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Scientific Reports

Fractional Young double-slit numerical experiment with Gaussian wavepackets

Mahboubeh Ghalandari, M. Solaimani

Published Nov 10, 2020• 6 citations
Publisher

Abstract

In the present work, we consider the transmission properties of a Gaussian wavepacket when transmits through few double and multi-slit systems in a fractional medium. For this purpose, we have solved the two-dimensional fractional Schrodinger equation utilizing a split-step Fourier method. Then, we have investigated the effects of different parameters such as the number of slits, slit width, barrier width, layer width, layer heights, fractional order, and wavepacket width on the transmission coefficient, and wavepacket evolution.

DOI
10.1038/s41598-020-76512-5

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In the present work, we consider the transmission properties of a Gaussian wavepacket when transmits through few double and multi-slit systems in a fractional medium. For this purpose, we have solved the two-dimensional fractional Schrodinger equation utilizing a split-step Fourier method. Then, we have investigated the effects of different parameters such as the number of slits, slit width, barrier width, layer width, layer heights, fractional order, and wavepacket width on the transmission coefficient, and wavepacket evolution.
In this study, we investigate the transport properties of Airy and Hermit-Gaussian wavepackets traveling through a Gaussian potential well in the standard and fractional media. We use a split step Fourier method to solve the corresponding two-dimensional fractional nonlinear linear Schrodinger equation. We study the interference phenomenon, Huygens principle and trapping properties of the system in different situations. For this purpose, the position of the system has also selected inside the potential well to consider the wavepacket evolution. Then, the effect of the well and incident wavepackets parameters on the evolution the transport properties of employed wavepackets have properly been considered.
We investigate a traveling Gaussian wave packet transport through a rectangular quantum barrier of lévy crystals in fractional quantum mechanics formalism. We study both standard and fractional Schrödinger equations in linear and nonlinear regimes by using a split-step finite difference (SSFD) method. We evaluate the reflection, trapping, and transmission coefficients of the wave packet and the wave packet spreading by using time-dependent inverse participation ratio (IPR) and second moment. By simultaneously adjusting the fractional and nonlinear terms, we create sharp pulses, which is an essential issue in optoelectronic devices. We illustrate that the effects of barrier height and width on the transmission coefficient are strangely different for the standard and fractional Schrödinger equations. We observe fortunately soliton-like localized wave packets in the fractional regime. Thus, we can effectively control the behavior of the wave evolution by adjusting the available parameters, which can excite new ideas in optics.
In this work, we have investigated the Gaussian and Airy wave packets colliding on the Dirac delta potentials. We have used the time-dependent space-fractional Schrodinger equation and solved it by using the slit step finite difference method. Here, we have presented some exclusive exotic propagation properties of Dirac delta potential that cannot be observed for other very similar potentials such as one-dimensional coulomb potential. We can now rectify any number of colliding wave packets provided that the correct parameters adjustment is possible. We have also addressed the wave packet speed control, wave packet splitting, wave packet rectification through collision process, wave packet dispersion, etc. The effects of different parameters such as the nonlinearity, fractitionality, dispersion, etc. on the wave packet-delta potential collision are also considered.