Reconfigurable nonlinear Pancharatnam-Berry diffractive optics with photopatterned ferroelectric nematics.

Planar optical elements incorporating space-varying Pancharatnam-Berry phase have revolutionized the manipulation of light fields by enabling continuous control over amplitude, phase, and polarization. While previous research focusing on linear functionalities using apolar liquid crystals (LCs) has attracted much attention, extending this concept to the nonlinear regime offers unprecedented opportunities for advanced optical processing. Here, we demonstrate the reconfigurable nonlinear Pancharatnam-Berry LC diffractive optics in photopatterned ion-doped ferroelectric nematics. By customizing the spatial phase distribution of efficient second-harmonic excitation, we accomplish programmable beam steering of various optical states towards predefined diffraction directions. Experimental results reveal continuous evolution of diffraction orders, intensity distributions, and polarization states under electrically varying splay conditions, consistent with our theoretical predictions. This work opens new avenues for designing reconfigurable nonlinear beam shaping and steering devices with potential applications in advanced optical and quantum information processing.