Within the Markov approximation, we introduce a novel class of random media which can produce a scattered field with optical lattice patterns. It is shown that the array dimension, lobes intensity profile, and the periodicity of the optical lattice can be flexibly controlled by altering the correlation parameters of scattering potential of the random medium. In addition, a new method for designing random media is proposed. It is shown that the convolution of any two legitimate degrees of potential correlation can lead to a new degree of potential correlation corresponding to a new scattered intensity distribution. An example of a novel family of random media is cited to demonstrate the result.
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