Compact-density Matrix Formalism Research Articles

Impurity related optical properties in tuned quantum dot/ring systems

ABSTRACTIn this paper, we explore the linear, third-order nonlinear, and total optical absorption coefficient (OAC) and refractive index change coefficient (RICC) of a GaAs doped quantum dot/quantum ring (QD/QR) with parabolic-inverse squared potential in conjunction with modified Gaussian confinement and taking into account the presence of on-centre shallow donor and or acceptor impurity. Calculations are done via the compact density matrix formalism and the iterative method. The two-dimensional parabolic QD/QR is subjected to uniform magnetic field oriented perpendicularly to the plane of the structure. The energy levels and wave function are derived within the framework of effective-mass and parabolic band approximation. The results exhibit that the OACs and RICC are clearly affected by different parameters of the applied confinement, strength of magnetic field, and the presence of impurity. The variation of confinement potential, nature of impurity, dot radius, cyclotron frequency of the parabolic confinement potential, and geometric parameter of the on-centre repulsive potential lead to either a red-shift or a blue-shift of the resonant peaks of the OACs and of the maximum and minimum of the RICC together with significant variations of the magnitudes of these resonant structures.

Single- and double-resonant enhancement of second-harmonic generation in asymmetric AlGaN/GaN/AlGaN quantum well heterostructures

The second-harmonic generation susceptibility is theoretically investigated based on the compact density-matrix formalism in two- and three-level AlGaN/GaN systems. The electronic states and their related wave functions were calculated by solving self-consistently the Schrödinger–Poisson equations within the effective mass and Hartree approximations. The presence of spontaneous and piezoelectric polarizations is taken into account in the modeling part. It was revealed from the relevant results that (i) the second-order susceptibility shows a multiple peak structure due to intersubband and their corresponding virtual transitions, (ii) the use of a back doping as well as the optimization of the layer widths in delta-doped AlGaN/GaN asymmetric quantum wells improved considerably the second-harmonic susceptibility, and (iii) the three-level AlGaN/GaN system is the most efficient structure, which generates the second-harmonic with a significant intensity up to 4.36 × 10−5 mV−1. Numerical results of the present work could lay the basis for research in AlGaN-related optoelectronic device applications.

Effects temperature, pressure and spin–orbit interaction simultaneously on third harmonic generation of wedge-shaped quantum dots

In the present paper, we have studied the effects of temperature and pressure simultaneously on the third harmonic generation (THG) of a GaAs wedge-shaped quantum dot under the influence of spin–orbit interaction (SOI). For this purpose, we have used analytical expression for THG obtained by the compact-density matrix formalism. THG has been calculated for different temperatures and pressures under SOI. According to the obtained results, it is found that (i) THG shows a red shift of peak position in the presence of SOI. (ii) THG shifts toward higher energies with increasing temperature and considering the SOI. (iii) THG moves to lower energies with increasing pressure and considering the SOI.

Numerical modelling of electronic and optical properties of isolated and self-assembled InAs/InP quantum dots

In the present work, we are interested for an isolated and self-assembled InAs/InP quantum dots with a dome cross-section. We have tried to study the electronic and optical properties in the quantum dot by using an efficient and simple method. This numerical method is based on the coordinate transformation and the finite difference method (FDM). The influence of the parameters introduced in the mathematical function, is studied on the size, the shape and the number of the quantum dot. The electron, and heavy hole energy levels as well as their interband transition energies are also investigated. The linear, third-order nonlinear and total interband optical absorption coefficients and refractive index changes are investigated as a function of photon energy with varying height dot (H) and the incident optical intensity (I). The analytical expressions of these optical properties are obtained by using the compact-density matrix formalism.

Influence of the position dependent effective mass on the nonlinear optical properties in semiparabolic and parabolic quantum well with applied magnetic field

In the current work, the nonlinear optical properties in GaAs/Ga1−xAlxAs semiparabolic and parabolic quantum well(QW) with constant effective mass(CEM) and position dependent effective mass(PDEM) are estimated for different applied magnetic field. In this regard, we have obtained the analytical expressions of the nonlinear rectification(OR), second harmonic generation(SHG), third harmonic generation(THG), optical absorption coefficients(OACs), and refractive index changes(RICs) by using the compact density matrix formalism. Simultaneously, we obtain the reliable energy eigenvalues and their corresponding eigenfunctions via the finite difference method. According to the obtained results, it is found that: (1)the correct inclusion of PDEM is the cause of a noticeable difference in nonlinear optical properties with respect to the use of CEM. (2)the applied magnetic field bear substantial technological importance in the process of nonlinear optical properties modulation.

