Fig. 3
Gradient nonlinear Pancharatnam-Berry LC devices. a Scheme of linear and nonlinear optical modulation based on the fabricated FNLC device with a splay angle of \({\rm{\pi }}\). The upper-left inset schematically depicts the alignment configuration of the system, while the lower-left inset illustrates the nonlinear Raman-Nath diffraction mechanism, which facilitates transverse phase matching through periodic modulation of nonlinear susceptibility. In the right panel, the red and white arrows correspond to the propagations of SHW and FW, respectively. b Polarizing optical microscope images of defect-free gradient polarity patterns of ion-doped FNLCs during the thermal annealing process. Iso: isotropic phase; N: nematic phase; Nx: mesophase; Scale bar: 250 μm. c–e Polarizing optical microscope characterizations of the polar LC arrangement in the device. These images include (c) an enlarged texture, (d) an image under the cross-polarizing optical microscope with a full wave plate insertion, e two images of rotating the analyzer in opposite directions with the included angles of 75° and 105° between the polarizer and analyzer. f Polarizing optical microscope textures under an in-plane triangular-wave electric field (1 Hz, AC voltage 0.06 V·μm-1). The red and blue unidirectional arrows indicate the direction of the electric field. Scale bar: 100 μm. g, h Extracted intensity profiles from the textures in (e) and (f). Red and blue sets of arrows in (h) denote the corresponding orientations of polar LC directors
