For paraxial approximant, we get the following equation:
here a =2k0nre f ,
From Equation 119, we get
Thus, the unknown at field φ l + 1 at z + Δz is related to the known field φ l at z as follows:
Using Equation 127 we finally can get the unknown field φ l + 1 at z + Δz from the known field φ l
If we consider FEM we get,
Thus, we can rewrite Equation 127 as
The element matrices [ M e] and [ K e] are defined by Equation 100 and Equation 99, respectively.