.86 A and 407 A cm⁻², the maximum output power (P_out,p) is 109 mW, the power consumption (P_in,p) is 13.10 W. The maximum pulsed operation temperature (T_p) is 120 K. Whereas, in CW mode and at 30 K, the values of the threshold current (I_th,cw), threshold current density (J_th,cw), the maximum output power (P_out,cw), the power consumption (P_in,cw) are 0.94 A, 452 A cm⁻², 21 mW, and 11.10 W, respectively. The maximum CW operation temperature (T_cw) is 45 K. The device performances degrade considerably in CW, implying the severe influence of heat accumulation. Considering the intrinsic low thermal conductivity of the active region, a practical approach to improve T_cw is to reduce the power consumption. However, simply decreasing the number of microlasers in the array will cause severe in-plane leakage, as already implied in Fig. 1(e).

 

Fig. 3. Comparison of the pulsed and CW operations of a quasi-BIC microlaser array, where w = 12.1 µm, δw = 0.2 µm, Λ=60.0 µm. (a) and (b) are the pulsed and CW emission spectra, respectively. (c) and (d) show respectively the pulsed and CW L-I-V curves measured at different temperatures.

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2.2 Hybrid quasi-BIC microlaser arrays

To improve T_cw, it is necessary to minimize the pumping area and keep low threshold current density. To this aim, we propose a hybrid-BIC microlaser array. As schematically shown in Figs. 4(a) and 4(b), the hybrid-BIC device contains a biased few-periods quasi-BIC array in the center, and an unbiased array on each side. In the unbiased array, there is a SiO₂ isolating layer underneath the top metallic layer of the ridge. The unbiased array consists of N_p periods of ridge with the periodicity Λ_p and the ridge width w_p, and supports a high-Q band-edge spoof SPP mode (see the Supplement 1 for more details). Since the SPP mode is far below the light cone, the E_z field is tightly bound on the surface of the array, with only a weak part penetrating into the unbiased active region. Because of the nearly vanishing group velocity, the band-edge SPP mode is perfectly confined with an extremely high Q_cav and a high Q_tot (see the Supplement 1). Moreover, the frequency of the SPP mode can be precisely tuned by changing the periodicity Λ_p.

 

Fig. 4. Concept of the hybrid-BIC microlaser array. (a) and (b) schematics of the device and its 2D cross-section. A biased few-periods quasi-BIC array is surrounded by an unbiased array (periodicity Λ_p, ridge width w_p, number of period N_p) on each side. (c) and (d) calculated electric field (E_z and E_x) of the hybrid-BIC. The parameters of the central array are N = 3, Λ=60.0 µm, w = 12.1 µm, δw = 0.1 µm. The parameters of the unbiased array are Λ_p= 34.3 µm, w_p =17.6 µm, and N_p =14. The eigenfrequency and the Q_cav of the hybrid-BIC are 3.16 THz and 2400, respectively.

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The device is designed such that the quasi-BIC is in resonance with the high-Q SPP mode, i.e., the two modes have nearly the same frequency and their field profiles match partially with each other. As a result, the field leaking out of the central quasi-BIC array (in the array direction) will be transformed efficiently into the SPP mode in the unbiased array. Thanks to the high Q_cav of the latter, the field oscillates in the unbiased array and is reinjected into the central quasi-BIC array. We name this supermode as the hybrid-BIC.

Figures 4(c) and 4(d) show the field distribution of a 3-periods hybrid-BIC (the central quasi-BIC array contains only N = 3 periods), with the device parameters given in the caption of Fig. 4. Figure 4(c) shows that, the E_z field is mainly confined in the near field of the whole structure, which results in a low calculated α_w of 1.28 cm⁻¹, a low α_// of 0.02 cm⁻¹, but also a low Γ of 5.2%. Because of the low Γ, δw is selected as 0.1 µm to guarantee relatively low α_rad (0.1 cm⁻¹) and thus the low threshold. Consequently, the threshold gain of the hybrid-BIC is calculated to be 27 cm⁻¹, which is only slightly higher than that of the optimized 22-periods quasi-BIC array (δw = 0.2 µm). Strikingly, the pumping area of the 3-periods hybrid-BIC device is only about one seventh of the 22-periods quasi-BIC array.

