The nonlinear optical rectification coefficient of quantum dots and rings with a repulsive scattering center

We make a rigorous exploration of profiles of nonlinear optical rectification (NOR) coefficient of impurity doped quantum dots (QDs) in presence and absence of noise. We have exploited Gaussian white noise in the present study. The quantum dot is doped with Gaussian impurity. Noise has been introduced to the system additively and multiplicatively. A perpendicular magnetic field serves as a confinement source and a static external electric field has been applied. The NOR profiles have been monitored as a function of incident photon energy when several important parameters such as electric field strength, magnetic field strength, confinement energy, dopant location, relaxation time, Al concentration, dopant potential, and noise strength assume different values. In addition, the role of mode of application of noise (additive/multiplicative) on the NOR profiles has also been examined thoroughly. The NOR profiles are found to be endowed with interesting observations such as shift of peak position and maximization/minimization of peak intensity. However, presence of noise prominently alters the features of NOR profiles through some interesting manifestations and often induces one photon resonance enhancement. Furthermore, the mode of application of noise (additive/multiplicative) also controls the NOR profiles in disparate as well as often contrasting manners. The observations indicate possibilities of tailoring the NOR coefficient of doped QD systems in presence of noise which bears tremendous technological importance.

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

The linear and nonlinear intraband optical absorption coefficients in GaAs three-dimensional single quantum rings are investigated. Taking into account the combined effects of hydrostatic pressure and electric field, applied along the growth direction of the heterostructure, the energies of the ground and first excited states of a donor impurity have been found using the effective mass approximation and a variational method. The energies of these states are examined as functions of the dimensions of the structure, electric field, and hydrostatic pressure. We have also investigated the dependencies of the linear, nonlinear, and total optical absorption coefficients as a function of incident photon energy for several configurations of the system. It is found that the variation of distinct sizes of the structure leads to either a redshift and/or a blueshift of the resonant peaks of the intraband optical spectrum. In addition, we have found that the application of an electric field leads to a redshift, whereas the influence of hydrostatic pressure leads to a blueshift (in the case of on-ring-center donor impurity position) of the resonant peaks of the intraband optical spectrum.

Polydiacethylene copolymers having different polymer backbone were synthesized consisting of same chromophore, such as dispersed red 19. Effects of polymer backbone on second-order nonlinear optical coefficients were investigated. The thin films of polydiacethylene were prepared by coating on soda-lime glass substrate and poled by corona poling at elevating temperature. The second-order NLO coefficients d33 of the films were measured by in situ second-harmonic generation measurements and Maker fringe measurements. The d33/d31 were deduced as 6.0 and 2.3 for polymer having p-cinnamate backbone and polymer having m-cinnamate at 1064 nm fundamental wavelength, respectively. The orientation order parameter is strongly depends on polymer backbone. To understand the temperature effects to the orientation thermal stability of polydiacethylene, the decay of second harmonic generation intensity were measured. The depoling experimental results showed that the orientation stability of p-cinnamate backbone is higher than that of m-cinnamate backbone. The order parameter and SHG decay of copolymer were also investigated.

The problem of saturation of intersubband absorption and optical rectification in asymmetric quantum wells is discussed theoretically using the density matrix formalism. The effects of the electron-electron interaction are taken into account. It is shown that near the resonance the spectral shapes of the nonlinear optical absorption coefficient and the nonlinear optical rectification coefficient are very similar. In the absence of the electron-electron interaction the spectral responses are nearly Lorentzian. The electron-electron interaction plays an important role in heavy doped systems. In structures with large spatial separation of the ground and the excited states wave functions, the depolarization effect is small and the absorption spectrum is affected mainly by the electrostatic Coulomb interaction. This interaction shifts the absorption peak to higher energy by an amount depending on the intensity of the incident light and leads to the significant distortion (asymmetry) of the line.

We consider the several phenomena which are taking place in Quantum Dots (QD) and Quantum Rings (QR): The connection of the Quantum Chaos (QC) with the reflection symmetry of the QD, Disappearance of the QC in the tunnel coupled chaotic QD, electron localization and transition between Double Concentric QR in the transverse magnetic field, transition of electron from QR to the QD located in the center of QR. Basis of this consideration is the effective Schr\"odinger equation for the corresponding systems.

