Among several optical devices in integrated optics, the fundamental characteristics of collinear optical switching devices have been studied about optical dielectric waveguides. Conventional waveguide-type acousto-optic (A-O) devices use collinear and longitudinal interactions with mode coupling based on the Bragg condition between optical waves and surface acoustic waves (SAW). Collinear A-O devices of the waveguide-type show sufficient performance for wavelength-selective switching with narrow bandwidths. However, in these collinear A-O devices, interaction time is several microseconds for 10 mm waveguide device length. In A-O devices of optical waveguides using transverse A-O interaction, where SAW propagates transversely to optical wave propagation direction, SAW propagation lengths needed for complete A-O interaction may become 10 µm and interaction time may be several nanoseconds. In this paper, fundamental characteristics of the transverse A-O interaction are studied as an electromagnetic boundary value problem. Refractive indices in optical waveguides induced by A-O effects with SAW are shown by sine functions. Wave field characteristics in periodic structures for transverse directions are analyzed by analytic method of Hill's equations for transverse spectral functions. Electromagnetic fields in regions with periodic structures are discussed by the Mathieu functions and the perturbation method. Dispersion characteristics of A-O eigen modes are studied for wavelengths of optical waves and SAW, with A-O coefficients.