Solution (source code)

= Solution

A transverse static <electric field> can induce <linear birefringence> through the <electro-optic Kerr effect>. Define its coefficient by $\Delta n=\lambda_0 K E_{\rm dc}^2$, with the <principal axes> parallel and perpendicular to the applied field. A <length> $d_K$ then gives $\delta_K=2\pi Kd_KE_{\rm dc}^2$.

For input polarized at $45^\circ$ to those axes, switching from zero retardation to $|\delta_K|=\pi/2$ switches linear to <circular polarization>. Other input angles generally become elliptical, and axis-aligned input stays linear. The required field magnitude for the lowest-order setting is
$$
\boxed{|E_{\rm dc}|=\frac1{\sqrt{4|K|d_K}}.}
$$
\b[A Kerr cell is suitable as a switchable <quarter-wave plate>.] The field can be changed electronically without mechanically rotating the axes; actual switching time depends on the material response and driving circuit. This is induced <linear birefringence>, not polarization-selective absorption.<The Feynman Lectures on Physics, Volume I by Richard Feynman and others>[§33–3, final paragraphs: an applied electric field produces birefringence and electrical light switching in a Kerr cell]{ref}