Canonical Equations of Optical Hysteresis

The work was carried out within the context of a competitive ideology of creating the element base of digital optical computers (transphasors, optical switches, memory elements) built on a basis other than the Fabry–Perot interferometer. Mathematical models of stationary (problem I) and non-stationary (problem II) four-beam laser interaction in optically nonlinear media are considered in detail. Problem (I) is the system of ordinary differential equations with specified boundary conditions. Problem (II) is the system of integro-differential equations with boundary conditions. We introduced the original sought-for functions z ( x ) and u ( z , t ) , υ ( z , t ) (II). As a result, the problem (I) is reduced to solving a simple transcendental equation (canonical equation of optical hysteresis). The problem (II) is reduced to solving a system of two nonlinear integral equations for the amplitudes of interference patterns (the canonical system of equations of non-stationary optical hysteresis).