Abstract

We demonstrate a ring resonator pumped with photorefractive gain that implements two classes of Lotka–Volterra dynamics: winner-takes-all and the voter's paradox. By using two additional photorefractive crystals, we program the coupling among five modes of the resonator. One version of the system is five-fold multistable: Any one, but only one, of the five modes can oscillate at any one time. The mode is selected with an injected signal. In another version of mode coupling, the modes undergo a continuous cycle though the five modes—thus, a steady state is never reached. The coupling is achieved by placing one photorefractive medium in a Fourier plane of two copies of the resonator modes, which are formed by a beam splitter. The two copies of the modes interact again in an image plane. For winner-takes-all, every mode couples to itself in the image plane. For voter's paradox, every mode couples to its neighbor.

© 1990 Optical Society of America