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Journal of Huaqiao University

Third-order Nonlinear Susceptibility in a nc-Si/SiO_2 Spherical Quantum Dot

Yang Xiao-ru

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Under the effective mass approximation,the electron state is considered to be confined within a nc-Si/SiO2 spherical quantum dot with infinite barrier,and by using the compact density matrix method,the analytic expression for the resonant third-order susceptibilities was derived.According to numerical simulation,the relation of the third-order susceptibilities with quantum dot dimension,incident photo energy and various relaxation rate was discussed.The result shows that the third-order susceptibilities strongly depends on quantum dot dimensions,incident photon energy and various relaxation rate.The third-order susceptibilities increases with an increase in quantum dot dimension and incident photo energy and a decrease in various relaxation rate.

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Under the effective mass approximation,the electron state is considered to be confined within a nc-Si/SiO2 spherical quantum dot with infinite barrier,and by using the compact density matrix method,the analytic expression for the resonant third-order susceptibilities was derived.According to numerical simulation,the relation of the third-order susceptibilities with quantum dot dimension,incident photo energy and various relaxation rate was discussed.The result shows that the third-order susceptibilities strongly depends on quantum dot dimensions,incident photon energy and various relaxation rate.The third-order susceptibilities increases with an increase in quantum dot dimension and incident photo energy and a decrease in various relaxation rate.
In this study, the linear and third-order nonlinear optical absorption coefficients of intersublevel transitions have been calculated for a spherical CdS/SiO2 quantum dot (QD) with infinite and different finite confining potential by using the density matrix formalism. The electron eigenenergies and the corresponding wavefunctions have been determined by the variational method under the effective mass approximation. We have investigated the effects of the incident optical intensity, QD radius, and confinement potential on the intersublevel optical absorption coefficients. It is found that the size of the dot and depth of the confinement have a great effect on the linear, the nonlinear, and the total absorption coefficients. Also, the total optical absorption saturation intensity is controlled by the strength of the confinement or the incident optical intensity.
In recent years,the subject of optical nonlinearity in semiconductor quantum confined structures such as quantum wires and quantum dots has attracted a considerable attention because of their relevance for studying practical applications and as a probe for the electronic structure of media.It has been shown that the low dimensional quantum systems present very large nonlinear optical susceptibilities .Theoretically,most of the studies on quantum dots are focused on spherical quantum dots for simplicity.The shape of quantum dot depends on growth conditions.In fact,quantum dots are better described as thin disk or cylinder.In the present work third order nonlinear optical susceptibilities in disk shaped quantum dots due to resonant intersubband transition are analyzed by a compact density matrix approach.It has rarely been discussed in literatures.Firstly,we consider an electron moving in a quantum disk whose radius R is very large compared to its thickness d .For simplicity,we assume that the isotropic effective mass approximation is valid within the disk and that the inner potential is null while the outer confining potential is approximately infinite.Using the adiabatic approximation we solve the three dimensional Schrdinger equation and obtain the analytical expressions of wave functions and energy levels in cylindrical coordinates.Secondly,we consider the system is excited by an electromagnetic field with frequency ω. The electromagnetic field is incident with a polarization vector normal to the disk.We treat H′=ezE(t) as a perturbation term.By using the compact density matrix method,we derive a general formula for third order nonlinear optical susceptibilites employing a four level model in quantum disk.Finally,numerical results are illustrated for a typical GaAs quantum disk.We calculate the third order nonlinear optical susceptibilities as a function of the disk thickness.It is shown that the third order nonlinear optical susceptibilities in quantum disk are 10～100 times larger than that in quantum well for various disk thickness.Furthermore,if we choose an optimized thickness of quantum disk,we could obtain a quite large refractive index with a comparatively small absorption coefficient.Therefore,we suggest that the quantum dots would be an excellent system in the field of optical communications and optical switching.
Abstract This paper systematically explores the third-order nonlinear optical properties and modulation mechanisms of a spherical quantum dot system confined by a Mie-type potential. We analytically solve the Schrödinger equation with Nikiforov–Uvarov method based on effective mass approximation to obtain the eigenenergies and wave function of the system. Subsequently, key third-order nonlinear optical parameters, including the third-harmonic generation (THG) coefficient, total optical absorption coefficients, and refractive index changes, are derived via the density matrix formalism. The results indicate that the nonlinear optical responses strongly depend on the geometric dimensions and the microscopic confinement parameters. By adjusting these parameters, effective control over the THG coefficient can be achieved. Furthermore, this study reveals the significant modulation effects of environmental factors. The synergistic influence of quantum dot size, confinement potential, and environmental interactions is systematically analyzed, providing a theoretical basis for designing high-performance nonlinear optical devices based on quantum dots.
Linear and nonlinear optical absorptions in one-dimensional semi-parabolic quantum dot is investigated. The analytical expression of linear and third-order nonlinear optical absorption coefficients are obtained by using compact density-matrix approach and iterative method. Numerical results are presented for an GaAs/AlGaAs quantum dot and the dependence on the quantum confinement of the semi-parabolic quantum dot, the incident optical intensity, and on the relaxation rate are also investigated. The results indicate that the optical absorption coefficients are strongly influenced by the confining frequency, relaxation time, and the incident optical intensity, respectively. However, their influences for the linear optical absorption, third-order nonlinear optical absorption, and the total optical absorption are different. We think our theoretical study may make a great contribution to experimental studies and may open up new opportunities for practical exploitation of the quantum-size effect in optical devices.
The current study looks at how the Kratzer confinement potential affects the linear, third-order nonlinear, and total optical absorption coefficients (ACs) of a single electron in a multilayered spherical quantum dot (MSQD) by using the finite element method within the effective mass approximation. The variation of the transition energy has been investigated for two allowed transitions, 1p-2s and 2s-2p. Furthermore, we investigated the variation of the linear, third-order nonlinear, and total optical absorption coefficients as a function of the incident photon energy for several transitions while accounting for the effect of the Kratzer confinement potential. The findings show that the optical ACs and transition energy are strongly influenced by the Kratzer confinement potential.
We study the modification of the linear, third-order, and fifth-order susceptibilities of a quantum dot that is coupled to a spherical metallic nanoparticle. We calculate the susceptibilities with a density matrix approach and calculate the modified spontaneous emission rate of the quantum dot due to the Purcell effect next to the metallic nanosphere using a boundary element method. We show that the strong variation of the spontaneous decay rates of the quantum dot near the metallic nanosphere can be used for tailoring the linear, third-order, and fifth-order susceptibilities. Specifically, the Purcell modified spontaneous decay rate leads to strong alteration (enhancement or suppression) of the linear and the nonlinear susceptibilities. The specific type of alteration depends on the distance of the quantum dot from the surface of the nanosphere and the direction of the electric dipole moment of the quantum dot. The strong influence of the pure dephasing rate of the quantum dot on the modification of the optical susceptibilities is also analyzed.