Second harmonic generation in a two-dimensional diatomic lattice

Gonçalves, Andreia

doi:10.1103/physrevb.62.14105

Cited by 4 publications

(5 citation statements)

References 8 publications

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“…In all these cases, the generated second harmonic was considered to be non-resonant with the fundamental harmonic. The resonant case needs to be treated separately using the condition of three-wave-interaction, which has been carried out for generic dispersive hyperbolic differential equations [43] and periodic lattices [28,20]. In addition, nonlinearity also gives rise to sub-harmonics, which have been studied in precompressed monoatomic granular chains by Tournat et al [49].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear waves in lattice materials: Adaptively augmented directivity and functionality enhancement by modal mixing

Ganesh

Gonella

2017

Journal of the Mechanics and Physics of Solids

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The motive of this work is to understand the complex spatial characteristics of finite-amplitude elastic wave propagation in periodic structures and leverage the unique opportunities offered by nonlinearity to activate complementary functionalities and design adaptive spatial wave manipulators. The underlying assumption is that the magnitude of wave propagation is small with respect to the length scale of the structure under consideration, albeit large enough to elicit the effects of finite-deformation. We demonstrate that the interplay of dispersion, nonlinearity and modal complexity involved in the generation and propagation of higher harmonics gives rise to secondary wave packets that feature multiple characteristics, one of which conforms to the dispersion relation of the corresponding linear structure. This provides an opportunity to engineer desired wave characteristics through a geometric and topological design of the unit cell, and results in the ability to activate complementary functionalities, typical of high frequency regimes, while operating at low frequencies of excitation -an effect seldom observed in linear periodic structures. The ability to design adaptive switches is demonstrated here using lattice configurations whose response is characterized by geometric and/or material nonlinearities.

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Section: Introductionmentioning

confidence: 99%

“…Under such conditions, additional constraints need to be incorporated to determine the forced solution (similar to the group velocity constraint imposed for the fundamental harmonic). Typically, a three-wave-interaction model is assumed to study resonant second harmonic generation[29,20], which will not be considered in this work.…”

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confidence: 99%

Nonlinear waves in lattice materials: Adaptively augmented directivity and functionality enhancement by modal mixing

Ganesh

Gonella

2017

Journal of the Mechanics and Physics of Solids

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“…The most well-known signature of finite-amplitude wave propagation is the generation of harmonics [13], a feature which, in conjunction with dispersion, is commonly employed as an inspection and characterization tool in Non-Destructive Evaluation (NDE) techniques [14][15][16]. While the concept of harmonic generation has also been explored in nonlinear periodic structures [17,18], its complete implications on the spatial characteristics of wave propagation have only been marginally studied. In this regard, we recently carried out a theoretical and numerical investigation of granular phononic crystals [19] and nonlinear lattices [20], where we have shown that the onset of nonlinear mechanisms (obtained, for example, by increasing the amplitude of excitation) can be effectively used to stretch the frequency signature of the wave response and distribute it over multiple modes, thereby activating a mixture of (possibly complementary) modal characteristics and enabling functionalities associated with high-frequency optical modes, even while operating in the low-frequency regime.…”

