Nonlinear optical rectification of hydrogenic impurity in a disk-like parabolic quantum dot: The role of applied magnetic field

We report a detailed theoretical study of the effect of combined electric and magnetic field on the nonlinear optical rectification of a hydrogenic impurity, confined in a two dimensional disk-like quantum dot, with parabolic confinement potential. We use the compact density matrix formalism and iterative method to obtain nonlinear optical rectification and absorption coefficients. To find energy levels and wave functions, we employ exact diagonalization method in the effective mass approximation. As main result, we found that the transition energy from ground to first excited state redshifts with increasing the magnetic field while blueshifts for transition from ground to second excited state, moreover, for former transition, nonlinear optical rectification coefficient decreases with increasing magnetic field in contrast to that occurs for latter one.     

施加电场的半抛物量子阱中的二阶非线性光学极化率

利用量子力学中的紧致密度矩阵方法,研究了施加电场的半抛物量子阱中的二阶非线性光学极化率(光整流系数),得到了此系统的光整流系数的解析表达式.数值计算的结果表明,随着电场强度的增加,光整流系数几乎线性随之增加,而且在同样的电场强度及抛物束缚势频率作用下,半抛物量子阱模型中的光整流系数比抛物量子阱模型中的值大一个数量级,这是由于我们所选模型本身的非对称性以及电场进一步使这种非对称性增强的缘故.     

Nonlinear optical rectification of a hydrogenic impurity in a disc-like quantum dot

An investigation of the nonlinear optical rectification of a hydrogenic impurity, which is in a two-dimensional disc-like quantum dot (QD) with parabolic confinement potential, has been performed by using the perturbation method in the effective mass approximation. Both the electric field and the confinement effects on the energy are investigated in detail. The results are presented as a function of the incident photon energy for the different values of the confinement strength and the electric field. It is found that the nonlinear optical properties of hydrogenic impurity states in a disc-like QD are strongly affected by the confinement strength and the electric field.     

Effects of an electric field on the confined hydrogen impurity states in a spherical parabolic quantum dot

In this paper, we studied the effects of an electric field on a hydrogenic impurity confined in a spherical parabolic quantum dot using nondegenerate and degenerate perturbation methods. The binding energies of the ground and three low-excited states are calculated as a function of the confinement strength and as a function of the intensity of an applied electric field. Moreover, we computed the oscillator strength and the second-order nonlinear optical rectification coefficient based on the computed energies and wave functions. The results show that the electric and optical properties of hydrogenic impurity states are strongly affected by the confinement strength and the applied electric field.     

加偏置电场的双曲线量子阱中的光整流效应

用量子力学中密度矩阵算符理论导出了加偏置电场的双曲线量子阱中光整流系数的解析表达式.并以典型的GaAs双曲线量子阱为例进行了数值计算。研究结果表明,该势阱中的光整流系数与势阱的形状和偏置电场的强度有关。通过调节势阱参量a以及外加偏置电场,在该势阱中可获得一个大的光整流系数.     

Nonlinear optical rectification in parabolic quantum dots in the presence of electric and magnetic fields

The optical rectification (OR) coefficient in a parabolic quantum dots (QDs) subject to applied electric and magnetic fields is theoretically investigated in the framework of the compact-density-matrix approach and an iterative method. The confined wave functions and energies of electrons in the QDs are calculated in the effective-mass approximation. Numerical results are presented for typical GaAs/AlGaAs parabolic QDs. These results show that the OR coefficient strongly depends on the radius of QDs and the magnitude of electric and magnetic fields. And the peak shifts to the aspect of high energy when considering the influence of electric and magnetic fields.     

