Abstract
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.
Highlights
Axisymmetrically-polarized modes, such as a radially-polarized (RP) mode and an azimuthally-polarized (AP) mode, have attracted considerable attention for application to laser processing [1,2,3,4,5,6], spectroscopy of a ring shaped material [7], super-resolution microscopy [8], particle acceleration [9], laser trapping [10], and telecommunications [11, 12]
To analyze the nonlinear propagation of |s = +1|l = −1 optical vortex (OV) pulses in a uniaxial crystal, we from the linear values derive the changes of S1E and Vspace
The self-phase modulation (SPM) and XPM effects can be analyzed through ΔVspace the phase modulation effects involving beam-divergence change modify beam overlap of these modes
Summary
Axisymmetrically-polarized modes, such as a radially-polarized (RP) mode and an azimuthally-polarized (AP) mode, have attracted considerable attention for application to laser processing [1,2,3,4,5,6], spectroscopy of a ring shaped material [7], super-resolution microscopy [8], particle acceleration [9], laser trapping [10], and telecommunications [11, 12] They have annular-shaped intensity profile owing to the polarization singularity in the beam center.
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