Visualization of electromagnetic-wave polarization evolution using the Poincaré sphere.

For the first time to the best of our knowledge, we derive expressions for coordinates of the trajectory on the Poincaré sphere that represent polarization evolution in an arbitrary beam of completely polarized light. Our work substantially extends the mapping function of the Poincaré sphere, and opens up new possibilities for its use in optics. In particular, the obtained expressions allow one to visualize the results of the finite-difference time-domain modeling of light propagation through birefringent crystals, including simulations of polarization rotation experienced by ultrashort pulses in nonlinear media.