Unified Homogenization of Photonic/Phononic Crystals: Controllable First-band Negative Refraction

TL;DR

This paper introduces a unified homogenization method for photonic and phononic crystals that accurately reproduces their band structures and demonstrates controllable negative refraction on the first pass band, enabling new wave manipulation possibilities.

Contribution

It presents the first unified approach to homogenize photonic and phononic crystals, accurately capturing their band structures and enabling control over negative refraction phenomena.

Findings

Homogenized parameters exactly reproduce band structures.

Negative refraction can be controlled over a wide frequency range.

Homogenized medium exhibits diverse refraction behaviors depending on frequency.

Abstract

It is shown, for the first time, that negative refraction with positive phase velocity refraction can be realized (and controlled) over a wide range of frequency on the first (lowest) pass band of simple photonic and phononic crystals. First a unified approach is presented to accurately, efficiently, and uniquely produce the homogenized effective material properties of doubly periodic phononic crystals for anti-plane shear (SH) and photonic crystals for transverse electric (TE) and transverse magnetic (TM) electromagnetic Bloch-form waves in such a manner that they exactly reproduce the band structure of the composite over any desired frequency band. Then the correspondence between phononic and photonic field equations is established and their effective homogenized material parameters are calculated. Finally illustrative examples are worked out for each case, revealing a rich body of refractive characteristics of these crystals, and showing by means of these examples that the homogenized effective parameters do yield the exact results, and that the resulting homogenized medium does in fact embody exactly the actual band structure and dispersive properties of the considered phononic/photonic crystal. As a consequence when the homogenized medium is placed in contact with a normal homogeneous half-space, it could display, even on the first pass band, positive, negative, or even no energy refraction depending on the frequency and wave vector of plane waves incident from the normal homogeneous solid to the interface.