Eikonal Analysis of the Boundaryless Beam Propagation Method

The boundaryless beam propagation method has been reported to suffer from reflections due to frequency aliasing. We propose an alternate explanation of reflection in the method, based on eikonal analysis of the wave equation in the mapped space, and show that reflection starts much before aliasing happens. We theoretically predict the reflection coefficient profile in a simulation and introduce an internal absorbing boundary condition (ABC), where reflection becomes appreciable. The a priori knowledge of the window size of the ABC does away with the arbitrariness in the design of such boundaries. Finally, we use the boundaryless scheme with the ABC to successfully model a dielectric bend.