Compact-density Matrix Formalism Research Articles

Energy spectrum and optical properties in a double parabolic quantum ring: Effects of the impurity, the magnetic field and the spin–orbit interaction

In this letter, the energy spectrum in a concentric double quantum rings(CDQRs) with a parabolic confinement under the influence of the spin–orbit interactions (SOIs), the magnetic field and the hydrogenic donor impurity has been investigated by diagonalizing the Hamiltonian matrix and applying the perturbation theory. Then the optical absorption coefficients (OACs) are calculated through the scheme of compact density-matrix formalism. A discussion of the different intensity of the two SOIs is conducted. Meanwhile, the effects of different factors on the total OACs with different incident light polarization angles have also been investigated, in which the bleaching effects are found.

Investigation of nonlinear optical rectification within multilayer wurtzite InGaN/GaN cylindrical quantum dots under the impact of temperature and pressure

We have looked numerically at variations of the nonlinear optical rectification (NOR) for an impurity donor localized in a wurtzite Inx0Ga1−x0N/GaN multilayer cylindrical quantum dots (MLCQDs), which is under the effect of hydrostatic pressure and temperature. Using the effective mass approximation, the compact density matrix formalism, we have solved the Schrödinger equation by the finite element method (FEniCS Project) . Firstly, we consider the impact of altering the polarization direction of the incident electromagnetic radiation. Specifically, we explore two distinct scenarios: axial, along the growth axis of the structure, and circular, across the cross-section of the cylinder. From our investigation, we found that the nonlinear optical rectification is determined by two main parameters: the transition energy, which is mainly related to quantum confinement, and the geometrical factor that depends on the distribution of the electron wave functions. The NOR experiences a blueshift with an increase in hydrostatic pressure or indium composition, and a redshift with an increase in temperature or quantum dot radius, where the impurity is located in the center of the upper QD. Furthermore, the results show that the amplitude and resonance peak position of NOR are significantly influenced by varying the impurity’s position and the barrier width.

Tailoring of the nonlinear optical rectification in vertically and laterally coupled InxGa1-xAs/GaAs quantum dots for Tera-hertz applications: Under In/Ga inter-diffusion, indium segregation, and strains effects

We numerically investigate the Nonlinear Optical Rectification (NOR) of two laterally coupled lens-shaped InxGa1-xAs/GaAs quantum dots and two layers of InxGa1-xAs/GaAs coupled QDs along the growth axis. In addition, we have examined the impact of applying an external electric field, hydrostatic pressure, and temperature on the NOR under indium segregation inside the wetting layer (WL) and In/Ga inter-diffusion in the QD region. The three-dimensional Schrödinger equation (3D) is solved numerically using the finite difference method (FDM) within the framework of the effective mass. We have used the compact density matrix formalism to compute the NOR coefficient. Our findings reveal that the indium segregation and inter-diffusion phenomena significantly affect the NOR coefficient and should be considered appropriately. It is also found that the lateral and vertical coupling thicknesses significantly impact the NOR coefficient, and the structure under investigation has a resonant behavior in the terahertz domain (0.1–10 THz). Moreover, obtained results reveal that the applied electric field orientation and intensity significantly affect the NOR magnitude. Therefore, the NOR intensity reaches the maximum value, χ(0)(2)=50.10-7m/V, for a negative applied electric field, F = −10 kV/cm. Additionally, it was shown that the increase in the hydrostatic pressure shifts the NOR spectrum to higher energies (blue-shift), whereas increasing temperature has the contrary effect. It is worth noting that the NOR magnitude and its attributed resonance energy can be adjusted for THz devices with a good choice of the external factors mentioned above.

