The limits for complete photonic bandgaps in low-contrast media

TL;DR

This paper investigates the minimal refractive index contrast needed for complete photonic bandgaps in structured media, deriving an analytical estimate and supporting it with numerical simulations in 2D and 3D.

Contribution

It introduces an analytical estimation of the optimal number of Bragg peaks for achieving CPBGs at low index contrasts in 2D and 3D structures.

Findings

Analytical estimate predicts optimal number of Bragg peaks for CPBGs.

Numerical simulations support the estimation in 2D structures.

Demonstrated near 10 dB emission suppression in 3D with low index contrast.

Abstract

The minimal refractive index contrast to obtain a complete photonic bandgap (CPBG) in structured media was not identified so far. We address this problem by considering distributed quasicrystals in with arbitrary number and positions of Bragg peaks in reciprocal space. For these structures an analytical estimation is derived which predicts that there is an optimal number of Bragg peaks for any refractive index contrast and finite CPBGs for an arbitrarily small refractive index contrast in 2D and 3D. Results of numerical simulations of dipole emission in 2D structures support our estimation. In 3D an emission suppression of almost 10 dB was demonstrated with a refractive index contrast of 1.6. The reason for residual leakage in 3D structures has to be further investigated.