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confidence: 99%

Experimental evidence of directivity-enhancing mechanisms in nonlinear lattices

Ganesh

Gonella

2017

Applied Physics Letters

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In this letter, we experimentally investigate the directional characteristics of propagating, finiteamplitude wave packets in lattice materials, with an emphasis on the functionality enhancement due to the nonlinearly-generated higher harmonics. To this end, we subject a thin, periodically perforated sheet to out-of-plane harmonic excitations, and we design a systematic measurement and data processing routine that leverages the full-wavefield reconstruction capabilities of a laser vibrometer to precisely delineate the effects of nonlinearity. We demonstrate experimentally that the interplay of dispersion, nonlinearity, and modal complexity which is involved in the generation and propagation of higher harmonics gives rise to secondary wave packets with characteristics that conform to the dispersion relation of the corresponding linear structure. Furthermore, these nonlinearly generated wave features display modal and directional characteristics that are complementary to those exhibited by the fundamental harmonic, thus resulting in an augmentation of the functionality landscape of the lattice. These results provide proof of concept for the possibility to engineer the nonlinear wave response of mechanical metamaterials through a geometric and topological design of the unit cell. Periodic structures and materials feature an intrinsic ability to impede wave propagation within certain frequency ranges referred to as bandgaps [1,2], which allows them to effectively function as vibration filters and waveguides [3,4]. Another related, but significantly less explored effect is their frequency-dependent spatial directivity [5], by which propagating wave packets travel with anisotropic characteristics and display patterns whose morphology depends on the frequency of excitation. When periodic structures experience finitedeformations, both bandgaps and directivity become amplitude-dependent [6,7], thereby endowing the structure with the ability to adapt to changes in operating conditions. On the other hand, nonlinear periodic structures can also be tuned to elicit complementary responses without changes in the operating condition [8], a feature that is commonly exploited to design tunable vibration filters [9]. Finally, the availability of nonlinear mechanisms also results in the ability to realize devices such as acoustic diodes and rectifiers [10][11][12], by triggering nonreciprocal effects that are seldom possible in their linear counterparts. The most well-known signature of finite-amplitude wave propagation is the generation of harmonics [13], a feature which, in conjunction with dispersion, is commonly employed as an inspection and characterization tool in Non-Destructive Evaluation (NDE) techniques [14][15][16]. While the concept of harmonic generation has also been explored in nonlinear periodic structures [17,18], its complete implications on the spatial characteristics of wave propagation have only been marginally studied. In this regard, we recently carried out a theoretical and numerical investigation of granula...

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“…In particular, the velocities are orthogonal. [19,32,52,84] In the case of second-order harmonic generation, when equation ( 15) satisfies the condition ω(2𝑞) = 2ω(𝑞), one arrives at the system of equations for the solvability condition of third order in the hierarchy of exponentials.…”

Section: Model and The Mathematical Background 21 The Envelope Equati...mentioning

confidence: 99%

“…Conclaves et al have reported an important phenomenon of resonant mode interactions observed in 2D diatomic lattices with a complex network. [32] The existence of intrinsic gap mode in 3D anharmonic diatomic lattices with realistic potentials has been explored in Refs. [33] and [34].…”

Section: Introductionmentioning

confidence: 99%

Oscillating multidromion excitations in higher-dimensional nonlinear lattice with intersite and external on-site potentials using symbolic computation

Srividya¹,

Kavitha²,

Ravichandran³

et al. 2014

Chinese Phys. B

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We show by an extensive method of quasi-discrete multiple-scale approximation that nonlinear multi-dimensional lattice waves subjected to intersite and external on-site potentials are found to be governed by (N +1)-dimensional nonlinear Schrödinger (NLS) equation. In particular, the resonant mode interaction of (2+1)-dimensional NLS equation has been identified and the theory allows the inclusion of transverse effect. We apply the exponential function method to the (2+1)dimensional NLS equation and obtain the class of soliton solutions with a purely algebraic computational method. Notably, we discuss in detail the effects of the external on-site potentials on the explicit form of the soliton solution generated recursively. Under the action of the external on-site potentials, the model presents a rich variety of oscillating multidromion patterns propagating in the system.

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Second harmonic generation in a two-dimensional diatomic lattice

Cited by 4 publications

References 8 publications

Nonlinear waves in lattice materials: Adaptively augmented directivity and functionality enhancement by modal mixing

Nonlinear waves in lattice materials: Adaptively augmented directivity and functionality enhancement by modal mixing

Experimental evidence of directivity-enhancing mechanisms in nonlinear lattices

Oscillating multidromion excitations in higher-dimensional nonlinear lattice with intersite and external on-site potentials using symbolic computation

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