Simulation of the evolution of laser beams in impurity carbon nanotubes using the Madelung approach

The relevance of modeling the interaction of electromagnetic waves with various materials exhibiting nonlinear properties is increasing every year. In this work, we studied the dynamics of laser beams propagating in a medium of single-walled carbon nanotubes with impurities, placed in a dielectric. By multilevel impurity, we mean an impurity whose energy levels are separated from the conduction band and valence band in carbon nanotubes and lie inside the band gap of the dielectric medium. The novelty of this work lies in the development of a model for the evolution of electromagnetic radiation in the infrared range is constructed using the Madelung transform for the nonlinear Schrödinger equation, the numerical implementation of which is carried out using the smoothed-particle hydrodynamics. The influence of impurity parameters on the laser beam propagation in a given medium, namely, the energy of electron transitions from impurity levels to the first and second sublattices of nanotubes, is analyzed.