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Optical Bistability, Switching Waves and Pattern Formation in Nonlinear Microcavities

O. G. Romanov

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

Finite-difference time-domain method for numerical solution of Maxwell equations has been applied to the problem of interaction of light beams with microcavities filled with the media exhibiting Kerr nonlinearity.The evolution of spatial-temporal structure of the light beams has been analyzed in the mode of optical bistability.The dynamics of transverse switching waves and the peculiarities of pattern formation in the cross-section of the light beams has have been analyzed numerically.

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Finite-difference time-domain method for numerical solution of Maxwell equations has been applied to the problem of interaction of light beams with microcavities filled with the media exhibiting Kerr nonlinearity.The evolution of spatial-temporal structure of the light beams has been analyzed in the mode of optical bistability.The dynamics of transverse switching waves and the peculiarities of pattern formation in the cross-section of the light beams has have been analyzed numerically.
This thesis presents the theory of the driven optical ring cavity containing a nonlinear material. First, an overview of the history of bistability and spatial solitons in driven nonlinear cavities is outlined. Then, the basic theory of the optical Kerr effect is presented and two of its consequences are outlined: optical bistability and spatial solitons. Within this background, the mirror feedback model is derived from the Maxwell-Bloch equations and considerations of the classical optics of the cavity. This model is analytically shown to exhibit bistability in the plane wave case. The mean-field model is subsequently derived by applying the mean-field limit to the Maxwell-Bloch equations and the cavity optics. In addition, the mean-field model is analytically shown to exhibit bistability in the plane wave case. Numerical simulations are performed on the mean-field model demonstrating the existence of: (i) plane wave bistability, (ii) transverse modulational bistability, (iii) the ability to “switch†between bistable states in both the plane wave and modulated case, (iv) instabilities in the modulated case and (v) the possibility for optimization of the switching process. Finally, an application of bistable driven cavities is explored: an all-optical digital information processor and storage device.
The shift of optical cavity modes oscillates due to the time-varying refractive index under Kerr nonlinearity. To reveal its impact on bistability, we present a time-average approach that includes this dynamic shift characteristic in the expression of nonlinear transmission. It predicts the monotonous decrease of the maximum transmission with the increase of the frequency detuning. Also, the frequency detuning to start bistability should be corrected as about 2. Our analyses are supported by the simulations based on the finite-difference time-domain technique.
Bistability due to the nonlinearity of an optical material has been studied recently and investigated for its potential high-speed all-optical signal-processing applications. As a result, accurate modeling techniques are required for design purposes. In this paper, the finite-difference time-domain (FDTD) method is applied to the modeling of optical bistability caused by the saturable Kerr effect of a GaAs–GaAlAs MQW-like material. A recursive finite-difference formulation for the saturable Kerr properties of the material is derived, and a physically realizable Fabry–Perot etalon is simulated. The numerical results demonstrate the effectiveness of the FDTD method for bistability modeling, and thus provide the foundations for further work and simulation of more complicated and realistic bistable structures. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 21: 165–168, 1999.
We discuss instabilities of the fundamental single-transverse-mode solution and the formation of new transverse spatial patterns in optical systems, containing nonlinearly absorbing two-level media using two transverse cavity geometries (rectangular and cylindrical). Under the appropriate approximations, these two models can be described by the same set of dynamical equations. Though the equations for the two models differ in their coefficients, their dynamical solutions are comparable. We find hysteresis phenomena associated with transitions in the transverse structure of the intensity which are completely different from the steady-state bistability and hysteresis found in theories of single-mode operation.
Effect of relaxation time on the performance of photonic crystal optical bistable switches based on Kerr nolinearity is discussed. This paper deals with optical pulses with the duration of about 50 ps. In such cases the steady state response of the optical device can be used to approximate the pulse evolution if the nonlinearity is assumed instantaneous, hence analytical solutions such as the coupled mode theory can be used to obtain the time evolution of the electromagnetic fields. However if the relaxation time of the material nonlinear response is also considered, changes in the power levels and in the shape of the hystersis loop is observed. In this case, we use the nonlinear finite difference time domain method (NL-FDTD) to follow the system dynamics and get the bistability hystersis loop. Codes are developed to analyze the instantaneous Kerr materials and the Kerr materials with finite response times. Depending on the material, the relaxation times of the order of 1-10fs should be considered in studying bistability to obtain the right shape of the output pulses. It is observed that the relaxation leads to larger input power and threshold and hence degrades the performance of the switch in pulse shaping.