What Causes Violation of Snell's Law in Linear Birefringent Crystals?

[enotstrebor]

In a linear birefringent crystal, if light enters parallel to a face that has been cut so that it is at an angle to the optical axis, the o-ray continues parallel to the face but the e-ray travels at an angle to the face in violation of Snell's Law.

Question --- Is there any explanation for the source cause of this violation?

(The answer is not the difference in index of refraction for the e-ray! The e-ray index can be higher or lower than that of the o-ray. It does alway bend the in-optical axis-plane polarized ray, but why not always bend the o-ray instead?)

 

[Andy Resnick]

heh... it's not called the 'extraordinary wave' for no reason.

To get to the root of the question, one needs to understand light propagation in crystals- that is, the index of refraction varies with direction. Born and Wolf covers this very well in chapter 15 (7th edition), so to summarize, the wave equation admits two solutions.

The general solution is quite complicated- it's a 4th order polynomial, but for some crystal geometries (uniaxial) this reduces to a solution where the velocity is independent of direction (ordinary wave) and one where is does (extraordinary wave). The speeds of the two waves are identical when they travel along the optical axis.

The next level of complication is biaxial crystals; this leads to conical refraction (among other phenomena).

The wiki site is not that great; It's worth checking out Born and Wolf.

 

[pallidin]

Andy, I hope this isn't a stupid question/wording:

If a single visible-light photon enters a birefringent crystal, does the photon split?

 

[Andy Resnick]

If I understand what you are getting at, then the results should be similar to that obtained by single photons + polarizers. That said, I have no idea what "really" happens in that situation.

 

[enotstrebor]

heh... it's not called the 'extraordinary wave' for no reason.

To get to the root of the question, one needs to understand light propagation in crystals- that is, the index of refraction varies with direction. Born and Wolf covers this very well in chapter 15 (7th edition), so to summarize, the wave equation admits two solutions.

....It's worth checking out Born and Wolf.

The question I asked is about the e-ray violating Snell's Law. Light enters perpendicular to the crystal face but changes angle.

As far as I know, the two solutions to the wave equations due to the fact that the index of refraction varies with direction (resulting in different velocities) does not require the e-ray to bend at the interface.

However I will check out Born and Wolf.

Thanks

 

[jrlaguna]

There is no violation of Snell's law in birefringent materials... Please, give citation. The parallel and perpendicular polarizations travel with different refractive indices, that's all... but both of them fulfill Snell's law!