Fig. 2: Structured light towards multiple DoFs and higher dimensions.

a High-order PS representation of two-DoF 2D vector beams. b SU(2) PS representation of complex ray-wave geometric modes. c The Majorana sphere exploits hidden dimensions to extend complex structured Gaussian modes. Adapted from ref. 18. d Spatial vector beams with spatially dependent polarisation pattern. e Spatio-temporal vortex pulses with transverse OAM at space-time. f Flying electromagnetic toroidal pulses as space-time-polarisation non-separable states