Analysis of Band Effects in One-Dimensional Periodic Lattices Using an Enhanced Homogenization Method

Abstract

Optical elements based on periodic lattices are important components in optics and photonics. Numerical analysis methods such as rigorous coupled-wave analysis are widely utilized to investigate these structures. Despite the high precision of numerical methods, the intricate periodicity of lattices hinders comprehensive physical analysis, emphasizing the need for effective homogenization techniques. The most common method, Rytov-based homogenization, is limited to binary-symmetrical lattices and prone to errors under oblique incidence. However, these traditional techniques remain prevalent due to the lack of better alternatives. This article introduces a novel homogenization technique that overcomes the limitations of Rytov-based methods and addresses the intricate periodicity of photonic lattices. It provides comprehensive physical insights by calculating the effective refractive index (n_g), particularly focusing on the challenging TM polarization. This homogenization technique can predict quasi-bound states in the continuum and guided-mode resonance spectral locations, and elucidate band effects such as mode crossing, and mode anti-crossing for any type of rectangular one-dimensional grating. The study examines an intricate asymmetrical multipart grating with asymmetry arising from both oblique incidence and asymmetrical profile arrangement. Notably, it reveals phenomena like invisible band flips and invisible bandgaps, which are crucial for understanding photonic band structures and are undetectable by numerical methods.