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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Optimal bistable switching in nonlinear photonic crystals

Marin Soljacic A, Mihai Ibanescu A, Steven G. Johnson, Yoel Fink, John D. Joannopoulos

Published Nov 11, 2002• 361 citations
Publisher

Abstract

We present an analytical model and numerical experiments to describe optimal bistable switching in a nonlinear photonic crystal system. It is proved that only three parameters are needed to characterize a bistable switch: the resonant frequency omega(res), the quality factor Q, and parameter kappa that measures nonlinear "feedback strength." A photonic crystal enables the device to operate in single-mode fashion, as if it were effectively one dimensional. This provides optimal control over the input and output and facilitates further large-scale optical integration.

DOI
10.1103/physreve.66.055601

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We present an analytical model and numerical experiments to describe optimal bistable switching in a nonlinear photonic crystal system. It is proved that only three parameters are needed to characterize a bistable switch: the resonant frequency omega(res), the quality factor Q, and parameter kappa that measures nonlinear "feedback strength." A photonic crystal enables the device to operate in single-mode fashion, as if it were effectively one dimensional. This provides optimal control over the input and output and facilitates further large-scale optical integration.
We present an analytical model and numerical experiments to describe optimal bistable switching involving photonic crystals nonlinear cavity. The involving photonic crystals nonlinear cavity is particularly suitable for large-scale all-optical integration. It is interesting to show that the refractive index of the system can be altered by the incident intensity when the incident frequency is tuned to the evanescent mode and the cavity contains a nonlinear Kerr medium. The response of this system to high-intensity incident waves is studied in detail. A cavity host a localized mode at 1.55 um with a Q of 4000 and a mode volume of 0.055 um3, we predict the onset of bistable reflection at incident powers of ~40 mW. The downstream reflections lead to hysteresis loops in the reflectivity that are topologically distinct from conventional Lorentzian-derived loops characteristic of isolated Fabry-Perot cavities. We provide a stability argument that reveals the unstable branches of these unique hysteresis loops, and we illustrate some of the rich bistable behaviors that can be engineered with such downstream sources, this fact may be used to obtain more flexibility in designing nonlinear devices.
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 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 designed and manufactured an optical bistability waveguide device based on nonlinear one-dimensional photonic crystal used CdS_xSe_(1-x) doped glass. This kind of semiconductor doped glass has large nonlinear refractive index and nonlinear fast response time. The distribution of refractive index of the nonlinear one-dimensional photonic crystal waveguide satisfies sine function. We obtained the nonlinear photonic crystal waveguide by exposure holography and etching techniques. Length of the photonic crystal waveguide is about 3 mm. The height of the peak-groove of the waveguide is 0.1 μm. According to our design, the center of bandgap of the one-dimensional photonic crystal lies at 514.5 nm while the power density of the incident light, the incident light was reflected by the photonic crystal. When the power density of the incident light increasing, the bandgap is shifting to the direc-tion of short wavelength due to the decreasing of the refractive index with the increasing of the incident power density, so more incident light is transmitted. In experiment, we used an active mode-locking pulse of Ar ion laser as the light source which wavelength is 514.5 nm, repeating frequency is 82 MHz and pulse width is 200 ps. The light beam was coupled into the device by prism with a laser average power of 1.28 W (in the case of nonlinear saturation operation, optimum coupling efficiency is about 6%). Pulse wave forms of incident light and transmitted from sample were recorded in turn by 7 904 oscilloscope. The optical bistability curve of input power density and output one is fitted by computer. We obtained the threshold power density of bistable switch to be 1.60×10~5 W/cm~2 (it is equivalent to average power of 77 mW) and both the rise and fall time are 63 ps. We used the Finite Difference Time Domain Method to obtain the characteristics of the bandgap shift with the incident power density increasing of the nonlinear photonic crystal and calculate the optical bistability curve of this device. In theory, the threshold power density of bistable switch is about 1.40×10~5 W/cm~2 and the switch time is about 50 ps. The theoretical results agree well with the experimental ones. This device is a new and feasible one for optical information process and optical computing in the future.
The general nonlinear behavior of multiple cascaded resonators is analyzed by using the coupled-mode theory in time and then compared to a single resonator from the viewpoint of optical bistable operation. Our analysis reveals that from the perspective of switching intensity, the multiple resonator structure is more advantageous than the single resonator with an equivalently increasing quality factor. It is also shown that a switching intensity-response time product, suggested as a performance metric for optical bistable devices, decreases linearly as the number of cascaded resonators increases. The effect of couplingnresonators is equivalent to a single resonator device withn-time increased quality factor in terms of the performance metric. The coupled-mode theory analysis is confirmed by a numerical study of the bistable operation of one-dimensional photonic crystal resonator structures using the finite-difference time-domain method.