Ukrainian Journal of Physical Optics 

Volume 22, Issue 4, 2021
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Optical solitons in fibre Bragg gratings with third- and fourth-order dispersive reflectivities

1Yakup Yıldırım, 2,3,4,5Anjan Biswas, 5Padmaja Guggilla, 5Salam Khan, 3Hashim M. Alshehri and 6Milivoj R. Belic

1Department of Mathematics, Faculty of Arts and Sciences, Near East   University, 99138 Nicosia, Cyprus
2Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Hwy, Moscow–115409, Russian Federation
3Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah–21589, Saudi Arabia
4Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa–0204, Pretoria, South Africa
5Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762–4900, USA
6Institute of Physics Belgrade, Pregrevica 118, 11080 Zemun, Serbia

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Abstract. For the first time in the field of nonlinear optics, we address cubic–quartic solitons appearing in the fibre Bragg gratings with dispersive reflectivity for four different cases of nonlinear refractive-index structures. A complete spectrum of single solitons, together with some straddled solitons, emerges from the integration scheme adopted by us, which is the approach of sine–Gordon equation. 

Keywords: solitons; Bragg gratings; sine–Gordon equation method

UDC: 535.32
Ukr. J. Phys. Opt. 22 239-254
doi: 10.3116/16091833/22/4/239/2021
Received: 22.10.2021

Анотація. Вперше в нелінійній оптиці розглянуто кубічно-квартичні солітони, які з’являються у волоконних бреггівських ґратках з дисперсійною відбивною здатністю для чотирьох різних випадків структур з нелінійним показником заломлення. Із прийнятої нами схеми інтегрування, яка є підходом рівняння синус–Гордона, випливає повний спектр одиничних солітонів, разом із деякими розмежованими солітонами.

Ключові слова: солітони; решітки Брегга; Метод рівняння синус–Гордона
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