Abstract
This work concerns the modelling of the dynamics of polarisation of a centrosymmetric material subjected to an amplitude-modulated excitation (AME). The dynamic equation obtained for the polarisation is the Duffing equation with nonlinearities of orders 3 and 5. With the multiple scale method, the nonlinear resonances are studied. Periodic, multiperiodic, quasiperiodic and chaotic behaviour have been checked using the bifurcation diagram, Lyapunov exponent, phase space, Poincaré section and vibrational resonance using the fourth-order Runge–Kutta integration algorithm. The effects of various parameters of polarisation are analysed and very interesting results are obtained. The results obtained by the analytical methods are validated and complemented by the numerical simulations.
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V C Long, H N Viet, M Trippenbach and K D Xuan, Comput. Meth. Sci. Technol. 14, 1 (2008)
D V Valovik, J. Opt. 19, 115502 (2017)
R W Boyd, Nonlinear optics, 2nd Edn (Academic Press, 2003)
D L Mills, Nonlinear optics: Basic concepts (Springer, 1991)
Y R Shen, The principles of nonlinear optics (Wiley, New York, 1984)
B N Delone, Basics of interaction of laser radiation with matter (Editions Frontières, 1993)
N N Akhmediev and A Ankevich, Solitons, nonlinear pulses and beams (Chapman and Hall, London, 1997)
A D Boardman, P Egan, F Lederer, U Langbein and D Mihalache, Third-Order nonlinear electromagnetic (TE and TM guided waves edited by H-E Ponath and G Stegeman (NorthHolland, Amsterdam), Reprinted from Nonlinear Surface Electromagnetic Phenomena, 1991
C Ainamon, C H Miwadinou, A V Monwanou and J B Chabi Orou, Appl. Phys. Res. 6(6), 74 (2014)
R W Boyd, Non linear optique, 3rd Edn (Academic Press, 2008)
P N Eleonskii, L G Oganes’yants and V P Silin, Sov. Phys. JETP 35, 44 (1972)
T O Roy-Layinde, U E Vincent, S A Abolade, O O Popoola, J A Laoye and P V E McClintock, Phil. Trans. Roy. Soc. A Math. Phys. Eng. Sci. 379, 2192 (2021)
S Rajasekar and M A F Sanjuán, Nonlinear resonances, in: Springer series in synergetics (Springer, Switzerland, 2016)
V M Gandhimathi, S Rajasekar and J Kurths, Phys. Lett. A 360, 279 (2006)
M I Dykman, D G Luchinsky, R Mannella, P V E McClintock, N D Stein and N G Stocks, Nuovo Cimento D 17, 661 (1995)
M I Dykman and P V E McClintock, Nature 391, 344 (1998)
S Guruparan, B Ravindran Durai Nayagam, V Ravichandran, V Chinnathambi and S Rajasekar, Chem. Sci. Rev. Lett. 4 (15), 870 (2015)
J H Yang, M A F Sanjuan, C J Wang and H Zhu, J. Appl. Nonlinear Dyn. 4, 397 (2015)
C Yao, Y Liu and M Zhan, Phys. Rev. E 83, 061122-1 (2011)
P S Landa and P V E McClintock, J. Phys. A: Math. Gen. 33, L 433 (2000)
A V Monwanou, A A Koukpémèdji, C Ainamon, P R Nwagoum Tuwa, C H Miwadinou and J B Chabi Orou, Complexity 2020, 8823458 (2020)
M Bartuccelli, G Gentile and J A Wright, Chaos 26, 083108 (2016)
H G Enjieu Kadji, R B Nana Nbendjo, J B Chabi Orou and P K Talla, Phys. Plasmas 15, 032308-1 (2007)
H G Enjieu Kadji, J B Chabi Orou and P Woafo, Phys. Scr. 77, 025503 (2008)
C H Miwadinou, L A Hinvi, A V Monwanou and J B Chabi Orou, Nonlinear Dyn. 88, 97 (2017)
T P Chang, Math. Prob. Eng. 3769870, 1 (2017)
J J Zebrowski, K Grudzinski, T Buchner, P Kuklik, J Gac, G Gielerak, P Sanders and R Baranowski, Chaos 17, 015121 (2007)
C H Miwadinou, A V Monwanou, A L Hinvi and J B Chabi Orou, Chaos Solitons Fractals 113, 89 (2018)
A Chudzik, P Perlikowski, A Stefanski and T Kapitaniak, Int. J. Bifurc. Chaos 21, 1907 (2011)
G F Kuiate, S T Kingni, V Kamdoum Tamba and P K Talla, Chin. J. Phys. 56, 2560 (2018)
S T Kingni, V-T Pham, S Jafari and P Woafo, Chaos Solitons Fractals 99, 209 (2017)
C H Miwadinou, A V Monwanou, A L Hinvi and J B Chabi Orou, Pramana – J . Phys. 93, 80 (2018)
V K Tamba, S T Kingni, G F Kuiate, H B Fotsin and P K Talla, Pramana – J. Phys. 91, 1 (2018)
A H Nayfey and D T Mook, Nonlinear oscillations (John Wiley and Sons, New York, 1979)
C Hayashi, Nonlinear oscillations in physical systems (McGraw-Hill Inc, New York, 1964)
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The authors thank very much the anonymous referees whose useful criticisms, and suggestions have helped strengthen the content and the quality of the paper. The authors sincerely thank The World Academy of Sciences (TWAS) for the advancement of science in develo** countries for the Research Grant No. 20-307 RG/PHYS/AF/AC-G-FR3240314170.
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Ainamon, C., Hinvi, L.A., Patinvoh, F.C. et al. Influence of amplitude-modulated excitation on the dynamic behaviour of polarisation of a material. Pramana - J Phys 95, 170 (2021). https://doi.org/10.1007/s12043-021-02168-z
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DOI: https://doi.org/10.1007/s12043-021-02168-z