Linear and Nonlinear Optical Properties of Spherical Quantum Dots:Effects of Hydrogenic Impurity and Conduction Band Non-Parabolicity

Simultaneous effects of an on-center hydrogenic impurity and band edge non-parabolicity on intersubband optical absorption coefficients and refractive index changes of a typical GaAs/Al x Ga 1 x As spherical quantum dot are theoretically investigated,using the Luttinger-Kohn effective mass equation.So,electronic structure and optical properties of the system are studied by means of the matrix diagonalization technique and compact density matrix approach,respectively.Finally,effects of an impurity,band edge non-parabolicity,incident light intensity and the dot size on the linear,the third-order nonlinear and the total optical absorption coefficients and refractive index changes are investigated.Our results indicate that,the magnitudes of these optical quantities increase and their peaks shift to higher energies as the influences of the impurity and the band edge non-parabolicity are considered.Moreover,incident light intensity and the dot size have considerable effects on the optical absorption coefficients and refractive index changes.     

Electronic structure and nonlinear optical properties of a two-dimensional hexagonal quantum dot

In this work electronic structure, the linear and the third-order nonlinear refractive index changes as well as optical absorption coefficients of a two-dimensional hexagonal quantum dot are investigated. Energy eigenvalues and eigenfunctions of the system are calculated by the matrix diagonalization technique, and optical properties are also obtained using the compact density matrix approach. As our results indicate, both the dot size and the confinement potential have a great influence on the intersubband energy intervals, the transition probability and consequently, the linear and the third-order nonlinear refractive index changes and optical absorption coefficients.     

Nonlinear optical properties of an off-center donor in a quantum dot under applied magnetic field

The nonlinear optical properties of an off-center hydrogenic donor in a two-dimensional quantum dot under applied magnetic field are investigated in detail by using the matrix diagonalization method. Based on the computed energies and wave functions, the linear, third-order and total optical absorption coefficients as well as the refractive index changes have been examined between the ground state (L=0) and the first excited state (L=1). The results show that the ion position, the applied magnetic field, the confinement frequency, and the incident optical intensity have an important influence on the nonlinear optical properties of off-center donors.     

Intersubband optical absorption coefficients and refractive index changes in modulation-doped asymmetric double quantum well

The linear and the third-order nonlinear optical absorption coefficients and refractive index changes in a modulation-doped asymmetric double quantum well are studied theoretically. The electron energy levels and the envelope wave functions in this structure are calculated by the Schrödinger and Poisson equations self-consistently in the effective mass approximation. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. In this regard, the linear, nonlinear and total intersubband absorption coefficients and refractive index changes are investigated as a function of right-well width (Lw₂) of asymmetric double quantum well. Our results show that the total absorption coefficients and refractive index changes shift toward higher energies as the right-well width decreases. In addition, the total optical absorption coefficients and refractive index changes is strongly dependent on the incident optical intensity.     

Exciton optical absorption coefficients and refractive index changes in a strained InAs/GaAs quantum wire: The effect of the magnetic field

Magnetic field induced exciton binding energy is investigated in a strained InAs/GaAs quantum wire within the framework of single band effective mass approximation. The strain contribution to the potential is determined through deformation potentials. The interband emission energy of strained InAs/GaAs wire is investigated in the influence of magnetic field with the various structural parameters. Magnetic field induced photoionization cross section of the exciton is studied. The total optical absorption and the refractive index changes as a function of normalized photon energy between the ground and the first excited state in the presence of magnetic field are analyzed. The optical absorption coefficients and the refractive index changes strongly depend on the incident optical intensity and the magnetic field. The occurred blueshift of the resonant peak due to the magnetic field will give the information about the variation of two energy levels in the quantum well wire. The optical absorption coefficients and the refractive index changes are strongly dependent on the incident optical intensity and the magnetic field.     

Study of optical properties in a cubic quantum dot

In this paper, the effect of hydrostatic pressure on both the intersubband optical absorption coefficients and the refractive index changes is studied for typical GaAs/Al _x  Ga_1?x As cubic quantum dot. We use analytical expressions for the linear and third-order nonlinear intersubband absorption coefficients and refractive index changes obtained by the compact-density matrix formalism. The linear, third-order nonlinear, and total intersubband absorption coefficients and refractive index changes are calculated at different pressures as a function of the photon energy with known values of box length (L), the incident optical intensity (I), and Al concentration (x). According to the results obtained from the present work, we have found that the pressure plays an important role in the intersubband optical absorption coefficient and refractive index changes in a cubic quantum dot.     

