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Optics Express

Dynamic shift effect on bistability in nonlinear optical microcavities

Xu-Sheng Lin, Quan Shi, Xuhong Cai, Nian-Shun Zhao, Sheng Lan

Published Jan 1, 2006• 3 citations
Publisher

Abstract

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.

DOI
10.1364/oe.14.006794

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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.
Based on Fabry-Perot cavity's theories and efficiency refractive index,the optical bistability of a nonlinear microcavity is studied,and the corresponding mathematical formula are deduced.The theoretical curves are well fitted with those of numerical simulation in other papers.The investigation shows that appropriate frequency-shifting should be preset on the incident light in order to produce bistability for a nonlinear system.If the system is composed of focusing nonlinear medium,the frequency must be redshifted, otherwise it must be blue-shifted.The magnitude of critical shifting is 0.866 times of the width of microcavity resonance mode.
It is known that two-wave coupling in photorefractive crystal may result in an intensity-dependent phase shift as well as energy transfer between the two waves without phase crosstalk. In a sense, this kind of phase shift is similar to the intensity-dependent refractive-index effects in Kerr media. Consequently, optical bistability can be established in an optical cavity with a photorefractive crystal. We formulate the model and get the expected bistable transmission with numerical simulations. Several cases, including that of the codirectional coupling and the contradirectional coupling, are considered. The effects of the photorefractive crystal’s distribution absorption and the spatial phase shift between the index grating and the light interference pattern in the crystal on the nonlinear transmission characteristics have also been studied. It is interesting to note that the output of the pumping wave is dependent on the cavity intensity and thus shows bistable behavior with respect to the cavity input as well.
In the last chapter, we examined the effect of cubic nonlinearity on selfrefraction of an optical beam. We have also seen that the presence of a quadratic nonlinearity can also contribute to change in the profile of a Gaussian beam in a crystal. In this chapter we will see how the effect of nonlinearity, alongwith the proper feedback, can give rise to optical bistability and hysteresis. This is not unexpected as hysteresis and bistability are also observed in nonlinear electronic circuits with feedback, such as in the Schmitt trigger, as well as in hybrid optical devices, such as an acoustooptic device with feedback (Banerjee and Poon, 1991). In what follows, we will examine two different types of optically bistable devices based on optical nonlinearities. The first is a nonlinear ring resonator comprising a two-level gain medium as the nonlinear element. We will treat both absorptive and dispersive bistability. Absorptive bistability is the case when the incident optical frequency is close to or equal to the transition frequency of the atoms from one level to another. In this case, the absorption coefficient becomes a nonlinear function of the incident intensity. On the other hand, if the frequencies are far apart, the medium behaves like a Kerr-type material and the system exhibits what is called dispersive bistability. In this case the material can be modeled by an effective n2 or v (3), meaning that the refractive index becomes a nonlinear function of the optical intensity. The second configurationwewill examine is a linear-nonlinear interface. In this case, the interface provides the feedback due to refractive index mismatch. In fact, the reflection coefficient (as well as the transmission coefficient) is modified due to the nonlinearity, which, as we shall see later, is responsible for demonstrating optical switching and bistability.
Optical Kerr nonlinearity is central to optical bistability in high-Q microcavities. Here, we show that optical Kerr nonlinearities in Fabry Perot resonators can also result in self-focusing effects, that can substantially modify the Q-factors of the resonators. For the studied cavities, up to five-fold increase in Q-factors is predicted, attributed to reduction of sidewall leakage, confirmed via simulations performed on curved cavities. We also show that for high Q-factor cavities, the higher-order Kerr effect can become relevant already at modest input intensities scaling inversely with Q-factor for a particular n2/n4 ratio. We investigate numerically the role of higher-order Kerr effect on optical bistability responses and find that its inclusion can shift the bistability threshold to higher input intensities than predicted by the standard n2-only model.