- #1

Paul Colby

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I've been looking at the optics of ##\alpha##-quartz which comes in two parities, left and right. Quartz is optically active which means that the plane of a linearly polarized beam propagating along the optic axis is rotated by an angle proportional to the distance traveled. I would like to express this in terms of tensor constitutive parameters, ##\epsilon_{nm}## and ##\mu_{nm}##. Here is where this runs aground. Crystal symmetry limits the form of the permittivity tensor to the form,

##\epsilon_{nm} = \left(\begin{array}{ccc}\epsilon_{a}&0&0\cr 0&\epsilon_{a}&0\cr 0 & 0 & \epsilon_{b}\end{array}\right)##

The very same symmetry arguments would require,

##\mu_{nm} = \left(\begin{array}{ccc}\mu_{a}&0&0\cr 0&\mu_{a}&0\cr 0 & 0 & \mu_{b}\end{array}\right)##

Okay, for a beam propagating along the optic (##z##-axis) no optical activity can be generated from constitutive relations of this form? What gives?