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Journal of the Optical Society of America B

Multistability and associative memory in a phase-conjugating resonator

Marcus S. Cohen

Published Jan 1, 1991• 0 citations
Publisher

Abstract

I derive and analyze coupled-mode equations for a double phase-conjugating resonator that is loaded with a volume-holographic recording medium in which multiplexed images have been stored. If the only nonlinearity present is the saturating gain of the conjugators, there is no multistability: The most deeply imprinted image always wins the competition for saturation. If several images are imprinted with equal depth, any slowly varying superposition of these images is neutrally stable. However, if a nonlinearity, arising from a space-charge-dependent cubic polarization, is present the resonator does exhibit multiple basins of stability that correspond to the faithful reconstruction of each stored image. The momentary injection of an initial image will tip the system into the basin that corresponds to the stored image that it most closely resembles, even if that image is not the most deeply imprinted one.

DOI
10.1364/josab.8.000106

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I derive and analyze coupled-mode equations for a double phase-conjugating resonator that is loaded with a volume-holographic recording medium in which multiplexed images have been stored. If the only nonlinearity present is the saturating gain of the conjugators, there is no multistability: The most deeply imprinted image always wins the competition for saturation. If several images are imprinted with equal depth, any slowly varying superposition of these images is neutrally stable. However, if a nonlinearity, arising from a space-charge-dependent cubic polarization, is present the resonator does exhibit multiple basins of stability that correspond to the faithful reconstruction of each stored image. The momentary injection of an initial image will tip the system into the basin that corresponds to the stored image that it most closely resembles, even if that image is not the most deeply imprinted one.
One can construct a memory having associative characteristics using optical resonators with an internal gain medium. The device operates on the principle that an optical resonator employing a holographic grating can have user prescribed eigenmodes. Information that is to be recalled is contained in the hologram. Each information entity (e.g. an image of a cat) defines an eigenmode of the resonator. The stored information is accessed by injecting partial information (e.g. an image of the cat's ear) into the resonator. The appropriate eigenmode is selected through a competitive process in a gain medium placed inside the resonator. With a net gain greater than one, the gain amplifies the field belonging to the eigenmode that most resembles the injected field; the other eigenmodes are suppressed via the competition for the gain. One can expect this device to display several intriguing features such as recall transitions and creativity. I will discuss some of the general properties of this class of devices and present the results from a series of experiments with a simple holographic resonator employing photorefractive gain.
We demonstrate a new method to implement holographic associative memory based on a coherently induced double phase conjugate mirror that has phase-conjugate reflectivity larger than unity for weak reference signal over a large range of pumping-reference intensity ratio. The phase conjugator, operated with a copper-doped KNSBN crystal, serves as a novel nonlinear feedback and gain element for the associative memory system. A vanadium-doped KNSBN crystal as storage medium improves the response speed of the holographic recording process. A stored image has been completely retrieved when a partial input addresses the associative memory system.
A high capacity associative memory would find applications in computing and perhaps lend some insight into the understanding of collective neural networks and human memory. In this work an entirely optical associative memory device is proposed. The device operates on the principle that an optical resonator employing a holographic grating can have user prescribed eigenmodes. Information which is to be recalled is contained in the hologram. Each information entity (e.g., an image of a cat) defines an eigenmode of the resonator. The stored information is accessed by injecting partial information (e.g., an image of the cat’s ear) into the resonator. The appropriate eigenmode is selected through a competitive process in a gain medium placed inside the resonator. With a net gain greater than one, the gain amplifies the field belonging to the eigenmode which most resembles the injected field; the other eigenmodes are suppressed via the competition for the gain. The principles underlying the proposed device are outlined and the issues which must be addressed are delineated.
A coherent optical memory is described. The device operates on the principle that an optical resonator employing a holographic grating can have user-prescribed eigenmodes. Each information entity (e.g., an image of a cat) defines an eigenmode of the resonator. The stored information is accessed by injecting partial information (e.g., an image of the cat’s ear) into the resonator. A gain medium internal to the resonator amplifies the field belonging to the eigenmode that most resembles the injected field; the other eigenmodes are suppressed through a competition for the gain. A simple optical memory exhibiting associative recall is demonstrated.
A programmable optical resonator is one in which a hologram assumes the role of one of the mirrors of an ordinary optical resonator. A holographic recording medium allows the optical electric field eigenmodes of the resonator to be user-defined. Interest in this kind of resonator stems from their potential as associative optical memories. When the holographic medium is a photorefractive or other real-time recording medium, the resonator can learn, recall, and forget programmed information. Recall is achieved by placing a gain medium, such as an externally pumped photorefractive crystal, inside the resonator. The gain medium excites eigenmodes of the resonator. Using LiNbO3 as the recording medium and pumped BaTiO3 as the gain medium we have been able to store and recall complicated images as eigenmodes of a resonator.
Optical bistability in resonators containing a nonlinear gyrotropic isotropic medium is analyzed by studying the dependence of the bifurcation intensity of the incident radiation on its ellipticity. It is found that if the gyrotropy is weak, this dependence may have symmetry-induced singular points or turning points. The stable radiation states in the resonator formed near a singular or turning point differ in respect of the polarization and are due to the evolution of the polarization instability. Bifurcation curves are plotted for a ring resonator containing a medium with a cubic nonlinearity. The form of these curves changes appreciably as the gyrotropy is increased. The change in the resonator transmission accompanying changes in the gyrotropy is studied.