Optical second harmonic generation in asymmetric double triangular quantum wells

The second harmonic generation (SHG) in the asymmetric double triangular quantum wells (DTQWs) is investigated theoretically. The dependence of the SHG coefficient on the right-well width of the DTQWs is studied, and the influence of the applied electric field on SHG coefficient is also taken into account. The analytical expression of the SHG coefficient is analyzed by using the compact density-matrix approach and the iterative method. Finally, the numerical calculations are presented for the typical GaAs/Al_xGa_1−xAs asymmetric DTQWs. The results show that the calculated SHG coefficient in this coupled system can reach the magnitude of 10⁻⁵ m/V, 1–2 orders of magnitude higher than that in step quantum well, and that in double square quantum wells. Moreover, the SHG coefficient is not a monotonic function of the right-well width, but has complex relationship with it. The calculated results also reveal that an applied electric field has a great influence on the SHG coefficient. Applying an appropriate electric field to a DTQW with a wider right well can induce a sharper peak of the SHG coefficient due to the double-resonant enhancement.     

Nonlinear optical rectification in asymmetric double triangular quantum wells

The nonlinear optical rectification (OR) in the asymmetric double triangular quantum wells (DTQWs) is investigated theoretically. The dependence of OR on the right-well width of the DTQWs is studied, and the influence of the applied electric field on OR is also taken into account. The analytical expression of the OR susceptibility is analyzed by using the compact density-matrix approach and the iterative method and the numerical calculations are presented for the typical GaAs/Al_xGa_1-xAs asymmetric DTQWs. The results show that the OR susceptibility obtained in this coupled system can reach the magnitude of 10^-3 m/V, 2-3 orders of magnitude higher than that in single quantum systems. Moreover, the OR susceptibility is not a monotonic function of the width of the right well, but has complex relationship with it. The calculated results also reveal that an applied electric field has a great influence on the OR susceptibility. Applying an appropriate electric field to a quasi-symmetric or symmetric DTQW can result in a larger OR susceptibility as compared with that obtained in an optimal asymmetric DTQW without electric field.     

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.     

Electric field induced exciton binding energy and its non-linear optical properties in a narrow InSb/InGaxSb1−x quantum dot

The effect of electric field on the binding energy, interband emission energy and the non-linear optical properties of exciton as a function of dot radius in an InSb/InGa_xSb_1?x quantum dot are investigated. Numerical calculations are carried out using single band effective mass approximation variationally to compute the exciton binding energy and optical properties are obtained using the compact density matrix approach. The dependence of the nonlinear optical processes on the dot sizes is investigated for various electric field strength. The linear, third order non-linear optical absorption coefficients, susceptibility values and the refractive index changes of electric field induced exciton as a function of photon energy are obtained. It is found that electric field and the geometrical confinement have great influence on the optical properties of dots.     

Linear and nonlinear optical absorption coefficients in inverse parabolic quantum wells under static external electric field

In the present theoretical study, the linear and third-order nonlinear optical absorption coefficients have been calculated in GaAs/Ga_1−x Al _x As inverse parabolic quantum wells (single and double) subjected to an external electric field. Our calculations are based on the potential morphing method in the effective mass approximation. The systematic theoretical investigation contains results with all possible combinations of the involved parameters, as quantum well width, quantum barrier width, Al concentration at each well center and magnitude of the external electric field. Our results indicate that in most cases investigated, the increase of the electric field blue-shifts the peak positions of the total absorption coefficient. In all cases studied it became apparent that the incident optical intensity considerably affects the total absorption coefficient.     

Nonlinear optical rectification in asymmetric coupled quantum wells

The optical rectification (OR) in the asymmetric coupled quantum wells (ACQWs) is calculated theoretically. The dependence of the OR on the width of the right-well and the barrier is studied. The analytical expression of the optical rectification coefficient is obtained by using the compact density-matrix approach and the iterative method, and the numerical calculations are presented for a typical GaAs/Al_xGa_1 − xAs ACQW. The results obtained show that the OR efficient can reach the magnitude of 10⁻⁴ m/V in this ACQW system, which is 1-2 orders higher than that in single quantum systems. Moreover, the OR coefficient is strongly dependent on the widths of the barrier and the right-well of the ACQWs. An appropriate choice for the width of the barrier and the right-well of the ACQWs can induce a larger OR coefficient.     

Linear and nonlinear optical properties in a semiconductor quantum well under intense laser radiation: Effects of applied electromagnetic fields

In this work we are studying the intense laser effects on the electron-related linear and nonlinear optical properties in GaAs–Ga_1?xAl_xAs quantum wells under applied electric and magnetic fields. The calculated quantities include linear optical absorption coefficient and relative change of the refractive index, as well as their corresponding third-order nonlinear corrections. The nonlinear optical rectification and the second and third harmonic generation coefficients are also reported. The DC applied electric field is oriented along the hererostructure growth direction whereas the magnetic field is taken in-plane. The calculations make use of the density matrix formalism to express the different orders of the dielectric susceptibility. Additionally, the model includes the effective mass and parabolic band approximations. The intense laser effects upon the system enter through the Floquet method that modifies the confinement potential associated to the heterostructure. The results correspond to several configurations of the dimensions of the quantum well, the applied electric and magnetic fields, and the incident intense laser radiation. They suggest that the nonlinear optical absorption and optical rectification are nonmonotone functions of the dimensions of the heterostructure and of the external perturbations considered in this work.     

