Numerical treatment of disorder in PHC slabs

TL;DR

This paper develops numerical simulation methods for Photonic Crystal structures with disorder, demonstrating their effectiveness in predicting quality factors and the impact of irregularities on waveguide performance.

Contribution

It introduces a Bloch-mode expansion formalism for large disordered PHC structures, enabling accurate simulations of disorder effects on quality factors and mode broadening.

Findings

Disorder can significantly reduce quality factors to match experimental values.

Correlation length of irregularities affects mode broadening and loss rates.

The method accurately predicts effects of disorder in PHC cavities and waveguides.

Abstract

This work concentrates on numerical simulations of Photonic Crystal structures using basis-expansion methods, with a main focus on simulating disorder. The plane-wave and guided-mode expansions are outlined as tools to compute the Bloch modes of a structure, on the basis of which the Bloch-mode expansion formalism is outlined - the latter allowing for simulations of large structures in presence of disorder. As a first illustration of the method, we apply it to three gentle-confinement cavities, to obtain results for their quality factors similar to the theoretically predicted in the literature. Furthermore, we compute that random disorder can drive those factors down to the experimentally measured values. As a second application, we study the effect of irregular hole shapes in a PHC waveguide, and find that the correlation length of the irregularity (i.e. the typical scale of the roughness of the features) matters: for higher correlation lengths, the computed modes show both higher band broadening and higher loss rates.