Interest of improved three-point formulas for finite-difference modeling of optical devices

摘要

The accuracy of finite-difference computations is limited by the errors inherent in the classical three-point formula for (#)↑（2）↓（x） (of order h ↑(2)) and in the discretizafion of discontinuities in the refractive indea. (of order from h↑(0) to h↑(2)). Various improvements are reviewed and analyzed, both for normalmede derivations and for the beam propagation method (BPM). For the BPM it seems that sophisticated discrotizations for discontinuities have a limited interest, whereas using a h ↑(4)-accurate three-point formula for （#）↑（2）↓（x） often allows the use of fewer grid points and hence faster computations; also it makes the opera/ion of transpt arent boundaries with Béronger layers considerably more efficient. Finally, the permittivity shbuld always be averaged mesh by mesh. # 1997 Optical Society of America [S0740-3232(97)00512:7]