Group velocity and energy transport velocity near the band edge of a disordered coupled cavity waveguide: an analytical approach

We develop an analytical approach to theoretically investigate light speed propagation near the band edge of a coupled cavity waveguide in the presence of residual disorder. This approach that is based on a mean field theory allows us to define the domains of validity of the group velocity and the energy transport velocity concepts as well as a guideline to minimize the role of the residual disorder. Inspired by an analogy with the theory of multiple scattering of classical wave, we derive an analytical formula for the energy transport velocity in periodic photonic structures. Whereas the group velocity diverges near the band edge in the presence of any amount of residual disorder, we show that the energy transport velocity mainly follows the ideal group velocity of the unperturbed structure except for very strong disturbances out of the scope of the presented model.