Research Article

Chirped gap solitons in fiber Bragg gratings with polynomial law of nonlinear refractive index

¹ College of Applied Sciences, University of Technology and Applied Sciences, P.O. Box 14, Ibri 516, Oman
² Department of Mathematics, Sultan Qaboos University, P.O.Box 36, Al-Khod 123, Muscat, Oman
³ Independent Researcher, Madison, AL 35758, USA
⁴ Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245, USA
⁵ Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
⁶ Department of Applied Sciences, Cross-Border Faculty, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati 800201, Romania
⁷ Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, Pretoria, South Africa

^* Corresponding author: khalil.ibr@cas.edu.om

Received: 18 February 2023
Accepted: 27 April 2023

Abstract

The objective of the present study is to examine the behaviors of chirped optical solitons in fiber Bragg gratings (BGs) with dispersive reflectivity. The form of nonlinear refractive index represents polynomial law nonlinearity. By virtue of phase-matching condition, the discussed model of coupled nonlinear Schrödinger equation is reduced to an integrable form. Consequently, chirped optical solitons having various profiles such as W-shaped, bright, dark, kink and anti-kink solitons are derived. Further to this, the chirp associated with these soliton structures are extracted. The impact of dispersive reflectivity, self-phase modulation and cross-phase modulation on the pulse propagation is investigated and it is induced that the changes of self-phase modulation and cross-phase modulation cause a marked rise in soliton amplitude which is subject to minor variations by dispersive reflectivity. The physical evolutions of chirped optical solitons are described along with the corresponding chirp to pave the way for possible applications in the field of fiber BGs.