Function Photonic Crystals

TL;DR

This paper introduces a new class of function photonic crystals with spatially varying refractive indices, analyzing their optical properties and demonstrating their ability to produce tunable band gaps compared to conventional photonic crystals.

Contribution

The paper proposes a novel concept of function photonic crystals with position-dependent refractive indices and derives their light propagation equations in multiple dimensions.

Findings

Function photonic crystals can have adjustable band gap widths.

Dispersion relations differ significantly from conventional photonic crystals.

Tunable optical properties are achievable through different refractive index distributions.

Abstract

In the paper, we present a new kind of function photonic crystals, which refractive index is a function of space position. Unlike conventional PCs, which structure grow from two materials, A and B, with different dielectric constants $\epsilon_{A}$ and $\epsilon_{B}$. By Fermat principle, we give the motion equations of light in one-dimensional, two-dimensional and three-dimensional function photonic crystals. For one-dimensional function photonic crystals, we study the dispersion relation, band gap structure and transmissivity, and compare them with conventional photonic crystals. By choosing various refractive index distribution function $n(z)$, we can obtain more width or more narrow band gap structure than conventional photonic crystals.