Effect of applied electric field on the nonlinear optical properties of modulation-doped GaAs/AlxGa1-xAs double quantum well

In the present study, the effects of varying doping concentration and applied electric field on the intersubband-related optical absorption and relative refractive index change coefficients in modulation-doped GaAs/AlxGa1-xAs double quantum wells are theoretically investigated. The allowed energy levels and the corresponding wave-functions are calculated by solving the Schrödinger and Poisson equations self-consistently within the framework of the effective-mass and parabolic band approximations. The optical coefficients are evaluated using the compact density matrix formalism within an iterative procedure. The numerical results are presented for two different doping concentration and several values of the electric field. They show that both the peak position and the magnitude of the calculated total optical absorption coefficients and refractive index changes are significantly affected by the applied electric field and the doping concentration. The treatment is suitable to consider the general problem with different wells and barrier sizes, although the barrier width should preferably be small enough as to allow for an effective inter-well coupling.

A theoretical evaluation of optical properties of InAs/InP quantum wire with a dome cross-section

In the present work, we have theoretically studied the optical properties of a InAs quantum wire with dome cross section. We have used a numerical method which is based on a combination of coordinate transformation and the finite difference method. For this purpose, we have used analytical expressions for optical properties obtained by the compact-density matrix formalism. We have evaluated the linear, non-linear and the total absorption coefficients between the ground state for electron and heavy hole as a function of photon energy. The linear, non-linear and total refractive index changes are also investigated. These optical properties are determined with varying the incident optical intensity and the height of the wire.

Electric field and impurity effect on nonlinear optical rectification of a double cone like quantum dot

In this work, we have investigated the effect of electric field and impurity position on nonlinear optical rectification of a double cone like quantum dot in the effective mass approximation and by using compact density-matrix formalism. We have calculated the energy levels and wave functions using finite element method (FEM) in the presence of impurity and influence of electric field. The results show that: (i) the binding energy changes with the impurity position and it is changed by the applied electric field, (ii) nonlinear optical rectification peak position of this system present the blue or red shift due to the applied electric field and changing the impurity position. (iii) for low electric field, impurity position plays an important role in electronic and optical properties, but for larger electric field, impurity position role becomes non-significant. (iv) the optical rectification changes due to the impurity position and the electric field are considerable.

The effect of Rashba spin-orbit interaction on electronic and optical properties of a double ring-shaped quantum dot

In this work, we analytically study the effects of the Rashba spin-orbit interaction (SOI) and magnetic field on energy levels and optical properties of a double ring-shaped quantum dot. For this purpose, we first solve the Schrödinger equation and obtain the energy eigenvalues and the wave functions. Then, we use analytical expressions for optical properties obtained by the compact-density matrix formalism. We calculate the total refractive index change and total absorption in the presence of applied magnetic field and Rashba SOI. It is found that the energy levels strongly depend on the combined effects of the Rashba SOI and the applied magnetic field. The energy levels split into two branches, spin-up and spin-down states, due to the Rashba spin-obit interaction. The peak positions of both optical properties shift towards higher energies with increasing the magnetic field and Rashba parameter.

Effects of anisotropy on the optical rectification of a disk-like quantum dot with donor impurity in external electric and magnetic fields

Based on the compact density matrix formalism and the effective mass approximation, optical rectification of a disk-like quantum dot in the presence of impurity has been studied, in this work. The effects of applied magnetics and electric fields and its direction on the optical rectification of an elliptic anisotropic quantum dot are analyzed in details. Our results show that the optical rectification is strongly affected by the anisotropy degree and the direction of the electric field. Also, we found that the binding energies of on-center impurity can be tuned with direction of electric field and anisotropy degree.

