Parametric Solitons in Two-Dimensional Lattices of Purely Nonlinear Origin

Gallo, Katia; Pasquazi, Alessia; Stivala, Salvatore; Assanto, Gaetano

doi:10.1103/physrevlett.100.053901

Cited by 42 publications

(21 citation statements)

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“…That is, we examine whether ILMs can be generated and, especially, stabilized by subharmonic and/or parametric driving which is homogeneous in space. So far, this type of question seems to have been considered chiefly in the context of continuous media [10], or for parametric driving [11][12][13], and has been principally theoretical in nature. In this Letter, we demonstrate experimentally and corroborate through theoretical modeling and numerical computation, and, when possible, infusing analytical insights, that ILMs can indeed be generated and stabilized via subharmonic forcing.…”

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Generation of Localized Modes in an Electrical Lattice Using Subharmonic Driving

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We show experimentally and numerically that an intrinsic localized mode (ILM) can be stably produced (and experimentally observed) via subharmonic, spatially homogeneous driving in the context of a nonlinear electrical lattice. The precise nonlinear spatial response of the system has been seen to depend on the relative location in frequency between the driver frequency, ! d , and the bottom of the linear dispersion curve, ! 0 . If ! d =2 lies just below ! 0 , then a single ILM can be generated in a 32-node lattice, whereas, when ! d =2 lies within the dispersion band, a spatially extended waveform resembling a train of ILMs results. To our knowledge, and despite its apparently broad relevance, such an experimental observation of subharmonically driven ILMs has not been previously reported. DOI: 10.1103/PhysRevLett.108.084101 PACS numbers: 05.45.Yv, 63.20.Pw, 63.20.Ry It is well known that a damped nonlinear oscillator can respond at its intrinsic resonance frequency when it is driven at a multiple of that frequency. A direct example of such subharmonic driving is provided by the driven Van der Pol oscillator, where the ratio of response to driver frequency is exactly 1=3 [1,2]. Many other nonlinear oscillators exhibit similar subharmonic resonances (the Duffing oscillator being another extensively studied example). In fact, subharmonic response must be seen as a fairly generic property of nonlinear oscillators. Alternatively, a nonlinear oscillator with a parameter modulated at a particular frequency can also respond at a fraction of that frequency in what is called parametric excitation.What happens when such nonlinear oscillators are connected to one another in a regular lattice? In nonlinear lattices, an important generic phenomenon is the existence of self-trapped localized modes, known as intrinsic localized modes (ILMs) or discrete breathers. Such a mode represents an excitation which is (typically exponentially) spatially localized over a limited range of lattice nodes and decays to zero far from these, and it is temporally periodic. In this regard, it can be thought of as an analog of the solitons of continuous media. However, the discreteness of the lattice introduces interesting variations to the problem, including, for instance, the fact that ILMs may be dynamically stable in any dimension. Here, we blend these two broadly significant aspects of nonlinear systems by addressing the following question: can subharmonic or parametric excitations, which figure so prominently in isolated nonlinear oscillators, carry over to the lattice setting? That is, we examine whether ILMs can be generated and, especially, stabilized by subharmonic and/or parametric driving which is homogeneous in space. So far, this type of question seems to have been considered chiefly in the context of continuous media [10], or for parametric driving [11][12][13], and has been principally theoretical in nature. In this Letter, we demonstrate experimentally and corroborate through theoretical modeling and numerical computation, an...

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Generation of Localized Modes in an Electrical Lattice Using Subharmonic Driving

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“…Second-order nonlinear optical processes can be enhanced via quasi-phase matching (QPM) in order to conserve momentum; in ferroelectric crystals (i.e. lithium niobate (LN) and lithium tantalate (LT)), this can be achieved by manipulating the quadratic susceptibility x (2) with a simple control of ferroelectric domain polarisation along the direction of light propagation [1]. Typically, an intense electric field is periodically applied along the optic axis (z) of the bulk crystal in order to obtain selective domain flipping.…”

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“…Optical waveguides, in this configuration, allow exploiting high intensity electromagnetic waves at low pump powers, extended propagation and interaction lengths, and controlled transverse profiles of the generated signal(s). Guided-wave and photonic lattice circuits based on parametric nonlinearities [2] can largely extend their functionalities by exploiting the periodic or quasi-periodic modulation of optical properties with tight spatial control and sub-micron resolution.…”

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Random quasi-phase matching in congruent lithium tantalate waveguides by proton exchange

et al. 2012

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“…PP-QPM is also crucial towards signal processing via quadratic cascading [5][6][7][8][9][10][11][12][13][14], including transverse light localization [15][16][17][18], wavelength shifting [19][20][21], unidirectional optical transmission [22,23]. A few parametric applications, such as backward second-harmonic generation (SHG), counterpropagating optical parametric oscillations and ultraviolet generation, require short periodicities of the nonlinear coefficient distribution, often below 1μm [24][25][26][27].…”

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Features of randomized electric-field assisted domain inversion in lithium tantalate

Stivala¹,

Buccheri²,

Curcio³

et al. 2011

Opt. Express

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Abstract:We report on bulk and guided-wave second-harmonic generation via random Quasi-Phase-Matching in Lithium Tantalate. By acquiring the far-field profiles at several wavelengths, we extract statistical information on the distribution of the quadratic nonlinearity as well as its average period, both at the surface and in the bulk of the sample. By investigating the distribution in the two regions we demonstrate a non-invasive approach to the study of poling dynamics. tuning and tolerances," IEEE J. Quantum Electron. 28(11), 2631-2654 (1992). 2. M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second harmonic generation," Appl. ©2011 Optical Society of America

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Parametric Solitons in Two-Dimensional Lattices of Purely Nonlinear Origin

Abstract: We demonstrate spatial solitons via twin-beam second-harmonic generation in hexagonal lattices realized by poling lithium niobate planar waveguides. These simultons can be steered by acting on power, direction, and wavelength of the fundamental frequency input.

Cited by 42 publications

References 38 publications

Generation of Localized Modes in an Electrical Lattice Using Subharmonic Driving

Generation of Localized Modes in an Electrical Lattice Using Subharmonic Driving

Random quasi-phase matching in congruent lithium tantalate waveguides by proton exchange

Features of randomized electric-field assisted domain inversion in lithium tantalate

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