Calculation of Linear and Nonlinear Intersubband Optical Absorptions in Electric-Field-Biased Semiparabolic Quantum Wells

By using the compact density matrix approach and iterative procedure, a detailed procedure for the calculation of the linear and nonlinear intersubband optical absorption coefficients is given in the electric-field-biased semi-parabolic quantum wells (QWs). The simple analytical formulas for the linear and nonlinear optical absorption coefficients in the systems are also deduced. Numerical result on typical GaAs materials shows that, the linear and nonlinear optical absorption coefficients sensitively depend on the applied electric field and the confined potential frequency of the semiparabolic QW systems as well as the incident optics beam intensity.     

Polaron Effect of a Two Electron Parabolic Quantum Dot

Polaron induced double electron in a quantum dot is investigated using the exact diagonalization techniques and the compact density-matrix approach. The dependence of nonlinear optical processes on the incident photon energies and the polaronic effect are brought out. The linear, third order non-linear optical absorption coefficients and the refractive index changes of singlet and triplet states as a function of photon energy are obtained with and without the inclusion of polaronic effect. It is found that the geometrical confinement and the effect of polaron have great influence on the optical properties of dots.     

Effect of size and indium-composition on linear and nonlinear optical absorption of InGaN/GaN lens-shaped quantum dot

Based on the Schr ¨odinger equation for envelope function in the effective mass approximation, linear and nonlinear optical absorption coefficients in a multi-subband lens quantum dot are investigated. The effects of quantum dot size on the interband and intraband transitions energy are also analyzed. The finite element method is used to calculate the eigenvalues and eigenfunctions. Strain and In-mole-fraction effects are also studied, and the results reveal that with the decrease of the In-mole fraction, the amplitudes of linear and nonlinear absorption coefficients increase. The present computed results show that the absorption coefficients of transitions between the first excited states are stronger than those of the ground states. In addition, it has been found that the quantum dot size affects the amplitudes and peak positions of linear and nonlinear absorption coefficients while the incident optical intensity strongly affects the nonlinear absorption coefficients.     

Linear and nonlinear optical absorption coefficients and binding energy of a spherical quantum dot

The binding energy and wavefunctions of the 1s, 1p, 1d and 1f energy states of a spherical quantum dot (QD) with parabolic potential were calculated by using a method which is a combination of the quantum genetic algorithm (QGA) and the Hartree–Fock–Roothaan (HFR) approach. In addition, the linear and the third-order nonlinear optical absorption coefficients based on optical transitions in QDs with and without impurity were calculated. The results show that the parabolic potential has a great effect not only on the binding energies and but also on the optical absorption coefficients. Moreover, the calculated results also reveal that the linear and nonlinear optical absorption coefficients are strongly affected by the existence of impurity and the incident optical intensity.     

Morse势阱中子带间的光吸收

研究了Morse势阱中子带间的光吸收,并且利用密度矩阵算符理论和迭代方法,推导出了线性和三阶非线性子带间的光吸收系数的解析表达式,然后以GaAs/AlGaAsMorse势阱为例进行数值计算。结果表明,线性吸收系数是正的,为总吸收系数作出积极的作用,而三阶非线性吸收为负,抵消了一部分线性吸收,进而得到总的吸收系数;吸收系数随着入射光强度的增大而减小,即出现吸收饱和现象;当势阱参数a增大时,吸收系数增大,即阱宽较窄时,系统吸收的能量较多。若要获得较大的光学吸收系数,就要输入较小的光场强度,并选择适当的势阱参数a和入射光频率。     

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.     

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.     

ZnS/CdSe量子点中线性和三阶非线性光吸收系数研究

在有效质量近似下,利用量子力学的密度矩阵理论,采用无限深势阱模型,从理论上研究了ZnS/CdSe柱型核壳结构量子点中线性和三阶非线性光吸收系数。导出了柱型量子点中线性和三阶非线性光学吸收系数的解析表达式,分析了该系统在不同条件下线性和三阶非线性光吸收系数与入射光频率之间的关系。改变系统的参数,该系统的光吸收系数呈规律性变化。计算结果表明:弛豫时间τ、入射光强I和壳半径R2对系统的吸收系数α有很大的影响,从而为实验上研究核壳结构量子点的非线性光学效应提供了必要的理论依据。     

Polaronic effects due to surface optical vibration modes in a freestanding cylindrical wurtzite nanowire

