Generalized model of anisotropic thermo-optic response on thin-film lithium niobate platform

Thermo-optic (TO) control is crucial for thin-film lithium niobate (TFLN) photonic integrated circuits (PICs), offering a simple and practical method for low-frequency and DC tuning while remaining compatible with high-frequency electro-optic (EO) modulation. In x-cut TFLN, the TO response is inherently anisotropic, depending on both waveguide propagation angle and polarization due to the mode-specific overlap of the electric field with the ordinary and extraordinary refractive index axes of the crystal. Despite its significance, a systematic and quantitative analysis of this anisotropy has remained elusive. Here, we present the first generalized analytical model that describes the anisotropic TO response as a function of polarization and arbitrary waveguide orientation, and rigorously validate it through numerical simulations and experiments. This study provides foundational insight into anisotropic thermal tuning and enables new opportunities for engineering energy-efficient and scalable photonic design in next-generation TFLN PICs.