 Modified rational approximants that can suppress the evanescent modes are now available.The accuracy of the BPM can be further improved, if you use the energy-conserving one-way model or the single-scatter one-way model.BPM is generally formulated as a solution to Helmholtz equation in a time-harmonic case, 


with the field written as, 

Now the spatial dependence of this field is written according to any one TE or TM polarizations

with the envelope 

Now the solution when replaced into the Helmholtz equation follows,

With the aim to calculate the field at all points of space for all times, we only need to compute the function
formula_7 for all space, and then we are able to reconstruct formula_8.