Linear and nonlinear intersubband optical absorption and refractive index changes of asymmetric double semi-parabolic quantum wells

The optical properties of the asymmetric double semi-parabolic quantum wells (DSPQWs) are investigated numerically for typical GaAs/Al_xGa_1−xAs. Optical properties are obtained using the compact density matrix approach. In this work, effects of the structure parameters such as the barrier width and the well widths on the optical properties of the asymmetric DSPQWs are investigated. The results show that the linear and nonlinear optical properties of asymmetric DSPQW are non-monotonic functions of these structure parameters. The behavior of the refractive index changes of asymmetric DSPQW with the variation of the barrier width is different substantially with that of symmetric DSPQW. Results reveal that the resonant peak values of the total absorption coefficient of asymmetric DSPQW is usually greater than that of symmetric DSPQW. Our calculations also show that the total absorption coefficient of asymmetric DSPQW is larger than that of asymmetric double square quantum well.     

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.     

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.     

Intense laser effects on nonlinear optical absorption and optical rectification in single quantum wells under applied electric and magnetic field

In this work the effects of intense laser on the electron-related nonlinear optical absorption and nonlinear optical rectification in GaAs-Ga_1−xAl_xAs quantum wells are studied under, applied electric and magnetic field. The electric field is applied along the growth direction of the quantum well whereas the magnetic field has been considered to be in-plane. The calculations were performed within the density matrix formalism with the use of the effective mass and parabolic band approximations. The intense laser effects are included through the Floquet method, by modifying the confining potential associated to the heterostructure. Results are presented for the nonlinear optical absorption, the nonlinear optical rectification and the resonant peak of these two optical processes. Several configurations of the dimensions of the quantum well, the applied electric and magnetic fields, and the incident intense laser radiation have been considered. The outcome of the calculation suggests that the nonlinear optical absorption and optical rectification are non-monotonic functions of the dimensions of the heterostructure and of the external perturbations considered in this work.     

Size dependent effective band gap,optical absorption coefficients and refractive index changes in a wide ZnS/Zn1−xMgxS strained quantum well

Exciton binding energy of a confined heavy hole exciton is investigated in a Zn_1−xMg_xS/ZnS/Zn_1−xMg_xS single strained quantum well with the inclusion of size dependent dielectric function for various Mg content. The effects of interaction between the exciton and the longitudinal optical phonon are brought out. The effect of exciton is described by the effective potential between the electron and hole. The interband emission energy as a function of well width is calculated for various Mg concentration with and without the inclusion of dielectric confinement. Non-linear optical properties are carried out using the compact density matrix approach. The dependence of nonlinear optical processes on the well width is investigated for different Mg concentration. The linear, third order non-linear optical absorption coefficients values and the refractive index changes of the exciton are calculated for different concentration of magnesium content. The results show that the exciton binding energy is found to exceed LO phonon energy of ZnS for x>0.2 and the incorporation of magnesium ions and the effect of phonon have great influence on the optical properties of ZnS/Zn_1−xMg_xS quantum wells.     

Intensity-dependent nonlinear optical properties in a modulation-doped single quantum well

In the present work, the changes in the intersubband optical absorption coefficients and the refractive index in a modulation-doped quantum well have been investigated theoretically. Within the envelope function approach and the effective mass approximation, the electronic structure of the quantum well is calculated from the self-consistent numerical solution of the coupled Schrödinger-Poisson equations. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. The numerical results GaAs/Al_xGa_1−xAs are presented for typical modulation-doped quantum well system. The linear, third-order nonlinear and total absorption and refractive index changes depending on the doping concentration are investigated as a function of the incident optical intensity and structure parameters, such as quantum well width and stoichiometric ratio. The results show that the doping concentration, the structure parameters and the incident optical intensity have a great effect on the optical characteristics of these structures.     

Nonlinear optical absorption and optical rectification in near-surface double quantum wells: combined effects of electric, magnetic fields and hydrostatic pressure

The theoretical study of the combined effects of electric and magnetic fields and hydrostatic pressure on the nonlinear optical absorption and rectification is presented for electrons confined within an asymmetrical GaAs?Ga_1-x Alx As double quantum well. The effective mass, parabolic band, and envelope function approaches are used as tools for the investigation. The electric field is taken to be oriented along the growth direction of the heterostructure and the magnetic field is applied parallel to the interfaces of the quantum wells. The pressure-induced mixing between the two lowest conduction bands is considered both in the low and high pressure regimes. According to the results obtained it can be concluded that the nonlinear optical absorption and rectification coefficients depend in a non-trivial way on some internal and external parameters such as the size of the quantum wells, the direction of applied electric field, the magnitude of hydrostatic pressure, the stoichiometry of the wells and barriers, and the intensity of the applied magnetic field.     

