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Journal of Lightwave Technology

Optical Bistability in Periodic Media with Third-, Fifth-, and Seventh-Order Nonlinearities

Yosia Yosia, Perry Ping Shum

Published Mar 1, 2007• 23 citations

Abstract

In this paper, the numerical studies on optical-bistability phenomena in third-, fifth-, and seventh-order nonlinear periodic media are presented. By cross-phase modulation with strong Gaussian pump, the continuous-wave probe transmission that operates in bistability regime can be permanently switched from low to high and vice versa using the property of the unstable state. While there is only one hysteresis in the third-order nonlinear periodic media, double hysteresis are observed in the nonlinear-transmission characteristics of pi phase-shifted periodic media with third-fifth and third-fifth-seventh-order nonlinearities. In the context of double hysteresis, unique-bistability regime is defined where the high state can be reached as input comes from low to high with fast enough rise time such that the output rises above the unstable state during its transient. Finally, all-optical transistor operation is shown as a prominent application of optical bistability based on the unstable-state principle

DOI: 10.1109/jlt.2006.890455

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In this paper, the numerical studies on optical-bistability phenomena in third-, fifth-, and seventh-order nonlinear periodic media are presented. By cross-phase modulation with strong Gaussian pump, the continuous-wave probe transmission that operates in bistability regime can be permanently switched from low to high and vice versa using the property of the unstable state. While there is only one hysteresis in the third-order nonlinear periodic media, double hysteresis are observed in the nonlinear-transmission characteristics of pi phase-shifted periodic media with third-fifth and third-fifth-seventh-order nonlinearities. In the context of double hysteresis, unique-bistability regime is defined where the high state can be reached as input comes from low to high with fast enough rise time such that the output rises above the unstable state during its transient. Finally, all-optical transistor operation is shown as a prominent application of optical bistability based on the unstable-state principle

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Multiple-scale analysis is employed for the study of nonlinear wave propagation in periodic layered media. In a first step, wave propagation in each individual layer is modeled by a corresponding equivalent nonlinear transmission line. The multiple-scale analysis is then employed to establish a system of nonlinear equations for the amplitudes of the forward and backward waves in the transmission lines of the model mentioned. This system of nonlinear equations is solved with the aid of a continuation technique for derivation of transmission characteristics of the periodic structure. To study optical bistability, a parameter-switching algorithm is utilized for obtaining the solutions of the system including both stable and unstable ones. For the sake of verification, we have also utilized a nonlinear finite-difference time-domain (NFDTD) method to analyze the wave propagation in the aforementioned structure. While there is an acceptable agreement between the bistability results obtained using our method and the NFDTD, there is a considerable difference between our results and the ones derived using the conventional coupled-mode theory.

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