Effects of electron–phonon interaction and impurity on optical properties of hexagonal-shaped quantum wires

We have investigated the influence of electron–phonon (e–p) interaction and hydrogenic donor impurity simultaneously on energy difference, binding energy, the linear, nonlinear and total refractive index changes and absorption coefficients of a hexagonal-shaped quantum wire. For this goal, we have used finite-element method (FEM), a compact density matrix approach and an iterative procedure. It is deduced that energy difference and binding energy decrease by changing the impurity position with and without e–p interaction. The dipole matrix elements have complex behaviours in the presence of impurity with and without e–p interaction. The refractive index changes and absorption coefficients increase and shift towards lower energies by enhancing a ₁ with central impurity. In the presence of central impurity, the absorption coefficients and refractive index changes enhance and shift toward higher energies when e–p interaction is considered.     

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.     

Quantum Wire with Triangle Cross Section: Optical Properties

In the present work, the optical properties of a GaAs quantum wire with equilateral triangle cross section are studied. For this purpose, we use analytical expressions for optical properties obtained by the compact-density matrix formalism. Here, we investigate the intersubband optical absorption coefficients and refractive index changes as a function of the triangle side (L) and the incident optical intensity (I). According to the obtained results, it is found that: (i) The total refractive index changes increase and shift towards lower energies when the triangle side increases. (ii) The total absorption coefficient decreases as the triangle side increases. Also, the resonance peak shifts towards lower energies by increasing the triangle side.     

Excited-state absorptions of an exciton confined in a quantum dot

The optical absorptions of an exciton with the higher excited states in a disc-like quantum dot are investigated. Calculations are made by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. With typical semiconducting GaAs based materials, the linear, third-order nonlinear, total optical absorption coefficients and refractive index changes have been calculated for the s–p, p–d, and d–f transitions. The results show that as the angular momentum quantum number of transitions increases, the absorption peaks shift towards lower energies and the absorption intensities increase.     

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.     

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.     

Linear and nonlinear optical properties in spherical quantum dots: Rosen-Morse potential

In this paper, we have studied optical properties of spherical quantum dots by using Rosen-Morse potential. In this regard, we have first solved the Schrodinger equation and obtained energy levels and wave functions by applying Nikiforov-Uvarov (NU) method. Then, by using density matrix method, we have applied analytical expressions for the linear and third-order nonlinear absorption coefficient and refractive index changes. The results show that the total refractive index changes and the absorption coefficients increase and shift towards higher by enhancing height potential.     

Excited state absorptions of an exciton bound to an ionized donor impurity in quantum dots

An investigation of an exciton bound in a parabolic two dimensional quantum dot by a donor impurity has been carried out by using the matrix diagonalization method and the compact density-matrix approach. The linear, third-order nonlinear, total optical absorption coefficients and refractive index changes have been calculated for the s-p, p-d, and d-f transitions. The results show that the parabolic potential has a great effect on the optical absorptions. The calculated results also reveal that as the angular momentum quantum numbers of transitions increase, the optical absorption and refractive index peaks shift towards lower energies and the absorption and refractive index intensities increase.     

Electron-related nonlinear optical properties of cylindrical quantum dot with the Rosen-Morse axial potential

We present a theoretical study on the effects of intense laser field(ILF) and static electric field on the linear and nonlinear optical properties of a cylindrical quantum dot with Rosen-Morse axial potential under the framework of effective mass and parabolic band approximations. This study also takes into account the effects of the structure parameters(η, V_1, and R). The analytical expressions of the linear, third-order nonlinear and total optical absorption coefficients(TOACs)and the relative refractive index changes(RRICs) are obtained by using the compact-densitymatrix approach. The results of numerical calculations show that the resonant peak position of the TOACs and RRICs shifts towards lower energies and the magnitude of the peak increases with the effect of the static electric field and ILF. In addition, it is observed that while the resonant energies of the TOACs and RRICs of system shift towards the higher(lower) energies with the enhancement of η, V_1, they decrease with the augmentation of R. Thus, the findings of this study show that the optical properties of the structure can be adjusted by changing the magnitude of structure parameters and applied external fields.     

