Influence of spin–orbit interaction,Zeeman effect and light polarisation on the electronic and optical properties of pseudo-elliptic quantum rings under magnetic field

ABSTRACT

We theoretically investigated the influences of the magnetic field and light polarisation on the electronic and optical properties of a GaAs/GaAlAs pseudo-elliptic quantum ring, modelled by an outer ellipsis and an inner circle, in the presence of the Rashba and Dresselhaus spin–orbit interactions and Zeeman effect. We show that Aharonov-Bohm oscillations of the energy spectrum are not affected by the presence of the Zeeman effect alone but, in the presence of Rashba and Dresselhaus spin–orbit couplings, the periodicity of certain levels becomes hardly definite. The Zeeman effect generally enhances/diminishes the separation levels produced by Rashba/Dresselhaus interactions (SOI) and when both types of SOI are considered, the effect depends on their relative strength. The magnetic field can trigger spin-flip for each type of spin–orbit interaction and Zeeman effect or their combination through anticrossings in the energy spectra. Our results reveal that the absorption spectra are very sensitive to the magnetic field and light polarisation. For all polarisations considered, the magnetic field increment leads to the redshift or blueshift of some particular peaks (an effect of this ring geometry) and a better separation of the peaks. The x-polarised light determines spectra with many small, but separated peaks while the circular polarised light leads to spectra with large peaks of high amplitude.     

Optical non-linearities associated to hydrogenic impurities in InAs/GaAs self-assembled quantum dots under applied electric fields

Abstract

The effects of the hydrogenic impurity on the electron-related non-linear optical processes in a InAs/GaAs dome-shaped quantum dot with a wetting layer under applied electric fields are studied within the density-matrix formalism. The one-electron energy levels and wave functions are calculated using the effective mass approximation and the finite element method. The non-linear optical absorption, relative refractive index change and non-linear optical rectification associated with interlevel transitions are calculated under a strong probe field excitation for both in-plane and z-polarisation of the incident light. According to our results as the electric field increases the absorption and dispersion peaks decrease and exhibit red shift. Hydrogenic impurity located at the origin induces a blue shift in the optical responses. For the optical absorption coefficient the peaks magnitude is enhanced by the impurity presence independent of the electric field strengths, whereas the non-linear optical rectification is larger in the case with impurity only for zero applied electric field.     

The nonlinear optical rectification of an ellipsoidal quantum dot with impurity in the presence of an electric field

We have performed theoretical calculation of second-order nonlinear optical rectification (OR) coefficient in a typical GaAs/AlGaAs QD with ellipsoidal confinement potential in the presence of an impurity and an applied electric field. Using an appropriate coordinate transformation and the perturbation theory, we have investigated the OR coefficient as a function of incident photon energy. Calculation results show that the values of OR coefficient increase with an increase of applied electric field. However, the values decrease with increases in confinement strength and ellipticity constant. Additionally, the presence of a donor impurity shifts the OR coefficient peak positions to higher energies (blueshift), contrary to that of an acceptor impurity.     

Nonlinear optical rectification of a hydrogenic impurity in a disc-like quantum dot

An investigation of the nonlinear optical rectification of a hydrogenic impurity, which is in a two-dimensional disc-like quantum dot (QD) with parabolic confinement potential, has been performed by using the perturbation method in the effective mass approximation. Both the electric field and the confinement effects on the energy are investigated in detail. The results are presented as a function of the incident photon energy for the different values of the confinement strength and the electric field. It is found that the nonlinear optical properties of hydrogenic impurity states in a disc-like QD are strongly affected by the confinement strength and the electric field.     

Nonlinear optical rectification of hydrogenic impurity in a disk-like parabolic quantum dot: The role of applied magnetic field

We report a detailed theoretical study of the effect of combined electric and magnetic field on the nonlinear optical rectification of a hydrogenic impurity, confined in a two dimensional disk-like quantum dot, with parabolic confinement potential. We use the compact density matrix formalism and iterative method to obtain nonlinear optical rectification and absorption coefficients. To find energy levels and wave functions, we employ exact diagonalization method in the effective mass approximation. As main result, we found that the transition energy from ground to first excited state redshifts with increasing the magnetic field while blueshifts for transition from ground to second excited state, moreover, for former transition, nonlinear optical rectification coefficient decreases with increasing magnetic field in contrast to that occurs for latter one.     

