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Journal of Nanoelectronics and Optoelectronics

Effects of the Magnetic Field on the Linear and Nonlinear Optical Absorption Coefficients and the Refractive Index Changes in a Spherical Quantum Dot

Muharrem Kırak, Sait Yılmaz, Mustafa Gençaslan

Published Dec 1, 2010• 8 citations
Publisher

Abstract

The linear and third-order nonlinear optical absorption coefficients (ACs) and the refractive index change (RIC) for a spherical quantum dot, having a hydrogenic impurity under an applied magnetic field have been theoretically studied. In numerical calculations, a variational scheme is adopted within effective mass approximation to determine the energy eigenvalues for the impurtiy. The variations of impurity binding energy with the dot radius, the linear and nonlinear ACs and RIC with the photon energy are investigated and effect of homogeneous magnetic field strength is discussed on these optical properties. It has been found that the binding energy, ACs and RIC are sensitively dependent on the magnetic field strength. Moreover, the calculated results also indicate that the absorption peak energies move to higher energies with increasing magnetic field.

DOI
10.1166/jno.2010.1126

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The linear and third-order nonlinear optical absorption coefficients (ACs) and the refractive index change (RIC) for a spherical quantum dot, having a hydrogenic impurity under an applied magnetic field have been theoretically studied. In numerical calculations, a variational scheme is adopted within effective mass approximation to determine the energy eigenvalues for the impurtiy. The variations of impurity binding energy with the dot radius, the linear and nonlinear ACs and RIC with the photon energy are investigated and effect of homogeneous magnetic field strength is discussed on these optical properties. It has been found that the binding energy, ACs and RIC are sensitively dependent on the magnetic field strength. Moreover, the calculated results also indicate that the absorption peak energies move to higher energies with increasing magnetic field.
The screened modified Kratzer potential (SMKP) model is utilized to scrutinize the impacts of an applied magnetic field (MF) on the binding energies and linear and nonlinear optical properties spherical GaAs quantum dot with donor impurity (DI). To accomplish this goal, we have used the diagonalization method to numerically solve the Schrödinger equation under the effective mass approximation for obtaining the electron energy levels and related electronic wave functions. The expressions used for evaluating linear, third-order nonlinear, and total optical absorption coefficients and relative refractive index changes were previously derived within the compact density matrix method. It has been shown here that the MF and DI impacts the characteristics of the absorption coefficients and the refractive index changes. This study's results will find application in optoelectronics and related areas.
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.
Confinement effects of Kratzer potential on a Wannier-Mott Exciton(W-M) are studied in a spherical quantum dot(QD) in the presence of a static magnetic field. Time independent Schro¨\ddot{o}o¨dinger equation is solved numerically to obtain the energy states. The excitonic transitions so realized have been used to explore the non-linear optical properties that are important for optical characterization of materials such as the optical absorption coefficients (ACs) and refractive index changes (RICs). Impact of magnetic field, strength of the laser field and transition parameters using familiar compact density matrix approach are also analyzed. It has been observed that optical properties get radically modified under confinement effects. Also, the shift of degeneracy of different excitonic energy levels with the magnetic field in confinement potential has been reported for the first time for W-M exciton in the spherical quantum dot, the study that may have crucial input to the literature and myriad of practical implications.
Linear and third order nonlinear optical absorption coefficients and refractive index changes of an on-center donor impurity in a spherical GaAs quantum dot which is located at the center of a cylindrical Ga 1 -x Al x As nano-wire, have been investigated under the simultaneous effect of electric field and laser radiation. The linear and third order nonlinear optical properties are calculated based on optical 1-2, 2-3 and 1-3 transitions by means of the compact density-matrix approach. The energy eigenvalues and corresponding wave functions are calculated using finite difference approximation and reliability of calculated wave functions is checked by computing orthogonality. It is shown that optical spectrum shifts towards lower and higher energies for 1-2 transition and shifts towards lower energies for 2-3 and 1-3 transitions as the electric field strength increases. The presence of laser field shifts absorption spectrum towards lower energies. In the absence of electric and laser field, the magnitude of absorption coefficient and refractive index changes increase in transitions between higher levels. Simultaneous presence of both electric field and laser radiation has great effect on magnitude of absorption coefficients and refractive index changes. The saturation in optical spectrum can be adjusted by electric field and laser radiation.
Abstract The effects of external magnetic field, hydrostatic pressure, temperature and radius of the quantum dots (QDs) on refractive index changes (RICs) of tuned QDs are studied in detail theoretically. In the framework of effective mass approximation, energy levels and wave functions are derived. Simultaneously, the nonlinear RICs are obtained by compact-density-matrix approach and iterative method. Then, the numerical simulations show that under various constraint factors, the resonant peak position of RICs moves to high energy or low energy, that is, blue shift or red shift, and the peak value of RICs will also alter with the change of parameters.