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Optica Acta International Journal of Optics

Switching in Optical Bistability by the Anharmonic Oscillator Model

Annabella Selloni, A. Quattropani, P. Schwendimann, H. Baltes

Published Jan 1, 1981• 5 citations
Publisher

Abstract

The response of a bistable optical system to a time-dependent driving field is studied in terms of a quartic anharmonic oscillator describing a non-linear medium. Dynamical lowering of the switching threshold is observed. The dispersive character of the model is confirmed.
DOI
10.1080/713820438

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The dynamical solution of the driven classical anharmonic (AH) oscillator is obtained through a region of optical bistability. The dynamical solution is observed to switch from the lowest to highest steady-state (SS) root near a SS turning point with evidence of critical slowing down. The solution of a widely used multiple-photon version of the AH model is also obtained and is found to give qualitatively similar behavior. The average number of photons observed dramatically increases in the bistable region and exhibits damped oscillations.
Optical bistability in nonlinear media is potentially useful because of its fast transition speed for all-optical logic operation [1-3]. The dynamics of these mirrorless systems have been described by a anharmonic Duffing oscillator [1-4]. After normalization the equation of motion is described by x + k x + x - f(x) = F sinwt, where k is the damping factor, F is the driving amplitude, w is the driving frequency and f(x) is a nonlinear function of x. Such a model predicts the existence of bistability under appropriate conditions [3]. It would be particularly important for this system to be tuned to some situation in order to efficiently generate these nonlinear phenomena. In this summary we would provide a global picture of possible dynamic behaviours in Eq.(1), which can be used as a guide line in real experiment.
Long-time behavior of transmitted and reflected field amplitude of optical bistability by a cavity including an absorptive resonant medium from an initial to a final steady state on switching the incident field is investigated by solving numerically the semiclassical dynamical equations without the mean-field approximation. The transmitted field amplitude as a function of time is monotonic as a whole, and an oscillatory character is seen on it in a shorter period. The dynamical character such as the oscillation amplitude and the duration of a whole process depend strongly on two parameters included in the equations.
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.