Generalized homogenization method for subwavelength periodic lattices

Periodic photonic lattices based on Guided-Mode Resonance (GMR) enable the manipulation of the incident light, making them essential components in a plethora of optical elements including filters, sensors, lasers, and polarizers. The GMR is regarded as a resonance phenomenon in the resonant-subwavelength regime of periodic lattices. We present a method that homogenizes these periodic structures in the subwavelength regime and provides an appropriate analytical interpretation of the resonance effect. Here, we propose a technique based on utilizing the dispersion relation for homogenization, which can be applied to multi-part period lattices under oblique incidence. The effect of asymmetry and emergence of the odd/even modes, not considered in previous methods, will also be taken into account and discussed. As a result of this analytical procedure, resonance lines are obtained, which are useful in designing optical elements such as wideband/narrowband reflectors and polarizers.