A vertical-cavity surface-emitting laser (VCSEL) is easily made into a two-dimensional array to improve its output power. However, if the near-field complex amplitude output cannot be stabilized in the lowest supermode generated by the fundamental transverse mode, the spot cannot converge on the center normal of the far-field array geometry, and the energy will be diverged. The external cavity is prepared for the VCSEL array, and the output of the array can be stabilized in the lowest order supermode generated by the fundamental transverse mode by supermode control through diffraction coupling. In this study, the parallel-coupled model for the 2-dimensional VCSEL array based on Fresnel diffraction integration was established and used to numerically calculate and analyze the influence on the supermodes’ thresholds of different array distributions, array elements’ transverse modes and duty ratios versus the length of the external cavity. The simulation results show that the square array provides a wider range of external cavity control length ($0.2d^2/\lambda$ and approximately $0.9 \mathrm{to} 1.0d^2/\lambda$). The lowest supermode of the fundamental transverse mode can be outputted. For the regular hexagonal array with the length of the external cavity of $0.15d^2/\lambda$ and $0.6d^2/\lambda$. The results have important reference significance for the design of an external cavity VCSEL array, which can control the supermode and obtain VCSEL coherent array beams with high power and near diffraction limits.

In-phase coherent vertical cavity surface emitting laser (VCSEL) arrays have desirable properties for highbrightness laser applications. We employ mutual injection feedback modeling of ring VCSEL arrays with fractional Talbot cavity to select their supermodes. An analysis of the effects of Talbot cavity lengths on engineering the coupling coefficient and gain threshold for in-phase mode operation is provided through the overlapping integrals of optical field distributions. An example design for 24-element arrays with a fractional Talbot cavity is presented, and the in-phase far-field distribution is obtained. This provides a potential method for fabricating Bessel Gaussian beams using larger ring VCSEL arrays.

Compressed Sensing (CS) has emerged as an efficient framework for sensor-based data acquisition and reconstruction, and is now widely employed in image processing. Deep unfolding networks integrate deep neural networks with optimization algorithms, emerging as a prevalent approach for image CS by enhancing interpretability and reconstruction performance. However, most existing deep unfolding networks suffer from insufficient integration and utilization of feature information during the iterative process. To address this limitation and achieve the goal of fusing complementary information to form a richer and finer feature representation, we propose an Iterative Shrinking-Threshold Algorithm (ISTA)-based deep unfolding network with optimized feature aggregation architecture for high-quality image CS, dubbed ISTOF-Net. By introducing a feature aggregation architecture, ISTOF-Net enhances both the integration and utilization of local detail features and global structural features. Specifically, in the reconstruction module, we design a novel Optimized Feature Aggregation Module (OFAM), which combines global structural features with local detail features, enhancing their integration and utilization through feature modulation and attention mechanisms. Moreover, we introduce auxiliary Convolutional Module (CM) to further refine and enhance fine image details. In addition, we adopt a lightweight network design, effectively reducing both computational complexity and reconstruction time. Experimental results on datasets acquired by image sensors and on remote sensing image demonstrate that ISTOF-Net outperforms state-of-the-art methods in both reconstruction quality and efficiency. Its high performance and lightweight design make ISTOF-Net ideal for sensor-based imaging systems that demand data compression and rapid imaging.

Chip-scale, kilowatt-scale peak-power short-pulse lasers are becoming increasingly important for applications in various fields. This study systematically explores the cascaded energy conversion and oscillation characteristics of vertically integrated composite cavity VCSEL with cascaded energy conversion, aiming to establish what we believe to be a novel route to achieve kilowatt-level high peak power short-pulse monolithically integrated lasers. In this paper, the stable oscillation conditions under different feedback coefficient and signal gain are investigated based on equivalent resonator theory. By deriving simultaneous coupled rate equations, the dynamics process on coupled oscillation in composite cavity are explored and the effective regime for achieving high peak power laser is uncovered. The effects of the reflectivity of the P-DBR R₂ and the absorption rate of the Nd:YAG A_Nd on the laser oscillation characteristics are further revealed analytically. Stable pulses with a highest peak power of 137.1 kW, a maximum pulse energy of 24.9 µJ, a pulse width of 123.7 ps are achieved in the vertically integrated composite cavity VCSEL within a 100 µm aperture. Additionally, by utilizing expanded 2D coherent VCSEL arrays with high beam quality, we obtained a maximum pulse energy up to 83.9 mJ with a slope efficiency of 0.54 W/A. Our work provides an avenue for steering on-chip integration and developing believed to be novel laser arrays capable of operating at high peak powers exceeding kilowatts, with potential applications in remote laser detection and ranging.

本文对环形激光阵列的Talbot效应进行了研究，利用Gyrator正则变换推导了极坐标下环形激光阵列的Talbot效应和自成像条件，并进一步分析了其在分数Talbot距离处的成像规律。通过FDTD Solutions软件对环形激光阵列在分数Talbot距离处的空间分布、相位分布进行模拟，得到与理论计算相一致的结果。通过与一维激光阵列分数Talbot效应的空间分布、相位分布情况进行对比分析，环形激光阵列可有效消除了一维激光阵列的Talbot边缘效应，获得等光强分布的Talbot自再现像，扩展了Talbot效应在环形激光相干阵列锁相的应用。

To mitigate the central heat accumulation in vertical-cavity surface-emitting laser (VCSEL) arrays during operation, homogenize the temperature field distribution, and enhance the overall output power of the laser array, this article establishes a 3-D thermoelectric coupling physical model. The study investigates the impact of missing units at different positions within the array on thermal crosstalk and proposes an algorithm aimed at minimizing the difference in the array’s thermal coupling factor matrix. The effectiveness of this algorithm in homogenizing the array’s thermal distribution is verified through thermal simulations. Various array configurations with different layouts are designed and fabricated, and the power–current characteristics and spectral data of the devices before and after optimization are successfully obtained. For the optimized $3\times 3$ and $5\times 5$ arrays, the peak powers reach 150.1 and 175.4 mW, respectively. The photoelectric conversion efficiency is improved by 23.92% and 13.63% compared to the pre-optimization state. Moreover, the optimized array structures reduce the wavelength redshift by 3.29 and 1.24 nm. By optimizing the layout of VCSEL array units, the optimized devices exhibit superior thermal characteristics.