Spurious modes in the DuFort-Frankel finite-difference beam propagation method

In this letter, we analyze the DuFort-Frankel beam propagation method (BPM) which is a modification to the known explicit finite-difference beam propagation method (EFD-BPM) and found that there are some precautions that must he taken before using the method. The accuracy and the efficiency of this method has been shown and compared with the most popular FD-BPMs.