The ground-state polaron self-trapped energy and effective mass due to the surface optical (SO) phonon modes in a freestanding wurtzite GaN nanowire (NW) were studied by means of the Lee–Low–Pines variational approach. Based on the dielectric continuum and Loudon’s uniaxial crystal models, the polar optical phonon modes in the one-dimensional (1D) systems are analyzed, and the vibrating spectra of SO modes and electron–SO phonon coupling functions are discussed and analyzed. The calculations on the ground-state polaron self-trapped energy and correction of effective mass due to the SO phonon modes in the 1D GaN NWs reveal that the polaron self-trapped energy and correction of effective mass are far larger than those in 1D GaAs NW systems. The reasons resulting in this obvious difference in the two 1D structures are mainly due to the different electron–phonon coupling constants and electron effective masses of bulk materials constituting the two types of 1D confined system. Finally, the polaronic properties of the wurtzite 1D GaN NWs have been compared with those of the wurtzite GaN-based two-dimensional quantum wells. The physical origination of these characteristics and their distinction in the different-dimensionality systems has been analyzed in depth.     

Nonlinear intersubband optical absorption in semiparabolic quantum wells

The linear and third-order nonlinear optical absorptions in semiparabolic quantum wells are studied in detail. Analytic formulas for the linear and third-order nonlinear optical absorption coefficients are obtained using the compact density matrix approach. Based on this model, numerical results are presented for typical GaAs/AlGaAs semiparabolic quantum wells. The results show that the factors of the incident optical intensity and the semiparabolic confinement frequency have great influences on the total optical absorption coefficients.     

加偏置电场的双曲线量子阱中线性与三阶非线性光学吸收系数的计算

利用紧致密度矩阵近似方法,研究了加偏置电场双曲线量子阱中的线性与三阶非线性光学吸收系数. 得到了该系统中的线性与三阶非线性光学吸收系数的解析表达式.分析了势阱的形状、外加电场的大小以及入射光场的强度对吸收系数的影响规律. 文章以典型的AlxGa1－xAs/ GaAs双曲线量子阱为例作了数值计算.结果表明：随着势阱宽度的增加,系统的吸收系数将减小;随着外加电场的增加,系统的非对称性增加,系统的吸收系数将增加;随着外加光场强度的增加,系统的吸收系数将减小,并且当光强增加到一定值时会出现明显的饱和吸收现象,这一结论为进一步的实验研究提供了相应的理论依据.     

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 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.     

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.     

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.     

Electron-phonon interaction effect on optical absorption in cylindrical quantum wires

Electron-phonon interaction effects on linear and nonlinear optical absorption in cylindrical quantum wires are investigated. The linear and nonlinear optical absorption coefficients are obtained by using compact-density-matrix approach and iterative method, and the numerical results are presented for GaAs/AlAs cylindrical quantum-well wires. The results show that electron-phonon interaction not only influences the relaxation rate but also distinctly influences the wave functions and energies of the electron. The correction of electron-phonon interaction effect on the wave functions of the electron dominates the values of absorption coefficients. Moreover, the correction of electron-phonon interaction effect on the energies of the electron makes the absorption peaks blue shift and become wider.     

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.     

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.     

Nonlinear optical absorption in graded quantum wells modulated by electric field and intense laser field

The laser field dependence of the linear and nonlinear intersubband optical absorption in a graded quantum well (GQW) under an applied electric field is investigated in the effective mass approximation. In our calculations, the position and the magnitude of the linear and total absorption coefficients depend on the laser parameter and electric field strength. The resonant peak of total absorption coefficient can be bleached at sufficiently high incident optical intensities. Such a dependence of the exciting optical intensity on the external field strengths in GQWs can be very useful for several potential device applications.     

Calculation of linear and nonlinear optical absorption coefficients of a spherical quantum dot with parabolic potential

In the effective mass approximation, we calculated the binding energy and wave function for the 1s-, 1p-, 1d- and 1f-states of a spherical quantum dot (QD) with parabolic potential by using a combination of quantum genetic algorithm (QGA) and Hartree-Fock-Roothaan (HFR) method. In addition, we also investigated the linear and the third-order nonlinear optical absorption coefficients as a function of the incident photon energy for the 1s-1p, 1p-1d and 1d-1f transitions. Our results are shown that the existence of impurity has great influence on optical absorption coefficients. Moreover, the optical absorption coefficients are strongly affected by the incident optical intensity, relaxation time, parabolic potential and dot radius.