Influence of the intense laser field on optical absorption coefficients and refractive index changes in the double trigonometric quantum wells

In this letter, the effect of the intense laser field on optical properties in the unique double trigonometric quantum wells has been investigated by applying the KH transformation. The Schrdinger equation is solved to obtain the energy levels and the wave functions of this system. Then the optical absorption coefficients (OACs) and refractive index changes (RICs) are calculated through the scheme of the compact density-matrix formalism. The results show that the OACs and RICs undergo a blue-shift first, followed by a red-shift, as the intensity of the laser field is enhanced. Furthermore, features of various transition total OACs are also discussed, which are also affected by the laser field.

Spectral features and optical absorption of vertically stacked V-groove quantum wires

The spectral features and the linear, nonlinear, and total optical absorption coefficients of two realistic mathrm {GaAs/Ga}_{1-x}{mathrm{Al}}_x{mathrm{As}} vertically stacked V-groove quantum wires confining electronic states were theoretically studied. The compact density matrix formalism and the finite element method were used as solution frameworks. The influence of the barrier width, inter-sidewall angle, the crescent thickness of the stack, and the influence of a static electric field on the energy spectrum and the optical coefficients is addressed. Increasing the crescent thickness (inter-sidewall angle) leads to a reduction (non-monotonous increase) of the energy values, while the presence of a static electric field leads to controllable stark-like patterns. In all cases, anti-crossing points are reported. By increasing the crescent thickness, inter-sidewall angle, or barrier width, a non-monotonous blue-/red-shift of the resonant peaks of the optical absorption is observed. In addition, the results in asymmetric/symmetric vertically coupled V-groove quantum wire systems suggest that the quantum tunneling phenomenon can be linked to the enhancement of the total optical absorption due to the possibility of the generation of dipole moments by higher electron mobility. Thus, optical fields oriented along the growth direction enhance the optical absorption. Furthermore, the absorption coefficient maximum is drastically modified by varying the inter-sidewall angle, and even the evolution tendency can be inverted due to the anti-crossing points in the energy spectra. Since the obtained resonant peaks are located below 20 meV in the spectra, the analyzed system could be interesting for exploring and designing new Terahertz devices.

Nonlinear optical characteristics of thermodynamic effects- and electric field-triggered Mathieu quantum dot

In this work, the total refractive index (TRICs) and total absorption coefficients (TACs) of a spherical quantum dot with the Mathieu potential encompassement, generated by using InxGa1−xAs/GaAs heterostructure, and including hydrogenic impurity in its center, under the influence of the temperature, hydrostatic pressure and external electric field are investigated. The compact density matrix formalism and the iterative method are employed to compute the nonlinear optical features. The relevant eigenvalue equation of the Mathieu quantum dot (MQD) is solved by constructing a tridiagonal matrix formalism, within the effective mass approach. As well as the response of TRICs and TACs to external parameters, the alterations concerning structure parameters such as doping concentration and restriction width are also examined. To the best of our knowledge, the external influences and structural parameters on the optical specifications of MQD containing the central impurity are theoretically taken into consideration, for the first time, in the present work. Determining the optimality of optical properties arising from structural and external parameter changes is crucial in terms of providing a theoretical basis for the experimental production and practical use of MQD.

Optical properties of Al x Ga1−x As/GaAs Woods–Saxon quantum well in the presence of hydrostatic pressure and applied electric field

The third harmonic generation (THG), linear and nonlinear optical absorption coefficients (OACs), and refractive index changes (RICs) are investigated in a Woods–Saxon quantum well (QW) modulated by the hydrostatic pressure and applied electric field. The effect of non-uniform aluminum doping (position-dependent effective mass (PDEM)) on the mass of the system is discussed, and further to explore the influence of PDEM on the nonlinear THG, OACs, and RICs of the Woods–Saxon QW. These nonlinear optical properties above are obtained using the compact-density matrix formalism. The electron states in a Woods–Saxon QW under the constant effective mass (CEM) and PDEM are calculated by solving the Schrödinger equation via the finite difference technique. The contributions from competing effects of the hydrostatic pressure and applied electric field to the nonlinear optical properties with CEM and PDEM are reported, as well as the comparison with each other. The observations reveal that the regulation of external fields and the influence of PDEM play an important role in the photoelectric properties of QW.

