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Abstract
Increasing the power of a quantum cascade laser by widening laser ridges will lead to the degradation of the beam quality because of the operation of high-order transverse modes. We report on a phase-locked array scheme of terahertz quantum cascade laser (THz QCL) utilizing Talbot effect. By adjusting the absorbing boundary width of each ridge in the array, stable operation of the fundamental supermode is realized. A five-element array shows 4 times power amplification than that of a single ridge device. Due to the large power amplification efficiency, stable mode selection, and simple fabricating process, the phase-locked array scheme is very promising to further improve the performance of THz QCL.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High power radiation sources are highly desired for applications such as trace gas detection [1], spectroscopy [2], and imaging [3,4]. As a compact coherent source with bright radiation [5–8], quantum cascade laser (QCL) has undergone a rapid development. Intensive studies have been devoted to improve the output power and beam quality for terahertz (THz) QCL, such as longitudinal phase-locking array [9], phase-locked pair [10], sampled grating [11], and hybrid gratings [12].
Scaling up the area of the active region is the most direct method to increase the output power. Nevertheless, the increase of ridge width will not only exacerbate heat accumulation, but also cause the operation on high-order transverse modes, which deteriorates the beam quality [8]. Multiple Fabry-Perot (F-P) cavities arranged in parallel can improve heat dissipation while realizing total power amplification. However, the light emitting from each cavity is incoherent, which limits its applications.
Talbot effect has been implemented in near-infrared lasers [13–15] and mid-infrared QCLs [16–20]. An array of coherent lasers can produce self-images after a certain propagation distance [21] which is called the Talbot length ${Z_t} = {2n{d^2}} {/} {\lambda_0}$, where $n$ is the refractive index of material, ${\lambda _0}$ is the wavelength of light in vacuum, $d$ is the center-to-center spacing between adjacent elements. In this paper, we report on a phase-locked array scheme based on Talbot effect to improve the performance of THz QCL. We demonstrated the first QCL array integrated with Talbot cavity in the terahertz frequency range (THz-Talbot-QCL), which achieved 4 times power amplification for an array with five coherent ridges. Considering the power amplification efficiency (78%) and stable mode selection performance, such a device shows great application potential.
2. Methods
Figure 1(a) shows the 3D schematic of the THz-Talbot-QCL. This array contains five elements with 100 µm ridge width. The center-to-center spacing between adjacent ridges is 220 µm and the cavity length is 2 mm. Figure 1(b) is a representative scanning electron microscope (SEM) image of the THz-Talbot-QCL. For describing the operation mechanism of the device, Fig. 1(c) exhibits the electric field distribution of the THz-Talbot-QCL obtained by finite element method (FEM) simulation. As shown in the red dashed box in Fig. 1(c), each ridge in the array operates in the same phase, thereby forming constructive interference and enhancing the light brightness with high beam quality.
Fig. 1. (a) Schematic of the THz-Talbot-QCL. (b) SEM image of the THz-Talbot-QCL. The absorbing boundary widths for the five ridges are 10/6/2/6/10 µm, respectively. The cavity length and the ridge width of each ridge element in the array are 2 mm and 100 µm, respectively. (c) 2D simulation of the electric field distribution for the THz-Talbot-QCL.
The light is coupled from the ridge array into the slab-like waveguide mode of the Talbot cavity, reflected by the back facet, and then recoupled back to the ridge array. When the length of the Talbot cavity is set to ${Z_t} / 8$, the light operating in the fundamental supermode will show an image of the Talbot effect at ${Z_t} / 4$, that is, at the junction between the array and the Talbot cavity after being reflected by the back facet [22]. In this process, Talbot cavity has different coupling efficiencies for each order of supermodes. The larger coupling efficiency means the lower threshold gain. The total number of supermodes in the phase-locked array is always equal to the number of array elements [23]. Therefore, an array with five ridges will have five supermodes: fundamental supermode (N = 1) to the fifth-order supermode (N = 5). Figure 2(a) shows the simulated coupling efficiency [18] versus the length of the Talbot cavity at 4.3 THz with the ridge width of 100 µm and the center-to-center spacing of 220 µm. Since the coupling efficiencies of second-, fourth- and fifth-order supermodes are significantly low, we only analyze the fundamental supermode and the third-order supermode. Comparing the coupling efficiency of the fundamental supermode (N = 1, red line) and the third-order supermode (N = 3, blue line), we choose the length of the Talbot cavity to be 621 µm $({Z_t} / 8)$, which shows the largest modal discrimination for selecting the fundamental supermode. For determining the center-to-center spacing between adjacent ridges, the increase of it will lead to the increase of Talbot length and thus the increase of device size, while the decrease of it will lead to the deterioration of mode selection ability, as shown in Fig. 2(b). As a compromise, we choose the center-to-center spacing to be 220 µm.
