Light transport regimes in slow light photonic crystal waveguides
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.