Since its invention in 1994, the performance of quantum cascade lasers (QCLs) has greatly improved, gradually becoming one of the most important light sources in the mid-infrared and terahertz (THz) region^[1−4]. Currently, the most direct method for enhancing the power of QCLs is to enlarge the ridge width, hence increasing the area of the gain region. However, simply widening the ridge causes deterioration of the beam quality, and leads to multi-lobed transverse mode lasing^{[5, 6]}. Phase-locked arrays operating in the in-phase mode (also known as coherent arrays) have become one of the most effective methods for achieving high power and high beam quality QCLs. This technique allows for power enhancement while maintaining high brightness.

Phase-locked array has been used in the near-infrared and mid-infrared semiconductor lasers^[7−10], and later widely applied in the THz region^{[11, 12]}. A phase-locked array refers to the coupling formed between different elements, thus maintaining a certain phase relationship. To improve the power performance of THz QCLs, many significant works have been done. Chang et al.^[13] implemented phase locking of two distributed feedback (DFB) lasers using evanescent-wave coupling, where 1.7 times power amplification was achieved. Kao et al.^[14] utilized leaky-wave coupling, successfully phase-locked multiple surface emitting DFB lasers via carefully designed "phase sector", thereby achieving high-quality far-field. In evanescent-wave coupled and leaky-wave coupled phase-locked arrays, the coupling of elements generally requires the element spacing smaller than the wavelength, which causes heat accumulation in the active region, thereby affecting the performance. Diffraction-wave coupling has been widely used in the near-infrared phase-locked arrays^{[15, 16]}, wherein diffracted light is reflected back into each element, utilizing the Talbot effect to achieve coupling between array elements. Therefore, the elements of phase-locked array that utilizes diffraction-wave coupling via the Talbot effect can make spacing larger, which can prevent heat from local accumulation. The Talbot effect refers to the phenomenon where diffracted light re-presents its initial waveforms after traveling a certain distance, with its self-imaging length ZT=2nd2/λ0, where n is refractive index, d is the center-to-center spacing between adjacent elements, and λ0 is free-space wavelength. Compared with near-infrared semiconductor lasers, THz QCLs have longer wavelengths, resulting in shorter self-imaging lengths and making external mirror-based phase-locked arrays for these lasers challenging. Recently, we utilized an on-chip integration method to fabricate the diffraction-wave coupled phase-locked array of THz QCLs, a four-times multimode power amplification was achieved with a five-elements Talbot array device^[17]. However, according to the principle of the Talbot effect, the self-imaging length varies with lasing wavelength, making the Talbot cavity more suitable for coupling single-mode lasers.

In this work, we achieved diffraction-wave coupling in five-elements array, through on-chip integration with a Talbot cavity. The Talbot cavity facet reflects the light back to the ridge array direction and achieves self-imaging in the array, thereby achieving phase-locked operation of five ridges. The first-order buried DFB gratings are fabricated on each ridge to ensure the single-mode operation of the device. The five-elements DFB array accomplished a single-mode output power of 108 mW, 4.9 times the power of the single ridge DFB device. The spacing between adjacent ridges is set as 220 μm, far larger than the free-space wavelength, which not only prevents heat accumulation, but also reduces the coupling efficiency of higher-order supermodes, resulting in a high-brightness far-field distribution. This scheme validates the superiority of the Talbot effect for enhancing the single-mode power, providing a new method for high-power single-mode THz QCLs.

Figs. 1(a) and 1(b) show the three-dimension (3D) structure diagrams of the five-elements DFB array device with ridge width of 94 μm, which consists of five ridges with first-order buried DFB gratings and a Talbot cavity. The total length of the device is 3 mm, and the length of the Talbot cavity is selected to be 624 μm (about ZT/8), so that the diffraction waveform at ZT/4 is coupled back to the ridge array. The two edges of each ridge were uncovered by metal, serving as the absorption boundary to suppress the higher-order transverse mode, and the absorption boundary width of the five ridges is set to 10/6/2/6/10 μm to ensure the stable fundamental supermode operation. Because higher-order supermodes spread in the edge region of the array, we can enhance the loss difference between the fundamental supermode and higher-order supermodes by using a wider absorbing boundary width for the edge ridges^[17]. Figs. 1(c) and 1(d) exhibit the images of the buried DFB grating captured by a 3D microscope. Excellent etching morphology can be seen, and the etching depth is around 600 nm. Fig. 1(e) is scanning electron microscope image of the array device.

We use the first-order buried DFB grating with periodic length Λ = 9.40 μm and duty cycle σ = 50% based on finite element method (FEM) simulation for a 4.3 THz device, to ensure single-mode operation. A 50 μm wide highly doped GaAs layer near the back facet of the Talbot cavity is left uncovered by metal, to provide a longitudinal absorption boundary, for eliminating the disturbance of mode resonance caused by reflection of THz wave on the back facet.