Hydrostatic pressure and electric and magnetic field effects on the binding energy of a hydrogenic donor impurity in InAs Pöschl-Teller quantum ring

We consider the effects of electric and magnetic fields as well as of hydrostatic pressure on the donor binding energy in InAs Pöschl-Teller quantum rings. The ground state energy and the electron wave function are calculated within the effective mass and parabolic band approximations, using the variational method. The binding energy dependencies on the electric field strength and the hydrostatic pressure are reported for different values of quantum ring size and shape, the parameters of the Pöschl-Teller confining potential, and the magnetic field induction. The results show that the binding energy is an increasing or decreasing function of the electric field, depending on the chosen parameters of the confining potential. Also, we have observed that the binding energy is an increasing/decreasing function of hydrostatic pressure/magnetic field induction. Likewise, the impurity binding energy behaves as an increasing/decreasing function of the inner/outer radii of the quantum ring nanostructure.     

Donor-bound electron states in a two-dimensional quantum ring under uniform magnetic field

The electron states in a two-dimensional GaAs/AlGaAs quantum ring are theoretically studied in effective mass approximation. On-centre donor impurity and uniform magnetic field perpendicular to the ring plane are taken into account. The energy spectrum with different angular momentum changes dramatically with the geometry of the ring. The donor impurity reduces the energies with an almost fixed value; however, the magnetic field alters energies in a more complex way. For example, energy levels under magnetic field will cross each other when increasing the inner radius and outer radius of the ring, leading to the fact that the arrangement of energy levels is distinct in certain geometry of the ring. Moreover, energy levels with negative angular momentum exhibit the non-monotonous dependence on the increasing magnetic field.     

Nonlinear optical properties in a nanoring: quantum size and magnetic field effect

We have studied the nonlinear optical absorption and the nonlinear optical rectification of an exciton in a nanoring in the presence of magnetic flux. The calculation results show that one can control the properties of nonlinear optical absorption and nonlinear optical rectification of a nanoring by tuning the outer and inner radius. Moreover, we find that the nonlinear optical properties of a nanoring can be modulated by the magnetic flux through the nanoring.     

Polaron effect on the optical rectification in spherical quantum dots with electric field

The polaron effect on the optical rectification in spherical quantum dots with a shallow hydrogenic impurity in the presence of electric field is theoretically investigated by taking into account the interactions of the electrons with both confined and surface optical phonons. Besides, the interaction between impurity and phonons is also considered. Numerical calculations are presented for typical Zn_(1-x)Cd_xSe/ZnSe material. It is found that the polaronic effect or electric field leads to the redshifted resonant peaks of the optical rectification coefficients. It is also found that the peak values of the optical rectification coefficients with the polaronic effect are larger than without the polaronic effect, especially for smaller Cd concentrations or stronger electric field.     

Eccentricity effects on the quantum confinement in double quantum rings

This work presents a theoretical study of the energy spectrum of GaAs/AlGaAs concentric double quantum rings, under an applied magnetic field directed perpendicular to the ring plane. The Schrödinger equation for this system is solved in a realistic model consisting of rings with finite barrier potentials. Numerical results show that increasing the magnetic field intensity leads to oscillations in the ground state energy which, in contrast to the usual Aharonov-Bohm oscillations, do not have a well defined period, due to the coupling between inner and outer ring states. However, when one considers an elliptical geometry for the rings, the energy spectra of the inner and outer ring states are decoupled and the periodicity of the oscillations is recovered.     

