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Bistability of Nonlinear Photonic Crystal Microring Resonators

Tahereh Ahmadi Tameh, Babak Memarzadeh Isfahani, Nosrat Granpayeh, A. R. Maleki Javan

Published Jan 1, 2009• 3 citations
OpenAlex

Abstract

In this paper, two structures of nonlinear photonic crystal microring resonator have been analyzed by the flnite-difierence time-domain method and their optical bistability curves have been derived. In a modifled structure, by increasing the interaction of the lightwave and material, the optical bistability threshold is decreased to one third of that of flrst structure.

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arXiv:physics/0605156•Physical Review E•Oct 5, 2006•101 citations
In this paper, two structures of nonlinear photonic crystal microring resonator have been analyzed by the flnite-difierence time-domain method and their optical bistability curves have been derived. In a modifled structure, by increasing the interaction of the lightwave and material, the optical bistability threshold is decreased to one third of that of flrst structure.
We describe the optical bistability phenomenon in a silicon-on-insulator microring resonators device by using an analytical theory, which includes both linear and nonlinear effects such as two-photon absorption, Kerr effect, free carrier and thermo-optic effect (TOE). We show that the bistable switching threshold and the hysteresis loop width can be tuned by geometrical parameters of the device and by the nonlinear parameters. The accuracy of the analytical approach is verified by comparing the spectrum responds with the predicting data from a commercial finite-difference time-domain software tool, and a very close agreement is found between the two when TOE is incorporated in analytical theory. In addition, our analysis reveals that a new type of hysteresis loop occurs at low input intensity. The mode suppression of the designed device by Vernier effect for tunable filter applications is also briefly discussed.
Over the past few decades, optical ring resonators have attracted a considerable amount of attention as versatile elements for a wide range of applications ranging from telecommunication and sensing to basic scientific research [1,2]. The silicon-on-insulator (SOI) material system is a mature fabrication technique and provides the ability to implement microring resonators. In addition, the high confinement of light and the large third-order nonlinearity of silicon at wavelengths in the near infrared, typically around 1.4-1.6 µm, can be utilized for a number of applications by microring resonator devices [3,4]. The optical bistability observed in silicon-based microring resonators have been theoretically investigated and numerically simulated through various sophisticated techniques [5-9]. However, only recently unifying analytical theories regarding nonlinear effects of optical bistability in microring resonators in terms of a slowly varying envelope approach have been reported [10,11]. Previously, we analytically described the nonlinear response of microring resonators consisting of an add-drop filter with feedback and showed that Fano lineshapes can be adjusted by the resonator parameters [12]. In this chapter, we extend our work to examine the optical bistabililty in such microring resonators and test the analytical results with those predicted by the OptiFDTD software package.
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.
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.