Relation between optical functions

We measure reflection R in the expreiment.

Using R we can calculation the phase shift:

θ(ω) = ω/π ∫ log(√(R/R₀))/(ω₀²-ω²)dω₀

Given R and θ as functions of ω, one can calculate all the optical functions.

1) n and k (refractive index and extinction factor):

because R=((n-1)²+k²)/((n+1)²+k²)

k²=4n/(1-R)-(n+1)²

therefore:

n=(1-R)/(1+R+2*√(R)cos(θ))

hence:

k=√(R(n+1)²-(n-1)²)/√(1-R)

2) other functions:

ε₁=n²-k²;

ε₂=2nk

σ₁=ε₂*ω*ε₀

α=k*ω/c, where c is the speed of light