Lithium niobate photonic integration represents a cutting-edge technology driving advancements in high-speed optical communication and optical information processing. On-chip power splitters are essential components in photonic integrated circuits. However, most traditional design schemes for power splitters are based on known physical effects. Geometries are typically determined by empirical models and optimized through fine-tuning of characteristic parameters. As a result, conventional designs have limited flexibility, which hinders further device integration. Unlike traditional design methods, the inverse design approach mathematically formulates the physical problem and employs various intelligent algorithms to iteratively compute the device structure based on the desired performance. This method fully explores the entire parameter space, overcoming conventional structural constraints and enabling the design of smaller, higher-performance optical devices. However, lithium niobate is an anisotropic material, meaning that the transmission characteristics of light waves within the device depend on the crystal orientation and propagation direction, necessitating future study of inverse design approaches for lithium niobate-based devices. In this paper, we incorporate the anisotropic properties of lithium niobate into the inverse design of 1×2 power splitters with different splitting ratios, utilizing both X-cut and Z-cut lithium niobate thin-film platforms. We compare the performance differences of power splitters with different crystal orientations to promote the application of inverse design methodology in highly integrated lithium niobate photonic circuits.

The device design area is divided into an M×N grid of equal-sized pixel cells. Each pixel has two possible states: etched (coded as 0) and unetched (coded as 1). In the simulation, the refractive index of lithium niobate is represented as a 3×3 diagonal matrix. The design process combines the DBS algorithm and 3D FDTD analysis, where the DBS algorithm iteratively generates new matrix states, and 3D FDTD evaluates the device’s figure of merit (FOM). The optimization continues until the target performance is reached or the maximum iteration count is achieved, at which point the final device structure is recorded.

The inverse design of power splitters on a Z-cut/X-propagation lithium niobate thin-film platform is conducted. When the target ratio is 1∶1, the insertion losses of the optimized devices within the 1500?1600 nm wavelength range for three sizes (L₁×L₂=2.86 μm×2.42 μm, 2.86 μm×2.86 μm, 2.86 μm×3.30 μm) are 0.135 dB?0.188 dB (Δ_IL=0.053 dB), 0.070 dB?0.097 dB (Δ_IL=0.027 dB), and 0.030 dB?0.060 dB (Δ_IL=0.030 dB), respectively (Fig. 4). As shown, all optimized devices exhibit low insertion loss (ξ_IL<0.2 dB), with IL showing minimal variation with the incident light wavelength (Δ_IL<0.06 dB). When the target ratio is 1∶2, the input light wave is unevenly split into the two output waveguides, and the splitting ratio of the device closely matches the ideal target value, while the overall insertion loss remains below 0.22 dB (Fig. 5). Next, the inverse design of power splitters is carried out on an X-cut/Y-propagation lithium niobate thin-film platform. When the target ratio is 1∶1, the insertion losses of the optimized devices in the 1500?1600 nm wavelength range are 0.206 dB?0.258 dB (Δ_IL=0.052 dB), 0.100 dB?0.135 dB (Δ_IL=0.035 dB), 0.057 dB?0.077 dB (Δ_IL=0.020 dB), respectively (Fig. 6). When the target ratio is 1∶2, the insertion loss of the device varies between 0.243?0.307 dB (Fig. 7).

In this paper, the inverse design of low-loss, compact 1×2 power splitters is carried out based on an anisotropic lithium niobate thin-film platform. The effects of design area sizes, splitting ratios, and crystal orientations on the inverse design results are also investigated. Firstly, three different sizes of 1∶1 and 1∶2 power splitters (2.86 μm×2.42 μm, 2.86 μm×2.86 μm, and 2.86 μm×3.30 μm) are designed on Z-cut/X-propagation and X-cut/Y-propagation lithium niobate thin-film platforms, respectively. The simulation results show that the devices exhibit low-loss characteristics within the 1500?1600 nm wavelength range. For a device size of 2.86 μm×2.86 μm, the insertion losses of the 1∶1 and 1∶2 power splitters are less than 0.14 dB and 0.31 dB, respectively, with the splitting ratios within the 100 nm operating bandwidth closely matching the target values, meeting the design requirements. The larger the design area size and the higher the number of pixels, the greater the design freedom, allowing for lower device loss, although this increases the simulation time. The inverse design results of the Z-cut/X-propagation and X-cut/Y-propagation lithium niobate thin-film platform are compared. The results indicate that devices designed based on the Z-cut/X-propagation platform are more likely to achieve lower loss due to the anisotropy of the lithium niobate crystals when TE-mode light waves are incident.