Effect of rainbow gravity, PDM, and external magnetic field on optical properties and energy spectra of GaAs quantum dot

The Klein–Gordon equation in cosmic strings within RG spacetime under the influence of an external magnetic field and Coulomb potential for position-dependent mass (PDM) particles is investigated using the Nikivorof-Uvarov (NU) method. Energy levels and wave functions are obtained from the solution of the Klein–Gordon system with PDM particles. We apply three rainbow functions to calculate the energy and optical properties of refractive index coefficient (RIC) and absorption coefficient (AC) for GaAs quantum dot (QD). Our results show that the linear, third-order nonlinear, and total RIC and AC increase and shift toward higher energies as the magnetic field increases for all three pairs of rainbow functions. Similarly, the linear, third-order nonlinear, and total RIC and AC increase and shift toward lower energies as the parameters of the rainbow function and PDM increase for all three pairs of rainbow functions. Furthermore, the total RIC and AC decrease as the optical intensity increases for all three pairs of rainbow functions. The values of linear, third-order nonlinear, total RIC, and AC for both positive and negative energies are symmetric for rainbow function 1 compared to the other rainbow functions. This is due to the influence of the energy value of GaAs QD rainbow function 1, both positive and negative energies are symmetrical compared to other rainbow functions.