# Optics and Polarization

#### clougb

Hi everyone, I am a little bit confused on a concept relating to optics. If we have an interferometer (lets say a Sagnac interferometer) after the two beams traverse equal paths and recombine, the S and P polarizations are in phase but orthogonal. Does this mean that the light is essentially a linear polarization with an angle of 45 degrees (assuming the magnitude of each polarization component is equal). I understand by lagging one component of either polarization we get elliptical polarization or circular in the event that you lag one component by pi/2, but I do not understand how 2 beams with the same phase and orthogonal polarizations can interfere (it is said to be done with a linear polarizer).

Thanks for your help!

-Ben

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#### Andy Resnick

There are some subtle aspects I may be missing from your post, but orthogonal polarization states cannot in general interfere. The experiment to check would be simple- set up a Michaelson/Mach-Zender interferometer and place a half-wave plate in one arm (and maybe a glass plate in the other to compensate). Use laser light, which is linearly polarized, and rotate the half-wave plate to rotate the polarization state of one arm. The interfence fringes should modulate in intensity.

Some subtlety comes in because any polarization state can be decomposed into two orthogonal states (linear is a superposition of left- and right-handed circular, for example), so the reference arm can almost always interfere with a component of the test arm.

#### clougb

Hi and thanks for your reply! I have heard that by having two perpendicular linear polarizations which are in phase, you can "phase demodulate" by using a quarter wave plate and linear polarizer to cause these two beams to interfere. I am still a bit confused how a circular polarization (after the quarter wave plate) would transmit through a linear polarizer. Since the vertical and horizontal components of the wave are phase delayed by pi/2, what sort of intensity would you expect to see at the output when the linear polarizer is oriented at 45 degrees with respect to the optical axis? Would the intensity remain constant as you rotate the linear polarizer since both components for circularly polarized light are the same?

#### Lambduh

Check this thing out if you don't have a linear polarizer, quarter-wave plate, and a laser to play with.

http://demonstrations.wolfram.com/PolarizationOfAnOpticalWaveThroughPolarizersAndWavePlates/

If you don't have Mathematica you can just install the player to use it. (there are actually a lot of cool applets to play with)

A circularly polarized wave that goes through a linear polarizer becomes linearly polarized once again. A simple linear polarizer basically only allows one direction of polarization to pass through due to it's internal structure. In one direction the electric field causes electrons to move in the atoms aligned and energy is lost from the wave, while in the other direction it is free to pass through. http://en.wikipedia.org/wiki/Polarizer

And yes a circularly polarized wave that goes through a linear polarizer will transmit the same irradiance no matter what angle the polarizer is rotated to.

#### Andy Resnick

Hi and thanks for your reply! I have heard that by having two perpendicular linear polarizations which are in phase, you can "phase demodulate" by using a quarter wave plate and linear polarizer to cause these two beams to interfere. I am still a bit confused how a circular polarization (after the quarter wave plate) would transmit through a linear polarizer. Since the vertical and horizontal components of the wave are phase delayed by pi/2, what sort of intensity would you expect to see at the output when the linear polarizer is oriented at 45 degrees with respect to the optical axis? Would the intensity remain constant as you rotate the linear polarizer since both components for circularly polarized light are the same?

Let me make sure I understand your setup: 2 beams, each linearly polarized, with one beam polarized in (say) 'x' and the other in 'y'. One beam ('y') goes through a 1/4 wave plate oriented to produce circular polarization and then a linear polarizer oriented in 'x' to select a linear state, and you want to know if the two beams interfere? And then you also want to know if the beams will still interfere as the linear polarizer is rotated?

#### clougb

Thanks Lambduh, that was very helpful! Andy, you are pretty much correct. The two states of linear polarization are from the two paths of an interferometer, once they are split using a polarizing beam splitter and traverse equal paths, they again recombine on a non-polarizing beam splitter, then both travel through a quarter wave plate (now circular polarization) and then through a linear polarizer oriented at 45 degrees. What I wanted to better understand is how these initially in phase but perpendicular linear polarizations (one along x, other along y) can be made to interfere using the quarter wave plate and linear polarizer.

Thanks again!

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