For a cavity, the influence of waveguide loss αw on threshold gain gth can be expressed by the threshold conditions of lasers^[18]

1gth=αwΓ+αradΓ,

where αrad is the radiation loss, Γ is the optical confinement factor, αw/Γ represents the contribution of waveguide loss to threshold gain. Fig. 2 shows that the frequency difference between the two band edge modes increases as the etching depth increases, which means that the grating distribution feedback effect is enhanced. However, the increase of the etching depth also leads to the increase of αw/Γ, which results in the increase of threshold gain. Therefore, we set the etching depth detch as 600 nm. At this etching depth, the difference of αw/Γ between the high-frequency (Hf) band edge mode and the low-frequency (Lf) band edge mode reaches 14.4 cm^–1, which can ensure the stable single-mode operation of the laser in the high-frequency mode.

The devices were fabricated on a QCL wafer that was grown using molecular beam epitaxy (MBE) and exhibited spectral gain in the range of 4.2–4.4 THz. Before the rest of the processes begin, the first-order DFB grating is fabricated by wet etching with H₃PO₄ : H₂O₂ : H₂O etchant in 1 : 1 : 10. To form the ridge array and Talbot cavity, the wafer was processed by inductively coupled plasma (ICP) dry etching. Near the two edges of each ridge, as well as on the bottom contact layer, a sequence of Ge/Au/Ni/Au (26/54/15/150 nm) was deposited with a narrow metal width of 5 μm to minimize optic loss. Ohmic contact was achieved through thermal annealing at 360 °C for 1 min under a nitrogen atmosphere. A metallic layer of Ti/Au (10/700 nm) was evaporated, leaving a highly doped GaAs layer of 10/6/2/6/10 μm uncovered on the edges of the five ridges. This region served as an absorbing boundary. The substrate was mechanically polished to a thickness of approximately 200 μm, and a Ti/Au (10/200 nm) layer was deposited on the back side of the processed wafer for soldering. Finally, the devices were cleaved to 3 mm length and soldered onto heat sinks.

Fig. 3 shows the performance of a representative DFB array device with five elements. The array device exhibits a single-mode emission at ~4.3 THz in all bias conditions with a side mode suppression ratio above 20 dB. A DFB single-ridge device with 94-μm-wide and 2.4-mm-long cavity was measured, which showed 22 mW peak optical power. For the five-elements DFB array device, a peak power of 108 mW was measured at 13 K, which exhibits a power amplification of 4.9 times compared with the DFB single-ridge device. Spectra taken at different currents (2.5–4.5 A) are plotted in Fig. 3(c). The robustness and capability for lithographic tuning of this scheme was verified by three devices with different grating periods Λ = 9.36/9.40/9.44 μm as shown in Fig. 3(d), which operate at 4.355/4.335/4.316 THz, respectively, with a similar mode effective refractive index of 3.68.

The far-field pattern of a representative array device is illustrated in Fig. 4, which was measured in pulse mode. The measurements were performed with a repetition frequency of 5 kHz and a pulse width of 2 μs. The device was positioned at the pivot point of a rotating arm. To detect signal, a highly sensitive Golay cell detector mounted on the rotating arm was employed. The collected data was then used to characterize the corresponding light intensity through a lock-in amplifier. Since the Golay cell detector is only capable of detecting low-frequency light, the repetition frequency was modulated to a low-frequency signal of 20 Hz using a signal generator. Fig. 4(a) presents the one-dimensional far-field distribution of the five-elements array device, measured in the ridge width direction (x direction). The measured distribution exhibits good agreement with the theoretical far-field distribution (blue dotted line). The slight broadening of the peak may be due to the large integral time of the lock-in amplifier, which reduces the measurement resolution. The lasing light of five elements have the same phase, and due to the principle of multi-slit Fraunhofer diffraction, the relatively divergent far-field envelope of each element converges into several peaks. This convergence significantly enhances the far-field brightness. The good fit between the experimental and simulated results also confirms the phase-locking effect of our Talbot integrated scheme. Figs. 4(b) and 4(c) show the far-field distribution at maximum peak power and half peak power, respectively. Fig. 4(d) displays the far-field distribution obtained through a two-dimensional Fourier transform calculation of the near-field distribution, as shown in Ref. [17]. In the x direction, there is a good agreement between the experimental and calculated results. The observed asymmetry and convergence of the measured far-field in the growth direction (y direction) can be attributed to the leakage of the light field to the substrate. This phenomenon is commonly observed in single-metal waveguide structure and is not caused by our array design. In fact, this phenomenon also exists in Fabry−Perot (F−P) devices with the same waveguide structure.

In conclusion, we present a diffraction-wave coupling scheme for single-mode power amplification. By on-chip integrating the ridge array with the Talbot cavity, the five-elements array obtained 108 mW of ~4.3 THz single-mode optical power in pulse mode, achieving nearly 5 times power amplification. Compared with leaky-wave coupling and evanescent-wave coupling, the diffraction-wave coupling scheme has a larger spacing between elements, which leads to better thermal performance. Stable and lithographic tunable single-mode and high brightness far-field distribution are achieved. The agreement between far-field distribution and simulation results, and the high efficiency of power amplification, prove the applicability of Talbot effect in the field of improving the single-mode power in THz QCLs.