Optical non-linearities associated to hydrogenic impurities in InAs/GaAs self-assembled quantum dots under applied electric fields

Abstract

The effects of the hydrogenic impurity on the electron-related non-linear optical processes in a InAs/GaAs dome-shaped quantum dot with a wetting layer under applied electric fields are studied within the density-matrix formalism. The one-electron energy levels and wave functions are calculated using the effective mass approximation and the finite element method. The non-linear optical absorption, relative refractive index change and non-linear optical rectification associated with interlevel transitions are calculated under a strong probe field excitation for both in-plane and z-polarisation of the incident light. According to our results as the electric field increases the absorption and dispersion peaks decrease and exhibit red shift. Hydrogenic impurity located at the origin induces a blue shift in the optical responses. For the optical absorption coefficient the peaks magnitude is enhanced by the impurity presence independent of the electric field strengths, whereas the non-linear optical rectification is larger in the case with impurity only for zero applied electric field.     

双波泵浦非对称量子阱的光学整流效应

为了实现基于光整流方式的室温下宽调谐高效率太赫兹源,设计了一种适于双波长CO2激光器共振子带跃迁泵浦的双阱嵌套形非对称量子阱结构,结构组分为Al0.5Ga0.5As/Ga As/Al0.2Ga0.8As,采用密度矩阵及迭代方法计算了其二阶非线性光整流系数χo(2)表达式,在导带为抛物线形和非抛物线形两种条件下对χo(2)进行对比研究。计算结果表明,其偶极跃迁矩阵元随量子阱总阱宽的增大而逐渐减小。当固定量子阱总阱宽及其中一束泵浦光波长不变时,χo(2)随着另一束泵浦光波长的增加,呈现出先增大后减小的变化趋势。当深阱为7 nm、总阱宽为23 nm、两束泵浦光相等为10.64μm时,χo(2)达到最大值5.925×10-6m/V;随着总阱宽的增大,χo(2)曲线呈现"红移"现象,其原因为量子限制效应导致了不同阱宽条件下的量子阱能级值差不同,从而造成满足泵浦光光子能量与能级差共振条件的变化。导带为抛物线形和非抛物线形两种条件下的χo(2)的最大值对应泵浦光波长基本相同,χo(2)数值上的差异主要由跃迁矩阵元的不同导致。     

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.     

Nonlinear optical properties of a Woods–Saxon quantum dot under an electric field

A theoretical study of the effect of the confining potential on the nonlinear optical properties of two dimensional quantum dots is performed. A three-parameter Woods–Saxon potential is used within the density matrix formalism. The control of confinement by three parameters and an applied electric field gives one quite an advantage in studying their effects on the nonlinear properties. The coefficients investigated include the optical rectification, second and third-harmonic generation and the change in the refractive index. Their dependence on the electric field values, dot size and the energy of the incoming photons is studied extensively.It is shown that the Woods–Saxon potential can be used to model the confinement in quantum dots with considerable success.     

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.     

Spherical quantum dot in modified Kratzer–Coulomb potential: study of optical rectification coefficients

We consider the effects of quantum dot radius, confinement potential depth and controllable effective mass on the optical rectification coefficient (ORC) in spherical quantum dots, which is confined with Modified Kratzer–Coulomb Potential (MKCP). Using the Nikiforov–Uvarov method and compact density matrix theory, the ground state energy, ORC and wave function of electrons under the combined action of many factors are calculated. The results show that they affect the optical rectification response from different angles, including the position of peak and formant.     

The nonlinear optical rectification of a confined exciton in a quantum dot

An exciton in a disc-like quantum dot (QD) with the parabolic confinement, under applied electric field, is studied within the framework of the effective-mass approximation. The nonlinear optical rectification between the ground and the first-excited states has been examined through the computed energies and wave functions in details for the excitons. The results show that the optical rectification susceptibility obtained in a disc-like QD reach the magnitude of 10⁻² m/V, which is 3-4 orders of magnitude higher than in one-dimensional QDs. It is found that the second-order nonlinear optical properties of exciton states in a QD are strongly affected by the confinement strength and the electric field.     

