Exact transparent boundary condition for the parabolic equation in a rectangular computational domain

• Published in: Journal of the Optical Society of America. A, Optics, image science, and vision Vol. 28; no. 3; p. 373
• Main Authors: Feshchenko, R M, Popov, A V
• Format: Journal Article
• Language: English
• Published: United States 01.03.2011
• ISSN: 1520-8532
• DOI: 10.1364/JOSAA.28.000373

In this paper, an exact three-dimensional transparent boundary condition for the parabolic wave equation in a rectangular computational domain is reported. It is a generalization of the well-known two-dimensional Basakov-Popov-Papadakis transparent boundary condition. It relates the boundary transversal derivative of the wave field at any given longitudinal position to the field values at all preceding computational steps. Several examples demonstrate propagation of light along simple structured optical fibers as well as in x-ray guiding structures. The proposed condition is simple and robust and can help to reduce the size of the computational domain considerably.