= Linear birefringence
<Linear birefringence> means that two orthogonal <linear polarizations> have different <refractive indices>. Their different propagation phases produce <phase retardation>. In a lossless <waveplate>, with fast-axis angle $\theta$ and slow-minus-fast retardation $\delta$, the <Jones matrix>, up to a common phase, is
$$
J_\delta(\theta)=R(-\theta)\begin{pmatrix}1&0\\0&e^{i\delta}\end{pmatrix}R(\theta),\qquad R(\theta)=\begin{pmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{pmatrix},
$$
using time dependence $e^{-i\omega t}$. <Circular birefringence> instead has circular eigenpolarizations.
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