# Obliquely incident waves on multiple dielectric interfaces

Discussion in 'Physics' started by DrNick, Feb 20, 2007.

1. ### DrNick Thread Starter Active Member

Dec 13, 2006
110
2
Does anyone know how to find the effective reflection coefficient for a EM wave hitting a multiple dielectric interface oblequely?

For example:
Code ( (Unknown Language)):
1.
2. eps1|   eps2    |   eps3
3.     |           |
4.     |           |
5.    z=0           d
6.
a wave is traveling in medium 1 with epsilon1 hitting at z=0, To find the input impedance at z=0, can i just use this formula:
Code ( (Unknown Language)):
1.
2. Zin=eda2 * [U]eda1 - j * eda2 * tan(B*d)[/U]
3.             eda2 - j * eda1 * tan(Bd)
4.
?

or do things get skrewed up by the angle of incidence != 0 degrees?

Thanks

Dec 13, 2006
110
2

3. ### Dave Retired Moderator

Nov 17, 2003
6,960
145
For two mediums M1 (e.g air) and M2 (e.g the medium to which you have interacted), isn't the answer to this related to Snell's Law:

Sin ψ = √ε1 Sin θ

You can use Fresnel's Law to deduce the reflection coefficient:

Γ = (√ε2 *Cosθ) - (√ε1 *Cosψ)

For nomal incidence, then Fresnel's Law simplifies to:

Γ = (√ε2) - (√ε1)

Dave

4. ### DrNick Thread Starter Active Member

Dec 13, 2006
110
2
Not exactly. I beleive the reflection coefficient is dependent on whether the incident wave's E field is perpindicular or parallel to the plane of incidence. But your equation might be a nice simplification of one of the fresnel formulas. I was just getting messed up by the multiple interfaces, but I think I've got it.

Thanks though.