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.     

Optical properties of AlxGa1−xAs/GaAs Woods–Saxon quantum well in the presence of hydrostatic pressure and applied electric field

The third harmonic generation (THG), linear and nonlinear optical absorption coefficients (OACs), and refractive index changes (RICs) are investigated in a Woods–Saxon quantum well (QW) modulated by the hydrostatic pressure and applied electric field. The effect of non-uniform aluminum doping (position-dependent effective mass (PDEM)) on the mass of the system is discussed, and further to explore the influence of PDEM on the nonlinear THG, OACs, and RICs of the Woods–Saxon QW. These nonlinear optical properties above are obtained using the compact-density matrix formalism. The electron states in a Woods–Saxon QW under the constant effective mass (CEM) and PDEM are calculated by solving the Schrödinger equation via the finite difference technique. The contributions from competing effects of the hydrostatic pressure and applied electric field to the nonlinear optical properties with CEM and PDEM are reported, as well as the comparison with each other. The observations reveal that the regulation of external fields and the influence of PDEM play an important role in the photoelectric properties of QW.     

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.     

Effects of hydrostatic pressure and temperature on the nonlinear optical properties of semiparabolic plus semi-inverse squared quantum wells

In this study, the effects of hydrostatic pressure and temperature on nonlinear optical rectification(OR), second-harmonic generation(SHG), third-harmonic generation(THG) and the linear,nonlinear, and total optical absorption coefficients(OACs) of a semiparabolic plus semi-inverse squared quantum well(QW) are theoretically investigated. The results show that hydrostatic pressure and temperature have significant effects on the optical properties of semiparabolic plus semi-inverse squared QWs, and that the energy levels and magnitudes of the resonant peaks of OR, SHG, THG, and the total OACs vary according to the shape of the limiting potential, the hydrostatic pressure, and the temperature. It is easily seen that the peak positions of the resonant peaks of OR, SHG, THG, and the total OACs in the semiparabolic plus semi-inverse squared QW show a red shift with increasing hydrostatic pressure, but a blue shift with increasing temperature. Therefore, the magnitude and position of the resonant peaks of OR, SHG, THG,and the total OACs can be adjusted by changing the hydrostatic pressure and the temperature,which promise a new degree of freedom in the tunability of various electro-optical devices.     

The effect of hydrostatic pressure,temperature and magnetic field on the nonlinear optical properties of asymmetrical Gaussian potential quantum wells

In this study, simultaneous effects of hydrostatic pressure, temperature and magnetic field on the linear and nonlinear intersubband optical absorption coefficients (OACs) and refractive index changes (RICs) in asymmetrical Gaussian potential quantum wells (QWs) are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy eigenvalues and their corresponding eigenfunctions of the system are calculated with the differential method. Our results show that the position and the magnitude of the resonant peaks of the nonlinear OACs and RICs depend strongly on the hydrostatic pressure, temperature and external magnetic field. This gives a new degree of freedom in various device applications based on the intersubband transitions of electrons.     

Studies on the Second-Order Nonlinear Optical Properties of Parabolic and Semi-parabolic Quantum Wells with Applied Electric Fields

Within the framework of compact density matrix approach and iterative procedure, a detailed procedure for the calculation of the second-harmonic generation (SHG) susceptibility tensor is given in the electric-field-biased parabolic and semi-parabolic quantum wells (QWs). The simple analytical formula for the SHG susceptibility in the systems is also deduced. Numerical results on typical AlGaAs/GaAs materials show that, for the same effective width, the SHG susceptibility in semi-parabolic QW is larger than that in parabolic QW due to the self-asymmetry of the semi-parabolic QW, and the applied electric field can make the SHG susceptibilities in both systems enhance remarkably. Moreover, the SHG susceptibility is also related to the parabolic confinement frequency and the relaxation rate of the systems.     

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.     

施加电场的半抛物量子阱中的电光效应

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电光效应。通过位移谐振子变换，得到了系统中的电子态的精确解。对典型的GaAs材料进行数值计算的结果表明，随着电场强度的增加，电光效应系数几乎线性随之增加；但是随着半抛物量子阱受限势频率的增加，电光效应系数单调地减小；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电光效应系数比抛物量子阱模型中的值大两个数量级，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。     

Polaron effects on the refractive index changes in cylindrical quantum dots with parabolic potential

The effect of electron-LO-phonon interaction on refractive index changes (RICs) for cylindrical quantum dots (CQDs) with an applied electric field is theoretically investigated. Analytic forms of the linear and third-order nonlinear the RICs are obtained for a cylindrical QD by using compact-density-matrix approach and iterative method, and the numerical results are presented for a GaAs cylinder quantum dot. The results show that the RICs coefficient is greatly enhanced and the peak shift to the aspect of high energy when considering the influence of electron-LO-phonon interaction.     

Two-colour mid-infrared absorption in InAs/GaSb type II and broken-gap quantum wells under gated electric field

We present a detailed theoretical study on optical properties of an InAs/GaSb-based type II and broken-gap quantum well (QW) in the presence of gated electric voltage. Two absorption peaks were observed through intraband transitions within the same material layer. The intensity of optical absorption induced by inter-layer transition is relatively weak due to a small overlap of electron and hole wavefunctions at InAs/GaSb interface. The applied electric field can open up new channels for optical transition and thus affect significantly the optical absorption by changing the overlap of the electron and hole wavefunctions as well as the transition channels. The obtained results suggest that InAs/GaSb-based type II and broken-gap QWs can be employed as two-colour photodetectors working at mid-infrared bandwidth at relatively high temperatures. More over, the bandwidth of the optical absorption can be tuned by the gated electric field.     