Fig. 2. (a) Calculated coupling efficiency versus the length of the Talbot cavity at 4.3 THz. To ensure the device operating on fundamental supermode (N = 1, red line), the length of the Talbot cavity is set to 621 µm $({Z_t} / 8)$. (b) Calculated coupling efficiency of the fundamental supermode and the third-order supermode versus the center-to-center spacing between adjacent ridges. The ridge width and the Talbot cavity length are 100 µm and 621 µm, respectively. (c) and (d) Calculated mode distribution of the fundamental supermode and the third-order supermode, respectively. Compared with the former, the latter is more spread in the edge ridges. (e) Waveguide loss of the fundamental supermode and the third-order supermode versus the absorbing boundary width of the middle ridge. From the edge ridge to the middle ridge, the absorbing boundary width decreased with an equal difference and that of the two edge ridges is 10 µm.
It should be noted that although the length of the Talbot cavity has been selected to have the largest coupling efficiency difference between the fundamental supermode and third-order supermode, the latter is still about 73% of the former, which leads to the unstable mode selection performance of the device. In order to achieve stable fundamental supermode operation, further enhance the loss difference between the fundamental supermode and the third-order supermode is needed. We calculated the mode distribution of the fundamental supermode and the third-order supermode, as shown in Fig. 2(c) and Fig. 2(d), respectively. Significant difference in mode distribution is observed. The mode distribution of the fundamental supermode is more concentrated in the central region of the array, while the third-order supermode is spread in the edge region. Thus, we can enlarge the loss difference between the fundamental supermode and the third-order supermode by using a narrower absorbing boundary width for the middle ridge and a wider absorbing boundary width for the edge ridges. The absorbing boundary is high-loss and composed by the high-doped GaAs layer uncovered by metal. Figure 2(e) shows the waveguide loss of the fundamental supermode and third-order supermode versus the absorbing boundary width of the middle ridge based on FEM simulation. From the edge ridge to the middle ridge, the absorbing boundary width decreased with an equal difference and that of the two edge ridges is 10 µm. It can be seen that the waveguide loss of the fundamental supermode decreased much faster than that of the third-order supermode when decreasing the absorbing boundary width of the middle ridge. Therefore, in order to further enhance the loss difference between the fundamental supermode and the third-order supermode, we set the absorbing boundary width as 10/6/2/6/10 µm for the five ridges in the array, respectively.
The devices were fabricated on QCL wafer grown by solid-source molecular beam epitaxy (MBE), with spectral gain at 4.2-4.4 THz. The wafer was processed by inductively coupled plasma (ICP) dry etching to form the ridge array and Talbot cavity. A sequence of Ge/Au/Ni/Au (26/54/15/150 nm) was deposited near the two edges on each ridge (with metal width of only 5 µm for reducing the loss caused by Ni), as well as on the bottom contact layer to provide ohmic contact via thermal annealing at 360°C for 1 minute under nitrogen atmosphere. Ti/Au (10/300 nm) was evaporated to form the metallic layer, with 10/6/2/6/10 µm highly doped GaAs layer left uncovered on the edges of the five ridges, respectively, serving as absorbing boundary. Following mechanically polishing the substrate down to about 200 µm, Ti/Au (10/200 nm) was deposited on the back side of the processed wafer for soldering. Finally, the devices were cleaved to desired length and In-soldered on heat sinks.
3. Results and discussion
As shown in the simulation of Fig. 1(c), when the ridge array operates on the fundamental supermode, ridges form constructive interference with same phase. Figure 3(a) shows the transverse near-field distribution of the red box in Fig. 1(c). The vertical and horizontal axes represent the near-field intensity and the lateral position of each ridge in the array, respectively. The five peaks with different intensities represent five ridges at different positions. The far-field distribution can be obtained by Fourier transform of the near-field intensity
with where ${x_0}$ is a half of the total transverse dimension of ridge array, ${E_{near}}$ is the near-field electric field varying with the lateral position $x$, $\theta$ is the angle of far field, ${k_0}$ is the wave number in vacuum, and ${I_{far}}$ is the far-field intensity corresponding to $\theta$. The calculated far-field pattern is shown in Fig. 3(b). It should be noted that although the light emitted by the phase-locked array operating in the fundamental supermode is in-phase, the far-field pattern is not a single lobe, but with several equally spaced weak lobes in addition to the strong lobe at 0° position, which can be explained by the multi-slit Fraunhofer diffraction effect [23] where $F(\theta )$ is the far-field intensity distribution of the phase-locked array, $I(\theta )$ is the far-field intensity of an individual element in the phase-locked array, and $G(\theta )$ represents the multi-slit Fraunhofer diffraction effect. The interval $\Delta \theta$ between adjacent lobes can be calculated by where ${\lambda _0}$ is the wavelength in vacuum, and $d$ is the center-to-center spacing between the adjacent elements. The full width at half maximum (FWHM) of each lobe $\theta$ can be calculated by where $a$ is the total width of the ridge array. Therefore, for the device operating at 4.3 THz, the calculated FWHM $\theta$ and the interval $\Delta \theta$ are 4° and 18.5°, in agreement with the far-field pattern obtained by Fourier transform of the near-field distribution, as shown in Fig. 3(b).Fig. 3. (a) Near-field distribution of the array from FEM simulation. (b) Far-field pattern calculated by Fourier transform of the near-field distribution.
