We generate photonic bandgaps (PBGs) in dielectric slab waveguides by exciting their acoustic plate eigenmodes of submicron wavelength. We investigate the optical forbidden bands below the light line where the slab interfaces and index of refraction are periodically modulated by the acoustic fields. Results show that multiple scattering through the enhanced periodic acousto-optic (AO) interaction opens Bragg PBGs. A tunable bandgap width and transmittance are achieved. Transmitted optical waves are found to incur strong nonlinear modulation through AO interaction by a multiphonon exchange mechanism. The applications include tunable optomechanical and AO devices.