Abstract

Self-organization is a term often used to characterize physical systems that exhibit spatial or temporal pattern formation, particularly those system that are associated with phase transitions. Thus a freezing liquid that crystallizes at a lower temperature, a laser that breaks into coherent oscillation above threshold, and a magnetic spin glass that forms stable spatial patterns below a critical temperature can all be considered self-organizing systems. Self-organization is also used to refer to neural networks, real or artificial, that learn without a teacher, or some other form of supervisor, indicating what is to be learned. Self-organizing neural networks extract information from their input environment and subsequently process information according to their history. The processing behavior and capability of self-organizing networks are often remarkable as well as useful. Inspired by the work in network models, we have developed some photorefractive optical self-organizing systems that learn on their own to process information. While the information sense of self-organization is from neural networks, we have found that these systems also exhibit the properties of physical self-organizing systems. Phase transitions in physical systems are governed by some critical parameter, temperature in the case of a thermodynamic system, gain in the case of a laser, for example. In our systems, the critical parameter is the Shannon information entropy at the input: If the entropy is sufficiently low, then our systems will “freeze out” the information and process it in some useful way. If the entropy is above a critical value, then the system “melts” and can do nothing at all with the input. The critical information entropy depends on an optical nonlinear gain of the system.

© 1992 Optical Society of America