On photonic band gaps in two-dimensional photonic crystal fibres. Analysis in the vicinity of the low-dielectric light line

TL;DR

This paper analyzes the existence and characteristics of photonic band gaps near the light line in two-dimensional photonic crystal fibres, providing mathematical insights applicable to low-contrast and various fibre geometries.

Contribution

It offers a mathematical analysis of photonic band gaps near the light line, including asymptotic results for ARROW fibres, without assuming specific dielectric contrast ratios.

Findings

Photonic band gaps exist near the light line in 2D photonic crystal fibres.

Asymptotic analysis demonstrates low-frequency band gaps in ARROW fibres.

Results apply to both low and moderate dielectric contrast models.

Abstract

We consider `off-axis' electromagnetic wave propagation down the homogeneous direction of a low-loss two-dimensional periodic dielectric (or photonic crystal fibre) near the light line of the low-dielectric material constituent. Numerous physical and numerical experiments demonstrate the presence of photonic band gaps in the vicinity of this `critical' light line. We mathematically analyse the existence of photonic band gaps near the line and characterise them in terms of frequency gaps in the spectrum of the Maxwell equations restricted to the line. We apply the results to both one-dimensional photonic crystal fibres, and a genuinely two-dimensional photonic crystal fibres with `thin' inclusions, namely ``ARROW'' fibres. In the case of ARROW fibres, by an asymptotic analysis, in terms of the small inclusion parameter, we demonstrate the existence of low frequency photonic band gaps. It is important to note that our analysis does not assume any specific ratio between the dielectric contrasts; as a result, moderate or even low contrast models are fully encompassed. Similarly, no limiting assumptions are imposed on the wave propagation constant along the fibre.