Eur. Phys. J. B 77, 147-152 (2010)
https://doi.org/10.1140/epjb/e2010-00250-y

Emergence of semi-localized Anderson modes in a disordered photonic crystal as a result of overlap probability^*

Department of Physics, College of Sciences, Shiraz University, Shiraz, 71454, Iran

Corresponding author: ^a montakhab@shirazu.ac.ir

Received: 10 November 2009
Revised: 7 June 2010
Published online: 13 August 2010

Abstract

In this paper we study the effect of positional randomness on transmissional properties of a two dimensional photonic crystal as a function of a randomness parameter α (α = 0 completely ordered, α = 1 completely disordered). We use finite-difference time-domain (FDTD) method to solve the Maxwell's equations in such a medium numerically. We consider two situations: first a 90° bent photonic crystal wave-guide and second a centrally pulsed photonic crystal micro-cavity. We plot various figures for each case which characterize the effect of randomness quantitatively. More specifically, in the wave-guide situation, we show that the general shape of the normalized total output energy is a Gaussian function of randomness with wavelength-dependent width. For centrally pulsed PC, the output energy curves display extremum behavior both as a function of time as well as randomness. We explain these effects in terms of two distinct but simultaneous effects which emerge with increasing randomness, namely the creation of semi-localized modes and the shrinking (and eventual destruction) of the photonic band-gaps. Semi-localized (i.e. Anderson localized) modes are seen to arise as a synchronization of internal modes within a cluster of randomly positioned dielectric nano-particles. The general trend we observe shows a sharp change of behavior in the intermediate randomness regime (i.e. α ≈ 0.5) which we attribute to a similar behavior in the underlying overlap probability of nano-particles.