Highly efficient absorbing boundary conditions for the beam propagation method

Two kinds of absorbing boundary conditions for the finite difference BPM are investigated, namely the operation of Berenger layers and the use of a mere nth-order differential relation with constant coefficients (UABC-n). Practical formulas are given for their implementation and their optimization is discussed, Their efficiency is demonstrated in 2-D test problems where the Hadley technique fails, Berenger layers with 5 to 10 points or 6th-order UABC should be useful for most practical problems. The extra numerical cost in 3-D problems should be either near negligible (UABC) or quite moderate (Berenger layers).