The optical power of the THz-Talbot-QCL devices were measured by a Thomas Keating absolute terahertz power meter with a pulse width of 2 µs and repetition frequency of 5 kHz, without any corrections and focusing optics. Devices were fixed on the cold finger of a liquid helium cryostat. The optical spectrum was measured utilizing a Bruker Fourier transform infrared spectrometer. Figure 4 shows the performance of a representative THz-Talbot-QCL array with five elements and the inset provides its optical spectrum. A total peak power of 359 mW at 10 K and a maximum operating temperature of 105 K were obtained. The performance of a single ridge F-P device with 100µm-wide and 2mm-long cavity was also measured for comparison. This device showed a peak power of 92 mW at 10 K and a maximum operating temperature of 110 K. Compared with the single ridge F-P device, the THz-Talbot-QCL array exhibits a power amplification of ∼ 4 times with the average power amplification efficiency of 78%. Due to the advantage of the array structure in heat dissipation, the maximum operating temperature of the array device is only slightly lower than that of the single ridge F-P device. In addition to the five-element array, we also designed a three-element array device. The measured peak optical power is 223 mW at 10 K with 81% average power amplification efficiency, and the maximum operating temperature is 108 K, which further proves the stability and flexibility of the phase-locked array scheme.
Fig. 4. Measured lasing characteristics (P-I and I-V curves) and spectrum (inset) of a representative THz-Talbot-QCL array device with five ridges and P-I curves of a single ridge F-P device at varying temperatures.
The far-field distribution of the THz-Talbot-QCL was measured by a Golay cell detector for high sensitivity. The detector was fixed on the rotating table and scanned with a radius of 20 cm. The THz-Talbot-QCL array was operated in pulsed mode with a pulse width of 1 µs and repetition frequency of 10 kHz. A signal generator was exploited to electrically modulate the output optical signal to a lower repetition rate. Figure 5(a) shows the measured far-field pattern at peak optical power of the THz-Talbot-QCL array with five ridges by utilizing the voltage output of the lock-in amplifier to characterize the light intensity. The measured far-field pattern consists of a strong central lobe and two weak lobes in lateral direction. The interval between adjacent lobes is about 18°. Figure 5(b) provides the calculated far-field pattern by using 3D full wave FEM simulation. It can be seen that the measured far-field pattern is in good agreement with the simulation results in the lateral direction, which supports that multi-slit Fraunhofer diffraction effect occurs during the operation of phase-locked array and indicates that all five elements of the array are indeed in-phase. However, we also noticed that the FWHM of the measured far-field pattern in the vertical direction is much narrower than that of the simulation results, which may be due to the strong leakage of the light field into the substrate. The exact reason for that is still under investigation.
Fig. 5. (a) Measured 2D far-field pattern at peak optical power of the five-element array device. The interval between adjacent lobes is ∼ 18°. (b) Far-field pattern obtained by 3D full wave FEM simulation of the THz-Talbot-QCL.
In the future, an ideal single-lobe far-field might be achieved by reducing the center-to-center spacing between adjacent ridges and adjusting the absorbing boundary width to improve the stability of the fundamental supermode. Note that simply reducing the center-to-center spacing will reduce the loss difference between the fundamental supermode and the third-order supermode, resulting in the device fail to work stably in the desired fundamental supermode. This issue can be resolved by varying the absorbing boundary width to enhance the loss difference between different supermodes, thus achieving a powerful THz coherent source with single-lobe narrow divergence far-field.
4. Conclusion
In summary, we demonstrated the first quantum cascade laser array integrated with Talbot cavity in the terahertz frequency range. All devices stably operate on the fundamental supermode. The THz-Talbot-QCL array with five ridges achieves 4 times power amplification. In addition, we present a method to adjust the supermode loss by varying the absorbing boundary width instead of increasing the center-to-center spacing between adjacent ridges, which makes the ideal far-field pattern with single lobe possible. The large power amplification efficiency and simple fabrication process make this design very promising to develop high power THz QCL with high beam quality.
Funding
National Natural Science Foundation of China (61734006, 61835011, 61991430, 61874110); Key Program of the Chinese Academy of Sciences (XDB43000000, QYZDJ-SSW-JSC027).
Acknowledgments
The authors would like to thank Ping Liang and Ying Hu for their help in device processing.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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