Linear and nonlinear optical properties in single CuIn1−xGaxSe2 nanowire: Effects of size, incident intensity, relaxation time and Ga concentration

The linear and nonlinear optical properties of CuIn1−xGaxSe2 free standing nanowire have been studied by employing the compact-density matrix formalism and the effective mass approximation. Considering the system under the effect of the polarization vector of the incident light in both cases perpendicular and parallel to the axis of the nanowire, the systematic theoretical investigation contains results with all possible combinations of the involved parameters, such as incident light intensity, relaxation time, nanowire radius and Ga concentration. Our results show that in the case of the polarization vector perpendicular to the nanowire axis, the linear and nonlinear absorption coefficient and refractive index changes can be controlled by changing the nanowire radius, and the effect of Ga concentration is clearly apparent. In contrast, polarization along the nanowire axis allows for a very large absorption coefficient and control of the optical properties through the height, but minimal effect on the transition energy. The increase of the relaxation time as well as the intensity of the incident light has a major role in the nonlinearity effects, while the Ga concentration and the size of the structure influence the amplitude and the transition energy shift.

Electronic and optical properties of cubic quantum dots subjected to terahertz laser field

This study introduces the influence of linearly polarized terahertz laser field (TLF) on electronic and anisotropic optical absorption coefficients (OACs) related to the cubical quantum dots (CQDs). The energy levels and wave functions of the system are obtained by solving the Schrödinger equation within the framework of the effective-mass. The OACs are inferred from the scheme of compact density-matrix formalism. The results show that the laser correction parameters and polarization angle of TLF have a significant influence on the optical properties. As a key result, the modulation of anisotropic OACs of CQDs by terahertz laser field with different parameters is given.

Size-dependent interband optical properties of lens-shaped InAs/InP quantum wire

Using the combination of coordinate transformation and the finite difference method, we have studied theoretically, the optical absorption coefficient and the refractive index changes of the InAs/InP quantum wire, with a lens cross-section. For this purpose, we have used the analytical expressions for optical properties obtained by the compact-density matrix formalism. The evaluation has been performed in varying the dimension of the quantum wire and the incident optical intensity I. The obtained results show that the oscillator strength (transition life) increase (decrease) by increasing the height H. Also, the total absorption coefficient achieves a maximum value which corresponds to the energy difference of the two different electronic states and the resonant peaks shift toward the lower energies by increasing the height H.

Effect of magnetic field, size and donor position on the absorption coefficients related a donor within the core/shell/shell quantum dot

In this study, linear, nonlinear and total optical absorption coefficients related a single shallow donor atom confined in semiconductor core/shell/shell quantum dot heterostructure are researched in detail within the compact density matrix formalism approximation. For this purpose, firstly, the energies and the wavefunctions are computed by the diagonalization method in the effective mass approach. Moreover, the effects of size modulation, donor position and magnetic field are analyzed. The numerical results indicate that the linear and nonlinear parts of the absorption coefficients related with intersubband \(1s\rightarrow 1p\) and \(1p\rightarrow 1d\) donor transitions undergo significant changes.

Linear and nonlinear optical absorption coefficients and refractive index changes of zigzag quantum wells affected by terahertz laser field

This study introduces the influence of terahertz laser field on optical absorption coefficients (OACs) and refractive index changes (RICs) related to the quantum wells with zigzag confinement potential. The energy levels and wave functions of the system are obtained by solving the Schrödinger equation within the framework of the effective-mass. The OACs and RICs are inferred from the scheme of compact density-matrix formalism. The results show that the peak of OACs and RICs are modulated by terahertz laser field and the potential parameter of quantum wells.

