Can anyone help out with the following question? Suppose we have an incident linearly polarized plane wave, polarized in the z-direction and propagating in the x-direction, and it passes through two quarter wave plates (their surfaces normal to the x-axis), and the left plate causes the fields emerging from the other side to rotate in the counter-clockwise direction as seen in this animation, the right plate causes the emerging field to rotate clockwise. What would be the relation between the angles of the E-field vectors emerging from the plates at any given moment? For example, at a moment when the E-field at the front of the left plate is pointing in the +y direction, would the E-field from the right plate also be parallel to the y-axis, and if so would it point in +y or -y at that moment?
Ideally I'd like to find a reference giving a general relation between the fields hitting one side of the plate and the fields emerging from the other as a function both of time and the thickness of the plate. (In order for a quarter-wave plate to function properly does there have to be some relation between its thickness and the wavelength of the wave hitting it, or can it theoretically be arbitrarily thin and still work perfectly? Will the same plate work equally well at producing circularly polarized waves for incoming linearly polarized wave of different wavelengths?) But a general relation isn't really necessary for the question I'm exploring (which is about what would happen in the classical analogue of the quantum experiment shown in the slides that accompany this article), if anyone knows how to answer the question above it'd be helpful.
Ideally I'd like to find a reference giving a general relation between the fields hitting one side of the plate and the fields emerging from the other as a function both of time and the thickness of the plate. (In order for a quarter-wave plate to function properly does there have to be some relation between its thickness and the wavelength of the wave hitting it, or can it theoretically be arbitrarily thin and still work perfectly? Will the same plate work equally well at producing circularly polarized waves for incoming linearly polarized wave of different wavelengths?) But a general relation isn't really necessary for the question I'm exploring (which is about what would happen in the classical analogue of the quantum experiment shown in the slides that accompany this article), if anyone knows how to answer the question above it'd be helpful.