Generation of envelope and hole solitons in an experimental transmission line

Marquié, Patrick; Bilbault, Jean-Marie; Remoissenet, M.

doi:10.1103/physreve.49.828

Cited by 185 publications

(113 citation statements)

References 22 publications

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“…MI has been found in deep water [9,10], in plasmas [11][12][13], within laser light [8,14], in electrical transmission lines [15], and in Bose-Einstein condensates [16]. A linear stability analysis is typically performed to identify the instability criterion and to evaluate the initial growth rate of the sidebands.…”

Section: Introductionmentioning

confidence: 99%

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

et al. 2015

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Since the 1960s, the Benjamin-Feir (or modulation) instability (MI) has been considered as the selfmodulation of the continuous "envelope waves" with respect to small periodic perturbations that precedes the emergence of highly localized wave structures. Nowadays, the universal nature of MI is established through numerous observations in physics. However, even now, 50 years later, more practical but complex forms of this old physical phenomenon at the frontier of nonlinear wave theory have still not been revealed (i.e., when perturbations beyond simple harmonic are involved). Here, we report the evidence of the broadest class of creation and annihilation dynamics of MI, also called superregular breathers. Observations are done in two different branches of wave physics, namely, in optics and hydrodynamics. Based on the common framework of the nonlinear Schrödinger equation, this multidisciplinary approach proves universality and reversibility of nonlinear wave formations from localized perturbations for drastically different spatial and temporal scales.

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Section: Introductionmentioning

confidence: 99%

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

et al. 2015

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“…(6) and (7), we set ω=1.2ω 1 . The numerical calculation shows that E p,A increases with the amplitude (see Figure 6).…”

Section: Driving Amplitudementioning

confidence: 99%

“…This is shown in Figure 1. Each cell of the transmission lines has the usual form [6], which consists of one capacitor and two inductors. In Line a, the capacitor is nonlinear.…”

Section: Coupled Lc Transmission Linementioning

confidence: 99%

“…A variable capacitance diode, BB112, working at a DC voltage near V d =2.0 V, serves as the nonlinear capacitor. If |V n |<2.0 V, the capacitance is related to the AC voltage V n as follows [6]: where the parameters are C 0 =320 pF, α=0.21 V 1 and β=0.0197 V 2 . In Line b, the capacitor is linear, and C b =C 0 =320 pF.…”

Section: Coupled Lc Transmission Linementioning

confidence: 99%

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confidence: 99%

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Asymmetric energy flow in coupled nonlinear LC transmission line

Chen

Feng

et al. 2011

Chin. Sci. Bull.

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We constructed a coupled LC transmission line and studied the propagation of waves in it. We found asymmetric energy flow when we changed the driving conditions at the boundary. We analyzed this change and believe that it occurs because of the bandpass characteristics of the LC transmission line and high-order harmonic waves induced by nonlinearities. The LC transmission line could be used to simulate a microscopic crystal lattice. Therefore, we hope to observe thermal rectification in the system. We investigated the dependence of the system on different parameters, and then discussed the multi-frequency condition to aid in experimental verification. For numerical simulations of a coupled 1D lattice, it has been found that energy can flow through the channel from the high-temperature thermal bath to the lower-temperature bath in one direction. However, the lattice behaves as an insulator if the thermal baths are swapped. An experiment using a nanotube has shown this behavior with a 7% difference between heat fluxes in the two opposite directions [3]. However, nanotubes are not strictly 1D lattices in reality. In fact, we should be able to observe this abnormal phenomenon in experiments based on a macroscopic 1D lattice, which has the similar governing equations as the microscopic crystal lattice. In a macroscopic system, the energy of vibration (phonon) of each lattice can be measured directly. There are many types of macroscopic 1D lattice models, for example, pendulum chains [4] and nonlinear LC transmission lines [5]. While taking into account effect of thermal baths, we used the LC transmission line as our investigation model. The realization of random vibrations is much simpler to achieve with an electrical signal than in a mechanical system. In this work, we present a study of the propagation of waves in two coupled LC transmission lines, in which one line exhibits nonlinear transmission [5] and the other line is linear. First, we investigated monofrequency driving through numerical simulation and looked for possible abnormal energy transmission. Then we further discus multi-frequency driving (thermal bath) to aid ensuring experimental realization. Coupled LC transmission lineThe coupled LC transmission line that we studied contains two sub-lines (Lines a and b), which have the same structure but different parameters. They are coupled by an inductor, L int . This is shown in Figure 1. Each cell of the transmission lines has the usual form [6], which consists of one capacitor and two inductors. In Line a, the capacitor is nonlinear. A variable capacitance diode, BB112, working at a DC voltage near V d =2.0 V, serves as the nonlinear capacitor. If |V n |<2.0 V, the capacitance is related to the AC voltage V n as follows [6]:

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Phase Engineering Chirped Super Rogue Waves in a Nonlinear Transmission Network with Dispersive Elements

Kengne

Liu

2021

Advcd Theory and Sims

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A discrete nonlinear transmission network with dispersive element is considered. It is shown that the dynamics of slowly modulated waves propagating in this network are governed by a generalized cubic‐quintic nonlinear Schrödinger equation with self‐steepening and self‐frequency shift. Through the baseband modulational instability (MI) analysis, the conditions for this network to support the propagation of chirped super rogue waves (SRWs) are obtained. Based on the analytical rational solutions of the governed equation, chirped first‐ and second‐order super rogue waves are engineered in the nonlinear transmission network under consideration. The effects of the dispersive elements of the network on the chirped SRWs propagating in the network system are investigated. Particularly, it is shown that the introduction of the dispersive linear capacitance of the network enhances the baseband MI and both the derived SRWs and the corresponding frequency chirp are localized in both time and space. It is also shown that the structure of the frequency chirp depends strongly on the pulse self‐steepening and self‐frequency shift.

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Generation of envelope and hole solitons in an experimental transmission line

Cited by 185 publications

References 22 publications

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

Asymmetric energy flow in coupled nonlinear LC transmission line

Phase Engineering Chirped Super Rogue Waves in a Nonlinear Transmission Network with Dispersive Elements

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