Electric field effects on the linear and nonlinear intersubband optical properties of double semi-parabolic quantum wells

In this work, the effects of the electric field on the optical properties of the symmetric and 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. Our calculations for the asymmetric DSPQW show that the resonant peak values of the total refractive index change and total optical absorption coefficient are maximum for a certain value of the applied electric field, due to the anti-crossing effect. However, for the symmetric DSPQW, the resonant peak values of these optical properties decrease monotonically with increasing the applied electric field. Also, our results indicate that a larger value of the optical rectification coefficient of the symmetric DSPQW can be induced by applying a small electric field.     

Linear and nonlinear intersubband optical absorption in symmetric double semi-parabolic quantum wells

The linear and the nonlinear intersubband optical absorption in the symmetric double semi-parabolic quantum wells are investigated for typical GaAs/AlxGa1−xAs. Energy eigenvalues and eigenfunctions of an electron confined in finite potential double quantum wells are calculated by numerical methods from Schrödinger equation. Optical properties are obtained using the compact density matrix approach. In this work, the effects of the barrier width, the well width and the incident optical intensity on the optical properties of the symmetric double semi-parabolic quantum wells are investigated. Our results show that not only optical incident intensity but also structure parameters such as the barrier and the well width really affect the optical characteristics of these structures.     

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.     

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.     

Linear and nonlinear intersubband optical absorption in double triangular quantum wells

The linear and the third-order nonlinear optical absorptions in the asymmetric double triangular quantum wells (DTQWs) are investigated theoretically. The dependence of the optical absorption on the right-well width of the DTQWs is studied, and the influence of the applied electric field on the optical absorption is also taken into account. The analytical expressions of the linear and the nonlinear optical absorption coefficients are obtained by using the compact density-matrix approach and the iterative method. The numerical calculations are presented for the typical GaAs/Al_xGa_1?xAs asymmetric DTQWs. The results show that the linear as well as the nonlinear optical absorption coefficients are not a monotonous function of the right-well width, but have complex relationships with it. Moreover, the calculated results also reveal that applying an electric field to the DTQWs with a thinner right-well can enhance the linear optical absorption but has no prominent influence on the nonlinear optical absorption. In addition, the total optical absorption is strongly dependent on the incident optical intensity.     

Improvement in intersubband optical absorption and the effects of device parameter variations in quantum wells with an applied electric field

The intersubband optical absorption in symmetric and asymmetric, single and coupled, double GaAs/ Ga_{1 − x}Al_xAs quantum wells is calculated. The results have been obtained in the presence of a uniform electric field as a function of the potential symmetry, size of the quantum well, and coupling parameter of the wells. In coupled double quantum wells we obtain a large Stark effect that can be used to fabricate tuneable photodetectors. We show that the effect of an applied electric field on the intersubband optical absorption is similar to changes in the dimensions of the structure. This behaviour in the intersubband optical absorption for different wells and barrier geometries can be used to study these systems in regions of interest, without the need for the growth of many different samples.     

Linear and nonlinear intersubband optical absorption coefficients and refractive index changes in symmetric double semi-V-shaped quantum wells

In this study, the changes in the refractive index and intersubband optical absorption coefficients in symmetric double semi-V-shaped quantum wells are investigated theoretically. The energy levels and the envelope wave functions of an electron confined in finite potential double semi-V-shaped quantum wells are calculated within the effective-mass approximation framework. The analytical expressions of the refractive index and intersubband optical absorption coefficients are obtained using the compact density matrix approach. The effects of the incident optical intensity and structure parameters, such as the barrier width, confinement potential and the well width, on the optical properties of the double semi-V-shaped quantum wells are investigated. The numerical results show that both the incident optical intensity and structure paremeters have a great effect on the optical characteristics of these structures.     

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.     

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.     

Third-order nonlinear optical properties of excitonic state in a semiconductor quantum dot

By considering usual matrix procedures we examine how the exciton affects the nonlinear optical properties of 3-D semiconductor GaAs quantum dot. We calculate the third-order optical susceptibility of the GaAs (well) Al_xGaAs_1?x (barrier), and consequently the refractive index and the absorption coefficient. By increasing the Al content (x) in barrier material, carrier relaxation time is enhanced and the susceptibility peaks and their positions showed a blue shift, which agrees with the existing experimental work. For an anisotropic QD, the third-order nonlinear absorption coefficient depends strongly on the quantum dot width.     

Analytical expressions for asymmetric double quantum wells and their application to semiconductor heterostructures

Analytical solution of Schrödinger's equation for an asymmetric double quantum well structure is obtained for the first time in terms of a transcendental equation, roots of which give energy eigenstates and enable derivation of corresponding wave functions. Results obtained are in agreement with those reported in the literature by numerical methods and do away with the need of perturbation approximation used in such cases. As an example, GaAs/Al _x Ga_{1? x} As system has been discussed with respect to variations in barrier width, quantum well (QW) width, confining potential and material composition. The analysis shows that the coupled QWs can be matched for a given energy level to allow maximum transport between them by variation of one or more of these parameters so that the energy difference between it and the next nearest state is minimal. This condition shows a complete delocalization and the probability of finding the electron in the two QWs becomes equal, which amounts to an asymmetric system becoming symmetric with respect to probability density.     

Intersubband transitions in an asymmetric double quantum well

The intersubband optical absorption in an asymmetric double quantum well for different barrier widths and the right well widths are theoretically calculated within the framework of effective mass approximation. The results obtained show that the intersubband transitions and the energy levels in an asymmetric double quantum well can be importantly modified and controlled by the barrier width and the well width. The sensitivity to the barrier and well widths of the absorption coefficient can be used in various optical semiconductor device applications.     

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.     

Effect of position-dependent effective mass on linear and nonlinear optical properties of a cubic quantum dot

In this paper, we first obtain an analytic relation for studying the position-dependent effective mass in a GaAs/Al_xGa_1−xAs cubic quantum dot. Then, the effect of position-dependent effective mass on the intersubband optical absorption coefficient and the refractive index change in the quantum dot are studied. Our numerical calculations are performed using both a constant effective mass and the position-dependent effective mass. We calculate the linear, nonlinear and total intersubband absorption coefficient and refractive index change as a function of the incident optical intensity and structural parameters such as dot length. The results obtained from the present work show that spatially varying electron effective mass plays an important role in the intersubband optical absorption coefficient and refractive index change in a cubic quantum dot.     

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.     

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.     

Binding energies of excitons in symmetric and asymmetric quantum wells in a magnetic field

The binding energy of the exciton in the symmetric and asymmetric GaAs/Ga_1 − xAl_xAs quantum wells is calculated with the use of a variational approach. Results have been obtained as a function of the potential symmetry, and the size of the quantum well in the presence of an arbitrary magnetic field. The applied magnetic field is taken to be parallel to the axis of growth of the quantum well structure. The role of the asymmetric barriers, magnetic field, and well width in the excitonic binding is discussed as the tunability parameters of the GaAs/Ga_1 − xAl_xAs system.     

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.     

直接带隙Ge耦合双量子阱中的光吸收系数

在有效质量近似下,详细研究了直接带隙Ge/Ge Si耦合双量子阱中带间光跃迁吸收系数和阈值能量随量子阱结构参数的变化情况.结果表明:随着量子阱阱宽增大,带间光跃迁吸收强度会逐渐减弱,阈值能量减小,吸收曲线向低能方向移动,出现了红移现象.增强耦合量子阱间的耦合效应使得带间光吸收强度显著提升.此外,与非对称耦合量子阱相比,耦合效应对对称耦合量子阱中光吸收系数的影响更为显著.