# Elliptical Polarization (QM)

by Pedvi
Tags: elliptical, polarization
 P: 1 1. The problem statement, all variables and given/known data The state of the photons is: $$|\psi> = \frac{1}{\sqrt{1+r^2}}(|\psi_x> + r\exp{(i\alpha)}|\psi_y>)$$ Where the $$|\psi_x>$$ and $$|\psi_y>$$ are the linear polarization states in the x and y direction, respectively. They are elliptically polarized. I have to give the axes a,b of the ellipse, the angle of the major axis and the direction. 2. Relevant equations I made a change of "axes" to the right and left circular polarization states: $$|\psi_{R/L}> = \frac{1}{\sqrt{2}}(|\psi_x> \pm i|\psi_y>)$$ 3. The attempt at a solution The result of the change is: $$|\psi> = \frac{1}{\sqrt{2(1+r^2)}}(|\psi_R>(1-ir\exp{i\alpha}) + |\psi_L>(1+ir\exp{i\alpha}))$$ I don't really know how to follow, I don't understand if I have to use the Jones matrices or if there's an other way. I think all the necessary information is there. Could somebody give me some hints? (It's the first time I write here, sorry if I've made any mistake).