We review the fast Fourier transform beam propagation method (FFT-BPM)
that is commonly used to describe diffraction of electromagnetic wave
s and introduce a time-domain version that takes into account arbitrar
y longitudinal index profiles, as well as transverse effects. This met
hod can describe all relevant aspects of paraxial propagation in linea
r or nonlinear media. That is, the technique can handle transmission,
diffraction, and, in particular, reflection of electromagnetic waves.