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We proposed a model for adjusting Goosâ€"Hänchen (GH) shifts in a cavity with quantum dot (QD) nanostructure in this letter. The actual component of the susceptibility was studied by analytical solution of the coherence term of the density matrix elements, and the refractive index of the QD nanostructure was explored. We discovered that the intracavity medium became phase sensitive because of the electron tunneling action. As a result, the relative phase of applied lights may be used to manipulate the medium’s refraction index. The GH shifts in reflected and transmitted light beams in high refractive index QD nanostructures with diminishing probe absorption were next examined. We discovered that the GH shifts of reflected and transmitted lights are greatly influenced by the applied lights’ relative phase. We established that greater negative or positive GH shifts in reflected and transmitted photons are conceivable in the presence of electron tunneling. [ABSTRACT FROM AUTHOR]

In this study, the numerical solution of the ordinary kind of differential equation for a simple pendulum with large-angle of oscillation was introduced to obtain the time period. The analytical solution is obtained in terms of elliptic functions, and numerical solution of the problem was achieved by using two numerical quadrature methods, namely, Simpson's 3/8 and Boole's method. The period of a simple pendulum with large angle is presented. A comparison has been carried out between the analytical solution and the numerical integration results. In the case of error analysis, absolute and relative errors of the problem have been presented. A numerical algorithm has been developed by MATLAB software 2013R and used for analyzing the result. It is established that the results of the comparison guaranty the ability and the accuracy of the present method. [ABSTRACT FROM AUTHOR]