Polarization by Reflection — Question 6

Question 6

Analyzer misalignment leaks the dominant polarization of reflected glare

An unpolarized beam reflects from a horizontal dielectric surface in a vertical incidence plane. At the chosen angle its power reflectances are Rs=0.16 and Rp=0.01. An ideal analyzer in the reflected beam has its axis at angle phi from the p direction toward s. Normalize all powers to incident P0.

1. Derive the transmitted analyzer power and find the best suppression orientation.

2. Find the transmitted fraction for phi=10 degrees and compare it with the optimum.

Question 6 - Solution

Analyzer misalignment leaks the dominant polarization of reflected glare

(a) Method and calculation

$$P_{r,p}=R_pP_0/2,\quad P_{r,s}=R_sP_0/2.$$$$\boxed{P_A/P_0=\tfrac12(R_p\cos^2\phi+R_s\sin^2\phi)}.$$

(b) Interpretation and further calculation

$$R_p<R_s\Rightarrow\boxed{\phi=0,\quad P_{A,\min}/P_0=R_p/2=0.005}.$$$$\boxed{P_A(10^\circ)/P_0=0.00726153,\quad P_A(10^\circ)/P_{A,\min}=1.45231}.$$

Physical check

The s electric field is horizontal and perpendicular to the vertical incidence plane; the analyzer must transmit the transverse p direction to suppress it.