I want better understand this subject. I have a few questions about it? In which cases it is preferable to use matrices of Jones, and in which cases it is preferable to use matrices of Stoces to describe polarized light propagation through the numerous optical elements? What are the restrictions of both these models? Which similar models for same purpose are you know and can recommend? Thank you in advance!
One simple way to decide is to ask yourself if you the system you are modelling has unpolarised light. If so, then the Stokes formulation is easier to use.
The Jones matrix is more intuitive, and a bit easier to follow. One approach that we sometimes use in modelling is to use Stokes vectors as input (because that is what we measure). Convert to Jones vectors and use Jones matrix elements to calculate the changes in polarisation, which is often simpler. Then convert back to our observable (a Stokes vector).
Another consideration. Are you modelling light fields with orbital angular momentum? Then the beam has a complicated spatial phase profile. Now, a position dependent Stokes vector will probably accurately describe what you might measure with a pin hole and a polarimeter, but, the propagation of the light field through an optical system will require an extended Jones matrix description, rather than Stokes matrices.
Other than that, you should probably go with what you are most comfortable with.
Stokes vectors for horizontal and vertical polarization of light:
Linearly polarized (horizontal) : [ 1 1 0 0 ]
Linearly polarized (vertical) : [ 1 -1 0 0 ]
Jones vector for horizontal and vertical polarization of light:
[ 1 0 ] and [ 0 1 ]
If you are familiar with the Jones formalism, you see immediately, that any attempt to write down a Jones vector for unpolarized light, fails.
The Jones formalism applies only to 100% polarized light.
In case the light is partially polarized (like the sunlight scattered by the atmosphere) or unpolarized, only the Stokes formalism gives a complete description of the light's state of polarization.
The answer of Antoine Weis is correct. Parvins answer is not wrong. You can use Stokes Matrices for polarized and unpolarized light, but Jones matrices for polarized light only and they are easier to handle. The second part of Lee's answer is not correct. You can use Jones matrices also for light with radial/azimuthal polarization (angular momentum), but they depend on the azimuthal angle. See Xin et al Optics Letters Vol.39 (7), p.1984 (2014) "Generation of optical vortices by using spiral phase plates..."
Antoine Weis states correctly that Jones formalism applies to only polarized light. But it must be realized that the Stokes parameters are also insufficient to describe completely the Polarization states, if the considerations are not limited to only lowest order correlations, , , and . For example, if one detects light by having a polarizer followed by first a nonlinear crystal which generates second harmonic and then a detector of intensity of this second harmonic, one will be detecting essentially , where v is the analytic signal in the transmission mode of the polarizer, and even light beams other than those which are strictly unpolarized will exhibit the Stokes Parameters Sx = Sy = Sz =0. A simple example is seen when both vx and vy are assumed to have completely random phases but non-random amplitudes.
Polarized and unpolarized states are extremes and are easy to understand and work with, but the general polarization state which is neither polarized nor unpolarized presents difficulties when one does not exclude from consideration higher order correlations..