Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section
Winnie Otieno,
Hannington Oyoko
Issue:
Volume 6, Issue 3, September 2018
Pages:
25-30
Received:
2 September 2018
Accepted:
6 October 2018
Published:
29 October 2018
Abstract: In the present work, a theoretical study of the variation of the photoionization cross-section with the incident photon frequency and the axial position of a hydrogenic donor impurity in GaAs quantum well dot of square cross-section is carried out. In the calculation, a trial wave function in the effective mass approximation and a finite potential well is used. The wave function is constructed with an appropriate envelope wave function that satisfies the boundary conditions, i.e., the wave function vanishes at the boundary. A trial wave function is employed to calculate the total energy of the hydrogenic donor impurity in the ground state. The total energy is then minimized with respect to the variational parameter in the trial wave function to obtain the minimum energy. The minimized total energies are then used to determine the donor binding energies within the quantum dot. It is observed that for a quantum dot of constant cross-section, the binding energy increases with a decrease in dot length to a peak value; thereafter it decreases rapidly towards zero. The binding energies obtained are used to compute the photoionization cross-section of the hydrogenic donor impurity as a function of the incident photon frequency for different positions of the donor impurity. It is observed that the photoionization cross-sections rise steeply to their peaks from almost zero value then gradually decrease as the photon frequency increases until they become almost constant for very high photon frequencies. The photoionization cross-section peak is much higher for the hydrogenic donor impurity located closest to the centre of the quantum well dot than for donor impurity located farther away from the dot centre. This indicates that the photoionization cross-section is sensitive to the location of the donor impurity in the quantum dot and to the incident photon frequency.
Abstract: In the present work, a theoretical study of the variation of the photoionization cross-section with the incident photon frequency and the axial position of a hydrogenic donor impurity in GaAs quantum well dot of square cross-section is carried out. In the calculation, a trial wave function in the effective mass approximation and a finite potential ...
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Higher-Order Nonlinear Schrödinger Equation Family in Optical Fiber and Solitary Wave Solutions
Rodrique Njikue,
Jean Roger Bogning,
Timoleon Crépin Kofané
Issue:
Volume 6, Issue 3, September 2018
Pages:
31-41
Received:
19 August 2018
Accepted:
6 September 2018
Published:
14 December 2018
Abstract: In this paper, we modify with an appropriate analytical technique, the characteristics of the optical fiber through the modification of the coefficients of the highly nonlinear partial differential equation, which initially governs the dynamics of the propagation in such a wave guide. The procedure consists to assign arbitrary coefficients to the various terms of the established nonlinear partial differential equation, such as the one that embodies the propagation dynamics in a strongly nonlinear optical fiber and subsequently establishing the constraint equations linking these coefficients and thus the analys is makes it possible to enumerate the criteria for which obtaining the desired solutions is possible. These coefficients are like indicators which characterize the various modifications made in this medium of transmission. The nonlinear evolution equation that served as mathematical model for this study is the higher-order nonlinear Schrödinger equation which better describes the propagation of an ultrafast pulse in an optical fiber. The use of the Bogning-Djeumen Tchaho-Kofané method enabled not only to establish the constraint relations, but also the solitary wave solutions and plane wave solutions. We want through the results obtained in this article to give the specialists of the manufacture of transmission media such as optical fiber, to consider the modification of the properties of this wave guide during manufacture, depending on the type of signal that one wants to propagate in this case notably the solitary wave.
Abstract: In this paper, we modify with an appropriate analytical technique, the characteristics of the optical fiber through the modification of the coefficients of the highly nonlinear partial differential equation, which initially governs the dynamics of the propagation in such a wave guide. The procedure consists to assign arbitrary coefficients to the v...
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