Light diffraction by ultrasonic pulses: Analytical and numerical solutions of the extended Raman–Nath equations

Abstract

Light diffraction by ultrasonic pulses at normal incidence is studied as well in the Raman–Nath region (low frequencies) as in the Bragg region (high frequencies). Based on a generating function method, an analytical expression for the Raman–Nath-like diffraction has been derived and compared with earlier work. Only small corrections within its validity region were observed. In order to extend these existing theories toward higher frequencies, numerical expressions for the intensity of the diffracted light waves are obtained by means of the Laplace transform theory. This powerful method leads to the same results for Raman–Nath-like diffraction and can easily be applied for much higher frequencies, too. Examples are provided showing the frequency dependence of the ultrasound, the influence of the Raman–Nath parameter v, and the spectral composition of the pulse on the diffraction pattern. When the pulse approaches a continuous wave, both theories converge to known results. A general condition concerning the symmetry properties of the diffraction spectrum has been derived.