Polarization in Interferometry

[matheyrichs]

I'm working on a laser-based holographic interferometry system. Basically, I produce a linear fringe pattern with a Mach-Zender style interferometer setup. Then when I put a transparent sample in one of the beam pathways (cell cultures), I can determine the phase offset produced based on the deformation of these fringes.

So I've been having trouble getting a strong interference signal at my camera and a colleague recommended I polarize the laser light before sending it through the system in order to get stronger fringe intensity. He was absolutely right -- my fringes are much clearer than they used to be. I don't understand why this works. He tried to tell me that when two beams interfere that are the same polarization, the signal is better (obviously...) but he couldn't tell me why this was the case. I would think that if you have a superposition of 2 different polarizations and each one interferes similarly, shouldn't the interference term have the same intensity relative to the background signal??

Any explanation for why interferometers work better with linearly polarized light will be much appreciated!

Thanks!

 

[Andy Resnick]

You didn't describe your beamsplitter (prism, pellicle, etc), but in general, the more coherent the beam, the better the fringes. Selecting a single polarization state increases the coherence.

Some imaging systems exploit interference and polarization effects: DIC microscopy is one.

 

[matheyrichs]

I'm using 2 non-polarizing beam-splitter cubes, a HeNe and a DPSS laser.

I understand that interfering two beams of similar polarization will produce a better fringe pattern than interfering say one S- and one P-polarized wave together (should produce no interference). But it's not clear to me that interfering the superposition of an S&P polarization with a similar S&P polarization wave won't produce equally-good intereference fringes.

Maybe it's the mirrors in the system? Do silvered mirrors reflect S-polarizations at different efficiencies than P-polarizations? If that's the case, then I guess by choosing a single-polarization from the source I am eliminating waves that would not interfere with high-quality fringes, thus eliminating background signal?

 

[Andy Resnick]

Wait...you are using 2 lasers? I don't understand your layout... usually there's a single source. Assuming you are indeed using just one source...

Are you spatially filtering the light prior to the interferometer? That will dramatically improve the quality of the fringes.

Silvered mirrors (or anything, really) will have different reflection coefficients for s- and p- polarization states, but if you are at or near normal incidence the differences are negligible.

My understanding is that the two polarization states are independent from each other- so interfering mixtures of the two will not produce clean interference fringes.

Then there are environmental issues- vibration isolation, air currents, etc. I assume you already controlled those reasonably well?

 

[matheyrichs]

I'm actually only using one source at a time. But since a Mach-Zender interferometer has 2 different entry points, the two free faces of the input beam splitter, I'm using 2 lasers. This way I can take a holographic interferogram at a single wavelength, then using shutters switch wavelengths and create a second interferogram. My end-application is using the two wavelengths to resolve 2-pi ambiguities from my phase images without running complex & time consuming unwrapping algorithms. It's actually a nifty concept...

But I am not spatially filtering. That should and will probably be my next improvement to my system.

The table is floated, but I haven't dealt with air currents yet...

 

[TGarzarella]

Because the two beams weren't linearly polarized in your original set-up you were essentially working with 4 waves (two s-waves and two p-waves).

In principle, its possible to interfere the two beams, but they would have to be in precisely the same (elliptical) polarization state. This is because both s-waves must be equal in amplitude, and both p-waves must be equal in amplitude. Also, the phase delay between s and p waves must be the same in both beams to ensure that when the s-waves interfere, the p-waves would also interfere.

Another possible complication is if the sample your using has some birefringence. If that's the case, it would be difficult or impossible to get a clean interference pattern from both s and p waves.

By linearly polarizing the beams, you essentially work with only two beams and the situation is greatly simplified and easier to work with (even with birefringent material).

 

[Redbelly98]

If two linearly polarized beams are polarized at right angles to each other, there will be no interference fringes. Electric fields at right angles to each other can neither destructively interfere, nor constructively interfere.

If the two coherent beams are polarized in the exact same direction and have the same amplitude, you will get perfect interference fringes, i.e. they will go to zero intensity at the fringe minima.

For two beams that are a random mixture of polarizations there will still be a fringe pattern, but it will not go to zero at the minima. The fringes will appear somewhat "washed out".

Moral: keep the beams polarized, and polarized in the same direction, for the clearest interference fringes.

 

[matheyrichs]

Andy Resnick, TGarzarella, & RedBelly98,

Thanks a bunch for the explanations! I appreciate it!

- M