Exciton related nonlinear optical properties of quantum wires with a parabolic confinement

Semiconductor nanostructures, including quantum wells (QWs) and quantum dots (QDs), have been extensively studied owing to their pronounced nonlinear optical characteristics. In contrast, excitonic contributions to the nonlinear optical behavior of quantum well wires (QWWs) have received comparatively limited attention. This dissertation presents a theoretical analysis of excitons confined in QWWs under a parabolic potential, aiming to determine their nonlinear optical susceptibilities. The excitonic Schrödinger equation is formulated in cylindrical coordinates within the effective-mass approximation and solved analytically, both with and without including the Coulomb term as a perturbation. The analytical solutions provide explicit wave functions and energy eigenvalues that serve as the basis for calculating optical response functions. In this study, the linear and third-order nonlinear optical susceptibilities were evaluated using analytical expressions previously derived within the density-matrix formalism, allowing a detailed examination of optical rectification, refractive index changes, and optical absorption —essential for understanding the nonlinear response in these low-dimensional systems. The effects of key physical parameters—such as the confinement frequency of the potential, the strength of the applied static electric field, and the incident optical intensity—are systematically investigated. The results show that variations in these parameters significantly modify both the magnitude and spectral characteristics of the nonlinear optical response. Moreover, the inclusion of the Coulomb interaction markedly enhances excitonic contributions, shifting the resonance peaks and increasing the optical nonlinearity. The results of this study establish a clear theoretical basis for understanding and controlling nonlinear optical effects arising from excitons in parabolically confined quantum wire systems, providing useful guidance for the development of advanced optoelectronic and photonic devices.