Theory of disorder-induced multiple coherent scattering in photonic crystal waveguides

TL;DR

This paper develops a comprehensive theoretical framework combining Green function and coupled mode methods to analyze disorder-induced multiple scattering in slow-light photonic crystal waveguides, explaining experimental phenomena and revealing effects like localization.

Contribution

It extends existing optical scattering theory to fully three-dimensional, multiple scattering scenarios in photonic crystal waveguides, enabling detailed analysis of disorder effects.

Findings

Multiple scattering significantly affects waveguide transmission.

Disorder-induced localization is enhanced in slow light regimes.

The theory accurately reproduces experimental resonance features.

Abstract

We introduce a theoretical formalism to describe disorder-induced extrinsic scattering in slow-light photonic crystal waveguides. This work details and extends the optical scattering theory used in a recent \emph{Physical Review Letter} [M. Patterson \emph{et al.}, \emph{Phys. Rev. Lett.} \textbf{102}, 103901 (2009)] to describe coherent scattering phenomena and successfully explain complex experimental measurements. Our presented theory, that combines Green function and coupled mode methods, allows one to self-consistently account for arbitrary multiple scattering for the propagating electric field and recover experimental features such as resonances near the band edge. The technique is fully three-dimensional and can calculate the effects of disorder on the propagating field over thousands of unit cells. As an application of this theory, we explore various sample lengths and disordered instances, and demonstrate the profound effect of multiple scattering in the waveguide transmission. The spectra yield rich features associated with disorder-induced localization and multiple scattering, which are shown to be exasperated in the slow light propagation regime.