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

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Discussion Overview

The discussion revolves around the behavior of light in linear birefringent crystals, specifically addressing the apparent violation of Snell's Law when light enters at an angle to the optical axis. Participants explore the underlying causes of this phenomenon and the implications for light propagation in such materials.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that when light enters a birefringent crystal at an angle, the ordinary ray (o-ray) continues parallel to the face while the extraordinary ray (e-ray) bends, questioning the source of this behavior.
  • Another participant emphasizes the importance of understanding light propagation in crystals, mentioning that the index of refraction varies with direction and that the wave equation has two solutions, leading to different behaviors for the o-ray and e-ray.
  • A participant poses a question about the behavior of a single photon entering a birefringent crystal, inquiring whether it splits into different paths.
  • Another participant suggests that the situation with single photons may yield results similar to those observed with polarizers, but expresses uncertainty about the actual behavior of the photon in this context.
  • A later reply asserts that there is no violation of Snell's Law in birefringent materials, stating that both polarizations fulfill Snell's Law despite traveling at different refractive indices.

Areas of Agreement / Disagreement

Participants express differing views on whether Snell's Law is violated in birefringent materials. While some argue that the e-ray's behavior constitutes a violation, others contend that both rays adhere to Snell's Law, indicating an unresolved debate on this topic.

Contextual Notes

Participants reference the complexity of light propagation in crystals and the need for a deeper understanding of the wave equations involved. There are mentions of specific texts, such as Born and Wolf, which may provide further insights, but no consensus is reached regarding the implications for Snell's Law.

enotstrebor
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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?)
 
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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.
 
Andy, I hope this isn't a stupid question/wording:

If a single visible-light photon enters a birefringent crystal, does the photon split?
 
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.
 
Andy Resnick said:
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
 
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!
 

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