Control of polarization rotation in nonlinear propagation of fully-structured light

Knowing, and controlling, the spatial polarization distribution of a beam is of importance in applications such as optical tweezing, imaging, material processing and communications. Here we show how the polarization distribution is affected by both linear and nonlinear (self-focussing) propagation. We derive an analytical ex- pression for the polarization rotation of fully-structured light (FSL) beams during linear propagation and show that the observed rotation is due entirely to the difference in Gouy phase between the two eigenmodes comprising the FSL beams, in excellent agreement with numerical simulations. We also explore the effect of cross-phase modulation due to self-focusing (Kerr) nonlinearity and show that polarization rotation can be controlled by changing the eigenmodes of the superposition, and physical parameters such as the beam size, the amount of Kerr nonlinearity and the input power. Finally, we show that by biasing cylindrical vector (CV) beams to have elliptical polarization, we can vary the polarization state from radial through spiral to azimuthal using nonlinear propagation.