Abstract

The transient response of a coherent optical processor with feedback has been experimentally studied over the time period from the moment light first enters the system to when steady state operation is established. To facilitate this transient response study, a Blumlein-driven electrooptic gate was constructed to provide a square diagnostic pulse with nanosecond scale rise and fall time, as the characteristic circulation time through the processor is in the 10-nsec regime. Light at several discrete points of the 2-D output was measured with high-speed avalanche photodiodes and displayed on a fast oscilloscope. This technique is compared to previous work in which the entire 2-D optical output as a function of time was also obtained by incorporating a linear phase shifting wedge inside the optical processor at one of the Fourier transform locations. Spatial separation of the successive 2-D outputs then correspond to sequential circulation inside the Fabry-Perot. These experimental studies reveal interesting phenomena related to the evolution of an optically computed solution to a partial differential equation due to (a) consecutive additions of the feedback cycles, (b) feedback polarity, and (c) the processing or filtering functions inside the confocal Fabry-Perot. The time-dependent evolution can be utilized to add a third dimension of time to optical solution of 3-D partial differential equations.

© 1982 Optical Society of America

Coherent optical feedback for the analog solution of partial differential equations

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