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

This paper presents a precise study of second-order optical nonlinearity of uniaxially cold-drawn and poled ferroelectric Nylon 11 films. The effects of drawing and poling on refractive indices and second-order nonlinear optical coefficients have been investigated. Drawing caused increase of refractive index (n) parallel to the drawing direction nX, and decrease of n perpendicular to drawing direction in the plane of film nY, as well as decrease of n on the poling direction parallel to film thickness direction nZ. Poling caused significant increase of nZ and decrease of nY. These n results imply that poling aligns the molecular chains so that carbonyl groups in Nylon backbone orient in the poling direction (Z-axis). Cold-drawn and poled Nylon 11 films belong to the mm2 point group. Dependence of second-order harmonic generation (SHG) intensity on incidence angle, i.e., Maker fringe pattern, could be precisely fitted using five independent nonzero tensor components, d33, d32, d31, d15, and d24. However, Kleinman symmetry was not satisfied: d31≠d15 and d32≠d24. The tensor components d33, d31, d15, and d24 increase with increasing remanent polarization, whereas the value of d32 was negligibly small irrespective of the intensity of the remanent polarization. Tensor components of microscopic first-order hyperpolarizability, βzxx, βzyy, βzzz, βxxz, and βyyz were determined. Tensor component βzzz was the largest and βzxx had negative sign. Second-order nonlinearity was largely suppressed in the vicinity of the melting point of Nylon 11.

The zone-center phonons are calculated for rhombohedral $\mathrm{CsGe}{X}_{3}$ compounds with $X=\mathrm{I}$, Br, Cl using density functional perturbation theory in a plane-wave pseudopotential method. The infrared absorption and reflection spectra are simulated and show that the absorption has a strong contribution from the LO as well as TO modes. Both the lowest and highest IR active modes have strong oscillator strengths for each symmetry (${A}_{1}$ and $E$) and correspond to motions of either the Cs or Ge ions relative to the halogen ions. respectively. The intermediate modes have low oscillator strength because their mode pattern shows less clearly a dipole pattern. The polarization dependent Raman spectra for various backscattering configurations are simulated. Only the highest modes of each symmetry have a strong Raman intensity. The results for the Raman spectra are found to be in good agreement with the available experimental data for polycrystalline films when averaging over directions. The Born effective charges and high and low frequency dielectric tensors as well as the second-order nonlinear optical coefficients are calculated. The ratio of the static to the high-frequency dielectric constants are extremely high and analyzed in terms of the contribution of each mode to the Lyddane-Sachs-Teller relation. The nonlinear optical coefficients decrease strongly from I to Br to Cl in reverse order of the band gaps and are found to be consistent with available experimental results.

We have studied electron correlation effects in quantum dots and rings which include a repulsive scattering centre and aresubjected to a perpendicular magnetic field. The results for thedipole-allowed absorption spectrum show good qualitative agreement with the observed magnetoplasmon dispersion in similarsystems. This work provides a unified description of the electroncorrelations in quantum dots and quantum rings in a magnetic field. We also demonstrate that optical absorption is a direct route to explore the effects of impurity and interactions in a quantum ring.

The polaronic effect on the linear, third-order nonlinear and total optical absorption coefficients have been calculated in the case of GaAs/AlAs core/shell quantum dot, with the impurity is positioned at the central radial position of the GaAs shell. The calculations are realized in the framework of the effective mass approximation and the numerical results are obtained by using a variational method and an infinite confining potential. The results show that the polaronic effect has a great influence on optical properties of core/ shell quantum dot, he causes a red-shift of the nonlinear optical coefficients associated to light absorption. Also, the polaronic effect is enhanced with the decreasing of quantum dot radius.

A simple, approximate relation between the dispersion of the second-order nonlinear optical (SNLO) coefficient and first-order susceptibility has been derived using the well-known results of density-matrix calculation of quantum-mechanical theory. A new tensor of SNLO coefficient has been defined, which retains symmetries when the input beams are in the spectral range of transparency while the generated beam can also be in the spectral range of absorption. The validity of the relation has been checked for three ferroelectric crystals, KTP, LiNbO3 and KNbO3, which are transparent in the visible and near infrared, and for two semiconductors, GaP and GaAs, which absorb in the visible. Contrary to Miller’s law, the presented relation is in good agreement with measurements.

