The second, third harmonic generations and nonlinear optical rectification of the Mathieu quantum dot with the external electric, magnetic and laser field

In this study, the nonlinear optical properties of the In ������Ga1-������As/GaAs Mathieu quantum dot (MQD) are investigated for the first time, focusing on the nonlinear optical rectification (NOR), second harmonic generation (SHG), and third harmonic generation (THG). The effects of external fields such as the electric field, magnetic field, and laser radiation field on the nonlinear optical properties of MQD are examined, along with structural parameters such as quantum dot depth and width determined by the indium concentration. The motivation of the study is to explain the NOR, SHG, and THG characteristics of MQD in response to changes in external fields and structural factors. To investigate the effects of the laser field, the time-dependent part of the laser field is transferred to the potential energy term of the wave equation using the Kramers-Henneberger (KH) and dipole approximations, creating a laser-dressed potential. Then, the effective potential wave equation is solved using the tridiagonal matrix method. The effects of external fields and structural parameters of MQD on the NOR, SHG, and THG coefficients are discussed in detail. The optimality of the structure for device design and applications considering MQD is revealed, and alternative parameter analysis is conducted for this optimality.