Polaron effects on the optical absorption coefficients and refractive index changes in a square quantum well

The linear and nonlinear optical absorption coefficients and refractive index changes are obtained by using the compact density-matrix approach and an iterative procedure. With typical semiconducting GaAs materials, the linear, third-order nonlinear, total optical absorption coefficients and the optical refractive index have been examined. We find that the polaron effect has an important influence on the linear, third-order nonlinear, and total absorption coefficients as well as the refractive index changes.     

Hydrostatic pressure and temperature effects of an exciton-donor complex in quantum dots

Using the matrix diagonalization method and the compact density-matrix approach, we studied the combined effects of hydrostatic pressure and temperature on the electronic and optical properties of an exciton-donor complex in a disc-shaped quantum dot. We have calculated the binding energy and the oscillator strength of the intersubband 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 nonlinear and total optical absorption coefficients as well as the refractive index have been examined. We find that the ground state binding energy and the oscillator strength are strongly affected by the quantum dot radius, hydrostatic pressure and temperature. The results also show that the linear, third-order nonlinear and total absorption coefficients and refractive index changes strongly depend on temperature and hydrostatic pressure.     

Effect of pressure on intersubband optical absorption coefficients and refractive index changes in a V-groove quantum wire

In this paper, the effect of hydrostatic pressure on the intersubband optical absorption and the refractive index changes in a GaAs/Ga_1−xAl_xAs ridge quantum wire are studied. 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 investigated at different pressures as a function of photon energy with known values of width wire (b$b$), the incident optical intensity (I$I$), and the angle θ$\theta$. According to the results obtained from the present work, we have found that the pressure plays an important role in the intersubband optical absorption coefficients and refractive index changes in a V-groove quantum wire.     

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.     

Intense laser field effects on the linear and nonlinear intersubband optical properties of a semi-parabolic quantum well

By using the compact-density matrix approach, the effect of a nonresonant intense laser field on the linear and nonlinear optical absorptions based on intersubband transitions and the refractive index changes in an asymmetric semiconductor quantum well have been presented. Our results show that the peak position of the absorption coefficient is sensitive to intense laser field, the absorption maximum shifts towards lower energies for increasing intense laser field value. Also we observe as the intense laser field strength increases, the total refractive index change has been increased in magnitude and also shifted towards lower energies. The results indicate that linear and nonlinear optical properties of the low dimensional semiconductor heterostructures can be adjusted in a desired energy range by using intense laser field.     

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.     

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.     

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.     

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 linear and nonlinear intersubband optical absorption coefficients and refractive index changes in a V-shaped quantum well under the applied electric and magnetic fields

In this study, the changes in the optical absorption coefficients and the refractive index in a V-shaped quantum well have investigated theoretically. Within the effective mass approximation, the electronic structure of the V-shaped quantum well is calculated by numerical methods from the Schrödinger equation. Optical properties are obtained using the compact density-matrix approach. In the present work, the linear, third-order nonlinear and total absorption and refractive index changes investigated as a function of the quantum well width, the incident optical intensity, strengths of the magnetic and electric fields. Our results show that the magnetic and electric fields strengths, the quantum well width and incident optical intensity have a great effect on the optical characteristics of these structures.     

Intersubband resonant enhancement of the nonlinear optical properties in asymmetric (CdS/ZnSe) based quantum wells

In this work, the linear and nonlinear optical properties are studied theoretically in asymmetric (CdS/ZnSe/BeTe)/(ZnSe/BeTe) quantum wells. The electronic states are calculated using the envelope wave function approximation and the intersubband transition energies are studied as a function of CdS and ZnSe well thicknesses as well as doping concentration. The optimum parameters carrying out the transition energy 0.8 eV (1.55 μm wavelength) are given. Results are presented for the linear, the third order nonlinear optical absorption and the refractive index changes in the studied heterostructure. Results show that the changes in the linear and the third order nonlinear optical absorption as well as refractive index change are as important as the temperature is high, the nonlinear terms must be taken into consideration especially near the resonance.