CAREER: Efficient Ray-Based Methods for Modeling Wave Propagation

University Of Rochester, Rochester NY

Investigators

Abstract

Wave phenomena are central to physics and engineering. Modeling the propagation of waves, however, can be an analytical or computational challenge when the system, medium, or potential in which they propagate is complex. In these cases, the ray model is often used to obtain approximate solutions. For quantum mechanical wave functions, the "rays" correspond to classical particle trajectories. When ray information is used properly, it can give a very accurate description of wave propagation phenomena. While several ray-based methods for modeling the propagation of waves have been proposed, they often have problems and do not incorporate measures of their own accuracy The scientific goals of the work proposed here are to achieve a profound understanding of the validity of the ray model within wave theory, and to generate all-purpose ray-based methods that describe the propagation of waves in complex media with unprecedented accuracy and computational efficiency. This work will rely on two different and complementary frameworks. The first one, particularly suited for problems of wave propagation through inhomogeneous media for the case of small wavelengths, is based on assigning flexible, interconnected field contributions to the rays, such that their sum gives accurate field estimates that are asymptotically independent of the contributions' width. In preliminary studies, this framework has been shown to be free of the problems that plague other techniques, and to give estimates of great accuracy. Furthermore, a simple measure of the estimates' error is accessible. So far, this formalism has been applied only to test cases involving propagation of scalar waves in two-dimensional inhomogeneous media. In this project, the framework will be extended to describe realistic situations involving three (and higher) dimensional fields in complicated media presenting, for example, absorption, gain, and anisotropies. The application of the method to the solution of differential equations not related to wave phenomena will also be explored. The second framework relates to wave propagation in piecewise homogeneous media, and is particularly suited to the study of partially coherent fields. It is based on representations of wave fields that behave exactly as ray weights, obeying the free radiative transfer equation. These representations can reduce significantly the computation times needed for estimating the intensity, flux, or polarization of partially coherent fields in regions away from their sources. Analogous representations can be defined to describe waves in anisotropic, optically active, absorptive or gain media. These representations can also be used in the description of systems involving refraction and reflection at interfaces and of propagation through scattering media, although this might require some assumptions about the coherence properties of the field. The understanding of such assumptions will give insight into the applicability of the ray-based radiative transfer model. The principal investigator and graduate students will participate in technical conferences organized by minority societies, as well as in outreach events for the promotion of science to the general public, particularly to underrepresented groups. Collaboration with national and foreign researchers in several different areas will be instrumental in the achievement of the goals of this project. These links will be strengthened not only through joint projects but also through participation in the organization of crossdisciplinary workshops and conferences.