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Effects of ellipticity angle on soliton solutions and modulation instability spectra in two-core birefringent optical fibers

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Abstract

In this paper, we investigate a coupled nonlinear Schrodinger equation which describes the propagation the propagation of optical signal in a two core optical fiber. A rich variety of various types of solitary wave solutions are exhibited including dark, bright, dark-bright, kink, anti-kink, singular, combined singular, triangular periodic solutions, Jacobi elliptic function solutions, combined Jacobi elliptic function solutions and periodic singular wave soliton solutions are obtained through the auxiliary equation method. We also investigate the modulation instability (MI) in the considered system. The study of the MI gain spectrum is done in the normal and anomalous dispersive regimes. To show the real physical significance of the studied equations, some three dimensional (3D) and two dimensional (2D) figures of obtained solutions are plotted with the use of the Matlab software under the proper choice of arbitrary parameters.

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Authors and Affiliations

  1. Department of Physics, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon

    Bienvenue Dépélair,  Douvagaï, Alphonse Houwe & Gambo Betchewe

  2. Department of Marine Engineering, Limbe Nautical Arts and Fisheries Institute, P.O. Box 485, Limbe, Cameroon

    Alphonse Houwe

  3. Department of Physics, Higher Teachers’ Training College of Maroua, the University of Maroua, P.O. Box 55, Maroua, Cameroon

    Gambo Betchewe

  4. Department of Computer Engineering, Biruni University, Istanbul, Turkey

    Mustafa Inc

  5. Science Faculty, Department of Mathematics, Firat University, 23119, Elazig, Turkey

    Mustafa Inc

  6. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Mustafa Inc

  7. Department of Physics, Faculty of Science, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon

    Serge Y. Doka

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Appendix

Appendix

\(k_{11}=-{ K}+\alpha \,{ K}+1/2\,\beta _{{2}}{\Omega }^{2}+\sqrt{{ \frac{P}{1+{f}^{2}}}}f\delta \,{ K}+\gamma \,\sqrt{{\frac{P}{1 +{f}^{2}}}}f+\nu \,\sqrt{{\frac{P}{1+{f}^{2}}}}f{ K}\),

\(k_{12}=C+\lambda \,\sqrt{{\frac{Pf}{1+{f}^{2}}}}\),

\(k_{13}=\sqrt{{\frac{P}{1+{f}^{2}}}}f\delta \,{ K}+\gamma \,\sqrt{{ \frac{P}{1+{f}^{2}}}}f+\nu \,\sqrt{{\frac{P}{1+{f}^{2}}}}f{ K}\),

\(k_{14}=\lambda \,\sqrt{{\frac{Pf}{1+{f}^{2}}}}\),

\(k_{21}=-\sqrt{{\frac{P}{1+{f}^{2}}}}f\delta \,{ K}+\gamma \,\sqrt{{ \frac{P}{1+{f}^{2}}}}f-\nu \,\sqrt{{\frac{P}{1+{f}^{2}}}}f{ K}\),

\(k_{22}=\lambda \,\sqrt{{\frac{Pf}{1+{f}^{2}}}}\),

\(k_{23}=\gamma \,\sqrt{{\frac{P}{1+{f}^{2}}}}f-\sqrt{{\frac{P}{1+{f}^{2}}}} f\delta \,{ K}-\alpha \,{ K}-\nu \,\sqrt{{\frac{P}{1+{f}^ {2}}}}f{ K}+{ K}+1/2\,\beta _{{2}}{\Omega }^{2}\),

\(k_{24}=C+\lambda \,\sqrt{{\frac{Pf}{1+{f}^{2}}}}\),

\(k_{31}=C+\lambda \,\sqrt{{\frac{Pf}{1+{f}^{2}}}}\),

\(k_{32}=-{ K}+\gamma \,\sqrt{{\frac{P}{1+{f}^{2}}}}+\alpha \,{ K }+1/2\,\beta _{{2}}{\Omega }^{2}+\sqrt{{\frac{P}{1+{f}^{2}}}}\delta \,{K}+\nu \,\sqrt{{\frac{P}{1+{f}^{2}}}}{K}\),

\(k_{33}=\lambda \,\sqrt{{\frac{Pf}{1+{f}^{2}}}}\),

\(k_{34}=\nu \,\sqrt{{\frac{P}{1+{f}^{2}}}}{K}+\sqrt{{\frac{P}{1+{f} ^{2}}}}\delta \,{K}+\gamma \,\sqrt{{\frac{P}{1+{f}^{2}}}}\),

\(k_{41}=\lambda \,\sqrt{{\frac{Pf}{1+{f}^{2}}}}\),

\(k_{42}=-\sqrt{{\frac{P}{1+{f}^{2}}}}\delta \,{K}+\gamma \,\sqrt{{ \frac{P}{1+{f}^{2}}}}-\nu \,\sqrt{{\frac{P}{1+{f}^{2}}}}{K}\),

\(k_{43}=C+\lambda \,\sqrt{{\frac{Pf}{1+{f}^{2}}}}\),

\(k_{44}=\gamma \,\sqrt{{\frac{P}{1+{f}^{2}}}}-\alpha \,{K}-\sqrt{{ \frac{P}{1+{f}^{2}}}}\delta \,{K}+1/2\,\beta _{{2}}{\Omega }^{2} -\nu \,\sqrt{{\frac{P}{1+{f}^{2}}}}{K}+{K}\).

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Dépélair, B., Douvagaï, Houwe, A. et al. Effects of ellipticity angle on soliton solutions and modulation instability spectra in two-core birefringent optical fibers. Opt Quant Electron 53, 322 (2021). https://doi.org/10.1007/s11082-021-02938-4

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