Electromagnetic Pulse propagating at oblique angle to a dielectric interface

Consider a gaussian wave pulse propagating along the z-axis from region 1 with refractive index n1 and onto a dielectric interface y = m z (for all x). To the left of this dielectric interface, the refractive index is n2.

Devise an initial value computer algorithm to determine the time evolution of the reflected and transmitted electromagnetic fields for this pulse.

e.g., n1 = 1 , n2 = 2

initial profile (t = 0, with z0 < 0) Ex = E0 exp[-a (z-z0)^2] By = n1 * Ex Choose parameters so that the pulse width is at least a fact of 8 less than the z- domain of integration ( -L < z < L).

For the slope of the interface, one could choose m = 1.