Optical properties of a hydrogenic impurity in a confined Zn1−xCdxSe/ZnSe spherical quantum dot

The effect of longitudinal optical phonon field on the ground state and low lying-excited state energies of a hydrogenic impurity in a Zn_1−xCd_xSe/ZnSe strained quantum dot is investigated for various Cd content using the Aldrich-Bajaj effective potential. We consider the strain effect considering the internal electric field induced by the spontaneous and piezoelectric polarizations. Calculations have been performed using Bessel function as an orthonormal basis for different confinement potentials of barrier height. Polaron induced photoionization cross section of the hydrogenic impurity in the quantum dot is investigated. We study the oscillator strengths, the linear and third-order nonlinear optical absorption coefficients as a function of incident photon energy for 1s-1p and 1p-1d transitions with and without the polaronic effect. It is observed that the potential taking into account the effects of phonon makes the binding energies more than the obtained results using a Coulomb potential screened by a static dielectric constant and the optical properties of hydrogenic impurity in a quantum dot are strongly affected by the confining potential and the radii. It is also observed that the magnitude of the absorption coefficients increases for the transitions between higher levels with the inclusion of phonon effect.     

Effect of conduction band nonparabolicity on the optical properties in a single quantum well under hydrostatic pressure and electric field

The effect of conduction band nonparabolicity on the linear and nonlinear optical properties such as absorption coefficients, and changes in the refractive index are calculated in the Al_0.3Ga_0.7As/GaAs heterostructure-based symmetric rectangular quantum well under applied hydrostatic pressure and electric field. The electron envelope functions and energies are calculated in the effective mass equation including the conduction band nonparabolicity. The linear and nonlinear optical properties have been calculated in the density matrix formalism with two-level approximation. The conduction band nonparabolicity shifts the positions of the optical properties and decreases their strength compared to those without this correction. Both the optical properties are enhanced with the applied hydrostatic pressure. While the absorption coefficients are bleached under the combined effect of high pressure and electric field, the bleaching effect is reduced when nonparabolicity is included.     

Conduction band non-parabolicity effect on the optical absorption coefficient and refractive index changes of spherical quantum dots

Optical absorption coefficients and refractive index changes associated with intersubband transition in typical GaAs/Al_xGa_1−xAs spherical quantum dots are theoretically investigated, both in the presence and in the absence of the conduction band non-parabolicity effect. In this regard, the effect of band non-parabolicity on the eigenvalues and eigenfunctions of the dot has been performed using the Luttinger-Kohn effective mass equation. Also, by means of the compact-density-matrix approach the linear and nonlinear optical absorption coefficients and refractive index changes have been calculated. The results show that magnitudes of these quantities are decreased and the peaks are shifted to the lower energies as the influence of band non-parabolicity is considered.     

Built-in electric field effect on the linear and nonlinear intersubband optical absorptions in InGaN strained single quantum wells

Considering the strong built-in electric field (BEF) induced by the spontaneous and piezoelectric polarizations and the intrasubband relaxation, we investigate the linear and nonlinear intersubband optical absorptions in In_xGa_1-xN/Al_yGa_1-yN strained single quantum wells (QWs) by means of the density matrix formalism. Our numerical results show that the strong BEF is on the order of MV/cm, which can be modulated effectively by the In composition in the QW. This electric field greatly increases the electron energy difference between the ground and the first excited states. The electron wave functions are also significantly localized in the QW due to the BEF. The intersubband optical absorption peak sensitively depends on the compositions of In in the well layer and Al in the barrier layers. The intersubband absorption coefficient can be remarkably modified by the electron concentration and the incident optical intensity. The group-III nitride semiconductor QWs are suitable candidate for infrared photodetectors and near-infrared laser amplifiers.     

Exciton effects on the refractive index and optical absorption in wurtzite quantum wells via a fractional-dimensional space approach

The optical refractive index changes and absorption coefficients of quantum wells (QWs) are theoretically investigated with considering exciton effects within the framework of the fractional-dimensional space approach. The exciton wave functions and bound energies are obtained as a function of spatial dimensionality, and the dimension increases with the well width increasing. Then optical properties are obtained by using the compact-density matrix approach and an iterative method. Numerical results are presented for wurtzite ZnO/Mg_xZn_1−xO QWs. The calculated results show that the changes of refractive index and absorption coefficients are greatly enhanced due to the quantum confinement of exciton. And the smaller the QW width (dimension) is, the larger influence of exciton on the optical properties will be. Furthermore, the exciton effects make the resonant peaks move to a lower energy. In addition, the optical properties are related to the QW width, the incident optical intensity and carrier density.