Radiation pattern of a classical dipole in a photonic crystal: photon focusing

TL;DR

This paper analyzes how a classical dipole's radiation pattern is significantly altered within a photonic crystal, showing suppression and enhancement effects due to photon focusing, supported by asymptotic analysis and numerical simulations.

Contribution

It provides the first asymptotic analysis of dipole radiation in a photonic crystal with incomplete bandgap, revealing photon focusing effects and validating results with FDTD simulations.

Findings

Radiation is suppressed in the stopband direction.

Radiation is enhanced along the group velocity direction.

Asymptotic analysis agrees with numerical FDTD results.

Abstract

The asymptotic analysis of the radiation pattern of a classical dipole in a photonic crystal possessing an incomplete photonic bandgap is presented. The far-field radiation pattern demonstrates a strong modification with respect to the dipole radiation pattern in vacuum. Radiated power is suppressed in the direction of the spatial stopband and strongly enhanced in the direction of the group velocity, which is stationary with respect to a small variation of the wave vector. An effect of radiated power enhancement is explained in terms of \emph{photon focusing}. Numerical example is given for a square-lattice two-dimensional photonic crystal. Predictions of asymptotic analysis are substantiated with finite-difference time-domain calculations, revealing a reasonable agreement.