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We suggest a method for optimizing geometry of acousto-optic (AO) interactions in anisotropic crystalline materials. Within the framework of this method, one gets global maximums of AO figure of merit M2 and their spatial orientations, proceeding from so-called “extreme” indicative surfaces, which are obtained after finding such an acoustic wave propagation direction that maximizes the M2 parameter for each propagation direction of the incident electromagnetic wave. The method improves earlier indicative surface-based techniques in several aspects, particularly in properly accounting for the momentum conservation condition for the AO diffraction, and yields a higher accuracy in assessing spatial anisotropy of the AO effect. We have constructed the extreme surfaces of LiNbO3 crystals for all possible cases, including those of isotropic/anisotropic AO diffractions and longitudinal/transverse acoustic waves. The anisotropy of the AO figure of merit for LiNbO3 is analyzed for the acoustic frequencies 0.01–2.0 GHz and the light wavelengths 405–1444 nm. The absolute M2 maximums refer to ‘indirect crystal cuts' and are equal to 26.3 × 10−15 s3/kg at 2 GHz and 405 nm, and 15.4 × 10−15 s3/kg at 0.4 GHz and 1444 nm.
