Simultaneous Effects of External Electric Field and Conduction Band Nonparabolicity on Optical Properties of a GaAs Quantum Dot Embedded at the Center of a GaAlAs Nano-Wire
Gh. Safarpour, Mohammad Izadi, M. Novzari, E. Niknam, Mohammad Mehdi Golshan
An investigation of the optical properties of a GaAs spherical quantum dot which is located at the center of a Ga 1−x Al x As cylindrical nano-wire has been performed in the presence of an external electric held. The band nonparabolicity effect is also considered using the energy dependent effective mass approximation. The energy eigenvalues and corresponding wave functions are calculated by finite difference approximation and the reliability of calculated wave functions is checked by computing orthogonality. Using computed energy eigenvalues and wave functions, the linear, third-order nonlinear and total optical absorption coefficients and refractive index changes are examined in detail. It is found that (i) Presence of electric field causes both blue and red shifts in absorption spectrum; (ii) The absorption coefficients shift toward lower energies by taking into account the conduction band nonparabolicity; (iii) For large values of electric field the effect of conduction band nonparabolicity is less dominant and parabolic band is estimated correctly; (iv) In the presence of electric field and conduction band nonparabolicity the nonlinear term of absorption coefficient rapidly increases by increasing incident optical intensity. In other words, the saturation in optical spectrum occurs at lower incident optical intensities.
An investigation of the optical properties of a GaAs spherical quantum dot which is located at the center of a Ga 1−x Al x As cylindrical nano-wire has been performed in the presence of an external electric held. The band nonparabolicity effect is also considered using the energy dependent effective mass approximation. The energy eigenvalues and corresponding wave functions are calculated by finite difference approximation and the reliability of calculated wave functions is checked by computing orthogonality. Using computed energy eigenvalues and wave functions, the linear, third-order nonlinear and total optical absorption coefficients and refractive index changes are examined in detail. It is found that (i) Presence of electric field causes both blue and red shifts in absorption spectrum; (ii) The absorption coefficients shift toward lower energies by taking into account the conduction band nonparabolicity; (iii) For large values of electric field the effect of conduction band nonparabolicity is less dominant and parabolic band is estimated correctly; (iv) In the presence of electric field and conduction band nonparabolicity the nonlinear term of absorption coefficient rapidly increases by increasing incident optical intensity. In other words, the saturation in optical spectrum occurs at lower incident optical intensities.
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.
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.
The effect of geometrical anisotropy is numerically investigated on the linear and nonlinear optical refractive index changes of a GaAs quantum dot which is located at the center of a Ga1-xAlxAs cylindrical nano-wire. The finite difference approximation has been used for obtaining energy eigenvalues and corresponding wave functions. Also, the compact density matrix formalism is applied to investigate linear, third order nonlinear and total optical refractive index (RI) changes. The optical properties are calculated as a function of the incident photon energy for different ellipsoid aspect ratio and dot radius. The results clearly reveal that the dot anisotropy plays an important role in determining the magnitude of nonlinear RI changes which enable us to adjust saturation condition. We also found that the dot anisotropy shifts optical spectrum towards both lower and higher energies which depend on the shape of dot (spherical, prolate or oblate quantum dot) and dot radius.
Abstract We present a theoretical study on the effects of intense laser field (ILF) and static electric field on the linear and nonlinear optical properties of a cylindrical quantum dot with Rosen–Morse axial potential under the framework of effective mass and parabolic band approximations. This study also takes into account the effects of the structure parameters ( η , V 1 , and R ). The analytical expressions of the linear, third-order nonlinear and total optical absorption coefficients (TOACs) and the relative refractive index changes (RRICs) are obtained by using the compact-density-matrix approach. The results of numerical calculations show that the resonant peak position of the TOACs and RRICs shifts towards lower energies and the magnitude of the peak increases with the effect of the static electric field and ILF. In addition, it is observed that while the resonant energies of the TOACs and RRICs of system shift towards the higher (lower) energies with the enhancement of η , V 1 , they decrease with the augmentation of R . Thus, the findings of this study show that the optical properties of the structure can be adjusted by changing the magnitude of structure parameters and applied external fields.
In this present study, we have theoretically investigated the effect of applied external electric field and non-resonant intense laser field, as well as the adjustable physical parameters (A, M, and η) of the system, on the linear and nonlinear of GaAs/GaAlAs cylindrical quantum dot. The confinement potential of the quantum dot is composed of the axial potential with a Razavy-type quantum well in the z-direction, and the cylindrical-type potential in the radial direction. To achieve this goal, the wave functions, and the corresponding eigenvalues of the electron are investigated by resolving the time-independent Schrödinger equation using the diagonalisation technique in terms of the effective mass approximation. The linear and nonlinear optical properties’ expressions have been calculated with the help of the compact density matrix method. Our numerical results show that by changing the A, M, and η parameters, we can see a blueshift or redshift in the total optical absorption coefficients (TOACs) and relative refractive index changes (RRICs). Additionally, they are redshifted, and their extrema increase as the radius increases. The increase in electric field or laser field intensities generates a strong displacement of the resonant peak position towards the higher energies, diminishes the TOACs magnitude, and shrinks RRICs extrema. The model potential used in the computation is important, and the study of it will be practical in the development and research of nanostructures systems.
Abstract In our investigation, we analyzed the variations in both linear and nonlinear optical properties of the GaAs/GaAlAs single quantum well heterostructure with modified Lennard-Jones potential under the conditions where external fields and the adjustable physical parameters of the structure are changed. We get the solution of the Schrödinger equation for identifying the subband energy levels with their wave functions taking advantage of the diagonalization method, effective mass approach, and parabolic band model. As a result, we find that the changes in the applied external fields and structure parameters have effects on the total optical absorption coefficients and total relative refractive index changes. While the optical response becomes red-shifted with the increment of applied electric, magnetic and intense laser fields and the well width, it becomes blue-shifted with the increment of the well depth.