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- $(\mathrm{\Delta }n-)$ 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. $\mathrm{\Delta }n$ 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 $\mathrm{\Delta }n$ 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 $\mathrm{\Delta }n$ 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 $\mathrm{\Delta }n.$ As a result, it was found that the phase-shift arm can be designed short enough to achieve a compact ultrafast all-optical switch.

© 2004 Optical Society of America