Composite stokes singularities in coherently and incoherently superimposed vector optical fields

The composite Stokes singularities formed in the coherent and incoherent superposition of two vector monochromatic coherent optical fields are studied and compared analytically and numerically. It is shown that the dynamic behavior of composite Stokes singularities depends on the superposition scheme (coherent or incoherent superposition), initial spatial distributions of the two superimposed fields, and propagation distance, and for the coherent superposition additionally depends on the relative phase of the two fields. There exist S₁₂ (C-points), S₃₁, S₂₃ composite singularities, and L-lines, in particular, V-points and C-lines at the transverse plane. Generally, both V-points and C-lines are unstable. For the coherent superposition the degree of polarization P=1, whereas for the incoherent superposition P may be less than 1 and is variable upon propagation. The results are illustrated analytically and numerically.