Skip to main content
SpringerLink
Log in

Modulated waves patterns in the photovoltaic photorefractive crystal

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

In this paper, we investigated the propagation of the modulated waves (MWs) patterns with the effects of the external field (EF) in a photorefractive crystal. To do so, we use the coupled nonlinear Schrödinger equations and we apply the auxiliary equation method to point out four families of solutions such as bright, dark, combined bright-dark, and bright-bright soliton. We pointed out the effects of EF on the modulation instability growth rate. Throughout the numerical simulation, we show that EF can generate MWs patterns when the short and open circuit condition is considered in the case of bright soliton. However, when we consider dark soliton solution as an initial condition and we have only obtained the MW pattern in the case of a short circuit. It results in this study of the propagation of the MWs patterns and chaos-like motion for specific cell indexes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Availability of data and materials

Not applicable.

References

  • Abbagari, S., Houwe, A., Akinyemi, L., Saliou, Y., Bouetou, T.B.: Modulation instability gain and discrete soliton interaction in gyrotropic molecular chain. Chaos, Solitons Fractals 160, 1–7 (2022)

  • Ablowitz, M.J.: Nonlinear Dispersive Waves Assymtotic Analysis and Solitons. Cambridge University Press, Cambridge (2011)

    Book  MATH  Google Scholar 

  • Aguero, M., García-Salcedo, R., Socorro, J., Villagran, E.: Soliton structures in a molecular chain model with saturation. Int. J. Theor. Phys. 48, 670–683 (2009)

    Article  MATH  Google Scholar 

  • Akinyemi, L., Inc, M., Khater, M., Rezazadeh, H.: Dynamical behaviour of Chiral nonlinear Schrödinger equation. Opt. Quantum Electron. 54(3), 1–15 (2022)

    Article  Google Scholar 

  • Anisimovas, E., Račiũnas, M., Sträter, C., Eckardt, A., Spielman, I.B., Juzeliũnas, G.: Semi synthetic zigzag optical lattice for ultracold bosons. Phys. Rev. E 94, 1–8 (2016)

  • Castillo, M.D., Aguilar, P.A., Mondragon, J.J., Stepanov, S., Vysloukh, V.: Spatial solitons in photorefractive Bi\(_{12}\)TiO\(_{20}\) with drift mechanism of nonlinearity. Appl. Phys. Lett. 64, 408–410 (1994)

    Article  ADS  Google Scholar 

  • Chang, X., Xie, J., Wu, T., Tang, B.: Modulational instability and quantum discrete breather states of cold bosonic atoms in a zig-zag optical lattice. Int. J. Theor. Phys. 57(7), 2218–2232 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  • Dai, C.Q., Wang, Y.Y.: Coupled spatial periodic waves and solitons in the photovoltaic photorefractive crystal. Nonlinear Dyn. 102, 1733–1741 (2020)

    Article  Google Scholar 

  • Davidov, A.S.: Soliton in Molecular Systems, 2nd edn. Kluwer Academic Publishers, Dordrecht (1991)

    Book  Google Scholar 

  • Duree, G.C., Shultz, J.L., Salamo, G.J., Segev, M., Yariv, A., Crosignani, B., Porto, P.D., Sharp, E.J., Neurgaonkar, R.R.: Observation of self-trapping of an optical beam due to the photorefractive effect. Phys. Rev. Lett. 71, 533–536 (1993)

    Article  ADS  Google Scholar 

  • Geniet, F., Leon, J.: Energy transmission in the forbidden band gap of a nonlinear chain. Phys. Rev. L 89, 1–4 (2002)

  • Hou, C.F., Zhang, Y., Jiang, Y.Y., Pei, Y.B.: Photovoltaic solitons in two-photon photorefractive materials under open-circuit conditions. Opt. Commun. 273, 544–548 (2007)

    Article  ADS  Google Scholar 

  • Houwe, A., Abbagari, S., Almohsen, B., Betchewe, G., Inc, M., Doka, S.Y.: Chriped solitary waves of the perturbed Chen–Lee–Liu equation and modulation instability in optical mono mode fibers. Opt. Quantum Electron. 53, 1–12 (2021)