Exciton related optical absorption in a spherical quantum dot

An exciton in a spherical quantum dot is studied analytically within the effective mass approximation. A parabolic confinement under an electric field is considered. The linear and nonlinear optical absorption coefficients are calculated within the density matrix formalism. No assumptions are made about the strength of the confinement. It is shown how the competing mechanisms of the Coulomb interaction, the confinement and the applied static electric field affect the optical absorption.     

Static and dynamic study of magnetic properties in FeNi film on flexible substrate, effect of applied stresses

The influence of an external electric field on the binding energies of the ground state and excited states with the third-harmonic-generation (THG) coefficient for spherical quantum dot (QD) with parabolic confinement is investigated theoretically. The energy levels and wave functions of electronic states in the QDs are calculated using by variational method within the effective-mass approximation. The numerical results demonstrate that the THG coefficient very sensitively depends on the magnitude of the electric field and the radius of the QDs. In addition, the THG coefficient also depends on the relaxation rate of the spherical QD with parabolic confinement and the position of impurity.     

Intersubband optical absorption coefficients and refractive index changes in a parabolic cylinder quantum dot

Optical absorption coefficients and refractive index changes associated with intersubband transition in a parabolic cylinder quantum dot are theoretically investigated. In this regard, the electronic structure of the dot is studied using the one band effective mass theory, and by means of the compact-density matrix approach the linear and nonlinear optical absorption coefficients and refractive index changes are calculated. The effects of the size of the dot, optical intensity and electromagnetic field polarization on the optical absorption coefficient and refractive index changes are investigated. It is found that absorption and refractive index changes are strongly affected not only by the size of the dot but also by optical intensity and the electromagnetic field polarization.     

Impurity related optical properties in tuned quantum dot/ring systems

In this paper, we explore the linear, third-order nonlinear, and total optical absorption coefficient (OAC) and refractive index change coefficient (RICC) of a GaAs doped quantum dot/quantum ring (QD/QR) with parabolic-inverse squared potential in conjunction with modified Gaussian confinement and taking into account the presence of on-centre shallow donor and or acceptor impurity. Calculations are done via the compact density matrix formalism and the iterative method. The two-dimensional parabolic QD/QR is subjected to uniform magnetic field oriented perpendicularly to the plane of the structure. The energy levels and wave function are derived within the framework of effective-mass and parabolic band approximation. The results exhibit that the OACs and RICC are clearly affected by different parameters of the applied confinement, strength of magnetic field, and the presence of impurity. The variation of confinement potential, nature of impurity, dot radius, cyclotron frequency of the parabolic confinement potential, and geometric parameter of the on-centre repulsive potential lead to either a red-shift or a blue-shift of the resonant peaks of the OACs and of the maximum and minimum of the RICC together with significant variations of the magnitudes of these resonant structures.     

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.     

Simultaneous effects of spin-orbit interaction and external electric field on the linear and nonlinear optical properties of a cubic quantum dot

In this article simultaneous effects of external electric field and spin-orbit interaction on the linear and the nonlinear optical properties of a cubic quantum dot are studied. Based on the non- degenerate perturbation method, energy eigenvalues and eigenfunctions of the system under the influence of spin-orbit interaction are calculated. Furthermore, the linear and the nonlinear optical absorption coefficients and refractive index changes are obtained using the compact density matrix approach and iterative method. Our results show that, due to the spin-orbit interaction, resonant peak values of the optical absorption coefficients and refractive index changes decrease and occur at lower values of the incident photon energy. The variation of these optical parameters depend on the spin-orbit interaction strength, dot dimensions and external electric field.     

Optical rectification coefficient of a two-dimensional quantum pseudodot system

Optical rectification coefficient associated with intersubband transitions in a two-dimensional quantum pseudodot system, under the influence of an uniform magnetic field is theoretically investigated. In this regard, the compact-density matrix approach and an iterative method are used to find the optical rectification coefficient of the pseudodot system. We have investigated the effects of an external magnetic field, the geometrical size and the chemical potential of the pseudodot system on this coefficient. It is found that optical rectification coefficient is affected by the external magnetic field, the geometrical size and the chemical potential of the pseudodot system.