Approximate and Numerical Methods in Acousto-Optics. Part 1. Normal Incidence of the Light

摘要

The basic principles of acousto-optical diffraction in an isotropic medium are briefly reviewed. Focus is on the derivation of the Raman-Nath equations for the amplitudes of the diffracted light waves and on the physical meaning of the various parameters occurring in this diffraction problem. Three distinct methods for the numerical integration of the truncated Raman-Nath system are outlined: Raman-Nath's elementary theory, Merten's perturbation method, and the N-th order approximation method. For each of these methods, the theoretical results are compared with experimental data. An eigenvalue method and an operational method (due to Heaviside-Jeffreys) are used to integrate the truncated Raman-Nath system in the case of normal incidence of the light. Both methods lead to closed form expressions for the intensities of the diffracted light beams, which are easily implemented on a computer. A comparison of the various approximation methods is presented. Fifteen figures illustrate the validity of each method in comparison with experimental data obtained for different values of the parameters. By means of the Nth-order approximation method, some new results are obtained, indicating the relevance of the three regime parameters in distinguishing between Raman-Nath and Bragg diffraction. Examples are given of the exact and approximate integration of infinite and truncated Raman-Nath systems.