Polarization — Question 8

Question 8

A rotating analyzer doubles the mechanical rotation frequency

A beam contains unpolarized intensity Iu and linear intensity Ip polarized at angle alpha. An ideal analyzer rotates with angular speed Omega, so its axis angle is Omega t.

1. Express the transmitted intensity as a constant plus a sinusoidal term.

2. Given a measured mean intensity M and modulation amplitude B, infer total intensity, polarized intensity, and the admissible range of B.

Question 8 - Solution

A rotating analyzer doubles the mechanical rotation frequency

(a) Method and calculation

$$I(t)=I_u/2+I_p\cos^2(\Omega t-\alpha).$$$$\boxed{I(t)=(I_u+I_p)/2+(I_p/2)\cos(2\Omega t-2\alpha)}.$$

(b) Interpretation and further calculation

$$\boxed{I_{\mathrm{total}}=2M,\quad I_p=2B,\quad I_u=2(M-B)}.$$$$\boxed{0\le B\le M,\quad\mathcal P_L=B/M,\quad\omega_{\mathrm{modulation}}=2\Omega}.$$

Physical check

An analyzer axis repeats after half a turn, giving two intensity cycles per mechanical revolution.