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Optics Express

Analytical theory for the nonlinear optical response of a Kerr-type standing-wave cavity side-coupling to a MIM waveguide

Ye Liu, Fei Zhou, Qinghe Mao

Published Sep 27, 2013• 12 citations
Publisher

Abstract

In this article, an analytical theory to describe the nonlinear dynamic response characteristics of a typical SPP waveguide-cavity structure formed by a Kerr-type standing-wave cavity side-coupling to a metal-insulator-metal (MIM) waveguide is proposed by combining the temporal coupled mode theory and the Kerr nonlinearity. With the analytical theory, the optical bistability with the hysteresis behavior is successfully predicted, and the optical bistability evolutions and its dynamic physical mechanism are also phenomenologically analyzed. Moreover, the influence of the quality factors Q₀ and Q₁ on the first-turnning point (FTP) power of optical bistability and the bistable region width, the approaches to decrease the FTP power and to broaden the bistable region are also discussed in detail with our analytical theory. This work can help us understand the physical mechanism of the nonlinear dynamical response at nanoscale, and may be useful to design nonlinear nanophotonic systems for applications in ultra-compact all-optical devices and storages.

DOI
10.1364/oe.21.023687

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In this article, an analytical theory to describe the nonlinear dynamic response characteristics of a typical SPP waveguide-cavity structure formed by a Kerr-type standing-wave cavity side-coupling to a metal-insulator-metal (MIM) waveguide is proposed by combining the temporal coupled mode theory and the Kerr nonlinearity. With the analytical theory, the optical bistability with the hysteresis behavior is successfully predicted, and the optical bistability evolutions and its dynamic physical mechanism are also phenomenologically analyzed. Moreover, the influence of the quality factors Q₀ and Q₁ on the first-turnning point (FTP) power of optical bistability and the bistable region width, the approaches to decrease the FTP power and to broaden the bistable region are also discussed in detail with our analytical theory. This work can help us understand the physical mechanism of the nonlinear dynamical response at nanoscale, and may be useful to design nonlinear nanophotonic systems for applications in ultra-compact all-optical devices and storages.
Optical bistability at nanoscale is a promising way to realize optical switching, a key component of integrated nanophotonic devices. In this work we present an analytical model for optical bistability in a metal nano-antenna involving Kerr nonlinear medium based on detailed analysis of the correlation between the incident and extinction light intensity under surface plasmon resonance (SPR). The model allows one to construct a clear picture on how the threshold, contrast, and other characteristics of optical bistability are influenced by the nonlinear coefficient, incident light intensity, local field enhancement factor, SPR peak width, and other physical parameters of the nano-antenna. It shows that the key towards low threshold power and high contrast optical bistability in the nanosystem is to reduce the SPR peak width. This can be achieved by reducing the absorption of metal materials or introducing gain media into nanosystems.
Optical bistability with a hybrid silicon-plasmonic configuration consisting of a nonlinear traveling-wave (disk) resonator side-coupled with a bus waveguide is theoretically investigated. The nonlinear response is studied with a theoretical framework combining perturbation theory and temporal coupled-mode theory. For the CW case, a general closed-form expression is derived. The effect of the parameters entering in the expression on the bistability curve is thoroughly investigated, and the physical system is accordingly designed so as to exhibit minimum power threshold for bistability and maximum extinction ratio between bistable states. Finally, the temporal dynamics are assessed. The system can toggle between bistable states in approximately 5 ps and is thus suitable for ultrafast memory and switching applications.
We have investigated numerically an optical bistability effect based on an analog of electromagnetically induced transparency (EIT) in a nanoscale plasmonic waveguide-coupled resonator system. The system consists of a metal-insulator-metal waveguide side-coupled with a slot cavity and a nanodisk cavity containing Kerr nonlinear material. By finite-difference time-domain simulations, the EIT-like spectral peak has a redshift with an increase of the dielectric constant of the nanodisk cavity. More importantly, we have achieved an optical bistability with threshold intensity about three times lower than that of recent literature [Appl. Opt.50, 5287 (2011)]. The results show that our plasmonic structure can find more excellent application in highly integrated optical circuits, especially all-optical switching.
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 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.
In this study, we theoretically investigate the optical bistability (OB) in hybrid triple-cavity optomechanical systems (OMSs) composed of three coupled cavities (two optical cavities and one optomechanical cavity) in the presence of semiconductor quantum dot molecules and a Kerr medium with a Kerr coefficient of χ when the optomechanical cavity is driven by a pump laser with frequency ωp and the amplitude Ep, which results in optical pressure on the movable mirror of the OMS. The dynamical equations of motion for this triple-cavity hybrid system in the steady state limit are solved using the Heisenberg-Langevin equations to achieve OB. We have demonstrated that it is possible to adjust both the width of the hysteresis loop and the switching threshold by controlling the Kerr coefficient . t is found that by properly tuning the physical parameters, the bistable thresholds of the system can be switched on and switched off, which is useful for designing and optimizing sensitive all-optical switching .