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Microwave and Optical Technology Letters

Modeling of nonlinear bistability with the FDTD method

T. Hruskovec, Zhizhang David Chen

Published May 5, 1999• 1 citation
Publisher

Abstract

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.

DOI
10.1002/(sici)1098-2760(19990505)21:3<165::aid-mop3>3.0.co;2-u

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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.
The finite-difference time-domain (FDTD) method is applied to investigate the characteristics of nonlinear Fabry-Perot (FP) resonators in optical waveguide geometries. Our treatment, which is the extension of Tran's method developed to analyse the characteristics of nonlinear photonic crystals, correctly reproduces analytical results on optical bistabilities of the FP resonator provided by Chen and Mills in 1987. It is found that the minimum power required for optical bistabilities is significantry decreased by adopting the optical waveguide geometry, compared with the case of Chen and Mills, i.e., a conventional nonlinear FP interferometer.
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.
The influence of transverse effects on optical bistability in Fabry-Perot cavity filled with saturable absorber was numerically investigated. A simple model of singlet absorption was used on numerically solving the relationships between the input and output light fields. The proposed model corresponds well to organic compounds considered as novel optical materials with third-order optical nonlinearities. The proposed optically bistable systems were demonstrated for two organic dyes of fluorescein and rhodamine 6G dispersed in transparent solid matrices. Their optically bistable behaviour was anticipated considering the homogeneous and Gaussian distribution of light energy in the radial direction. Most notable cases are discussed related to the changes of the Gaussian beam radii, positive feedback conditions in the Fabry-Perot cavity and considering linear and nonlinear absorption parameters of the organic media. The simulation results enabled us to establish numerically thresholds of Fabry-Perot mirror reflectance and Gaussian beam radius for both nonlinear organic materials, above which absorptive optical bistability can occur. The results can be helpful in design of optical switches for all-optical communication networks.
Optical bistability can be obtained in nonlinear materials either with Fabry-Perot mirrors or without external feedback. When a material is placed between partially reflecting mirrors, a nonlinear Fabry-Perot etalon is formed with the etalon providing an external feedback. Optical bistability and gating occur as a result of a shift in the Fabry-Perot peak when the light intensity is increased (or when a second laser beam is introduced into the cavity). Optical bistability with the external feedback mechanism has been observed in many semiconductors such as bulk GaAs, GaAs-AIGaAs multiple-quantum-well (MQW) structures, InSb, InAs, CdS, CdHgTe, GaSe, and CuCI.
Theoretical analysis is presented to search for the purely absorptive optical bistability in a Fabry-Perot cavity filled with a saturable absorber. A simple model of singlet absorption is used on numerically solving the relationships between the input and output light fields. The proposed model corresponds well to organic compounds considered as novel optical materials with third-order optical nonlinearities. The effects of saturable absorber parameters on the output light characteristics are studied and purely absorptive optical bistabilities are shown numerically to search for bistable behaviour. The simulated results are indications for promising applications in optical switches for all-optical communication networks.