In experiment, we fabricated and measured a series of hybrid-BIC devices with different N (N= 2, 3 or 4), while all the other parameters are fixed and given in the caption of Fig. 5. Figure 5 shows the SEM picture of a 3-periods hybrid-BIC device and its performances measured in pulsed and CW modes, respectively. Figure 5(b) shows the pulsed L-I-V curves of the device. At 20 K, the values of I_th.p, J_th.p, P_in,p and P_out,p are 0.14 A, 413 A cm⁻², 2.28 W and 3.64 mW, respectively. T_p reaches to 109 K, close to that of the optimized 22-periods quasi-BIC device [see Fig. 3(c)]. Figure 5(c) shows the pulsed emission spectrum, confirming that the device operates in single mode with side mode suppression ratio (SMSR) about 24 dB.

 

Fig. 5. Laser performance of a 3-periods hybrid-BIC microlaser array, where Λ=60.0 µm, w = 12.1 µm, δw = 0.1 µm, Λ_p= 34.3 µm, w_p =17.6 µm, and N_p =14. (a) SEM pictures of the device. (b) L-I-V curves measured at different temperatures in pulsed mode. (c) shows the pulsed emission spectra. (d) and (e) are L-I-V curves and emission spectra measured in CW mode, respectively. (f) Far-field beam pattern measured at 20 K.

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Figure 5(d) shows the L-I-V curves of the same device measured in CW mode. At 20 K, the values of I_th,cw, J_th,cw, P_in,cw and P_out,cw are 0.14 A, 422 A cm⁻², 2.31 W, and 3.4 mW, respectively. More importantly, T_cw reaches to 79 K. Compared with the optimized 22-periods quasi-BIC device [see Fig. 3(d)], the 3-periods hybrid-BIC device does not degrade the threshold current density, but significantly reduces the threshold current and power consumption on the expense of output power. This explains the substantially increased T_cw for the 3-periods hybrid-BIC device. Figure 5(e) presents the CW emission spectrum, confirming single-mode emission with the SMSR about 29 dB. Figure 5(f) shows the measured beam pattern of the device, which features a main lobe with a low divergence of 17° × 17° and very weak side emission along the array direction. The weak side emission roots from the EM field distributed in the passive array.

2.3 Heat dissipation in the microlaser array

We quantitatively compared the heat dissipation of the quasi-BIC device (N = 22), the hybrid-BIC devices (N = 2, 3 or 4), and a reference FP-MM laser (a Fabry-Perot THz QC laser based on the metal-metal waveguide), all fabricated with the same material. The laser performances of the FP-MM laser and the hybrid-BIC devices (N = 2 or 4) are given in Supplement 1.

For the 3-periods hybrid-BIC device, Fig. 6(a) presents the variation of threshold current density as a function of heat-sink temperature in pulsed and CW modes, respectively. In pulsed mode (the pulse width is 1 µs, the repeat frequency is 10 kHz), the self-heating of the device is negligible and the temperature of the active region equals approximately to the heat-sink temperature. With the same threshold current density, the heat-sink temperatures under the CW condition (T_hs,cw) is less than that under the pulsed condition (T_hs,p), and the difference ($\Delta T = {T_{hs,p}} - {T_{hs,cw}}$) reflects the temperature increase in the active region due to the self-heating and can be described as [46]

Here, P_th is the threshold power density, and R_therm is area-normalized thermal resistance reflecting the temperature increase per unit power density loaded on the device. The triangles in Fig. 6(a) illustrate a transformation from the CW to the pulsed characteristics using R_therm as the fitting parameter. Figures 6(b) and 6(c) show the situations for the 22-periods quasi-BIC device and the FP-MM laser, respectively. Table 1 lists the deduced R_therm and other measured parameters of the related devices.

