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

JOSA B, Vol. 21, Issue 10, pp. 1833-1838 (2004)

http://dx.doi.org/10.1364/JOSAB.21.001833

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### 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.

© 2004 Optical Society of America

**OCIS Codes**

(230.3990) Optical devices : Micro-optical devices

(230.7400) Optical devices : Waveguides, slab

(320.7080) Ultrafast optics : Ultrafast devices

**Citation**

Yoshinori Watanabe, Noritsugu Yamamoto, Kazuhiro Komori, Hitoshi Nakamura, Yoshimasa Sugimoto, Yu Tanaka, Naoki Ikeda, Kiyoshi Asakawa, and Kuon Inoue, "Simulation of group-velocity-dependent phase shift induced by refractive-index change in an air-bridge-type AlGaAs two-dimensional photonic crystal slab waveguide," J. Opt. Soc. Am. B **21**, 1833-1838 (2004)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-21-10-1833

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