Polarization — Question 9

Question 9

Incoherent orthogonal beams and a circular wave share linear-analyzer readings

Compare two beams of the same total intensity I0: beam A is an equal incoherent mixture of x and y linear polarization; beam B is a coherent circular wave. Only an ideal linear analyzer is initially available.

1. Show that neither beam varies in transmitted intensity as the analyzer rotates.

2. Place a quarter-wave plate before the analyzer, with a phase delay chosen to convert beam B to linear polarization. Find the maximum and minimum readings for each beam.

Question 9 - Solution

Incoherent orthogonal beams and a circular wave share linear-analyzer readings

(a) Method and calculation

$$I_A(\theta)=\tfrac12I_0\cos^2\theta+\tfrac12I_0\sin^2\theta=I_0/2.$$$$\boxed{I_B(\theta)=I_0/2\quad\text{for all}\ \theta}.$$

(b) Interpretation and further calculation

$$\boxed{I_{A,\max}=I_{A,\min}=I_0/2}\quad\text{after the plate}.$$$$\boxed{I_{B,\max}=I_0,\quad I_{B,\min}=0}\quad\text{after conversion to linear}.$$

Physical check

A phase plate cannot create coherence between the independent components of A; it can change the relative phase of coherent B.