Reflectionless Beam Propagation on a Piecewise Linear Complex Domain

We describe a new class of transparent boundary conditions for beam-propagation simulation. The method is based on a transformation that breaks the original real-axis computational domain into a piecewise linear complex-plane contour, with higher-order analogues of Riemann–Cauchy conditions imposed at sharp corners of the contour. The resulting boundary conditions are extremely effective in terminating outgoing waves, and are easy to implement in an arbitrary beam-propagation method.