Polarization by Reflection — Question 4

Question 4

Brewster transmission is generally only partly polarized

An unpolarized beam of power P0 strikes a single lossless interface at Brewster incidence. Its s reflectance is Rs and its p reflectance is zero. A detector collects the entire transmitted beam. Define the transmitted degree of linear polarization as the power difference divided by the sum.

1. Find the transmitted s and p powers and total transmitted power.

2. Derive the degree of polarization and evaluate it when Rs=1/4.

Question 4 - Solution

Brewster transmission is generally only partly polarized

(a) Method and calculation

$$\boxed{P_{t,p}=P_0/2,\quad P_{t,s}=(1-R_s)P_0/2}.$$$$\boxed{P_t=P_0(1-R_s/2)}.$$

(b) Interpretation and further calculation

$$\mathcal P_t=\frac{P_{t,p}-P_{t,s}}{P_{t,p}+P_{t,s}}=\boxed{\frac{R_s}{2-R_s}}.$$$$R_s=1/4\Rightarrow\boxed{P_t/P_0=7/8,\quad\mathcal P_t=1/7}.$$

Physical check

The reflected beam is purely s, but the transmitted beam retains both components unless s transmission also vanishes.