= Retardation mechanism
<Birefringence> gives two orthogonal linear eigenpolarizations with different <refractive indices>, $n_f$ and $n_s$. They accumulate different <wave phases> through the same physical thickness $d$. Their relative <phase retardation> is
$$
\delta=\frac{\omega d}{c}(n_s-n_f)=\frac{2\pi d}{\lambda_0}(n_s-n_f),\qquad
\boxed{\delta=\pm\frac\pi2\pmod{2\pi}}.
$$
Here $\lambda_0$ is the <vacuum> <wavelength>. For the thinnest positive-retardance plate, $d=\lambda_0/[4(n_s-n_f)]$. The plate uses a difference in <phase velocity>, rather than differential <wave absorption>. Equal <wave amplitudes> along the two axes, obtained from input <linear polarization> at $45^\circ$ to them, acquire <phase quadrature> and become <circular polarization>. Reversing that conversion gives <linear polarization> from the corresponding circular input. A different input angle generally gives <elliptical polarization> on one pass.
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