An optical beam splitter is an important device for optical communication. It is mainly used to split optical signals and realize optical signal splitting and combination in transmission networks. Compared with traditional beam splitters, photonic crystal-based beam splitters have low transmission loss, large-angle beam splitting, small size, and easy integration, making them suitable for large-scale and high-density integration in modern communication. In recent years, research on photonic crystal-based optical beam splitters has mainly focused on enhancing the beam-splitting capacity of single-wavelength optical beam splitters, which has limited their application. Broadband photonic crystal beam splitters have become a current focus of research. In addition, few structures can achieve broadband beam splitting and flexible beam-splitting ratios simultaneously. A photonic crystal beam splitter that can achieve a flexible and designable splitting ratio within a wide bandwidth range is of great significance for the optical communication system. In this article, a broadband 1×3 photonic crystal beam splitter is proposed based on a 2D photonic crystal waveguide. By introducing a regulating dielectric column at the waveguide branch and optimizing its radius and offset, we can adjust the transmittance of each output port of the beam splitter. By introducing three sets of bandwidth-optimized dielectric columns on the inner side of the two branch waveguides and optimizing their radii, the broadband characteristics of the beam splitter can be achieved.

Currently, optimization of the structural parameters of broadband photonic crystal beam splitters mainly uses the control variable method, which is time consuming, inefficient, and only suitable for optimizing a small number of variables. To improve the performance of broadband photonic crystal beam splitters, multiple parameters must be adjusted simultaneously. Therefore, it is difficult to realize a broadband photonic crystal beam splitter with a flexible beam-splitting ratio and excellent beam-splitting performance using the traditional control variable method. In this study, a broadband photonic crystal 1×3 beam splitter was reversely designed based on the downhill-simplex algorithm. First, the effect of the radius and offset of the adjustable dielectric column on the transmittance of each port and the effect of the radius of the bandwidth-optimized dielectric column on the broadband characteristics were analyzed using the finite-difference time-domain method. Subsequently, the radius and offset of the modulating dielectric column and the radius of the bandwidth-optimized dielectric column were optimized using the downhill-simplex algorithm according to a specific target beam-splitting ratio, and a broadband photonic crystal 1×3 beam splitter with different beam splitting ratios was designed in reverse.

The results show that the inverse design of the 1×3 photonic crystal beam splitter based on the downhill-simplex algorithm not only improves the optimization efficiency of the photonic crystal beam splitter but also can provide a broadband beam splitter with excellent performance. The designed 1×3 isoperimetric beam splitter has an additional loss of less than 0.199 dB, uniformity of less than 0.119 dB, and response time within 0.5 ps in the bandwidth range of 1525‒1565 nm (Figs.8 and 11). The designed 1×3 unequal beam splitter has an additional loss of less than 0.177 dB, beam-splitting variance of less than 6.88×10^-4 in the bandwidth range of 1525‒1565 nm, and response time within 0.5 ps (Figs.9, 11, and 20, Table 3).

(1) This structure can achieve three output ports with different spectral ratios by adjusting only one dielectric column (R₁ in this study). (2) The designed beam splitter has a wide range of variation in beam-splitting ratio, and all three output ports can achieve a transmittance change of approximately 0.08‒0.75. (3) By adding three sets of dielectric columns to optimize the bandwidth, this structure can achieve good broadband characteristics throughout the entire C-band. (4) The combination of theoretical models and optimization algorithms improves the optimization efficiency of photonic crystal beam splitters, greatly reduces the optimization time, and makes high-performance broadband beam splitters possible. The beam splitter has a wide operating bandwidth, flexible beam-splitting ratio, excellent beam-splitting performance, wide range of beam-splitting ratios, and good prospects for future applications in all-optical communication networks, photonic high-density integration, etc.