BOUNDARY-CONDITIONS FOR THE FINITE-DIFFERENCE BEAM-PROPAGATION METHODBASED ON PLANE-WAVE SOLUTIONS OF THE FRESNEL EQUATION

Each particular implementation of the beam propagation method (BPM) re quires a special procedure allowing for radiation to leave the computa tional window. We propose a new approach to constructing the finite di fference schemes of the BPM at the boundary of the computational windo w, These schemes are independent of the computed fields and allow for a similar treatment of both interior and boundary points, The new appr oach can be further improved by correcting the field values at the bou ndary points according to Hadley's method. The algorithm is easy to im plement for both two- and three-dimensional structures. The new method considerably reduces computation times because the propagation matric es remain constant in longitudinally invariant sections, thus avoiding repeated LU-decompositions. The basic idea-establishing the finite di fference scheme such that locally exact, approximate, or plausible sol utions are recovered-may be of interest for other efforts to solve par tial differential equations by the finite difference method.