    Article  Google Scholar 

  • Houwe, A., Djorwe, P., Abbagari, S., Doka, S.Y., Nana Engo, S.G.: Discrete solitons in nonlinear optomechanical array. Chaos Solitons Fractals 154, 1–8 (2022)

    MathSciNet  MATH  Google Scholar 

  • Issa, S., Maïna, I., Tabi, C.B., Mohamadou, A., Fouda, H.P.E., Kofane, T.C.: Long-range modulated wave patterns in certain nonlinear saturation alpha-helical proteins. Eur. Phys. J. Plus 136, 1–21 (2021)

    Article  Google Scholar 

  • Katti, A.: Bright screening solitons in a photorefractive waveguide. Opt. Quantum Electron. 50, 1–10 (2018)

    Article  Google Scholar 

  • Katti, A.: Gaussian soliton pairs in an unbiased photorefractive crystal due to the pyroelectric effect. Eur. Phys. J. Plus 134, 1–11 (2019)

    Article  Google Scholar 

  • Katti, A.: Coupling of separate solitons in a series circuit of two photon photorefractive crystals exhibiting simultaneous quadratic and linear nonlinearities. Optik 206, 1–10 (2020)

  • Ke-Qing, L., Yanpeng, Z., Tiantong, T., Bo, L.: Incoherently coupled steady-state soliton pairs in biased photorefractive-photovoltaic materials. Phy. Rev. E 64, 1–9 (2001)

  • Ke-Qing, L., Wei, Z., Yan-Long, Y., Xiang-Ping, Z., Jin-Ping, L., Yan-Peng, Z.: Modulation instability of quasi-plane-wave optical beams in biased photorefractive photovoltaic crystals. Chin. Phys. Soc. 13, 2077–2081 (2004)

    Article  ADS  Google Scholar 

  • Konar, S., Shekhar, S., Hong, W.P.: Incoherently coupled two component screening photovoltaic solitons in two-photon photorefractive materials under the action of external field. Opt. Laser Technol. 42, 1294–1300 (2010a)

  • Konar, S., Shekhar, S., Shwetanshumala, S.: External electric field induced modulation instability of an electromagnetic beam in two-photon photorefractive materials. Opt. Laser Technol. 42, 1276–1281 (2010b)

  • Kong, L.Q., Liu, J., Jin, D.Q., Ding, D.J., Dai, C.Q.: Soliton dynamics in the three-spine α-helical protein with inhomogeneous effect. Nonlinear Dyn. 87, 83–92 (2017)

    Article  Google Scholar 

  • Koon, K.T.V., Leon, J., Marquié, P., Tchofo-Dinda, P.: Cutoff solitons and bistability of the discrete inductance-capacitance electrical line: theory and experiments. Phys. Rev. E 75, 1–8 (2007)

  • Liu, W., Yu, W., Yang, C., Liu, M., Zhang, Y., Lei, M.: Analytic solutions for the generalized complex Ginzburg–Landau equation in fiber lasers. Nonlinear Dyn. 89, 2933–2939 (2017)

    Article  MathSciNet  Google Scholar 

  • Mathanaranjan, T., Rezazadeh, H., Senol, M., Akinyemi, L.: Optical singular and dark solitons to the nonlinear Schrödinger equation in magneto-optic waveguides with anti-cubic nonlinearity. Opt. Quantum Electron. 53(12), 1–16 (2021)

    Article  Google Scholar 

  • Mirzazadeh, M., Akbulut, A., Taşcan, F., Akinyemi, L.: A novel integration approach to study the perturbed Biswas-Milovic equation with Kudryashov’s law of refractive index. Optik 252, 1–9 (2022)

  • Mohamed, M.S., Akinyemi, L., Najati, S.A., Elagan, S.K.: Abundant solitary wave solutions of the Chen–Lee–Liu equation via a novel analytical technique. Opt. Quantum Electron. 54(3), 1–14 (2022)