Off-centre impurity-related nonlinear optical absorption, second and third harmonic generation in a two-dimensional quantum ring under magnetic field

The effects of an off-centre donor impurity on the non-linear optical absorption, second and third harmonic generation in a GaAs two-dimensional disc-shaped quantum ring under magnetic field are investigated within the compact density-matrix formalism and the effective mass approximation. The results reveal that: (i) the absorption spectra extend on larger energy intervals at the increment of the magnetic field; (ii) the possibility of generating second harmonic response from the system is demonstrated for an impurity placed on the repulsive part of the confining potential; (iii) both second harmonic and third harmonic coefficients are one order of magnitude larger for an impurity placed on the repulsive part of the potential and are blue-shifted by the increment of the magnetic field regardless the impurity position.

Magnetic field control of absorption coefficient and group index in an impurity doped quantum disc

The electronic properties and optical characteristics – absorption coefficient, refractive index and group index – in an impurity doped pseudo-harmonic quantum disc subjected to an applied magnetic field are investigated. Numerical calculations are performed using the exact diagonalization technique and the compact density-matrix formalism. It is found that the chosen structure could be switched between a lambda-type and a ladder-type configuration by a proper tailoring of the magnetic field strength. Furthermore, the absorption profile and the associated slow light frequency range can be controlled not only by varying the control field amplitude and its detuning but also by changing the impurity position and the magnetic field strength.

Effects of electric field and structure on the electromagnetically induced transparency in double quantum dot

We theoretically investigated the effects of electric field and structural parameters of the confining potential on the optical properties of a GaAs/AlGaAs double quantum dot related to the occurrence of the electromagnetically induced transparency phenomenon, using the compact density-matrix formalism and the effective mass approximation. The dependences of the absorption coefficient, refraction index and light group velocity on the Rabi frequency of the control field, intensity of the static electric field, asymmetry parameter of the potential and dot dimension are discussed in detail. It is found that electromagnetically induced transparency occurs in the system for intermediate field values and its transparency window for probe field absorption and sub- and super-luminal frequency interval of the probe field are blueshifted by the increment of the electric field strength and dot dimension but are redshifted by the augment of the asymmetry parameter of the potential.

Combined effects of the intense laser field, electric and magnetic fields on the optical properties of n-type double δ-doped GaAs quantum well

In the present work, the effects of the non-resonant intense laser field, electric and magnetic fields on the optical properties, such as linear, third order nonlinear and the total optical absorption coefficient and refractive index changes associated with the intersubband transitions between the ground and the first excited states in the n-type double δ-doped GaAs quantum well is theoretically studied by solving the Schrödinger equation in the laser-dressed confinement potential within the framework of effective mass approximation. The analytical expressions of the linear and third-order nonlinear optical absorption coefficients and refractive index changes are obtained by using the compact-density matrix formalism. Our numerical results show that the optical absorption coefficient and refractive index change are quite sensitive to the applied external fields, such as non-resonant intense laser field, electric and magnetic fields. The obtained results can be applied for the design of various optoelectronic devices based on the intersubband transitions of electrons.

Optical properties of wedge-shaped quantum dots under Rashba spin–orbit interaction

In the present paper, the optical properties of a GaAs wedge-shaped quantum dot (QD) under the effect of Rashba spin–orbit interaction (SOI) are theoretically studied. For this purpose, we have used analytical expressions for optical properties obtained by the compact-density matrix formalism. The dependence of the optical absorption coefficients and refractive index changes on the strength of Rashba SOI for different angles and different radii of wedge-shaped QD has been studied. According to the obtained results, it is found that (i) the Rashba SOI does not have considerable effects on the refractive index changes maxima. (ii) The total absorption coefficient is increased and shifted towards higher energies with considering the Rashba SOI. (iii) The influence of Rashba SOI on the optical properties depends on the parameters such as apex angle and radius of the wedge-shaped QD.

