Giant anomalous self-steepening in photonic crystal waveguides

Self-steepening of optical pulses arises due to the dispersive contribution of the effective Kerr nonlinearity. In typical structures this response is on the order of a few femtoseconds with a fixed frequency response. In contrast, the effective Kerr nonlinearity in photonic crystal waveguides (PhCWGs) is largely determined by the geometrical parameters of the structure and is consequently tunable over a wide range. Here we show group-velocity (group-index) modulation leads to a previously unexplored physical mechanism for generating self-steepening. Further, we demonstrate that periodic media such as PhCWGs can exhibit self-steepening coefficients two orders of magnitude larger than typical systems. At these magnitudes the self-steepening strongly affects the nonlinear pulse dynamics even for picosecond pulses. Due to interaction with additional higher-order nonlinearities in the semiconductor materials under consideration, we employ a generalized nonlinear Schrödinger equation numerical model to describe the impact of self-steepening on the temporal and spectral properties of the optical pulses in practical systems, and define appropriate figures of merit. These results provide a theoretical description for recent experimental results presented by C. A. Husko et al. [Sci. Rep. 3, 1100 (2013)] and F. Raineri et al. [Phys. Rev. A 87, 041802 (2013)]. More generally, these observations apply to all periodic media due to the rapid group-velocity variation characteristic of these structures.