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I have read [1] that when the light enters a birefringent material with optical axis perpendicular to the plane of incidence that the angle of refraction of the extraordinary wave can be found by Snell's Law. My question is weather this holds independent of medium the light is in before it reaches the interface?

For example let us say the light is travelling from a birefringent material 1 to material 2. And material 2 has an optical axis perpendicular to the plane of incidence of the extraordinary wave. Can we use Snell's law independent of the direction of the axis in medium 1? Either way please can you explain.

References

[1] Fowles, G.R. 1975. Introduction to Modern Optics. 2nd ed. New York: Holt. Rineheart Wintson, INC.(p183)

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The observation you mention is a consequence of the fact that under the aforementioned conditions, the electric field of the s-polarisation (or, "TE") always remains parallel to the optical axis, no matter what the incidence angle is. If one substitutes the effective permittivity along the optical axis into the Snell law, it holds (for this polarisation only).

This special condition is maintained when you replace air with any isotropic medium, and even more generally, with an anisotropic medium where the optical axis is still perpendicular to the incidence plane.

Note that in most cases, the Snell law is not applicable in anisotropic media.

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  • $\begingroup$ Well, Snell's law still applies except when the Poynting vector is away from the direction of the wavefront (IIRC). Is that what you're referring to? $\endgroup$
    – Carl Witthoft
    Commented Apr 20, 2016 at 15:38
  • $\begingroup$ @CarlWitthoft Yes, in most cases, it is as you write. $\endgroup$
    – dominecf
    Commented Apr 20, 2016 at 19:44

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