# Flip of polarisation of light

Consider an optical experiment with photons or light pulses.

Is there an optical element that acts in the polarisation degree of freedom like the unitary $$U = \frac 1 {\sqrt 2} \begin{pmatrix} 1 & 1 \\ -1 & 1 \end{pmatrix}\quad \text ?$$ I choosed the basis such that $$|H\rangle = \begin{pmatrix} 1 \\ 0 \end{pmatrix}\;,\quad |V\rangle = \begin{pmatrix} 0 \\ 1 \end{pmatrix}$$

If yes, then a photon that passes this device twice would expirience a flip in the polarisation: $$U^2 = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}\;,$$ like $U|H\rangle = |V\rangle$ and $U|V\rangle = -|H\rangle$.

Does it exist?

• The result of passing through this element twice would be to "flip the polarization" - or if you like, it would be a 180 degree phase shift. That would just be a $\lambda/2$ element. But something that does this "after you pass through twice" is more interesting. What you are asking for is an element that rotates the polarization angle by 90 degrees. I have a hunch that you could achieve this with a birefringent element, but I'm not sure that can be done when you don't know the incident polarization angle. Commented Oct 16, 2014 at 14:25