Interferometer to measure refractive index of a gas

[Robsta]

Homework Statement

I've uploaded a diagram showing a two beam interferometer that can be used to monitor changes of refractive index in a gas cell. it is illuminated with monochromatic light of wavelength λ. The light is linearly horizontally polarised. The two polarizing beam splitters (PBS) pass vertical polarisation and reflect horizontal polarisation.

a) How should retarder 1 be configured to produce beams of equal intensity in the two interferometer arms?

b) Determine the orientation of polarisation which polaroid 1 should pass so that detector 1 can observe an optimally modulated interference pattern

c) Detector 2 should also observe an optimally modulated interference pattern. Determine the configuration of retarder 2 and polariser 2 that will produce an optimally modulated interference signal in which the phase difference of light from the two arms is changed from the phase difference observed on detector 1 by dφ

The Attempt at a Solution

a) I think retarder one wants to have its ordinary and extraordinary axes at 45 degrees to in incoming polarised light. This will split the light into two components, both polarised at 90 degrees to each other, of equal intensity.

These however won't be vertically and horizontally polarized, they'll be at 45 degrees to that.

b) I don't really see why the system needs two detectors. I see that the light going through the gas will acquire a phase shift due to the different refractive index of the gas. This will make circularly (or elliptically) polarised light at the detector. A polariser will just turn that into linearly polarised light. Will it produce an interference pattern?

I guess for a combination of the vertical light and the phase shifted horizontal light, the polariser should be at 45 degrees so as to combine the two.

c) I don't really see why detector two needs a retarder. Come to that, I dont' really see how the phase shift leads to an interference pattern at all rather than just circularly polarised light.

I'd appreciate any insight into this.

 

[andrevdh]

Look at the Application Examples at the bottom http://www.edmundoptics.com/technical-resources-center/optics/understanding-waveplates/
Also interference is produced by a path difference, in this case by the gas slowing the one beam down
and thus causing a phase difference between the two beams, which in effect is the same as a path difference.
How a laser interferometer works:
http://spie.org/x34353.xml