Effect of multiphoton absorption and free carriers in slow-light photonic crystal waveguides

We examine the effects of multiphoton absorption, free carriers, and disorder-induced linear scattering in slow-light photonic crystal waveguides. We derive an analytic formulation for self-phase modulation including the group velocity scaling of the nonlinear phase shift in materials limited by three-photon absorption as a representative nonlinear process. We investigate the role of free carriers and derive an approximate critical intensity at which these effects begin to strongly modify the optical field. This critical intensity is employed to determine an optimal group index for the self-phase modulation in the slow-light devices. These observations are confirmed with numerical modeling.