Properties of Fresnel's Interface Reflection Coefficients

phase shift δ

incidence angle ϕ

radius r

Let

w

denote an interface Fresnel reflection coefficient for

s

- or

p

-polarized light at an oblique angle of incidence

ϕ

and

z

denote the same coefficient at normal incidence. Then it can be shown that

w

is an analytic function of

z

that depends parametrically on the angle of incidence

ϕ

. Here

z=rexp(jδ)

, where

r

and

δ

are the normal-incidence amplitude reflectance and phase shift.

The figure shows the trajectories of the

s

-reflection coefficient in the complex

w

plane as the angle of incidence

ϕ

increases from 0 (normal incidence) to 90° (grazing incidence) for

0≤r≤1

and

0≤δ≤180°

. Each curve originates on the semicircle with radius

r

with a constant

δ

and ends at the point

(-1,0)

, moving counterclockwise.