The global maxima of the acousto-optic interaction are theoretically determined for CaWO₄ crystals by extreme surfaces method. As it is shown, the highest value of the acousto-optic figure of merit M₂ is equal to 14.0×10¹⁵ s³/kg and achieved in the case of the diffraction of ordinary or extraordinary light beam on the slow quasi-transversal acoustic wave. At that the incident light wave propagates close to c-axis of the crystal and the corresponding acoustic wave propagates in the direction close to the perpendicular one.
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