Nonlinear optical behavior of confined electrons under torsion and magnetic fields

In this work, we investigate the influence of torsion, Aharonov-Bohm flux, and external magnetic fields on the linear and nonlinear optical properties of a confined quantum system. The confinement potential is not assumed a priori, but emerges as a radial effective potential, analogous to a quantum dot, geometrically induced by the torsion of the material. Starting from an effective radial equation derived in a nontrivial geometric background, we analytically solve for the energy spectrum and wave functions. These solutions are then employed to evaluate the optical absorption coefficients and refractive index changes, including both linear and third-order nonlinear contributions. The formalism incorporates the electric dipole approximation and accounts for intensity-dependent effects such as saturation and spectral shifts. Our results reveal that torsion and topological parameters significantly modify the optical response, leading to tunable resonances and nontrivial dispersive behavior. This work highlights the potential of geometric and topological engineering in low-dimensional systems to control and enhance nonlinear optical phenomena.