Fabry–Pérot modes associated with hyperbolic-like dispersion in dielectric photonic crystals and demonstration of a bending angle sensor at microwave frequencies

The dispersion properties of metamaterials and photonic crystals (PhCs) lead to an intensive research in the development of cavity resonators for the confinement of electromagnetic (e-m) radiation. In this work, we investigate the formation of Fabry–Pérot (FP) modes associated with hyperbolic-like dispersion (HLD) regimes in two-dimensional dielectric PhCs. Conventionally, FP modes are formed using an optical etalon, in which electromagnetic (e-m) waves reflecting from a partially reflecting mirror separated by a distance can interfere constructively and form a resonating mode. The FP mode observed in dielectric PhCs is formed due to the interference of cylindrical wavefronts inside the PhC interface at HLD frequencies. The FP modes in PhCs are surface localized, in which maxima/minima of the electric field lies along the air–PhC interface as a standing wave pattern and decays in air medium. Projected bandstructure, Eigen Frequency Contours (EFC), phase and group index calculations are carried out to explain the formation of FP modes in PhCs under different coupling cases. By varying the PhC dimension, FP modes with different spatial profiles are witnessed and the role of source position in exciting specific mode is demonstrated. The observed FP modes in PhCs are compared with the FP mode in an ideal indefinite slab. Based on the FP resonance in PhCs, a sensing device capable of detecting a bending angle less than [Formula: see text] is demonstrated numerically. The FP modes in PhCs are scalable to other parts of e-m spectra so that the bending angle sensing can be extendable to terahertz and optical domains.