# Can circular polarized light be cancelled?

I can cancel the light output from an LED screen by placing a linear polarizer at 90 degrees from the linear polarizer built into the LED display. OLED displays use circular polarizers instead of linear polarizers; in what way can I cancel the light output from them?

A circularly polarized light state can be thought of as a superposition, with equal magnitude weights, of $x$ and $y$ linearly polarized light states, with the $y$ component either leading or lagging the $x$ by a quarter of a period. Therefore, you can extinguish a beam of such light with linear polarizers in several ways, of which two are:

Method 1

Pass the beam through a linear polarizer, of any arbitrary orientation. The output will be the component of the superposition orthogonal to that extinguished by the polarizer, i.e. it will be linearly polarized with polarization plane orthogonal to that extinguished by the polarizer. A second polarizer with polarization plane orthogonal to the first will then extinguish all the light, to within the imperfections of the polarizers.

Fun "magic trick": with the crossed polarizers blocking all the light, try putting a third linear polarizer in between the other two and rotating it. Now rotate the third and observe the output. The third polarizer now allows some light to pass through all three polarizers unless its polarization plane is aligned with the other two. This in my experience is the one polarization experiment that small children do not grow bored with swiftly. They love and find it enthralling.

exercise 1 Explain the "magic trick" and calculate the maximum amount of light, as a fraction of the input, to pass through the three polarizer system and what the middle polarizer's orientation has to be to achieve this maximum.

exercise 2 Show that the above method (with the two polarizers, not three) will always extinguish any light beam, no matter what the input polarization state and degree of polarization may be. Show that the magic trick works in the almost same way, no matter what the input light state may be (although some input light states - linear ones with extinguished polarization plane aligned with the first polarizer - will be altogether extinguished by the first polarizer).

Method 2

Use a birefringent crystal of a quarter wavelength delay (a quarter wave plate) between its slow and fast axes to bring the two linear components of the circular polarization state in-phase (i.e. delay the leading / lagging polarization state enough to get rid of the lead/lag).

The output is a linear polarization state, with plane of polarization making angle $\frac{\pi}{4}$ with the birefringent crystal's slow and fast axes. A linear polarizer aligned to this plane will now extinguish the light.

exercise 3 Investigate this setup for an arbitrary polarization state / degree of polarization input, showing that in this case there are only particular light states that are extinguished this time.