Optical properties of an off-center hydrogenic impurity in a spherical quantum dot with Gaussian potential

Optical absorption coefficients and refractive index changes associated with intersubband transition of an off-center hydrogenic impurity in a spherical quantum dot (QD) with Gaussian confinement potential are theoretically investigated. Our results show that the optical absorption coefficients in a spherical QD are 2–3 orders of magnitude higher than those in quantum wells and are 2–3 orders smaller than those in a disk-like QD. It is found that the optical absorptions and the optical refractive index are strongly affected not only by the confinement barrier height, dot radius but also by the position of the impurity.     

Nonlinear optical properties of a three-electron quantum dot with account of the Rashba spin–orbit interaction

In this study, a detailed investigation of the nonlinear optical properties such as optical absorption and refractive index change associated with intersubband transitions in a three-electron quantum dot in two dimensions in the presence of the Rashba spin–orbit interaction has been carried out. We present the exact wave functions and energy levels of the system. Numerical results on typical GaAs/AlGaAs materials show that the decrease of the quantum dot radius blueshifts and amplifies the absorption coefficients as well as the refractive index changes, as expected. Additionally, an increase of the optical intensity and relaxation time considerably changes the absorption coefficients and the refractive index changes.     

Laterally coupled circular quantum dots under applied electric field

The optical response of a system of two laterally coupled quantum dots with circular cross-sectional shape is investigated within the effective mass approximation, taking into account the effects of the change in the geometrical configuration, the application of an external static electric field, and the presence of a donor impurity center. The first-order dielectric susceptibility is calculated in order to derive the corresponding light absorption and relative refractive index coefficients. The possibility of tuning these optical properties by means of changes in the quantum dot symmetry and the electric field intensity is particularly discussed.     

Simultaneous effects of spin-orbit interaction and external electric field on the linear and nonlinear optical properties of a cubic quantum dot

In this article simultaneous effects of external electric field and spin-orbit interaction on the linear and the nonlinear optical properties of a cubic quantum dot are studied. Based on the non- degenerate perturbation method, energy eigenvalues and eigenfunctions of the system under the influence of spin-orbit interaction are calculated. Furthermore, the linear and the nonlinear optical absorption coefficients and refractive index changes are obtained using the compact density matrix approach and iterative method. Our results show that, due to the spin-orbit interaction, resonant peak values of the optical absorption coefficients and refractive index changes decrease and occur at lower values of the incident photon energy. The variation of these optical parameters depend on the spin-orbit interaction strength, dot dimensions and external electric field.     

Effect of magnetic fields on the linear and nonlinear intersubband optical absorption coefficients and refractive index changes in square and graded quantum wells

In this study, both the intersubband optical absorption coefficients and the refractive index changes as dependent on the magnetic field are calculated in square and graded quantum wells. Our results show that the position and the magnitude of the linear and total absorption coefficients and refractive index changes depend on the magnetic field strength and the shape of potential. The incident optical intensity has a great effect on the total absorption and refractive index changes.     

Size effects of an exciton–acceptor complex in quantum dots

In this study, a detailed investigation of the size effects of an exciton–acceptor complex in a disc-like quantum dot has been carried out by using the matrix diagonalization method and the compact density-matrix approach. We calculate the binding energy and the oscillator strength of intersubband quantum transition from the ground state into the first excited state as a function of the dot radius. Based on the computed energies and wave functions, the linear, third-order and total optical absorption coefficients as well as the refractive index have been examined between the ground and the first excited states. We find that the all absorption spectra and refractive index changes are strongly affected by the quantum dot size. However, for two cases of a smaller dot and a larger dot, the results of quantum size effects on the optical absorptions are opposite.     

Intersubband optical absorption coefficient changes and refractive index changes in a two-dimensional quantum pseudodot system

The optical absorption coefficient changes and refractive index changes associated with intersubband transitions in a two-dimensional quantum pseudodot system under the influence of a uniform magnetic field are theoretically investigated. In this regard, the electronic structure of the pseudodot system is studied using the one-band effective mass theory, and by means of the compact density matrix approach linear and nonlinear optical absorption coefficient and refractive index changes are calculated. The effects of an external magnetic field and the geometrical size of the pseudodot system on the optical absorption coefficient and refractive index changes are investigated. It is found that the absorption coefficient and refractive index changes are strongly affected not only by an external magnetic field but also by the geometrical size of the pseudodot system.     

Linear and nonlinear optical properties in a disk-shaped quantum dot with a parabolic potential plus a hyperbolic potential in a static magnetic field

Linear and nonlinear optical properties in a disk-shaped quantum dot (DSQD) with a parabolic potential plus a hyperbolic potential in a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron are obtained by three kinds of approximation methods. It is found that optical absorption coefficients and refractive index changes are not only by the characteristic parameters of the hyperbolic potential and the confinement frequency, but also by the magnetic field.     

