Theoretical studies on the optical absorption coefficients and refractive index changes in parabolic quantum dots in the presence of electric and magnetic fields

The optical absorption coefficients and the changes in the refractive index in GaAs/AlGaAs parabolic quantum dots(QDs) with applied electric and magnetic fields are studied in detail. Analytical expressions for the linear and nonlinear intersubband absorption coefficients and refractive index changes are obtained by using a compact density matrix approach and an iterative procedure. Finally, the calculated results show the incident optical intensity, the frequencies of the confined potential of the QDs and the applied electric and magnetic fields have a great influence on the optical absorption coefficients and refractive index changes in this system.     

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.     

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.     

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.     

Exciton optical absorption coefficients and refractive index changes in a strained InAs/GaAs quantum wire: The effect of the magnetic field

Magnetic field induced exciton binding energy is investigated in a strained InAs/GaAs quantum wire within the framework of single band effective mass approximation. The strain contribution to the potential is determined through deformation potentials. The interband emission energy of strained InAs/GaAs wire is investigated in the influence of magnetic field with the various structural parameters. Magnetic field induced photoionization cross section of the exciton is studied. The total optical absorption and the refractive index changes as a function of normalized photon energy between the ground and the first excited state in the presence of magnetic field are analyzed. The optical absorption coefficients and the refractive index changes strongly depend on the incident optical intensity and the magnetic field. The occurred blueshift of the resonant peak due to the magnetic field will give the information about the variation of two energy levels in the quantum well wire. The optical absorption coefficients and the refractive index changes are strongly dependent on the incident optical intensity and the magnetic field.     

Effects of external electric and magnetic fields on the linear and nonlinear intersubband optical properties of finite semi-parabolic quantum dots

In this work, influences of external electric and magnetic fields on the optical rectification coefficient, the linear and the third-order nonlinear optical absorption coefficients as well as refractive index changes of finite semi-parabolic quantum dots are investigated. In this regard, energy eigenvalues and eigenfunctions of the system are calculated numerically, and optical properties are obtained using the compact density matrix approach. The results show that external electric and magnetic fields have a great influence on these optical quantities.     

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.     

Effect of magnetic fields on the linear and nonlinear intersubband optical absorption coefficients and refractive index changes in square and graded quantum wells

In this study, both the intersubband optical absorption coefficients and the refractive index changes as dependent on the magnetic field are calculated in square and graded quantum wells. Our results show that the position and the magnitude of the linear and total absorption coefficients and refractive index changes depend on the magnetic field strength and the shape of potential. The incident optical intensity has a great effect on the total absorption and refractive index changes.     

Pressure induced optical absorption and refractive index changes of a shallow hydrogenic impurity in a quantum wire

Pressure induced binding energy of a hydrogenic impurity in an InAs/GaAs quantum wire is investigated. Calculations are performed using Bessel functions as an orthonormal basis within a single band effective mass approximation using variational method. Photoionization cross-section of the hydrogenic impurity in the influence of pressure is studied. The total optical absorption and the refractive index changes as a function of normalized photon energy between the ground and the first excited state in the presence of pressure are analyzed. The optical absorption coefficients and the refractive index changes strongly depend on the incident optical intensity and pressure. The occurred blue shift of the resonant peak due to the pressure gives the information about the variation of two energy levels in the quantum well wire. The optical absorption coefficients and the refractive index changes are strongly dependent on the incident optical intensity and the pressure.     

Linear and Nonlinear Intersubband Optical Absorptions and Refractive Index Changes in InGaN Strained Single Quantum Wells： Strong Built-in Electric Field Effects

Considering the strong built-in electric field （BEF） effects due to the spontaneous and piezoelectric polarizations, the intersubband optical absorptions and refractive index changes for an InxGa1-xN/AlyGa1-yN strained single quantum well are studied theoretically within the framework of the density matrix method and effective-mass approximation. The linear, third-order nonlinear and total absorption coefficients and refractive index changes are calculated as a function of the incident optical intensity and photon energy. Our results show that both the incident optical intensity and the strong BEF have great influence on the total absorptions and refractive index cllanges. The results are significant for designing some important photodetectors and the photonic crystal devices with adjustable photonic band structures.     

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.     

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.     

Nonlinear optical properties of an off-center donor in a quantum dot under applied magnetic field

The nonlinear optical properties of an off-center hydrogenic donor in a two-dimensional quantum dot under applied magnetic field are investigated in detail by using the matrix diagonalization method. Based on the computed energies and wave functions, the linear, third-order and total optical absorption coefficients as well as the refractive index changes have been examined between the ground state (L=0) and the first excited state (L=1). The results show that the ion position, the applied magnetic field, the confinement frequency, and the incident optical intensity have an important influence on the nonlinear optical properties of off-center donors.     

Morse势阱中线性和三阶非线性光折射率的改变

利用量子力学中的密度矩阵算符理论和迭代方法,导出莫尔斯（Morse）势阱中线性和三阶非线性光折射率改变的解析表达式,并以典型的GaAs／AlGaAs Morse势阱为例进行数值计算。数值结果表明,随着入射光强度增强,总的折射率改变将减少;随着势阱参数a的增大,总的折射率改变将减小;而随着载流子浓度的增加,总的折射率改变将增加。结果表明要获得较大的折射率改变,则需选取较小的入射光强度,较小的参数a,较大的载流子浓度,从而为实验研究提供理论依据。     

有限深V型势阱中总折射率的改变

研究了有限深V型势阱折射率改变,并且利用量子力学中的密度矩阵算符理论和迭代法导出了一次,三次谐波极化率系数.最后,以GaAs有限深V型势阱为例作了数值计算.数值结果表明,减少入射光强度,或增加电子浓度使总折射率改变变大.     

Electric field effect on the linear and nonlinear intersubband refractive index changes in asymmetrical semiparabolic and symmetrical parabolic quantum wells

By using the displacement harmonic variant method and the compact density matrix approach, the linear and nonlinear intersubband refractive index changes (RICs) in a semiparabolic quantum well (QW) with applied electric field have been investigated in detail. The simple analytical formulae for the linear and nonlinear RICs in the system were also deduced. The symmetrical parabolic QWs with applied electric fields were taken into account for comparison. Numerical calculations on typical GaAs QWs were performed. The dependence of the linear and nonlinear RICs on the incident optical intensity, the frequencies of the confined potential of the QWs and the strength of the applied electric field were discussed. Results reveal that the RICs in the semiparabolic quantum well system sensitively depend on these factors. The calculation also shows that the semiparabolic QW is a more ideal nonlinear optical system relative to the symmetric parabolic QW systems.     

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 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 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.     

Hydrostatic pressure on optical absorption and refractive index changes of a shallow hydrogenic impurity in a GaAs/GaAlAs quantum wire

The effect of hydrostatic pressure on the binding energy of a hydrogenic impurity in a GaAs/GaAlAs quantum wire is discussed. Calculations have been performed using Bessel functions as an orthonormal basis within a single band effective mass approximation. Pressure induced photoionization cross section of the hydrogenic impurity is investigated. The total optical absorption and the refractive index changes as a function of normalized photon energy between the ground and the first excited state in the presence of pressure are analysed. The optical absorption coefficients and the refractive index changes strongly depend on the incident optical intensity and the pressure.