In this thesis the optical properties of self-assembled III-V semiconductor nanostructures are investigated by analyzing the photoluminescence (PL) with and without an external magnetic field. The studied PL is a result of the recombination of electrons and holes confined in the nanostructures. In this thesis we directly correlate the size, shape, composition and topology of the nanostructures to their magnetic and optical properties and study the influence of an electrical contact in the close proximity of these nanostructures. One of the most interesting nanostructures are quantum dots (QDs), which are able to confine charge carriers in all three dimensions. Both the exciton g-factor gex and the exciton diamagnetic coefficient ad determine the behavior of excitons confined in a QD in a magnetic field and provide further insight in the energy level structure of these nanostructures. The exciton Zeeman splitting is proportional to gex and is a result of the different spin configurations of the electron and hole, which constitute the exciton. The diamagnetic shift is a result of the additional confinement provided by the magnetic field B, and is proportional adB2, where ad scales with the lateral extend of the quantum dot. PL experiments on a large ensemble of InAs/GaAs QDs, as well as on individual InAs/GaAs QDs are performed. For these dots ad and gex have been determined. Importantly, there is a trend between gex and the emission energy E0: for larger emission energy a more negative value of the exciton g-factor is observed. From the power and temperature dependence of the ensemble PL it is shown that the sample consists of QDs with different height, where the highest dots correspond to the smallest emission energies. Moreover, QDs with larger ad have a more positive g-factor. From this it is inferred that quantum dots with an overall larger size have a less negative value of gex. By implementing the QDs in a Schottky device in close proximity to an electrical contact it is possible to tune the charged state of the exciton in the dot. We show that charge-tunable InAs/GaAs quantum dots also allow to study many-body interactions between a localized QD state and a Fermi sea of electrons. As a result of these many-body interactions new optical transitions are observed in the PL spectra. The same chargetunable quantum dots are also investigated in a magnetic field. Instead of the positive diamagnetic shift observed for the majority of the quantum dots, two different types of negative diamagnetic shift are reported. The shallow character of our quantum dots causes a negative quadratic diamagnetic shift for the highly negatively charged exciton complexes in line with predictions for shallow quantum dots. The second type of negative diamagnetic shift is observed even for the neutral exciton and is strongly linearly dependent on the magnetic field. We also investigated quantum dots grown from different semiconductor materials. InAs/InP quantum dots are studied using AFM, X-STM, macro-PL and micro-PL. Macro PL and X-STM measurements show that the studied InAs/InP dots have a multimodal height distribution. Single quantum dot luminescence, carried out on a large number of dots, shows a strong correlation between exciton g-factor, diamagnetic coefficient and emission energy. In fact, the strong dependence of gex on the emission energy results in a sign change of the exciton g-factor. In correspondence with what we found on the InAs/GaAs QDs, we find that dots having a smaller overall size will have a more negative gex as compared to quantum dots of larger overall size. We also show that for several quantum dots the exciton g-factor is quenched. A theoretical model is used to calculate the effect of the quantum dot size on the g-factor. The model is both qualitatively and quantitatively in good agreement with the experimental obtained results. Nanostructures of a different topology are self-assembled InAs/GaAs quantum rings (QRs). Using magnetization measurements on a large ensemble of quantum rings we demonstrate the presence of the Aharonov-Bohm (AB) effect in these nanostructures. Moreover, a model based on the X-STM measurements on these nanostructures reproduces the magnetic field position of this oscillation. The optical properties of these QRs are investigated for magnetic fields up to 30T for a large ensemble of quantum rings and for individual rings. Although the excitonic AB effect is suppressed in these nanostructures, the ring character of our nanostructures gives rise to non-equidistant energy level splittings and into a magnetic field induced splitting of each excited state into two states in the ensemble PL. This is different to what has been observed in measurements on quantum dots. The calculations based on the same model show a qualitative agreement with the experimental data, and allow us to identify the different PL peaks. Furthermore, analyzing exciton lines with high resolution revealed an anomalous quadruplet splitting, which is different as the one reported for InAs/GaAs quantum dots. Although the origin of this splitting is still unclear, it is most likely related to the singlet to triplet transition of singly charged excitons. Finally the magneto-luminescence experiments on type II self-assembled InP/GaAs quantum dots are discussed. For these dots the hole is located outside the quantum dot, whereas the electron is confined inside the quantum dot creating a type II exciton. The magneto-luminescence of the ensemble of dots did not resolve any oscillatory behavior related to the AB effect in contrast to experiments reported on the same sample. Decisive magneto-luminescence measurements on individual dots did also not reveal any AB related phenomena within the experimental resolution of 40 µeV. These results show the necessity to study subtle magneto-luminescence properties of nanostructures on an individual dot level, rather than on a large ensemble of dots.

Laser-induced nonlinear optical rectification in a two-dimensional quantum pseudodot system

For the first time, exact analytical solutions of electronic wavefunctions in quantum ring-like structures are found using a symmetry-adapted coordinate system. In the case of an infinite potential barrier, it is related to a more general problem of finding resonance modes in a ring-like cavity. The solutions in the parabolic coordinate system are Bessel or confluent hypergeometric functions for quantum dot, ring and wire including objects with flat bases. The continuous evolution from the 0D quantum dot system to the perfect 1D quantum ring system is analysed. The electronic properties (energy levels, wavefunctions and density of states) are continuously followed during the dot to ring transformation until the limit of a perfect 1D quantum ring is reached. The creation of a ring structure by changing the material composition in a dot centre leads to a sharp variation in the energy levels of totally symmetric states. This is a consequence of the immediate build-up of a potential barrier energy in the centre of the ring. Finally the use of the structure of electronic levels to identify the signature of self-organized quantum rings when compared to quantum dots is proposed.