Exact transparent boundary condition for beam propagation in rectangular domain

In this paper we report an exact 3D transparent boundary condition for the parabolic equation in a rectangular computational domain. It is an exact generalization of the well known 2D transparent boundary condition. The condition is based on an assumption that any wave that reaches a boundary of the computational domain is lost. It relates a boundary value of the field at any given longitudinal position to the field values at the preceding computational steps. As an example propagation of light along a simple structured optical fiber is demonstrated. The proposed condition is simple and robust and reduces the size of the computational domain considerably.