The fractional comparative study of the non-linear directional couplers in non-linear optics
A new extended direct algebraic method is applied to extract new traveling wave solutions for non-linear directional couplers with the optical meta-materials. This model studies light distribution from the main fiber into other branch fibers, which can be one or more than one. So, for this reason, t...
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doaj-d4793d2217dc4896b97e0725530171aa2021-07-17T04:33:34ZengElsevierResults in Physics2211-37972021-08-0127104459The fractional comparative study of the non-linear directional couplers in non-linear opticsMuhammad Imran Asjad0Waqas Ali Faridi1khadijah M. Abualnaja2Adil Jhangeer3Hanaa Abu-Zinadah4Hijaz Ahmad5Department of Mathematics, University of Management and Technology, Lahore, PakistanDepartment of Mathematics, University of Management and Technology, Lahore, PakistanDepartment of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Mathematics, Namal Institute, Talagang Road, Mianwali 42250, PakistanUniversity of Jeddah, College of Science, Department of Statistics, Jeddah, Saudi ArabiaDepartment of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan; Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy; Corresponding author.A new extended direct algebraic method is applied to extract new traveling wave solutions for non-linear directional couplers with the optical meta-materials. This model studies light distribution from the main fiber into other branch fibers, which can be one or more than one. So, for this reason, twin couplers and multiple core couplers are studied in this paper. Further two cases in multiple core couplers namely multiple core couplers near the neighbor and multiple core couplers with a complete neighbor are exhaustively discussed. The non-linearity type that is considered here is Kerr Law. The obtained solutions set is more generalized than the existing solution as it is transformed into fractional-order derivative because it gives the solutions of problems with heavy tails or infinity fluctuations. Furthermore, the obtained solutions contain almost all types of solitons such as dark, bright, dark-bright, rational, periodic, breather, and singular soliton solutions, etc. Moreover, the obtained solutions are fractional solitons with Atangana-Baleanu and modified Riemann–Liouville fractional operator. These non-linear directional couplers also act as limiters in intensity-dependent switches. The propagation constants of the modes of a system are changed by non-linearity. In order to discuss the physical nature of couplers, 2D and 3D figures are also shown.http://www.sciencedirect.com/science/article/pii/S221137972100574XKerr lawtravelling wave solutionNew extended direct algebraic methodTwin couplerMultiple core couplerOptical meta-material |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Muhammad Imran Asjad Waqas Ali Faridi khadijah M. Abualnaja Adil Jhangeer Hanaa Abu-Zinadah Hijaz Ahmad |
spellingShingle |
Muhammad Imran Asjad Waqas Ali Faridi khadijah M. Abualnaja Adil Jhangeer Hanaa Abu-Zinadah Hijaz Ahmad The fractional comparative study of the non-linear directional couplers in non-linear optics Results in Physics Kerr law travelling wave solution New extended direct algebraic method Twin coupler Multiple core coupler Optical meta-material |
author_facet |
Muhammad Imran Asjad Waqas Ali Faridi khadijah M. Abualnaja Adil Jhangeer Hanaa Abu-Zinadah Hijaz Ahmad |
author_sort |
Muhammad Imran Asjad |
title |
The fractional comparative study of the non-linear directional couplers in non-linear optics |
title_short |
The fractional comparative study of the non-linear directional couplers in non-linear optics |
title_full |
The fractional comparative study of the non-linear directional couplers in non-linear optics |
title_fullStr |
The fractional comparative study of the non-linear directional couplers in non-linear optics |
title_full_unstemmed |
The fractional comparative study of the non-linear directional couplers in non-linear optics |
title_sort |
fractional comparative study of the non-linear directional couplers in non-linear optics |
publisher |
Elsevier |
series |
Results in Physics |
issn |
2211-3797 |
publishDate |
2021-08-01 |
description |
A new extended direct algebraic method is applied to extract new traveling wave solutions for non-linear directional couplers with the optical meta-materials. This model studies light distribution from the main fiber into other branch fibers, which can be one or more than one. So, for this reason, twin couplers and multiple core couplers are studied in this paper. Further two cases in multiple core couplers namely multiple core couplers near the neighbor and multiple core couplers with a complete neighbor are exhaustively discussed. The non-linearity type that is considered here is Kerr Law. The obtained solutions set is more generalized than the existing solution as it is transformed into fractional-order derivative because it gives the solutions of problems with heavy tails or infinity fluctuations. Furthermore, the obtained solutions contain almost all types of solitons such as dark, bright, dark-bright, rational, periodic, breather, and singular soliton solutions, etc. Moreover, the obtained solutions are fractional solitons with Atangana-Baleanu and modified Riemann–Liouville fractional operator. These non-linear directional couplers also act as limiters in intensity-dependent switches. The propagation constants of the modes of a system are changed by non-linearity. In order to discuss the physical nature of couplers, 2D and 3D figures are also shown. |
topic |
Kerr law travelling wave solution New extended direct algebraic method Twin coupler Multiple core coupler Optical meta-material |
url |
http://www.sciencedirect.com/science/article/pii/S221137972100574X |
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