Anisotropic Second-Harmonic Ince-Gaussian Beam Generation Using NbOBr₂ Holograms

Ince-Gaussian (IG) modes are a complete and orthogonal set of solutions to the paraxial wave equation in elliptic coordinates representing a continuous transition between Hermite-Gaussian modes and Laguerre-Gaussian modes. Chip-scale platforms to generate IG beams have great significance for various applications, including optical trapping and micromanipulation of particles, optical communication, and quantum optics. On the other hand, materials with high optical anisotropy are crucial for building polarization-sensitive optical devices. In this context, niobium oxide dihalides are a new class of ferroelectric materials exhibiting strong, tailorable, and highly anisotropic second-harmonic generation responses. Here, we report the generation of highly anisotropic second-harmonic IG beams using binary grating holograms patterned on ultrathin niobium oxide dibromide (NbOBr₂) flakes. Both even and odd IG beams with different mode indices are generated by encoding the phase profiles of the beams into the holograms. According to the polarization-dependent second-harmonic generation responses, the relative magnitudes of the second-order nonlinear susceptibility elements of NbOBr₂ crystal are extracted. The results presented here provide new directions for generating complex optical beams with potential applications in classical and quantum photonic integrated devices.