 

Fig. 6. Dependence of the threshold current density on the operating temperature for the 3-periods hybrid-BIC device (a), the 22-periods quasi-BIC device (b), and the FP-MM laser (c). The black squares and the red circles correspond to the measured J_th as a function of temperature under the pulsed and CW conditions, respectively. The triangles represent the transformation from the CW to the pulsed characteristics with the fitting value of R_therm.

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Table 1. The measured parameters and the deduced thermal resistance of the FP-MM, the quasi-BIC, and the hybrid-BIC devices. The values of I_th,cw, J_th,cw, P_in,cw, and P_out,cw were measured at 30 K for the quasi-BIC device, and measured at 20 K for the others.

View Table

The variation tendency of R_therm reveals the distinctions of heat dissipation among the three types of devices. First, for all devices, the lower R_therm corresponds to the lower (T_p -T_cw). Therefore, an important direction to increase T_cw is to reduce the area-normalized thermal resistance R_therm. Second, the values of R_therm of the quasi-BIC and hybrid-BIC devices are substantially lower than that of the FP-MM device, meaning that the discrete distribution of the heat sources (i.e., microlasers) facilitates the heat dissipation. Third, the less pumping area, the lower R_therm. Consequently, the few-periods hybrid-BIC microlaser array strongly suggests the laser configuration for high temperature CW operation. Balancing R_therm and the threshold current density, it turns out that the 3-periods hybrid-BIC device exhibits the highest T_cw of 79 K and its output power remains 3.4 mW in CW mode at 20 K. The comprehensive performances of the optimized hybrid-BIC device are comparable to the state-of-the-art of THz QCLs [23–28], in terms of the CW operating temperature, the output power, and the beam quality. It is worth noting that the two parameters – the maximum output power at low temperature (P_out,cw) and the maximum operating temperature (T_cw) – restrict each other. We can improve P_out,cw by increasing the asymmetric factor δw/w, but it will in turn increase the radiation loss and thus the threshold gain, resulting in the decrease of T_cw.

3. Conclusion

In conclusion, we realized continuous wave operation of 1D THz QC microlaser arrays that operate on various BIC states. Our work demonstrates the capability to comprehensively tailor the BIC states, including the radiation and in-plane Q-factors, the mode volume, and the radiation pattern. We also proved that the discrete distribution of the microlasers and the small pumping area facilitates the heat dissipation of the device. The results suggest a novel solution to improve the CW performance of THz QC lasers in terms of the operating temperature, the output power, and the beam quality.

4. Methods

4.1 Simulations

The simulations were implemented by full-wave finite element method (FEM) with a commercial solver of COMSOL Multiphysics. The complex refraction index of the active region and the metallic layers were computed by the Drude model. Frequency dependence of the material index was considered. During the calculation of Q_cav, the material losses were neglected, and only the field leakage was considered. During the calculation of Q_tot, the material loss, the radiation loss and the in-plane wave leakage are all considered.

4.2 Fabrication

The QCL active region is close to that reported work [47], and contains 180 stages with a total thickness of 11.8 µm. The fabrication was similar to that described in Ref. [46]. The only difference is that, in the unbiased region, an isolating SiO₂ layer was deposited on the top of the active region by means of PECVD and dry etching.

4.3 Measurement details

The spectral characteristics of the devices were performed using a Fourier transform infrared spectrometer (Bruker 80 V). The pulsed output power was measured by a Golay cell, and the CW output power was measured by Ophir 3A-P-THz detector. The detectors were calibrated by a Thomas Keating absolute THz power meter. The output power reported in this work is that collected by the detectors, without considering the collection efficiency of the measurement setup which is about 50% [48]. The far-field beam patterns were measured with the Golay cell detector, which was scanned on a 15-cm-radius sphere centered on the device surface.