A numerical analysis and expository interpretation of the diffraction of light by ultrasonic waves in the Bragg and Raman-Nath regimes using multiple scattering theory

In this paper, we examine some of the fundamental properties of Bragg and Raman-Nath diffraction of light by ultrasonic waves by revisiting the well-known multiple plane wave scattering theory developed by Korpel and Poon in 1980. The purpose is to provide a clear and unambiguous insight into the variety of physical and geometrical configurations associated with the process of optical diffraction from Bragg and Raman-Nath ultrasonic cells, treating each domain separately. Despite well-established theoretical models, there is a tendency to sometimes erroneously associate general Bragg domain diffraction (as opposed to exact Bragg diffraction where the incident angle is Bragg-matched and the interaction width is infinite) with only two diffracted orders that vary sinusoidally with peak phase shift of the light and distance of propagation. In numerical analyses of the coupled equations, there is also a tendency to sometimes limit the number of orders to a few lower ones. With the enthusiasm to arrive at a solution, this truncation is sometimes applied in the Raman-Nath regime as well. In doing so, higher Raman-Nath-scattered orders are implicitly assumed to be progressively weaker and, therefore, negligible. In complex acoustooptic systems, such approximations can lead to serious errors. With an aim toward rectifying these and other common misconceptions, a thorough numerical analysis of uniform plane wave acoustooptic diffraction in the two well-known regimes is presented and the limits of such analysis are examined.