Fresnel Equations

xiaoipower

Hi guys!

Was wondering if anyone was confident with Fresnel equations for a refractive index interface. From what I understand:

Assume incoming normal plane wave travelling in z-direction and polarised in x plane.

Assume z=0 is the plane that separates two materials: n_1 and n_2 (refractive index)

I think the Fresnel solution for the wave should go:

Ex = (for z>0) exp(-i*k0*n_1*z)+r*exp(i*k0*n_1*z)

(for z<0) t*exp(-i*k0*n_2*z)

the RED term representing the normal incident component and the GREEN term represents the reflected component which only exist in the n_1 half

and the BLUE term representing the transmitted component which only exists in the n_2 half.

I am uncertain about if I should be adding both the incident and reflected term (for z>0) as long as they are travelling in different directions or if I need to subtract them. i.e. should it be RED+GREEN or RED-GREEN? As I already have defined them to travel in opposite directions.

Any thoughts?

Many thanks!

vanhees71

You find the coefficients by solving for the boundary conditions at the surface between the two media. This can be found in any textbook on electrodynamics or optics.