Electric field effect on the second-order nonlinear optical properties in semiparabolic quantum wells

Electric field effect on the second-order nonlinear optical properties in semiparabolic quantum wells are studied theoretically. Both the second-harmonic generation susceptibility and nonlinear optical rectification depend dramatically on the direction and the strength of the electric field. Numerical results show that both the second-harmonic generation susceptibility and nonlinear optical rectification are always weakened as the electric field increases where the direction of the electric field is along the growth direction of the quantum wells, which is in contrast to the conventional case. However, the second-harmonic generation susceptibility is weakened, but the nonlinear optical rectification is strengthened as the electric field increases where the direction of the electric field is against the growth direction of the quantum wells. Also it is the blue (or red) shift of the resonance that is induced by increasing of the electric field when the direction of the electric field is along (or against) the growth direction of the quantum wells. Finally, the resonant peak and its corresponding to the resonant energy are also taken into account.     

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.     

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.     

Contactless electroreflectance spectroscopy of optical transitions in low dimensional semiconductor structures

The authors present the application of contactless electroreflectance (CER) spectroscopy to study optical transitions in low dimensional semiconductor structures including quantum wells (QWs), step-like QWs, quantum dots (QDs), quantum dashes (QDashes), QDs and QDashes embedded in a QW, and QDashes coupled with a QW. For QWs optical transitions between the ground and excited states as well as optical transitions in QW barriers and step-like barriers have been clearly observed in CER spectra. Energies of these transitions have been compared with theoretical calculations and in this way the band structure has been determined for the investigated QWs. For QD and QDash structures optical transitions in QDs and QDashes as well as optical transitions in the wetting layer have been identified. For QDs and QDashes surrounded by a QW, in addition to energies of QD and QDash transitions, energies of optical transitions in the surrounded QW have been measured and the band structure has been determined for the surrounded QW. Finally some differences, which can be observed in CER and photo-reflectance spectra, have been presented and discussed for selected QW and QD structures.     

Excitonic optical absorption in wurtzite InGaN/GaN quantum wells

Within the framework of the effective-mass and envelope function theory, exciton states and optical properties in wurtzite (WZ) InGaN/GaN quantum wells (QWs) are investigated theoretically considering the built-in electric field effects. Numerical results show that the built-in electric field, well width and in composition have obvious influences on exciton states and optical properties in WZ InGaN/GaN QWs. The built-in electric field caused by polarizations leads to a remarkable reduction of the ground-state exciton binding energy, the interband transition energy and the integrated absorption probability in WZ InGaN/GaN QWs with any well width and In composition. In particular, the integrated absorption probability is zero in WZ InGaN/GaN QWs with any In composition and well width L > 4 nm. In addition, the competition effects between quantum confinement and the built-in electric field (between quantum size and the built-in electric field) on exciton states and optical properties have also been investigated.     

Effect of Quantum Well Width Reduction for GaInNAs/GaAs Lasers

We investigated the function of the quantum well (QW) width for laser characteristics especially for reduction of the well width. We pointed out that such reduction has almost no influence on the optical gain or the carrier overflow for a large conduction band offset system, such as GaInNAs QWs. A thin QW is advantageous for suppression of the carrier overflow to the higher quantized energy levels which results in good temperature and gain characteristics. Thin GaInNAs QWs is a good candidate for an active layer structure of the lasers utilized in the next optical communication systems.     

Internal electric fields due to piezoelectric and spontaneous polarizations in CdZnO/MgZnO quantum well with various applied electric field effects

The strain-induced piezoelectric polarization and the spontaneous polarization can be reduced effectively using the applied electric field in the CdZnO/ZnMgO quantum well (QW) structure with high Cd composition. That is, optical properties as a function of internal and external fields in the CdZnO/ZnMgO QW with various applied electric field result in the increased optical gain due to the fact that the QW potential profile is flattened as a result of the compensation of the internal field by the reverse field as confirmed. These results demonstrate that a high-performance optical device operation can be realized in CdZnO/MgZnO QW structures by reducing the droop phenomenon.     

Donor impurity states in direct-gap SiGe quantum well: Applied electric field and quantum size effects

Within the framework of the effective-mass approximation and variational procedure, competition effects between applied electric field and quantum size on donor impurity states in the direct-gap Ge/SiGe quantum well (QW) have been investigated theoretically. Numerical results show that the applied electric field (quantum size) dominates electron and impurity states in direct-gap Ge/SiGe QW with large (small) well width. Moreover, the competition effects also induce that the donor binding energies show obviously different behaviors with respect to electric field in the QW with different well widths. In particular, when the impurity is located at left boundary of the QW, the donor binding energy is insensitive to the variation of well width when well width is large for any electric field case.     

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.     

Effect of In-segregation on subbands in GaInNAs/GaAs quantum wells emission around 1.3 and 1.55 micron

The effect of In-segregation on optical properties in 7.5-nm GaInNAs/GaAs single quantum well (QW) is studied theoretically. The nominal (In, N) contents in the QW are chosen to be (0.35, 0.015) and (0.39, 0.03) for the emission wavelengths around 1.3 and 1.55 μm, respectively. Muraki’s model is used to model the composition profiles in the QWs. In-plane strain, confinement potential, and subband energy levels of the QW are calculated using multi-band effective mass theory. We show a space-indirect transition between light holes localized in indium deficient region and electrons localized in indium rich region of the quantum well. Our results show that the optical transition energies are approximately constant for the segregation efficiencies smaller than 0.7 in both QWs.