6533b852fe1ef96bd12ab35d

RESEARCH PRODUCT

Energy transmission in the gap of nonlinear media triggered by deterministic and stochastic driving

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International audience; These past years, a growing interest has been devoted to the analysis of the response of nonlinearmedia to various excitations wether random or deterministic in order to better characterizetheir transmission properties [1, 2, 3]. Especially, since the introduction of the concept of soliton,the development of nonlinear electrical transmission lines has provided an efficient tool toexperimentally investigate the behaviour of these nonlinear waves [4]. Recently, some effortshave focused on the energy transmission in the gap of media obeying to equations deriving fromthe nonlinear Schr¨odinger model [5, 6]. Indeed, Geniet and Leon have shown that such nonlinearsystems, which present a natural forbidden band gap , can transmit energy of a signal even ifthe frequency is chosen in the gap [7]. Indeed, instead of the classical evanescent wave, whichis observed for weak amplitudes of the driving signal, nonlinear modes are triggered when thedriving amplitude exceeds a particular threshold. This effect, called supratransmission, has beenreported in various media ranging from optics to electronics [8, 9, 10, 11, 12].In this communication, we propose an overview of nonlinear supratransmission from bothnumerical and experimental points of view. We carried out our study in a Klein-Gordon electricallattice which exhibits Supratransmission [13]. Next, a numerical study is performed toreveal this effect in the sine-Gordon model where it is shown that noise can also trigger thiseffect [14]. We finally conclude by considering the influence of nonlinear coupling on the conditionof supratransmission triggering.Acknowledgements The authors thank the Regional Council of Burgundy for financial support(IRAP - Convention 2014-9201AAO49S01401 (SSTIC 6)).References[1] L., Gammaitoni, P. H¨anggi, P. Jung and F. Marcesoni, “Stochastic Resonance” Rev. Mod.Phys., 70, (1998).[2] B. Lindner, J. Garc´ıa-Ojalvo, A. Neiman, L. Schimansky-Geier, “Effects of noise in excitablesystems” Physics Reports 392, 321–424 (2004).[3] S. Flach, A. Gorbach, “Discrete breathers - Advances in theory and applications”, PhysicsReports 467 1-116 (2008).[4] M. Remoissenet, “Waves called solitons : concepts and experiments” (3rd revised and enlargededition), Springer-Verlag, Berlin 1999.[5] F. Geniet and J. Leon, “Energy Transmission in the forbidden band gap of a nonlinearChain” Phys. Rev. Lett. 89, 134102, (2002).[6] J. E. Macias-Dias, “Bistability of a two-dimensional Klein-Gordon system as a reliablemeans to transmit monochromatic waves: A numerical approach” Phys. Rev. E, 78, (2008).