Phase difference of HeNe laser in Lithium Niobate

[haigie123]

Homework Statement

I have a laser focused into a lithium niobate crystal and an analyzer placed after the crystal. The analyzer and laser are cross polarized.
I'm trying to derive the equation that relates the phase difference of the o-wave and e-wave after the analyzer. I know it is dependent on the thickness, d, of the crystal, the birefringent refractive indexes, n(e,o), and wavelength λ (here, 633nm).

Homework Equations

So far I'm aware the waves are split into two, of intensity (Eo/2)cos(wt±ε), where ε is the phase difference and Eo is the amplitude.

The Attempt at a Solution

I've tried combining the two, then doing the difference of two cosines, but this didn't get me far but I am sure this is the along the right lines... Suggestions or thoughts would be greatly appreciated!

 

[Jhero]

Dear fellow scientist,

Thank you for sharing your experiment and question with us. It sounds like you are working with a very interesting setup. The phase difference between the o-wave and e-wave after the analyzer can be related to the thickness of the crystal, the birefringent refractive indexes, and the wavelength using the following equation:

ε = (2πd/λ)(n(o) - n(e))

Where ε is the phase difference, d is the thickness of the crystal, n(o) and n(e) are the refractive indexes for the o-wave and e-wave, respectively, and λ is the wavelength. This equation is known as the phase retardation equation and is commonly used in optics to describe the phase difference between two waves passing through a birefringent material.

I hope this helps in your derivation. Please let me know if you have any further questions or need clarification on anything. Good luck with your experiment!