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.