Simulation of group-velocity-dependent phase shift induced by refractive-index change in an air-bridge-type AlGaAs two-dimensional photonic crystal slab waveguide

Abstract

We report on a theoretical study of a refractive-index-change- (Δn-) induced phase shift enhanced by the low group velocity in an air-bridge-type AlGaAs two-dimensional (2-D) photonic crystal (PC) slab waveguide. The calculation was based on a three-dimensional finite-difference time-domain method for the design of a phase-shift arm of the 2-D PC-based symmetric Mach–Zehnder- (SMZ-) type all-optical switch. Δn was assumed to be induced by an optical nonlinearity of InAs quantum dots embedded selectively in the phase-shift arm in the PC SMZ. By changing Δn from 0 to −0.01 and −0.1 for an even guided mode in the triangular-lattice single-line-defect waveguide in the PC SMZ, we calculated a group-velocity-dependent phase shift as well as a band diagram and a transmission spectrum. The result showed that the phase shift is almost inversely proportional to the group velocity. Taking into account Δn of approximately −0.001 predicted for actual InAs quantum dots, we evaluated the length of the phase-shift arm, necessary for the π phase shift in the PC SMZ, to be ~100 μm for a group velocity of 0.031c and a lattice constant of 0.36 μm at a wavelength of ~1.3 μm, where c is the light velocity in the vacuum. The length of the phase-shift arm was significantly reduced because of the low group velocity in spite of the small Δn. As a result, it was found that the phase-shift arm can be designed short enough to achieve a compact ultrafast all-optical switch.