Polarization by Reflection — Question 8

Question 8

Two Brewster reflections select the overlap of their s directions

An unpolarized beam of power P0 undergoes two successive Brewster reflections. Their s power reflectances are R1 and R2. In the plane transverse to the intermediate ray, the second s axis is rotated by phi from the first s axis. No other loss occurs between the interfaces.

1. Find the power in the twice-reflected beam.

2. Compare phi=60 degrees and phi=90 degrees with aligned incidence planes.

Question 8 - Solution

Two Brewster reflections select the overlap of their s directions

(a) Method and calculation

$$P_1=R_1P_0/2,\quad\mathbf E_1\parallel\hat s_1.$$$$P_2=R_2P_1|\hat s_1\cdot\hat s_2|^2=\boxed{\tfrac12R_1R_2P_0\cos^2\phi}.$$

(b) Interpretation and further calculation

$$\boxed{P_2(60^\circ)/P_2(0)=1/4}.$$$$\boxed{P_2(90^\circ)=0}.$$

Physical check

At crossed s axes, the first reflected polarization is p for the second interface and therefore has zero second reflection.