    Article  Google Scholar 

  • Muniyappan, A., Suruthi, A., Monisha, B., Sharon Leela, N., Vijaycharles, J.: Dromion-like structures in a cubic-quintic nonlinear Schrödinger equation using analytical methods. Nonlinear Dyn. 104, 1533–1544 (2021)

    Article  Google Scholar 

  • Ntiamoah, D., Ofori-Atta, W., Akinyemi, L.: The higher-order modified Korteweg–de Vries equation: its soliton, breather and approximate solutions. J. Ocean Eng. Sci. 1–12 (2022)

  • Primatarowa, M.T., Stoychev, K.T.: Soliton dynamics in gyrotropic molecular chains. Phys. Rev. B 49, 6634–6642 (1994)

    Article  ADS  Google Scholar 

  • Primatarowa, M.T., Stoychev, K.T., Kamburova, R.S.: Soliton dynamics in chiral molecular chains with first and third-neighbour interactions. Eur. Phys. J. B 29, 291–294 (2002)

    Article  ADS  Google Scholar 

  • Remoissenet, M.: Waves Called Solitons Concepts and Experiments, 2nd edn. Springer, Berlin (1996)

    Book  MATH  Google Scholar 

  • Seadawy, A.R.: Three-dimensional nonlinear modified Zakharov–Kuznetsov equation of ion-acoustic waves in a magnetized plasma. Comput. Math. Appl. 71, 201–212 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  • Simo, E., Kofane, T.C.: Nonlinear effects in molecular chains with two types of intramolecular vibrations. Phys. Rev. E 54, 2071–2076 (1996)

    Article  ADS  Google Scholar 

  • Stedman, G.E.: On chiral or gyrotropic optical effects. Phys. Lett. A 152, 19–20 (1991)

    Article  ADS  Google Scholar 

  • Sulaiman, T.A., Bulut, H.: Optical solitons and modulation instability analysis of the \((1+1)\)-dimensional coupled nonlinear Schrödinger equation. Commun. Theor. Phys. 72, 1–6 (2020)

  • Tabi, C.B.: Fractional unstable patterns of energy in a-helix proteins with long-range interactions. Chaos Solitons Fractals 116, 386–391 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  • Wang, L., Zhang, L.L., Zhu, Y.J., Qi, F.H., Wang, P., Guo, R., Li, M.: Modulational instability, nonautonomous characteristics and semirational solutions for the coupled nonlinear Schrödinger equations in inhomogeneous fibers. Commun. Nonlinear Sci. Numer. Simulat. 40, 216–237 (2016)

    Article  ADS  MATH  Google Scholar 

  • Zhang, Y., Hou, C., Zhan, K., Sun, X.: Incoherently coupled bright-dark photovoltaic soliton pairs based on two-photon photorefractive effect. Optik 122, 263–265 (2011)

    Article  ADS  Google Scholar 

Download references

Funding

No funding available for this project.

Author information

Authors and Affiliations

  1. Department of Mechanical Petroleum and Gas Engineering, National Advanced School of Mines and Petroleum Industries, University of Maroua, P.O. Box 46, Maroua, Cameroon

    Jérôme Dikwa

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

    Alphonse Houwe

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

    Alphonse Houwe

  4. Department of Basic Science, National Advanced School of Mines and Petroleum Industries, University of Maroua, P.O Box 08, Kaélé, Cameroon

    Souleymanou Abbagari

  5. Department of Mathematics, Lafayette College, Easton, PA, USA

    Lanre Akinyemi

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

    Mustafa Inc

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

    Mustafa Inc

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

    Mustafa Inc

Authors
  1. Jérôme Dikwa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alphonse Houwe
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Souleymanou Abbagari
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lanre Akinyemi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mustafa Inc
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The authors read and approved the final manuscript.

Corresponding authors

Correspondence to Alphonse Houwe or Lanre Akinyemi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethics approval

Not applicable.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dikwa, J., Houwe, A., Abbagari, S. et al. Modulated waves patterns in the photovoltaic photorefractive crystal. Opt Quant Electron 54, 842 (2022). https://doi.org/10.1007/s11082-022-04224-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-022-04224-3

Keywords

Search

Navigation