Refinement of the Transparent Boundary Condition for Wide Angle Beam Propagation Method

Abstract

The transparent boundary condition (TBC) [1] has greatly simplified the use of the Beam Propagation Method (BPM). Its primary advantage is that it is problem independent and can be applied with relative ease. Alternative boundary conditions have been studied in the past [2, 3], but they are suitable only for paraxial simulation. The TBC, on the other hand, makes it straightforward to adapt for wide angle BPM e.g. the Fade recursion method [4]. The different TBC methods all assume an outgoing plane wave at the boundaries, and they differ in how this plane wave is modelled. For low order Pade, the angles of incidence at the boundary are shallow and optical energy is typically well confined along the axis. Thus boundary anomalies becomes negligible due to these low fields. Higher Pade orders allow wider propagation angles, so it is more likely for large fields to reach the boundaries at sharper angles of incidence and in a less planar form, e.g. circular wave-fronts. We report a transparent boundary condition suitable for wide angle propagation (WA-TBC), and compare this with the TBC implemented by Hadley [1]. In this poster we systematically study how the outgoing waves appear at the boundaries as the Pade order is increased. The field does not have to be a single plane wave, but can be a superposition of many plane waves, which allows a more accurate representation at the boundary. The method is intuitive and simple to implement for high orders of Pade recursion.