Introduction Light propagation within anisotropic crystals

1 Introduction Light propagation within anisotropic crystals 

The surfaces seen on these photographs are known as ray velocity surfaces. For all uniaxial anisotropic crystals, we have a double surface when the crystal has a positive optic sign (like quartz), the ellipsoid of revolution is enclosed by the sphere, but if the crystal is optically negative (like calcite), the ellipsoid encloses the sphere. The assumption that the form of the variation of velocity for the extraordinary disturbance in uniaxial crystals is ellipsoidal was 

The wave fronts transmitted within the crystal are the envelopes of all the surfaces representing the secondary wavelets thus the +1 wave fronts in the crystal are given by the common tangents to extreme secondary wavelets. We see from the figure that there are two parallel wave fronts travelling in the crystal represented by tu and lm for the ordinary and extraordinary waves respectively, and that the wave normal direction is common both to them and the incident waves. It is also clear that the two parallel wave fronts travel with different speeds for they are at different positions within the crystal the extraordinary wave fronts advance faster than the ordinary wave fronts (rn rt). In order to locate the images of the dot formed by the two waves, we must now consider the direction of advance of a given point on the front physically this is what is meant by the ray directions within the crystal. 

It is instructive to pursue the interpretation of the calcite rhomb experiment beyond the simple Huyghenian construction to learn something about the polarization of the transmitted light. The electromagnetic theory of light requires that the electric vector shall be contained in the plane of the wave front. The ordinary disturbances vibrate perpendicular to a principal section. Also the extraordinary disturbance must vibrate in the principal section plane. 

It is apparent from this that the vibration direction for the transmitted extraordinary waves is not generally perpendicular to the ray direction. 

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