The photorefractive transmission grating ring self-pumped phase-conjugate mirror is shown to be formally equivalent to a double phase-conjugate mirror with internal losses and equal-intensity input beams. These mirrors are also equivalent to a self-pumped phase conjugator consisting of a photorefractive crystal with one face highly reflecting. This result shows that all transmission grating self-pumped phase-conjugate mirrors, with the exception of the linear self-pumped phase conjugator, are topologically equivalent to a double phase-conjugate mirror. No similar equivalence can be shown for the reflection grating ring phase conjugator.
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