Intense laser effects on the optical properties of asymmetric GaAs double quantum dots under applied electric field

We investigated the combined effects of a non-resonant intense laser field and a static electric field on the electronic structure and the nonlinear optical properties (absorption, optical rectification) of a GaAs asymmetric double quantum dot under a strong probe field excitation. The calculations were performed within the compact density-matrix formalism under steady state conditions using the effective mass approximation. Our results show that: (i) the electronic structure and optical properties are sensitive to the dressed potential; (ii) under applied electric fields, an increase of the laser intensity induces a redshift of the optical absorption and rectification spectra; (iii) the augment of the electric field strength leads to a blueshift of the spectra; (iv) for high electric fields the optical spectra show a shoulder-like feature, related with the occurrence of an anti-crossing between the two first excited levels.     

Effects of an electric field on the confined hydrogen impurity states in a spherical parabolic quantum dot

In this paper, we studied the effects of an electric field on a hydrogenic impurity confined in a spherical parabolic quantum dot using nondegenerate and degenerate perturbation methods. The binding energies of the ground and three low-excited states are calculated as a function of the confinement strength and as a function of the intensity of an applied electric field. Moreover, we computed the oscillator strength and the second-order nonlinear optical rectification coefficient based on the computed energies and wave functions. The results show that the electric and optical properties of hydrogenic impurity states are strongly affected by the confinement strength and the applied electric field.     

Linear and nonlinear optical properties of strained GaN/AlN quantum dots: Effects of impurities,radii of QDs,and the incident optical intensity

The linear and nonlinear optical properties of cylinder GaN/AlN quantum dots with strain effects and impurity are investigated by taking into account the effects of the deformation potential and piezoelectric potential on the conduction band edge. The results are presented as a function of photon energies and QD radii. The optical absorption spectrum and refractive index changes have a blueshift in the presence of the impurity. With increasing distance of the impurity’s position along the growth direction, the peak values of the refractive index changes decrease and shift to higher photon energy. When the sizes of the QDs increase, redshift effects are observed and the relative amplitudes diminish. It can be found that the nonlinear effect becomes obvious with increase of the incident optical intensity. Then there is a “hole-burning” in the absorption coefficient spectra and two new peaks will appear in the total refractive index change spectrum when the optical intensity becomes larger enough. Finally it can be concluded that the intensity of the incident light and the position of the impurity play an important role in the linear and nonlinear optical properties.     

The polaron effect on the binding energy of a shallow donor impurity in quantum-well wires in an electric field

Using a variational technique, the effect of electron-longitudinal optical (LO) phonon interaction on the ground and the first few excited states of a hydrogenic impurity in a semiconductor quantum wire of rectangular cross section under an external electric field is studied theoretically for the impurity atom doped at various positions. The results for the binding energy as well as polaronic correction are obtained as a function of the size of the wire, the applied uniform electric field and the position of the impurity. It is found that the presence of optical phonons changes significantly the values of the impurity binding energies of the system. Taking into account the electron–LO phonon interaction the 1s→2p_y and 1s→2p_z transition energies are calculated as a function of applied electric field for different impurity positions.     

The effects of pressure and hydrogenic donor impurity on the linear and nonlinear optical properties of a GaAs/GaAlAs nanowire superlattice

The combined effects of hydrostatic pressure, presence and absence of hydrogenic donor impurity are investigated on the linear and nonlinear optical absorption coefficients and refractive index changes of a GaAs/Ga_1−xAl_xAs nanowire superlattice. The wave functions and corresponding eigenvalues are calculated using finite difference method in the framework of effective mass approximation. Analytical expressions for the linear and third order nonlinear optical absorption coefficients and refractive index changes are obtained by means of compact-density matrix formalism. The linear and third order nonlinear absorption coefficient and refractive index changes are presented as a function of photon energy for different values of hydrostatic pressure, incident photon intensity and relaxation time in the presence and absence of hydrogenic donor impurity. It is found that the linear and third order nonlinear absorption coefficients, refractive index changes and resonance energy are quite sensitive to the presence of impurity and applied hydrostatic pressure. Moreover, the saturation in optical spectrum and relaxation time can be adjusted by increasing pressure in presence of impurity whereas the effect of hydrostatic pressure is negligible in the case of absence of hydrogenic impurity.     

