= Pure-polarization preparation with two quarter-wave plates
Two rotatable ideal <quarter-wave plates> can transform a fixed <circular polarization> into any <pure polarization> represented by a <Jones vector>. Use time dependence $e^{-i\omega t}$, $Q(\theta)=R(-\theta)\operatorname{diag}(1,i)R(\theta)$ and input $J_L=(1,i)^T/\sqrt2$. Every target <polarization ellipse> can be written, up to a common phase, as $R(-\beta)(\cos\eta,i\sin\eta)^T$, with signed ellipticity angle $-\pi/4\leq\eta\leq\pi/4$. The first <quarter-wave plate> at $\theta_1=\beta+\eta+\pi/4$ produces <linear polarization> at $\beta+\eta$. The second, at $\theta_2=\beta$, therefore produces the required target. The two angles supply the two independent parameters of pure <polarization>.
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