Light transport regimes in slow light photonic crystal waveguides

Abstract

The dispersive properties of waves are strongly affected by inevitable residual disorder in man-made propagating media, in particular in the slow wave regime. By a direct measurement of the dispersion curve in $k$ space, we show that the nature of the guided modes in real photonic crystal waveguides undergoes an abrupt transition in the vicinity of a band edge. Such a transition that is not highlighted by standard optical transmission measurement, defines the limit where $k$ can be considered as a good quantum number. In the framework of a mean-field theory we propose a qualitative description of this effect and attribute it to the transition from the ``dispersive'' regime to the diffusive regime. In particular we prove that a scaling law exists between the strength of the disorder and the group velocity. As a result, for group velocities ${v}_{g}$ smaller than $c/25$ the diffusive contribution to the light transport is predominant. In this regime the group velocity ${v}_{g}$ loses its relevance and the energy transport velocity ${v}_{E}$ is the proper light speed to consider.