Threshold for conjugation of speckle beams by a double phase conjugate mirror

We find the theoretical threshold for phase conjugation of a pump beam with speckle structure by a double photorefractive phase conjugate mirror based on transmitting and reflecting gratings of a diffusion type. For a speckle beam the nonlinear dependence of the profile of light-induced optical nonuniformity on the local intensity profile reduces the readout efficiency and raises the threshold by as much as a factor of 1.5.