Tight-binding parameterization for photonic band gap materials

TL;DR

This paper extends the tight-binding method from electronic systems to classical photonic band gap materials, enabling accurate modeling of their band structures using fitted parameters.

Contribution

It introduces a tight-binding parameterization approach for photonic materials, demonstrating transferability and accuracy across various 2D lattice configurations.

Findings

Successfully reproduces band structures of different 2D photonic lattices

Shows transferability of TB parameters to defected structures

Validates the TB model against ab initio results

Abstract

The ideas of the linear combination of atomic orbitals (LCAO) method, well known from the study of electrons, is extended to the classical wave case. The Mie resonances of the isolated scatterer in the classical wave case, are analogous to the localized eigenstates in the electronic case. The matrix elements of the two-dimensional tight-binding (TB) Hamiltonian are obtained by fitting to ab initio results. The transferability of the TB model is tested by reproducing accurately the band structure of different 2D lattices, with and without defects, thus proving that the obtained TB parameters can be used to study other properties of the photonic band gap materials.