# Experimental calculation of Birefriengence

1. Aug 9, 2007

### MartingeWomble

I was wondering if any of you guys could help me.

Is there any simple way to set up an experiment to calculate the birefringence of a birefringent crystal? I've trudged through papers and the most helpful one was "Measuring birefringence properties using a wave plate and an analyzer" by Stewart R. M. Robertson.

unfortunately, I don't immediately see how to get a value for birefringence from his calculations.

Thanks!

2. Aug 9, 2007

### Claude Bile

Send a beam polarised at 45 degrees to the crystal axis through a crystal of known thickness and measuring the output polarisation. From the measurement of the output polarisation you can calculate the difference in path lengths of each the ordinary and extraordinary polarisations.

Alternatively you can send a beam through and see the difference in refraction angle of two polarisations, but the crystal has to be cut the right way to do this.

Failing both of these, you can try to phase match a 2nd order nonlinear process if you have a suitable laser at hand. You could work out the birefringence by measuring the optimal alignment angle wrt the crystal axis.

Claude.

3. Aug 10, 2007

### MartingeWomble

Hello Claude, and thank you for responding to my question!

would you have to measure output polarizations for separate beams (one for ordinary, another for extraordinary)? What if the deflection angle is very small? I'm not sure I understand how to calculate path lengths from polarization data.

Alternatively you can send a beam through and see the difference in refraction angle of two polarisations, but the crystal has to be cut the right way to do this.

Failing both of these, you can try to phase match a 2nd order nonlinear process if you have a suitable laser at hand. You could work out the birefringence by measuring the optimal alignment angle wrt the crystal axis.

All three of these seem like viable solutions, but I am unsure how to implement them. Are there readily available sources you could point me towards which explain this in greater detail? I appreciate your help and would like to learn more so I can ask more poignant questions!

4. Aug 13, 2007

### Claude Bile

No, I would keep everything colinear. The idea here is to measure the phase difference between the two orthogonal polarisations. This will determine whether you measure linearly, circularly or elliptically polarised light. The induced phase difference between each component will be a direct result of the difference in refractive index the two polarisations "see".
The simplest way I have seen this done is simply placing the crystal on an overhead projector and observing the "double-vision".
This process should be covered in most textbooks on optics, and certainly any on nonlinear optics. I can give a brief run-down as to how this works though.

I beam of sufficient energy at frequency f will generate a frequency at 2f in media with a crystalline structure of appropriate symmetry. For efficient conversion from f to 2f, the f beam and 2f beam need to be kept in phase. Since the natural material dispersion of a medium generally results in n(f) =/= n(2f), one must go to some lengths to ensure that the f and 2f beams are kept in phase. In a birefringent crystal, this can be done by sending the f beam at an angle to the crystal axis such that the ordinary refractive index at frequency f equals the extraordinary refractive index at 2f. The actual angle depends on the ordinary and extraordinary refractive indices, so if you know one you can work out the other.

Claude.