Applicability of the Effective Index Method for the Simulation of X-Cut LiNbO₃ Waveguides

Photonic integrated circuits (PIC) find applications in the fields of microwaves, telecoms and sensing. Generally, PICs are fabricated on a base of isotropic materials such as SOI, Si3N4, etc. However, for some applications, anisotropic substrates such as LiNbO3 are used. A thin film of LiNbO3 on an insulator (LNOI) is a promising material platform for complex high-speed PICs. The design and simulation of PICs on anisotropic materials should be performed using rigorous numerical methods based on Maxwell's equations. These methods are characterized by long calculation times for one simulation iteration. Since a large number of simulation iterations are performed during the PIC design, simulation methods based on approximations should be used. The effective index method (EIM) is an approximation-based method and is widely applied for simulations of isotropic waveguides. In this study, the applicability of EIM for simulations of anisotropic waveguides is analyzed. The results obtained by EIM are compared with the calculation results of a rigorous finite-difference frequency-domain (FDFD) method for evaluation of the EIM's applicability limits. In addition, radiation losses in waveguides with rough sidewalls are estimated using the Payne-Lacey model and EIM. The results demonstrate the applicability of EIM for the simulation of anisotropic LNOI-based waveguides with cross-section parameters specified in this paper.