Applied electric and magnetic fields effects on the nonlinear optical rectification and the carrier's transition lifetime in InAs/GaAs core/shell quantum dot

In this paper, we have focused our research on the design of a resonant lens-shaped InAs/GaAs core/shell quantum dot structure with intra-band transitions in the conduction band. We have studied the combined effects of the structural dimensions, the hydrostatic pressure (P), the temperature (T), the applied electric (F) and magnetic (B) fields on the nonlinear optical rectification (NOR) and the carrier's transition lifetime (τ). This study is done under the compact density matrix formalism and the effective mass approximation by using the Finite Difference Method (FDM). Obtained Results show that the NOR coefficient is improved by increasing the core radius, as the NOR magnitude increases and a red shift is achieved. Moreover, the application of an electric and a magnetic field enhances the NOR coefficient where its resonant energy exhibits a red shift (blue shift) with increasing the applied magnetic field (applied electric field). Besides, a comparative study between the core/shell structure and a single quantum dot, for B = 15 T, shows that the cap layer thickness can be controlled and reduced to obtain the optimized NOR coefficient. Consequently, our theoretical results will be useful for designing new optoelectronic core/shell devices with an improved performance by the adjustment of the applied external proofs.

Bound states and optical properties for Derjaguin-Landau-Verweij-Overbook potential

In the present work, bound states of the Schrodinger equation (SE) and the corresponding optical properties for Derjaguin-Landau-Verweij-Overbook (DLVO) potential are studied. For this goal, we first solved the SE using DLVO potential and obtained eigenfunctions and bound state energy eigenvalues for an arbitrary system. We used analytical expression for optical properties obtained by the compact-density matrix formalism. Here, we have investigated the intersubband optical absorption coefficients and refractive index changes.

Optical analysis of quantum dot with velocity‐dependent potential

AbstractIn this study, for the first time, the velocity‐dependent potential (VDP) effects on the total refractive index changes (TRICs) and the total absorption coefficients (TACs) of the parabolic quantum dot with spherical confinement, generated by GaAs/GaAlAs heterostructure, are comprehensively investigated. In order to obtain the subband energy spectra and the electronic wave function of the quantum dot system, the wave equation is numerically solved due to the VDP's complexity by using Runge‐Kutta‐Fehlberg method within the effective mass approximation. The nonlinear optical specifications of the quantum dot with velocity‐dependent potential (QDVDP) are analyzed using the compact density matrix formalism within the framework of the iterative method. To investigate the optical specifications of QDVDP, the isotropic form factor of VDP is taken into consideration as the harmonic oscillator type, F(r) = γρ0r2 (being γ and ρ0 are constants). Optical analysis is also executed for parabolic encompassing under the influence of VDP, as well as VDP, analyzing for TRICs and TACs of QDVDP, for which the result is quite a change compared to cases without VDP due to the symmetry‐breaking repercussion on system confinement of VDP. The main motivation of the present study is to clearly distinguish VDP effects on optical properties of the quantum dot, carrying out an analysis on optimal range and alternative parameter for optical properties.

Numerical modeling of linear and nonlinear optical properties in hexagonal core-shell shape ZnSe/ZnSxSe1-x quantum dot

In this paper, we have theoretically modeling a ZnSe/ZnSxSe1-x hexagonal core-shell quantum dot (CSQD). The optical and electronic properties of the quantum dot have been obtained by using a numerical method which is based on a combination of coordinate transformation and the finite difference method. The optical properties are obtained by an application of compact-density matrix formalism. The linear, nonlinear and total absorption coefficient, refractive index changes and susceptibilities between the ground state energy of the electron and the first excited state are investigated as a function of photon energy for different dimensions of CSQD, different values of incident optical intensity and different composition x.

