We all know farady effect is observed in linearly polarized wave when it passes through a dielectric medium and magnetic field is along the direction of propagation. Is this phenomenon observable in circularly polarized waves?
Circularly polarized wave travel through the medium with different phases. But as soon as they are out of the medium they retain their polarization. So basically a circularly polarized wave 's polarization is not affected but only it's phase. Whether we split circularly polarized wave into two linearly polarized wave and take the equation of form: $$E(z)=Ee^{i\left(\frac{2\pi z}{\lambda}+\phi\right)}\tag{1}$$
Frequency and wavelength remain same for the em wave when it is entering and when it is leaving the dielectric medium. Say the em wave is split into two linearly polarized waves- one is sine wave along $yz$ plane and the other is cosine wave along $xz$ plane. Both waves rotated by same angle due to faraday rotation because rotation is not dependent on plane polarization or phase of the wave. When we combine them again only the phase($\phi$) of circularly polarized wave changes. First question is this theory correct?
Second question is how do we calculate the change in phase. For example, a linearly polarized wave's change in polarization is given by experimental formula of becquerel equation(change in angle of $β=V \times B \times d$ Where $\beta$ is polarization, $V$ is verdet constant, $B$ is magnetic field and $d$ is length of dielectric, see the figure to get an idea ). Is there any experimental formula for circularly polarized waves?
Edit: I guess the change in phase of circularly polarized wave follows different equation as seen in the becquerel equation. I am unable to find any experimental data on this.