Light Field Distributions in One-dimensional Photonic Crystal Fibers

TL;DR

This paper analyzes the light field distribution in one-dimensional photonic crystal fibers, revealing a fundamental property of decay and periodicity in band gaps, applicable to various layered structures and elucidating the nature of photonic band gap guidance.

Contribution

It establishes a general property of light field distributions in 1D photonic crystal fibers, applicable regardless of layer complexity or index contrast, enhancing understanding of band gap guidance mechanisms.

Findings

Light field distribution in band gaps is a decaying factor times a periodic function.

The periodicity can match the medium's period or double it, depending on eigenvalue matrix trace.

Photonic band gap guidance is a form of total internal reflection.

Abstract

It is shown in this paper that the light field distribution in a band gap within periodic structures for one-dimensional photonic crystal fibers is described by a decaying factor multiplied by a periodical function that has the same period length as the one of the medium or has double the period length of the medium, depending on the sign of the trace of eigen value matrix. This fundamental property is applicable to any 1D planar periodic structures, no matter how many layers a unit cell has, what the contrast of refractive indices is, and whether the dielectric parameters in individual layers are homogeneous or inhomogeneous; it plays a significant role in understanding of numerical results in a number of previously published research works. It is also shown that, similar to the refractive index guidance in conventional optical fibers, the photonic band gap guidance is also a form of total internal reflection.