Linear and nonlinear intersubband optical absorption coefficients and refractive index changes in a quantum box with finite confining potential

In this work, both the intersubband optical absorption coefficients and the refractive index changes are calculated exactly in a quantum box. Analytical expressions for the linear and nonlinear intersubband absorption coefficients and refractive index changes are obtained by using the compact-density matrix approach. Numerical results are presented for typical GaAs/Al_xGa_1−x As quantum box system. The linear, third-order nonlinear and total absorption and refractive index changes are investigated as a function of the incident optical intensity and structure parameters such as box-edge length and stoichiometric ratio. Our results show that both the incident optical intensity and the structure parameters have a great effect on the total absorption and refractive index changes.     

Optical absorptions of a biexciton quantum dot

A investigation of the linear and nonlinear optical properties for intersubband electronic transitions associated with a biexciton in a quantum dot has been performed by using the method of few-body physics. The optical absorption coefficients and the refractive index changes have been examined based on the computed energies and wave functions. It is over two orders of magnitude higher than that obtained in an exciton quantum dot. The results show that the optical absorption saturation intensity can be controlled by the confinement potential frequency and the relaxation time.     

Polaron effect on the optical absorption and refractive index of an exciton in quantum dots

We have studied the optical absorption of an exciton and its refractive index in a disc-like quantum dot, taking into account of the confined longitudinal optical (LO) phonons. Calculations are performed in the framework of the effective-mass approximation using the compact density-matrix approach. With typical semiconducting GaAs materials, the linear, third-order nonlinear, total optical absorption coefficients and refractive index changes with and without considering the exciton-phonon interaction have been examined. By comparing the polaron effect of the two-electron quantum dot, it is found that the corrections due to the LO phonons on the optical absorption and refractive index are very important and cannot be ignored.     

Pressure induced optical absorption and refractive index changes of a shallow hydrogenic impurity in a quantum wire

Pressure induced binding energy of a hydrogenic impurity in an InAs/GaAs quantum wire is investigated. Calculations are performed using Bessel functions as an orthonormal basis within a single band effective mass approximation using variational method. Photoionization cross-section of the hydrogenic impurity in the influence of pressure is studied. The total optical absorption and the refractive index changes as a function of normalized photon energy between the ground and the first excited state in the presence of pressure are analyzed. The optical absorption coefficients and the refractive index changes strongly depend on the incident optical intensity and pressure. The occurred blue shift of the resonant peak due to the pressure gives the information about the variation of two energy levels in the quantum well wire. The optical absorption coefficients and the refractive index changes are strongly dependent on the incident optical intensity and the pressure.     

Nonlinear optical properties of a three-dimensional anisotropic quantum dot

The linear and nonlinear optical properties in a three-dimensional anisotropic quantum dot subjected to a uniform magnetic field directed with respect to the $z$-axis have been investigated within the compact-density matrix formalism and the iterative method. The dependence of the linear and nonlinear optical properties on the characteristic frequency of the parabolic potential, on the magnetic field, and on the incident optical intensity is studied in detail. Moreover, taking into account the position-dependent effective mass, the dependence of the linear and nonlinear optical properties on the dot radius is investigated. The results show that the optical absorption coefficients (ACs) and refractive index (RI) changes of the anisotropic quantum dot (QD) are strongly affected by these factors, and the position effect also plays an important role in the optical ACs and RI changes of the anisotropic QD.     

Simultaneous Effects of External Electric Field and Conduction Band Nonparabolicity on Optical Properties of a GaAs Quantum Dot Embedded at the Center of a GaAlAs Nano-Wire

An investigation of the optical properties of a GaAs spherical quantum dot which is located at the center of a Ga1-xAlx As cylindrical nano-wire has been performed in the presence of an external electric field. The band nonparabolieity effect is also considered using the energy dependent effective mass approximation. The energy eigenvalues and corresponding wave functions are calculated by finite difference approximation and the reliability of calculated wave functions is checked by computing orthogonality. Using computed energy eigenvalues and wave functions, the linear, third-order nonlinear and total optical absorption coefficients and refractive index changes are examined in detail. It is found that （i） Presence of electric field causes both blue and red shifts in absorption spectrum; （ii） The absorption coefficients shift toward lower energies by taking into account the conduction band nonparabolicity; （iii） For large values of electric field the effect of conduction band nonparabolieity is less dominant and parabolic band is estimated correctly; （iv） In the presence of electric field and conduction band nonparabolicity the nonlinear term of absorption coefficient rapidly increases by increasing incident optical intensity. In other words, the saturation in optical spectrum occurs at lower incident optical intensities.