Quantitative analysis on the optical kerr impact and third harmonic generation in beltrami-shaped curved graphene

We present a comprehensive analysis of the optical attributes of graphene sheets with charge carriers residing on a curved substrate. In particular, we focus on the fascinating case of Beltrami geometry and provide an explicit parametrization for this curved two-dimensional surface. By employing the massless Dirac description that is characteristic of graphene, we investigate the impact of the curved geometry on the optical properties within the sample. Our findings reveal that the optical properties of the system are highly sensitive to several key factors, namely the Beltrami radius, surface radius, chemical potential and relaxation time. The numerical findings demonstrate that the optical characteristics of Beltrami-shaped graphene differ significantly from those of regular graphene due to the curved geometry. This distinction opens up exciting possibilities for exploring new optical phenomena and designing graphene-based devices with customized optical properties.