Periodicity enclosed in boundaries: local density of states in photonic clusters

V Prosentsov,A Lagendijk

doi:10.1364/oe.16.006974

Abstract

We have studied the effect of the boundaries on the local density of states (LDOS) in one-, two-, and three-dimensional finite size photonic structures. The LDOS was calculated with the help of the local perturbation method (LPM) and a new LPM-Bloch method using periodicity of the system. The methods are applicable for the clusters made of small (relative to the incident wavelength) particles or for the clusters which can be considered as made of such particles. It was demonstrated that the LPM-Bloch method is an accurate numerical tool for calculation of the LDOS in the finite size photonic structures with weak interference.

Highlights

It is well known in physics that sometimes it takes much less effort to study an ideal infinite system than a finite one
The impact of the boundary on the local density of states (LDOS) and the frequency (Lamb) shift was investigated in the work [1] for two-dimensional photonic crystals
In this paper we will compare the two methods for the case when the results of the local perturbation method (LPM) are exact. For this purpose we study LDOS in the clusters made of particles which are small compared to the incident wavelength

Summary

Introduction

It is well known in physics that sometimes it takes much less effort to study an ideal infinite system than a finite one. The method is based on the assumption that the scatterers (or particles forming the scatterers) are small compared to the incident wavelength and that fields inside a cluster are almost periodic, implicitly implying what the boundary effects are weak. In this paper we will compare the two methods for the case when the results of the LPM are exact (with the high numerical accuracy) For this purpose we study LDOS in the clusters made of particles which are small compared to the incident wavelength (see [4] for comparison between LPM and exact results). It is interesting to note that in the work [5] the LDOS was studied for the finite photonic structures with the help of the periodic boundary conditions (PBC). From a calculation with the PBC it is difficult to extract the properties of a realistic cluster

Theory of the LPM-Bloch method

Numerical examples

Scalar case

Vector case

Conclusions