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Journal of Lightwave Technology

Bistability by Slow Light Photonic Crystal Waveguide

Lei Dai, Chun Jiang

Published Dec 16, 2009• 7 citations
Publisher

Abstract

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.

DOI
10.1109/jlt.2009.2038599

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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 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.
A photonic crystal waveguide-cavity structure with a partially reflecting element is exploited to achieve optical bistability. Analysis of the theoretical model and validation of the numerical simulation indicate that this structure shows an asymmetrical lineshape and a novel switching characteristic, with the nonlinear transmission power varying sharply in a very narrow linewidth range. The characteristic power can be decreased from 6.35 mW/μm of the symmetrical lineshape to 0.604 mW/μm of the asymmetrical one. Through the study of the quality factor of the cavity, the results show that the lower switch power of an asymmetrical lineshape is essentially due to the increased Q-factor, which causes more and more energy to be stored in the cavity.
Optical bistability with low power and large modulation depth is observed in the silicon 2D photonic crystal 3 defect-long (L3) cavity coupling with a photonic crystal waveguide experimentally. The cavity-waveguide resonator system operates under the critical coupling condition. The triangular line shape of the cavity resonance and the hysteresis loop of the system is observed. The switching contrast is 7.7 dB and the modulation depth is 0.70 at the switching power of -12.1 dBm. A nonlinear coupled mode model is established to analyze the behavior of the cavity, and numerical simulation results are in good agreement with the experiment results.
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
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.