Strongly Localized State of a Photon at the Intersection of the Phase Slips in 2D Photonic Crystal with Low Contrast of Dielectric Constant

TL;DR

This paper demonstrates that in a 2D photonic crystal with low dielectric contrast, strong photon localization can be achieved at the intersection of phase slips for specific geometries, resulting in high-quality bound modes.

Contribution

It introduces a method to localize photons strongly in low-contrast 2D photonic crystals using phase slips, identifying a specific 'magic' cylinder radius for optimal confinement.

Findings

Bound photon mode lifetime exceeds 10^6 at the magic radius

Small deviations from the magic radius cause significant damping

Localization occurs despite absence of a bandgap

Abstract

Two-dimensional photonic crystal with a rectangular symmetry and low contrast (< 1) of the dielectric constant is considered. We demonstrate that, despite the {\em absence} of a bandgap, strong localization of a photon can be achieved for certain ``magic'' geometries of a unit cell by introducing two $\pi/2$ phase slips along the major axes. Long-living photon mode is bound to the intersection of the phase slips. We calculate analytically the lifetime of this mode for the simplest geometry -- a square lattice of cylinders of a radius, $r$. We find the magic radius, $r_c$, of a cylinder to be 43.10 percent of the lattice constant. For this value of $r$, the quality factor of the bound mode exceeds $10^6$. Small ($\sim 1%$) deviation of $r$ from $r_c$ results in a drastic damping of the bound mode.