Electric field-induced nonlinear optical properties of a hydrogenic impurity in a GaAs/GaAlAs quantum dot: effects of spin–orbit interactions

Nonlinear optical properties, optical rectification coefficients and the second-order and third-order harmonic generation coefficients as a function of photon energy are dealt in a GaAs/Ga_0.8Al_0.2As quantum dot in the presence of electric field and the spin–orbit interactions. The Dresselhaus and the Rashba spin–orbit interactions are added in the Hamiltonian. The electric field-induced photoionization cross section with the normalized photon energy for an on-centre donor impurity in the quantum dot is studied. The effect of nonparabolicity is included in the Hamiltonian. The spin–orbit interaction as a function of photon energy is investigated. The computations are carried out within the framework of the single band effective mass approximation using variational technique and the compact density approach. It is found that the spin–orbit interaction coefficients show strong effects on the resonant position of harmonic generations. The results are compared with the recent investigations.     

Noise-driven optical absorption coefficients of impurity doped quantum dots

We make an extensive investigation of linear, third-order nonlinear, and total optical absorption coefficients (ACs) of impurity doped quantum dots (QDs) in presence and absence of noise. The noise invoked in the present study is a Gaussian white noise. The quantum dot is doped with repulsive Gaussian impurity. Noise has been introduced to the system additively and multiplicatively. A perpendicular magnetic field acts as a source of confinement and a static external electric field has been applied. The AC profiles have been studied as a function of incident photon energy when several important parameters such as optical intensity, electric field strength, magnetic field strength, confinement energy, dopant location, relaxation time, Al concentration, dopant potential, and noise strength take on different values. In addition, the role of mode of application of noise (additive/multiplicative) on the AC profiles has also been analyzed meticulously. The AC profiles often consist of a number of interesting observations such as one photon resonance enhancement, shift of AC peak position, variation of AC peak intensity, and bleaching of AC peak. However, presence of noise alters the features of AC profiles and leads to some interesting manifestations. Multiplicative noise brings about more complexity in the AC profiles than its additive counterpart. The observations indeed illuminate several useful aspects in the study of linear and nonlinear optical properties of doped QD systems, specially in presence of noise. The findings are expected to be quite relevant from a technological perspective.     

Effects of applied electric and magnetic fields on the nonlinear optical rectification and second-harmonic generation in a graded quantum well under intense laser field

In this present study, the effects of electric and magnetic fields on the nonlinear optical rectification and second-harmonic generation in a graded quantum well under intense laser field have been investigated theoretically. The energy eigenvalues and their corresponding eigenfunctions are obtained by solving Schrödinger equation within the framework of effective mass approximation. The analytic expressions for the optical properties are calculated by the compact-density-matrix approach and iterative method. The numerical results are presented for a typical GaAs/Ga_1?x Al _x As quantum well. The results show that the nonlinear optical rectification and second-harmonic generation coefficients are considerably affected by the electromagnetic fields and intense laser field.     

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.     

Electric field effect on the second-order nonlinear optical properties in semiparabolic quantum wells

Electric field effect on the second-order nonlinear optical properties in semiparabolic quantum wells are studied theoretically. Both the second-harmonic generation susceptibility and nonlinear optical rectification depend dramatically on the direction and the strength of the electric field. Numerical results show that both the second-harmonic generation susceptibility and nonlinear optical rectification are always weakened as the electric field increases where the direction of the electric field is along the growth direction of the quantum wells, which is in contrast to the conventional case. However, the second-harmonic generation susceptibility is weakened, but the nonlinear optical rectification is strengthened as the electric field increases where the direction of the electric field is against the growth direction of the quantum wells. Also it is the blue (or red) shift of the resonance that is induced by increasing of the electric field when the direction of the electric field is along (or against) the growth direction of the quantum wells. Finally, the resonant peak and its corresponding to the resonant energy are also taken into account.