Creating certain polarisations from light source

Question

I'm thinking about this situation:

Two plane polarized beams of light of equal intensity with polarizations that are mutually orthogonal are produced from a gas discharge lamp emitting nearly monochromatically at mean wavenumber ν and with bandwidth ∆ν using a polarizing beamsplitter.

I would like to create: 1) A circularly polarised beam 2) An unpolarised beam

I'm wondering are those 2 orthogonally polarised beam from the gas discharge lamp completely uncorrelated? In other words, just by combining them will give me "2) An unpolarised beam"?

and.. I got no idea how to create a circularly polarised beam. Any suggestions?

Answer 1

If you split a single lamp beam into horizontal and vertical beams, those two remain coherent. By delaying one by a half-wave, you can recombine them with the right phase relationship to make circularly polarized light.

If you have two independent beams, from two parts of the lamp, their phases are random. Recombine those and sometimes you have right-circular light, sometimes left, and sometimes linear at lots of different angles. This is all rapidly and randomly varying: quite similar to the random hence unpolarized light you started with.

Answer 2

For two polarized sources superimposing, the resultant beam has several parameters (relative: amplitudes, phase shifts, frequencies, and polarization angles.) Your desired setup fixes all but the latter, and changing that will only ever output another plane polarized beam. To get say a circular beam, you need a $\pi/2$ phase shift between the two. Here's an animated graph to illustrate the general case. All you to need to play with are the relative parameters. There are three plots: source 1, 2, and superimposed, as well as a particle trajectory for each.