A method for increasing the frequency shift of optical radiation by means of cascade acoustooptic diffraction of light is proposed and studied. The method is based on special features of anisotropic diffraction in an anisotropic medium and optical properties of gyrotropic media. Five-cascade diffraction of radiation from a He - Ne laser (λ=0.633 μm) in a TeO{sub}2 single crystal with efficiency of 8% was experimentally obtained.
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