On the Diffraction of Light by Ultrasonic Wave

The partial differential equation for the wave function in the problem of the diffraction of light by an ultrasonic wave is derived as the result of transformations and related approximations of the electrical field equation itself. It is shown that this way of treating the diffraction problem is equivalent to the generating function method applied to the Raman-Nath system of difference-differential equations for the amplitudes of the diffracted waves. This general method is worked out here for diffraction due to an amplitude-modulated ultrasonic wave, for which the symmetry properties of the diffraction pattern are also investigated with the help of the transformed wave equation. Afterwards the wave function is considered as a generating function for the amplitudes. The corresponding partial differential equation for this generator is solved exactly in the case of large ultrasonic wave lengths at oblique incidence of the light.