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Atoms

Tuning the Nonlinear Optical Properties of Quantum Dot by Noise-Anharmonicity Interaction

Debi Roy, Sk. Md. Arif, Swarnab Datta, Manas Ghosh

Published Oct 25, 2022• 4 citations
Publisher

Abstract

Current inspection rigorously explores the tuning of a few relevant nonlinear optical (NLO)properties of GaAs quantum dot (QD) under the stewardship of Gaussian noise-anharmonicity interplay. The NLO properties explored are total optical absorption coefficient (TOAC), total optical refractive index change (TORIC), nonlinear optical rectification (NOR), second harmonic generation (SHG), third harmonic generation (THG), DC-Kerr effect (DCKE), electro-absorption coefficient (EAC), group index (GI)and optical gain (OG). The route of application of noise (additive/multiplicative) to the QD, as well as the symmetry (odd/even) of the anharmonicity, influence the aforesaid NLO properties. These NLO properties exhibit steadfast growth, steadfast fall, maximization, minimization and saturation. The outcomes of the inspection appear to be quite pertinent in the context of the immense technological demand of QD, taking into account the combined impact of anharmonicity and noise.

DOI
10.3390/atoms10040122

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Current inspection rigorously explores the tuning of a few relevant nonlinear optical (NLO)properties of GaAs quantum dot (QD) under the stewardship of Gaussian noise-anharmonicity interplay. The NLO properties explored are total optical absorption coefficient (TOAC), total optical refractive index change (TORIC), nonlinear optical rectification (NOR), second harmonic generation (SHG), third harmonic generation (THG), DC-Kerr effect (DCKE), electro-absorption coefficient (EAC), group index (GI)and optical gain (OG). The route of application of noise (additive/multiplicative) to the QD, as well as the symmetry (odd/even) of the anharmonicity, influence the aforesaid NLO properties. These NLO properties exhibit steadfast growth, steadfast fall, maximization, minimization and saturation. The outcomes of the inspection appear to be quite pertinent in the context of the immense technological demand of QD, taking into account the combined impact of anharmonicity and noise.
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The study presents results of the linear and non-linear optical properties of GaAs quantum dots. The reported work aims to provide new results of the quantum dot optical properties confined in Hua plus modified Eckart (HPME) potential. To obtain analytical expressions for the energy eigenvalues and the wave functions, we solved the time-independent Schrödinger equation for the HPME potential by using the parametric Nikiforov-Uvarov (NU) method. Investigation of the linear, third-order nonlinear, and total absorption coefficients and refractive index changes was done with the help of the density matrix approach. The results showed that the energy decreases in a linear manner as the potential parameter, V0. Also, it is observed that as the barrier slope increases, the peaks of the linear, third-order linear, and total absorption coefficient tend to higher values of energy. Furthermore, as the barrier slope increases, the change in refractive indices increases, and their positions shift to higher energies. Additionally, an increase in the structure parameters and optical intensity greatly influences the absorption coefficients and the refractive index changes of the quantum dots.
The effects of quantum dot (QD) radius, incident light intensity, temperature and other factors on the optical absorption coefficients (OACs) of cylindrical QDs are investigated numerically for typical GaAs/Ga[Formula: see text]Al[Formula: see text]As. We theoretically studied the cylindrical QDs with like-inversely quadratic Hellmann potential and parabolic potential. The expressions for the energy levels and wave functions were obtained by the Nikiforov–Uvarov method, and then the expressions for the OACs were derived by using the density matrix theory and the iterative method. Finally, the results show that the structural and external parameters affect the sensitivity of the optical absorption properties by influencing the matrix elements and energy levels, and the quantum confinement effects affect their applicable frequencies, which makes the QD system easier to tune.
In the present work, we have studied numerically the second harmonic generation (SHG) and third harmonic generation (THG) in a cone-like quantum dot. For this purpose, we firstly obtained the energy levels and wave functions of this system. Then, we have used an expression for the SHG and THG by a compact density matrix approach and an iterative procedure. The SHG and THG enhance and shift toward lower energy by increasing the height h and vertex angle α. According to the results it is found that the structural parameters have great influence on the THG in this system.
I recent years, significant attention has been given to nonlinear optical phenomena, such as nonlinear optical absorption and dispersion, derived from a driven quantum transition of semiconductor nanostructures, such as semiconductor quantum wells, quantum disks and mainly quantum dots. An important issue that is widely studied is the effect of probe electromagnetic field intensity on the total (nonlinear) absorption coefficient and on the total (nonlinear) index of refraction. Some of the phenomena that are commonly found for large electromagnetic field intensities are the creation of a strong dip in the absorption spectrum near or at resonance (the so-called bleaching effect), negative absorption near or at resonance that leads to optical gain and the change of the slope of the total index of refraction near or at resonance from negative to positive that changes the behavior of the system from fast to slow light. Unfortunately, these phenomena do not exist and are artifacts of a common abuse of the theoretical methodology for the study of the total absorption coefficient and the total index of refraction. The main error is that the total absorption coefficient and the total index of refraction was initially derived from density matrix equations using perturbation theory and includes first-order (linear) as well as third-order (nonlinear) terms. This method gives correct results for small electromagnetic field intensities and it leads to saturation of absorption and dispersion in this regime. However, for larger intensities it gives the misleading results mentioned above due to either failure of the order of perturbation theory considered in the derivation of the total absorption coefficient and the total index of refraction or even failure of perturbation theory at all in the treatment of the problem. In this work, we revisit the problem of the total absorption coefficient and the total index of refraction in a symmetric semiconductor quantum dot structure (we choose the example of a core-shell quantum dot) under a strong probe field excitation. We use the two-level model, solve the relevant density matrix equations under the rotating wave approximation and under steady state conditions, and obtain the correct form of the nonlinear optical susceptibility that is then used for the derivation of the formulae of the total absorption coefficient and the total index of refraction under the interaction with a strong probe field. Actually, the commonly used perturbation theory formulae can be obtained by our formulae using a series expansion and keeping terms up to second order in electric field amplitude. We also derive the electronic structure of the quantum dot system by solving numerically the time-independent Schrodinger equation, under the effective mass approximation, using the potential morphing method and obtain the energy difference and the electric dipole matrix element for the relevant transitions of the quantum dot system. Then, for the specific quantum dot system we compare the results of the total absorption coefficient and the total index of refraction for the two methodologies (the perturbation result and our result) for different electromagnetic field intensities.
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.