Electromagnetically induced transparency in double quantum dot under intense laser and magnetic fields: from Λ to Ξ configuration

We theoretically investigated the effects of non-resonant intense laser and magnetic fields on the optical properties of asymmetric GaAs/AlGaAs double quantum dot related to the occurrence of electromagnetically induced transparency, using compact density-matrix formalism and effective mass approximation. The chosen structure has the advantage to present x-lambda(Λ)-configuration or y-ladder(Ξ)-configuration for EIT occurrence, depending on lasers polarization, at low values of the non-resonant laser, and to change the configuration from Λ to Ξ at the increase of the x-polarized non-resonant laser intensity. We discussed in detail the influences of the control laser field intensity, non-resonant laser strength and polarization, and magnetic field intensity on the absorption coefficient, refraction index and group index. It is found that: (i) the control laser or the non-resonant laser at the same control laser intensity influences more the system being in x-Ξ-configuration than in x-Λ-configuration and have intermediate effects on y-Ξ-configuration; (ii) the magnetic field has the greatest influence on the system being in x-Λ-configuration and the lowest for y-Ξ-configuration; (iii) the increment of the non-resonant intense laser or magnetic fields induces a red-shift of the transparency windows and sub (super) luminal frequency intervals for the Λ-configuration but a blue-shift for both Ξ-configurations.

Intense laser field effects on the intersubband optical absorption and refractive index change in the [formula omitted]-doped GaAs quantum wells

In this paper, we have investigated the effects of the non-resonant intense laser field on the electronic and optical properties such as linear, nonlinear and the total optical absorption coefficient and refractive index change for transitions between two lower-lying electronic states in the GaAs-based δ-doped quantum well. Within the effective mass approximation, we calculated the eigenvalues and corresponding eigenfunctions as a function of the intense laser parameter by solving the Schrödinger equation in the laser-dressed confinement potential. The analytical expressions of the linear and third-order non-linear optical absorption coefficients and refractive index changes are obtained by using the compact-density matrix formalism. The obtained results show that the separation between ground and first excited energy levels in the δ-doped quantum well decreases in energy by the increase of the laser field intensity and this effect leads to an optical red-shift in the intersubband transitions. This behavior gives us a new degree of freedom in tunability of different device applications based on the optical transitions.

Intense laser field-induced nonlinear optical properties of Morse quantum well

Abstractauthoren This paper investigates the effects of an intense laser field and electric field on the optical properties of quantum well represented by Morse potential. The non-resonant, high-frequency intense laser effects upon the system are treated within the framework of non-perturbative approach, modifying the confinement potential associated to the heterostructure. The analytical expressions of the linear and third-order nonlinear optical absorption coefficients and refractive index changes are obtained by using the compact-density matrix formalism. The results for a typical GaAs quantum well correspond to several configurations of the structural parameter, the strengths of the intense laser radiation, and the static electric field. Numerical results reveal the striking influence of the external fields on the magnitude and resonant peak energy positions of the optical absorption coefficients and refractive index changes. Besides, the control of intersubband optical transitions by the structure parameter seems feasible.

Effects of the structure asymmetry on optical responses in GaAs double quantum dots under intense laser and electric fields

The effects of the potential shape asymmetry on the nonlinear optical absorption and optical rectification in GaAs double quantum dots under intense non-resonant laser field and static electric field were investigated comparatively using the effective mass approximation and the compact density-matrix formalism under steady state conditions. The obtained results show that: (i) for both systems, the optical spectra are redshifted with the increase of the laser intensity only in the presence of the electric field, exceptions appearing at the highest considered laser intensity for both systems and at low laser field intensity for the asymmetric system; (ii) the augment of the static field intensity blueshifts the optical spectra of both systems; (iii) the spectra of the asymmetric system are displaced toward higher energies and show a shoulder-like feature at a given electric field value; (iv) the optical rectification spectra are more intense for the symmetric system.

Impurity-related nonlinear optical rectification in double quantum dot under electric field

The characteristics of donor-impurity-related nonlinear optical rectification in asymmetric double quantum dot under electric field are investigated within the compact density-matrix formalism and the effective mass approximation. The results show that: (i) the binding energy of the ground state varies strongly with the impurity position and it is raised or decreased by the applied field, depending on the impurity position; (ii) the optical rectification spectra are rather sensitive to the impurity position and the electric field intensity; (iii) the changes in the impurity position within the double quantum dot and the electric field value may induce red or blue shift of the resonant peaks of the nonlinear optical rectification.