Linear and third-order nonlinear optical properties of Germanene nanotubes

This study presents a comprehensive computational investigation of linear and nonlinear optical properties, including third harmonic generation, intensity-dependent refractive index, and DC Kerr effect, of zigzag Germanene nanotubes (GeNTs) with different radii. Calculations were performed using the tight-binding model, beyond the Dirac cone approximation. The linear optical susceptibility spectra reveal a distinct, radius- independent peak in the ultraviolet region, originating from dipole-allowed transitions across the entire Brillouin zone. Remarkably, the nonlinear optical response exhibits multiple resonant peaks below the band gap in the infrared regime, arising from one-, two-, and three-photon processes between valence and conduction states. The third-order nonlinear susceptibility demonstrates a strong dependence on the nanotube radius, with a red- shift in peak positions and an enhancement in peak intensities for larger radii. Variations in intensity and peak position are attributed to the distinct electronic structures of the GeNTs. These findings provide valuable insights into the design and optimization of GeNT-based nonlinear optical devices, enabling potential applications in frequency conversion, optical switching, and advanced photonic technologies.