Highly efficient transparent boundary conditions for finite difference beam propagation method at order four

The operation of highly efficient transparent boundary conditions for finite difference beam propagation method (BPM, Berenger layers and "UTBC-q") is extended to fourth-order finite difference discretization. The efficiency of Berenger layers is strongly enhanced; five-point layers can be considered a practical TBC for three-dimensional (3-D) computations. On the other hand, problems exist where UTBC-q fails.