Quarter wave plate made of anisotropic crystal

[Chen]

Hi,

I'm constructing an interferometry experiment, in which I'm using a Michelson-Morley-type interferometer. However, the only beam splitter I have which preserves polarization is physically small (a few mm), and so in my setup the beam in each arm is not split. The reflection off the mirror is completely, or extremely close to, normal. The input beam is linearly polarized.

I'd like to have the polarization plane of one of the beams reflected through some axis (doesn't matter which), with respect to the polarization of the beam in the second arm. Normally I'd use a half wave plate for this purpose, however since I can't split the beam in each arm, it would pass through the plate twice and the final result would be the same as if I had no plate at all.

So I thought, why not use a quarter wave plate instead? After the beam splitter, one of the beams would pass through the plate and change its polarization to something elliptic (because the polarization along one axis would gain a phase of pi/2). That beam would be reflected off the mirror, and pass through the plate again, and the polarization along the same axis would gain an additional phase of pi/2 and the total effect would be just that of a half wave plate.

However, I'm not sure that it would work, because in its second pass through the plate, the beam would be going in the opposite direction. So I thought it might be the case that the polarization which gained a phase of pi/2 in the first pass, would lose it in the second pass, and not gain an additional pi/2. Do you think that's the case? The material I'm using for the wave plates is Mica, optical quality.

Any input would be most welcome.

Thanks,
Chen

 

[Chen]

My first intuition is that it should work. The direction of propagation (up or down the same line) shouldn't make a difference. The fast and slow axes don't interchange when I send the beam into the crystal from the opposite direction, right? So the slow polarization should still be behind the fast one, and the end result should be the same.

What do you think?

 

[JeffKoch]

It'd help if you drew a picture of the setup, I'm not quite sure I follow.

 

[Chen]

Okay, this is the original setup I had in mind, in which I'd use a half-wave plate (HWP) in order to flip the polarization plane of one beam:

http://img402.imageshack.us/img402/1346/hwpwr2.png

However, since I don't have a non-polarizing beam-splitter (BS) big enough to support this setup, I have to resort to something like this:

http://img402.imageshack.us/img402/2092/qwpuv2.png

In which case I'd use a quarter-wave plate (QWP) in order to first turn the linear polarization into elliptical, and then on the way back it would be transformed into linear polarization, which is flipped relative to the original beam.

Think it'd work? The second setup also has the benefits of bouncing the beams off the mirrors at exactly 90 degrees, which would minimize any polarizing effects of the mirrors.

 

[JeffKoch]

The double-pass 1/4 waveplate will have the same effect as a single-pass 1/2 waveplate, so yes, they're equivilent. Try it and see, you may also find some interesting polarization and phase-shifting features due to the beamsplitter depending on what you're using.

 

[Chen]

Heh, "interesting" is the last word I'd use in that context. I'm trying to avoid any polarizing effects in the system, since the goal of the experiment is to see how rotating one beam's polarization with respect to the other affects the intereference pattern (well, its contrast anyway). I was originally instructed to use a Sagnac-type interferometer, but I was having much problem with the mirror reflections, which was at 45 degrees and extremely polarizing.

I'm on my way to the lab now, will report back. Thanks for the input.