Geometry-controlled Third Harmonic Generation in spherical quantum dot heterostructures in the presence of a magnetic field

Abstract

The paper describes the theoretical study of the Third Harmonic Generation (THG) in multilayered spherical quantum dots (MSQDs) subjected to an external magnetic field, emphasizing the role of structural geometry in this response. The intricate potential profiles and quantum confinement of these heterostructures are modeled by solving the time-independent Schrödinger Equation (SE) within the effective mass approximation via the Finite Element Method (FEM). This numerical technique accurately charts the electronic states and their wavefunctions as the core, shell, and well dimensions vary. By using the compact density matrix formalism, we calculate the third harmonic generation coefficient from the intersubband transitions among the confined electronic states. The results indicate that the nonlinear optical response varies significantly with the geometric parameters of the MSQDs as well as the magnetic field strength. Unlike previous studies that mainly investigated isolated effects of external fields or simplified confinement models, the present work systematically reveals the coupled influence of magnetic confinement and multilayer structural geometry on the THG response using the finite element method, providing a comprehensive understanding of geometry-dependent nonlinear optical behavior in realistic GaAs/AlGaAs heterostructures. Most importantly, varying the geometric parameters not only causes considerable shifts in the resonance peaks but also drastically changes the overall third harmonic generation magnitude. Specifically, increasing the core radius leads to a blue shift and a reduction in the magnitude of the THG peaks, whereas increasing the barrier and well widths results in red shifts and enhanced THG peak intensity. Furthermore, our results show that the applied magnetic field causes a blue shift in the THG peaks, where the shift rate depends on the geometric size of the MSQD, demonstrating a pronounced interplay between magnetic and quantum confinement. These results demonstrate that geometry engineering, combined with magnetic-field modulation, provides an efficient strategy for simultaneously controlling the resonance energy and enhancing the THG response. Therefore, the proposed multilayer quantum-dot architecture offers a promising platform for the development of highly tunable nonlinear optoelectronic devices, including frequency converters, optical switches, and integrated photonic components.