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Laser Physics

Kerr nonlinearity and nonlinear absorption coefficient in a four-level M-model cylindrical quantum dot under the phenomenon of electromagnetically induced transparency

Behjat Behroozian, Hassan Randjbar Askari

Published May 16, 2018• 5 citations
Publisher

Abstract

Abstract The Kerr nonlinearity and the nonlinear absorption coefficient in a four-level M-model of a GaAs cylindrical quantum dot (QD) with parabolic potential under electromagnetically induced transparency are investigated. By solving the density matrix equations in the steady-state, the third order susceptibility is obtained. Then, by using the real and imaginary parts of third order susceptibility, the Kerr nonlinearity and the nonlinear absorption coefficient, respectively, for this system are computed. The effects of the radius and height of the cylindrical QD are then investigated. In addition, the effects of the control laser fields on the Kerr nonlinearity and the nonlinear absorption coefficient are investigated.

DOI
10.1088/1555-6611/aab388

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Chinese Journal of Luminescence•Jan 1, 2001•1 citation
Abstract The Kerr nonlinearity and the nonlinear absorption coefficient in a four-level M-model of a GaAs cylindrical quantum dot (QD) with parabolic potential under electromagnetically induced transparency are investigated. By solving the density matrix equations in the steady-state, the third order susceptibility is obtained. Then, by using the real and imaginary parts of third order susceptibility, the Kerr nonlinearity and the nonlinear absorption coefficient, respectively, for this system are computed. The effects of the radius and height of the cylindrical QD are then investigated. In addition, the effects of the control laser fields on the Kerr nonlinearity and the nonlinear absorption coefficient are investigated.
In this paper, effect of the control and probe lasers polarization on generation of the double windows of electromagnetically induced transparency (EIT) and also on absorption coefficient in a W-type GaAs cylindrical quantum dot (QD) with parabolic potential are investigated. The Schrodinger equation is solved in method of effective mass. Dependence of EIT and absorption coefficient on radius and height of cylindrical QD, in the different polarization of the probe and control lasers are also investigated.
Abstract In this paper, linear and 3rd-order nonlinear group velocities of the probe laser field are investigated in a tripod-type four-level cylindrical quantum dot (TTFLCQD) with parabolic potential in electromagnetically induced transparency. The nonlinear refractive index for this system is calculated by obtaining the real part of the 1st and 3rd-order susceptibilities. Afterward, linear and 3rd-order nonlinear group velocities are found. The control lasers at z-polarization are applied to the system in order to investigate the linear and 3rd-order nonlinear group velocities and the results are discussed. The linear and 3rd-order nonlinear group velocities are compared at z-polarization. Furthermore, the effects of parameters of TTFLCQD and control lasers on linear and 3rd-order nonlinear group velocities are explored. Finally, 3rd-order nonlinear group velocity for z- and x-polarization is compared.
The effects of quantum dot (QD) radius, incident light intensity, temperature and other factors on the optical absorption coefficients (OACs) of cylindrical QDs are investigated numerically for typical GaAs/Ga[Formula: see text]Al[Formula: see text]As. We theoretically studied the cylindrical QDs with like-inversely quadratic Hellmann potential and parabolic potential. The expressions for the energy levels and wave functions were obtained by the Nikiforov–Uvarov method, and then the expressions for the OACs were derived by using the density matrix theory and the iterative method. Finally, the results show that the structural and external parameters affect the sensitivity of the optical absorption properties by influencing the matrix elements and energy levels, and the quantum confinement effects affect their applicable frequencies, which makes the QD system easier to tune.
We have introduced a Y-configuration model from the double-quantum-dot (QD) system to study third-order Kerr nonlinearity based on the density-matrix method. Inhomogeneity in QDs has been included in the calculations of the real (Kerr) and imaginary (absorption) parts of the density matrix, which has not been covered in the earlier Kerr calculations. Our system exhibits high controllability with a single parameter. Giant Kerr dispersion, propagation without distortion, wide electromagnetic-induced transparency, and switching between subluminal to superluminal propagation are obtained by tuning its fields. Controlling and cycling fields can also control the system in addition to the pump field.
We introduce a Y-configuration model for a double quantum dot (QD) system, which is modeled for Kerr nonlinearity using the density matrix theory. Inhomogeneity in QDs is included in the calculations of the real part (Kerr) and the imaginary part (absorption) of the density matrix, which has not been covered before in Kerr calculations. Five configurations are studied: Y, ladder, Λ, staircase, and weak probe. Frequency detunings, controlling fields, and phases are used to study the structures. Our system shows high controllability as well as a giant Kerr dispersion, propagation without distortion, wide electromagnetic induced transparency, and switching between subluminal to superluminal propagation by tuning its fields.
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.