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Communications in Theoretical Physics

Electron-related nonlinear optical properties of cylindrical quantum dot with the Rosen–Morse axial potential

Fatih Ungan, Mustafa Kemal Bahar, Suvajit Pal, Miguel Eduardo Mora-Ramos

Published Jun 24, 2020• 18 citations
Publisher

Abstract

Abstract We present a theoretical study on the effects of intense laser field (ILF) and static electric field on the linear and nonlinear optical properties of a cylindrical quantum dot with Rosen–Morse axial potential under the framework of effective mass and parabolic band approximations. This study also takes into account the effects of the structure parameters ( η , V 1 , and R ). The analytical expressions of the linear, third-order nonlinear and total optical absorption coefficients (TOACs) and the relative refractive index changes (RRICs) are obtained by using the compact-density-matrix approach. The results of numerical calculations show that the resonant peak position of the TOACs and RRICs shifts towards lower energies and the magnitude of the peak increases with the effect of the static electric field and ILF. In addition, it is observed that while the resonant energies of the TOACs and RRICs of system shift towards the higher (lower) energies with the enhancement of η , V 1 , they decrease with the augmentation of R . Thus, the findings of this study show that the optical properties of the structure can be adjusted by changing the magnitude of structure parameters and applied external fields.

DOI
10.1088/1572-9494/ab8a1d

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In this present study, we have theoretically investigated the effect of applied external electric field and non-resonant intense laser field, as well as the adjustable physical parameters (A, M, and η) of the system, on the linear and nonlinear of GaAs/GaAlAs cylindrical quantum dot. The confinement potential of the quantum dot is composed of the axial potential with a Razavy-type quantum well in the z-direction, and the cylindrical-type potential in the radial direction. To achieve this goal, the wave functions, and the corresponding eigenvalues of the electron are investigated by resolving the time-independent Schrödinger equation using the diagonalisation technique in terms of the effective mass approximation. The linear and nonlinear optical properties’ expressions have been calculated with the help of the compact density matrix method. Our numerical results show that by changing the A, M, and η parameters, we can see a blueshift or redshift in the total optical absorption coefficients (TOACs) and relative refractive index changes (RRICs). Additionally, they are redshifted, and their extrema increase as the radius increases. The increase in electric field or laser field intensities generates a strong displacement of the resonant peak position towards the higher energies, diminishes the TOACs magnitude, and shrinks RRICs extrema. The model potential used in the computation is important, and the study of it will be practical in the development and research of nanostructures systems.
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In this paper, we have studied optical properties of spherical quantum dots by using Rosen-Morse potential. In this regard, we have first solved the Schrodinger equation and obtained energy levels and wave functions by applying Nikiforov-Uvarov (NU) method. Then, by using density matrix method, we have applied analytical expressions for the linear and third-order nonlinear absorption coefficient and refractive index changes. The results show that the total refractive index changes and the absorption coefficients increase and shift towards higher by enhancing height potential.
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Abstract In this present study, the effects of electric, magnetic, and non-resonant intense laser field (ILF) on the linear, third-order nonlinear, and total optical absorption coefficients (TOACs) and relative refractive index changes (RRICs) of GaAs quantum well, having Hulthen confinement potential, were theoretically investigated. In addition, the dependence of the nonlinear optical properties in the structure on the optical intensity of incident photon and the inverse relaxation time was also calculated. To do this research, firstly the energy eigenvalues and eigenfunctions of the structure were calculated by using the effective mass and envelope function approaches. By using these calculated subband energy levels and wave functions belonging to these levels, the nonlinear optical properties of the system were obtained via the iterative method, within the compact density matrix approach framework. The obtained numerical results show that the optical properties of the considered system depend on the externally applied fields. With the applied external electric and magnetic field, the peak positions of TOACs and RRICs shift to higher energies, and the peak magnitudes increase. The high-frequency ILF applied to the structure shifts the peak positions of TOACs and RRICs initially towards higher energies and then towards lower energies and their peak sizes increase. These results show that the optical properties of the system can be adjusted purposively by changing the magnitude of applied external fields.
In this paper, we have researched the electronic and optical properties of cylindrical quantum dot structures by selecting four different hyperbolic-type potentials in the axial direction under an axially-applied electric field. We have considered a position-dependent effective mass model in which both the smooth variation of the effective mass in the axial direction adjusted to the way the confining potentials change and its abrupt change in the radial direction have been considered in solving the eigenvalue differential equation. The calculations of the eigenvalue equation have been implemented considering both the Dirichlet conditions (zero flux) and the open boundary conditions (non-zero flux) in the planes perpendicular to the direction of the applied electric field, which guarantees the validity of the results presented in this study for quasi-steady states with extremely high lifetimes. We have used the diagonalization method combined with the finite element method to find the eigenvalues and eigenfunction of the confined electron in the cylindrical quantum dots. The numerical strategies that have been used for the solution of the differential equations allowed us to overcome the multiple problems that the boundary conditions present in the region of intersection of the flat and cylindrical faces that form the boundary of the heterostructure. To calculate the linear and third-order nonlinear optical absorption coefficients and relative changes in the refractive index, a two-level approach in the density matrix expansion is used. Our results show that the electronic and, therefore, optical properties of the structures focused on can be adjusted to obtain a suitable response for specific studies or goals by changing structural parameters such as the widths and depths of the potentials in the axial direction, as well as the electric field intensity.