Large Photonic Band Gaps in Certain Periodic and Quasi-Periodic Networks in two and three dimensions

TL;DR

This paper investigates photonic band gaps in 2D and 3D periodic and quasi-periodic networks of waveguides, revealing that gaps occur at anti-resonance frequencies of the fundamental loop.

Contribution

It demonstrates the existence of photonic band gaps linked to anti-resonant transmission in specific network structures, extending understanding to quasi-periodic systems.

Findings

Photonic band gaps only occur at anti-resonance frequencies.

Band gap positions are determined by anti-resonance in the fundamental loop.

Quasi-periodic networks also exhibit band gaps based on total transmission spectra.

Abstract

The photonic band structures in certain two- and three-dimensional periodic networks made of one-dimensional waveguides are studied by using the Floquet-Bloch theorem. We find that photonic band gaps exist only in those structures where the fundamental loop exhibits anti-resonant transmission. This is also true for quasi-periodic networks in two and three dimensions, where the photonic band structures are calculated from the spectra of total transmission arising from a source inside the samples. In all the cases we have studied, it is also found that the gap positions in a network are dictated by the frequencies at which the anti-resonance occurs.