Giant anomalous self-steepening in photonic crystal waveguides

TL;DR

This paper introduces a new physical mechanism for giant self-steepening in photonic crystal waveguides, driven by group-velocity modulation, leading to significantly enhanced nonlinear pulse effects in tunable, periodic media.

Contribution

It demonstrates for the first time that group-velocity modulation causes giant self-steepening in photonic crystal waveguides, with coefficients much larger than in conventional systems.

Findings

Self-steepening coefficients two orders of magnitude larger than typical systems.

Giant self-steepening significantly influences nonlinear pulse dynamics.

Theoretical model aligns with recent experimental results.

Abstract

Self-steepening of optical pulses arises due the dispersive contribution of the $\chi^{(3)}(\omega)$ Kerr nonlinearity. In typical structures this response is on the order of a few femtoseconds with a fixed frequency response. In contrast, the effective $\chi^{(3)}$ 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 self-steepening based on group-velocity (group-index) modulation for the first time, giving rise to a new physical mechanism for generating this effect. 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 Schr\"{o}dinger equation numerical model to describe the impact of self-steepening on the temporal and spectral properties of the optical pulses in practical systems, including new figures of merit. These results provide a theoretical description for recent experimental results presented in [Scientific Reports 3, 1100 (2013) and 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.