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The peculiarities have been studied of acoustooptic (AO) diffraction of quasi-nondiffracting vector Bessel light beams (BLB) on the ultrasound waves in optical gyrotropic cubic crystals. The system of coupled equations describing the process of acoustooptic interaction is solved, diffraction efficiency has been calculated. The mathematical description of AO interaction, which differs from the similar description for the plane optical waves means of two types of synchronism, is conducted. It isdoi:10.13189/ujpa.2015.090504 fatcat:uhkncd4x7jfgvn2djytkrmdvcq