Nonlinear coupling between axisymmetrically-polarized ultrashort optical pulses in a uniaxial crystal.

Nonlinear propagation of focused axisymmetrically-polarized ultrashort optical pulses along the optic axis in a uniaxial crystal is investigated experimentally and theoretically. The energy transfer between an azimuthally-polarized pulse and a radially-polarized pulse is observed. To analyze the nonlinear propagation, a general paraxial equation with a third-order nonlinearity for axisymmetrically-polarized pulses in a uniaxial crystal is derived and the extended Stokes parameters (ESPs) based on cylindrical coordinates are newly-introduced. The simulation results by using this equation, providing the calculated ESPs, well explain our experimental observations: 1) the energy transfer is attributed to the four-wave-mixing effect, reflecting the overlapping between the axisymmetrically polarized modes, 2) the variations of the polarization defined from the ESPs are clarified to be affected by the self- and the cross-phase modulations, which make the effective propagation length long or short.