With nano optical technology rapidly evolving, beam splitters are widely used in optical sensing [1,2], optical communication [[3], [4], [5]], optical storage [6], and waveguides [7,8]. Beam splitters have become an indispensable component of contemporary optical devices. To suit the demands of various fields, beam splitters with multifunctional beam-splitting characteristics and small volumes have received widespread attention [[9], [10], [11]]. Conventional beam splitters made of prisms or wave plates are challenging to use in tiny optical systems due to their hefty and cumbersome structure. In contrast, the grating beam splitter is not only easy to manufacture and modest in size, but it also has a high potential for beam separation. It set off a wave of research on grating beam splitters among researchers.

In recent years, two-dimensional gratings have garnered increased interest due to their ease of producing polarization-independent performance, which has a wide range of applications. Lu et al. described a polarization-insensitive two-dimensional grating beam splitter with conical frustum-shaped arrays [12]. Based on the finite element method, the reflective grating can achieve high reflective diffraction efficiencies of both TE and TM polarization. Huang et al. put forward a multi-channel 2D grating beam splitter with cylindrical arrays [13]. The nano-grating beam splitter has been optimized by the finite element method to achieve high-efficiency four channels and five channels at the wavelength of 1550 nm. Mao et al. investigated and designed an add-shaped grating with multiple zero-reference marks to solve the zero-reference position problem and the mean level of diffracted energy for four nonzero symmetrical orders reached 14% [14]. However, it is difficult for two-dimensional grating beam splitters to achieve multifunctional beam splitting. On the contrary, this is the advantage of one-dimensional grating beam splitters, which has received widespread attention from researchers. Zhu et al. proposed a dual-functional beam splitter in the 800 nm wavelength with a three-layer grating ridge [15]. The grating beam splitter transmits one channel at TE polarization and transmits two channels at TM polarization. Liu et al. reported a grating beam splitter with a connecting layer under a second Bragg incidence [16]. The beam splitter provides polarization selection capability, which can achieve TE-three/TM-two output with an excellent diffraction efficiency evenness. For applications with complex output requirements, one-dimensional gratings have obvious advantages. However, there are still relatively few studies that can simultaneously achieve both polarization selection and polarization independence functions.

In this study, we present a creative bidirectional trifunctional splitter with a two-sided structure. Through the implementation of the rigorous coupled-wave analysis (RCWA) [17] and simulated annealing algorithm (SAA) [18], this bidirectional trifunctional splitter tackles the problem of polarization independence and accomplishes effective polarization selection, which is difficult to achieve with two-dimensional gratings. The upper part of this bidirectional beam splitter can achieve TE-three/TM-two output, while the lower part can realize 4-port output for both polarizations. Aside from that, the grating ridge of this bidirectional reflective beam splitter is simpler than the previously reported multifunctional grating beam splitter, improving its suitability for production and fabrication. Tolerance analysis on various physical dimensions of this bidirectional trifunctional splitter is conducted, demonstrating excellent process deviation and enabling industrial applications. Moreover, in Sec. 3, we investigate the electromagnetic field distribution within the bidirectional trifunctional splitter using the simplified modal method (SMM) [19,20], which explains the energy coupling process within the bidirectional trifunctional splitter. Assisted by the finite element method (FEM) [21], the correctness of the numerical findings in the study has been greatly enhanced. The proposed bidirectional trifunctional splitter exhibits excellent performance characteristics and can be utilized in complex space environments and optical communication systems.