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arXiv:0804.4133 · Optics Express

Low-threshold bistability of slow light in photonic-crystal waveguides

Sergei F. Mingaleev, Andrey E. Miroshnichenko, Yuri S. Kivshar

Published Jan 1, 2007• 39 citations
arXivHTMLPDF

Abstract

We analyze the resonant transmission of light through a photonic-crystal waveguide side coupled to a Kerr nonlinear cavity, and demonstrate how to design the structure geometry for achieving bistability and all-optical switching at ultralow powers in the slow-light regime. We show that the resonance quality factor in such structures scales inversely proportional to the group velocity of light at the resonant frequency and thus grows indefinitely in the slow-light regime. Accordingly, the power threshold required for all-optical switching in such structures scales as a square of the group velocity, rapidly vanishing in the slow-light regime.

DOI
10.1364/oe.15.012380

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We analyze the resonant transmission of light through a photonic-crystal waveguide side coupled to a Kerr nonlinear cavity, and demonstrate how to design the structure geometry for achieving bistability and all-optical switching at ultralow powers in the slow-light regime. We show that the resonance quality factor in such structures scales inversely proportional to the group velocity of light at the resonant frequency and thus grows indefinitely in the slow-light regime. Accordingly, the power threshold required for all-optical switching in such structures scales as a square of the group velocity, rapidly vanishing in the slow-light regime.
We analyze the resonant linear and nonlinear transmission through a photonic crystal waveguide side-coupled to a Kerr-nonlinear photonic crystal resonator. First, we extend the standard coupled-mode theory analysis to photonic crystal structures and obtain explicit analytical expressions for the bistability thresholds and transmission coefficients which provide the basis for a detailed understanding of the possibilities associated with these structures. Next, we discuss limitations of standard coupled-mode theory and present an alternative analytical approach based on the effective discrete equations derived using a Green's function method. We find that the discrete nature of the photonic crystal waveguides allows a geometry-driven enhancement of nonlinear effects by shifting the resonator location relative to the waveguide, thus providing an additional control of resonant waveguide transmission and Fano resonances. We further demonstrate that this enhancement may result in the lowering of the bistability threshold and switching power of nonlinear devices by several orders of magnitude. Finally, we show that employing such enhancements is of paramount importance for the design of all-optical devices based on slow-light photonic crystal waveguides.
We study theoretically and numerically optical bistability in photonic crystal waveguide-cavity system with cavity holding multipole mode patterns. The elimination of dominant component of the radiation in cavity can reduce dramatically the scattering of light by cavity and can be used to achieve bistability at band edge. Numerical results performed by the finite-difference time-domain method indicate that the switch power can be reduced greatly that can be regarded as the improvement of quality-factor in cavity.
We demonstrate extremely low-power all-optical bistability by using photonic crystal linear resonators based on InGaAsP quantum-wells. Since the photonic crystal cavity has a high quality-factor and a small mode-volume, the photon density in the cavity is extremely high, which makes it possible to reduce the bistable power. The measured minimum bistable threshold power was 37 muW by using a fiber coupling technique, and the estimated nonlinear refractive index (n2) was -6.84times10-14m2/W at a wavelength of 1610.8 nm which is near the resonant wavelength of quantum-well. The low-power optical bistable operations in a single photonic crystal cavity open the possibility of integrated optical devices such as an all-optical memory and switch, based on photonic crystals