Studies on the nonlinear optical properties of two-step GaAs/Ga1−xAlxAs quantum well

In this paper, the numerical computation for the absorption coefficient and the relative refractive index change, considering the third order correction nonlinear optical properties, is reported. This study was performed for a symmetric two-step GaAs/Ga1−xAlxAs quantum well, subjected to a constant electric field applied along the growth direction z, and an in-plane constant magnetic field B. We also consider the intense laser field effect, characterized through the laser-dressing parameter α0. The electronic structure computation was obtained by working under the effective mass approximation and the Schödinger equation was solved by diagonalization procedure. The optical properties are calculated by using the well-established compact density matrix formalism expressions for the nonlinear optical properties of interest. In general, we found that the structural parameters, as the step-like potential or the central barrier, permit the resonant peak and the amplitude design. We also found that the system becomes more sensitive to electric than to magnetic field, and finally that the intense, non-resonant, laser field can strongly change the optical properties of interest. Our results indicate that the implementation of the step-like potential profile, experimentally feasible, enhance the optical properties of interest, that falls within the THz electromagnetic range, and can be used to design a photodetector, or even can be used for quantum cascade lasers design.

Intersubband resonant enhancement of second order-nonlinear susceptibility in asymmetric AlxGa1−xN/GaN double quantum wells

The present work aims at investigating the second-harmonic generation theoretically in asymmetric AlxGa1−xN/GaN double quantum wells based on a compact density-matrix formalism and a self-consistent approach. Calculations have been made using two- and three-level quantum well models. For this purpose, the electronic subbands and their related wave functions as well as the Fermi energy are computed in asymmetric AlxGa1−xN/GaN double quantum well heterostructures within the effective mass and Hartree approximations. From the given results, it was concluded as follows: (i) The susceptibility exhibits multiple peak structures originating from the intersubband and their corresponding virtual transitions. (ii) The second-order susceptibility strongly depends on the aluminum composition and on the planar-doping design in the barriers as well. (iii) The optimization of electron wave functions' overlaps considerably improved the second-harmonic generation. (iv) Double quantum well systems are revealed to be the most appropriate to generate the second harmonic with an efficient intensity at the suitable resonance frequency. Theoretically, the obtained results would make a useful contribution for experimental studies. From an applied viewpoint, they can open up new opportunities for AlxGa1−xN/GaN optoelectronic devices.

Nonlinear intersubband absorption coefficient in an AlxGa1−xAs/GaAs quantum cascade laser-like profile

In this work we perform a theoretical study on the nonlinear intersubband absorption response in a quantum cascade laser (QCL) profile-like heterostructure that consists of a triple AlxGa1−xAs/GaAs quantum well. In particular, we investigate the role of the central quantum well width, as well as the electric and magnetic field effects, on the intersubband optical properties of the system. Results on the electronic structure arise within the framework of the effective mass, and parabolic band approximations. The calculation also takes into account the effective mass mismatch in the kinetic energy and magnetic potential energy terms, in order to investigate the importance of the position dependence of this parameter. The conduction band offset ratio was determined using the model solid theory, considering strain effects. The expression from which we calculate the nonlinear optical response comes from the third-order dielectric susceptibility derived within the compact density matrix formalism. In general we have obtained that, as a function of the central well width and the applied magnetic field strength, the light absorption coefficient can exhibit red- and blue-shifts. Meanwhile, in the case of the application of an electric field only blue-shifts are observed. The effective mass mismatch is more significant for small applied magnetic fields, due to the difference in the resonant peak found in the absorption coefficient. In all cases it is found that the third-order correction is significant in value.

Tailoring the optical properties of quantum ring irradiated by THz laser

ABSTRACTThis study set out to introduce the optical nonlinearities of a intense laser-driven two-dimensional quantum ring subjected to external uniform magnetic field. Inclusion of the effect of non-resonant, high-frequency THz laser radiation is realised by the laser-dressed potential, whereas the total optical absorption coefficients, total relative refractive index changes and third-harmonic generation (THG) coefficient are inferred from the scheme of compact density-matrix formalism and iterative method. Our results reveal that the laser field smoothens the antidot region of the ring that consequences with remarkable modifications in the electronic structure and correspondingly the optical response of the system. We have found that the height and location of the resonant peaks of total optical absorption coefficient, total relative refractive index changes and THG coefficient can be controlled by the externally applied fields and system parameters. The tunability of the intersubband transitions could be beneficial for practical device application relying on the electronic optical transitions.