Fig. 2

Nonlinear diffraction simulations. a Schematic of the orientations of polar LC directors in periodic splay bands. The splay angle illustrates the variation of the director vectors within a single period, which is defined as the difference between the minimum and maximum orientational angles within one period of the polar LC grating, i.e., the splay angle \(\theta ={\alpha }_{m}-{\alpha }_{1}\). b, c Simulated nonlinearity phases and diffractions of SH signals for FW with horizontal polarization, vertical polarization, LHCP, and RHCP incidences, respectively. The nonlinearity phase describes the Pancharatnam-Berry phase generated from LCs with a specific director oriented at \(\alpha\). The blue arrows located at the bottom of b represent the polar LC directors corresponding to different α angles and various nonlinearity phases. The diffraction patterns in (c) map the diffractions of SH signals under different conditions, including different polar LC gratings with distinct splay angles and different incident polarizations