Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers

Law, D. C.; D'Ambroise, Jennie; Kevrekidis, P. G.; Kip, Detlef

doi:10.3390/photonics1040390

Cited by 8 publications

(26 citation statements)

References 28 publications

(43 reference statements)

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“…Later, in the context of asymmetric transmission of signals through non-linear asymmetric dimer layers, it was shown that multistability could be enhanced by weak saturation of the (cubic) on-site nonlinearity; this favors the nonreciprocal transmission and also yields opposite effects of the rectifying action for short/long wavelength signals [7,8]. A similar study was carried out for saturable nonlinear oligomer DNLS segments (N = 1, 2, 3) embedded in a linear Schrödinger chain [9]. Other relevant works concern the asymmetric wave transmission through oligomers with cubic-quintic on-site nonlinearity [10], and the enhancement of the non-reciprocal transmission under saturable cubic-quintic nonlinear responses for dimers [11].…”

Section: Introductionmentioning

confidence: 88%

“…The parameter γ n determines the strength of the local nonlinearity, which we take to have a standard cubic (Kerr) form, while n represents the nonlocal (inter-site) saturable nonlinearity. We saturate only the inter-site nonlinearity as the effect of saturating the on-site cubic nonlinearity has been addressed in earlier work [7][8][9]11]. β is the saturation parameter; in the unsaturated limit β = 0 we recover the DNLS model with cubic inter-site nonlinearity studied in [18] (relevant e.g.…”

Section: Modelmentioning

confidence: 99%

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Multichannel asymmetric transmission through a dimer defect with saturable inter-site nonlinearity

Wasay,

Johansson

2020

Preprint

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We consider the asymmetric transmission properties of a Discrete Nonlinear Schrödinger type dimer with a saturable nonlinear intersite coupling between the dimer sites, in addition to a cubic onsite nonlinearity and asymmetric linear onsite potentials. In contrast to previously studied cases with pure onsite nonlinearities, the transmission coefficient for stationary transmission is shown to be a multivalued function of the transmitted intensity, in regimes of low saturability and small or moderate transmitted intensity. The corresponding backward transfer map is analyzed analytically and numerically, and shown to have either one or three distinct solutions for saturable coupling, and zero or two solutions for the purely cubic nonlinear coupling. As saturation strength is increased, the multi-solution regimes disappear through bifurcations and the single-valued regime of the onsite model is recovered. The existence of multiple solution branches yields novel mechanisms for asymmetric left/right stationary transmission: in addition to shifts of the positions of transmission peaks, peaks for transmission in one direction may correspond to nonexistence of stationary solutions propagating in the opposite direction, at the corresponding branch and transmitted intensity. Moreover, one of these transmission channels behaves as a nearly perfect mirror for incoming signals. The linear stability of the stationary solutions is analyzed, and instabilities are typically observed, and illustrated by direct numerical simulations, in regimes with large transmission coefficient. Intersite nonlinearities are found to prevent the formation of a localized dimer mode in the instability-induced dynamics. Finally, the partial reflection and transmission of a Gaussian excitation is studied, and the asymmetric transmission properties are compared to previously studied onsite models.

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Section: Introductionmentioning

confidence: 88%

Section: Modelmentioning

confidence: 99%

Multichannel asymmetric transmission through a dimer defect with saturable inter-site nonlinearity

Wasay,

Johansson

2020

Preprint

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“…If D = i −1 δ and m = γ, eqs. (31), become the time dependent saturable nonlinear Schrödinger equation, [4]: 5 The equilibrium function in the d2q9 velocity scheme.…”

Section: The Construction Of the Nonlinear Schrödinger Equationmentioning

confidence: 99%

A solution of the two-dimensional Schrodinger equation

Fonseca¹

2016

imf

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In this work we solved the saturable nonlinear Schrödinger equation, in two dimensions, using the higher-order moment Lattice-Boltzmann (LB) technique, and working with the d2q9 velocity scheme. The approach is based on the introduction of the suitable nonlinear terms using the source terms in the LB's equations. Also, we adopt the He's semi-inverse approach in order to find solitary wave solutions. We get coherent structures.

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“…For example, for short and high peak power pulses, the field-induced change in the refractive index cannot be described by a Kerr-type nonlinearity, since it is influenced by higher-order nonlinearities such as saturable nonlinearity [24]. The saturation of the nonlinear response has been shown to have novel impacts on the dynamical properties of wave propagation in clean systems [24,25,26,27,28,29,30,31,32,33,34,35]. For instance, it has been pointed out that the saturable nonlinearity allows the existence of stable two-state solitons with the same time duration [24] and of breathers with high power [25].…”

Section: Introductionmentioning

confidence: 99%

“…In [26], genuinely localized travelling waves have been found in saturable nonlinear Schrödinger lattices for the first time. Furthermore, in recent papers, the authors have shown that there exists asymmetric wave propagation through saturable nonlinear oligomers and wave rectification devices can be produced based on such systems [34,35].…”

Section: Introductionmentioning

confidence: 99%

Anderson localization and saturable nonlinearity in one-dimensional disordered lattices

Nguyen

Kim

2017

Journal of Modern Optics

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We investigate numerically the propagation and the Anderson localization of plane waves in a one-dimensional lattice chain, where disorder and saturable nonlinearity are simultaneously present. Using a calculation scheme for solving the stationary discrete nonlinear Schrödinger equation in the fixed input case, the disorder-averaged logarithmic transmittance and the localization length are calculated in a numerically precise manner. The localization length is found to be a nonmonotonic function of the incident wave intensity, acquiring a minimum value at a certain finite intensity, due to saturation effects. For low incident intensities where the saturation effect is ineffective, the enhancement of localization due to Kerr-type nonlinearity occurs in a way similar to the case without saturation. For sufficiently high incident intensities, we find that the localization length is an increasing function of the incident wave intensity, which implies that localization is suppressed for stronger input intensities, and ultimately approaches a saturation value. This feature is associated with the fact that the nonlinear system is reduced to an effectively linear one, when either the incident wave intensity or the saturation parameter is sufficiently large. We also find that the nonlinear saturation effect is stronger and more pronounced when the energy of the incident wave is larger.

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Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers

Cited by 8 publications

References 28 publications

Multichannel asymmetric transmission through a dimer defect with saturable inter-site nonlinearity

Multichannel asymmetric transmission through a dimer defect with saturable inter-site nonlinearity

A solution of the two-dimensional Schrodinger equation

Anderson localization and saturable nonlinearity in one-dimensional disordered lattices

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