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Soviet Journal of Quantum Electronics

Optical transistors and bistable devices utilizing nonlinear transmission of light in systems with undirectional coupled waves

A. A. Maǐer

Published Nov 30, 1982• 111 citations
Publisher

Abstract

An analysis is made of nonlinear transmission (self-switching, self-modulation) of light in tunnel-coupled cubically nonlinear waveguides and other optical systems carrying unidirectional waves with a distributed coupling which become separated at the exit from a system if at least one of the waves travels in a medium with a cubic (Kerr) susceptibility. Optical transistors and bistable devices based on these systems are considered. The threshold energy of bistable devices based on coupled GaAs waveguides is ~10−10–10−9 J.

DOI
10.1070/qe1982v012n11abeh006159

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An analysis is made of nonlinear transmission (self-switching, self-modulation) of light in tunnel-coupled cubically nonlinear waveguides and other optical systems carrying unidirectional waves with a distributed coupling which become separated at the exit from a system if at least one of the waves travels in a medium with a cubic (Kerr) susceptibility. Optical transistors and bistable devices based on these systems are considered. The threshold energy of bistable devices based on coupled GaAs waveguides is ~10−10–10−9 J.
An investigation was made of the influence of the finite nonlinear response time, of the nonlinear dispersion of the group velocities, and of the dispersion of the coupling coefficient on self-switching of dome-shaped pulses in tunnel-coupled optical waveguides and other distributively coupled systems supporting unidirectional waves. Estimates are obtained of the maximum values of the parameters above which self-switching is perturbed. Relationships representing the influence of these parameters are determined graphically and partly interpreted. It is proposed to use the results in estimating the parameter of discrete optical transistors and logic devices pumped by a sequence of ultrashort pulses.
Bistable optical systems are of considerable interest to produce high-speed optical signal-processing devices. Among them, those that use a nonlinear optical medium are attractive because they allow the lowest possible switching time. By the use of a suitable electromagnetic resonance, the bistability threshold can be lowered to a reasonnable value, for the incident power. Keeping in mind that a bistable optical system should be well adapted to optical integration in a planar geometry, one is naturally confronted to a corrugated waveguide filled with a nonlinear (Kerr) medium.
A new use of gratings in nonlinear optics is presented, i.e., the realization of bistable components. The device studied here consist of grating couplers ruled on a Kerr nonlinear medium, which use the guided-wave resonance to increase the local field and thus the nonlinearities. The result is that they are intrinsic bistable optical systems with high-speed, low pumping thresholds, and geometry well adapted to optical integration. First, a linear electromagnetic study of the devices is presented. It follows optimizing the grating parameters in order to get the best coupling between the incident beam and the guided mode inside the corrugated waveguide. Then a graphical construction is given that demonstrates the bistable character of the system in nonlinear optics. Next a nonlinear analysis of the devices is rigorously derived from Maxwell equations. It states precisely the predictions of the graphical construction and allows comparison of the effectiveness of the guided-wave resonance with the surface plasmon resonance in order to reduce the threshold of bistability.
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.