Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica

Szameit, Alexander; Burghoff, Jonas; Pertsch, Thomas; Nolte, Stefan; Tünnermann, Andreas; Lederer, F.

doi:10.1364/oe.14.006055

Cited by 174 publications

(122 citation statements)

References 16 publications

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“…For instance, in Refs. [51,52] experiments showed that weak coupling was required to obtain nonlinear localized solutions at the surface of femtosecond laser written nonlinear square lattices. Having in mind that in dimerized Lieb lattice soliton solution bifurcates from the linear limit, its geometry can provide conditions for tailoring strength of coupling.…”

Section: Discussionmentioning

confidence: 99%

Localized gap modes in nonlinear dimerized Lieb lattices

et al. 2017

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Compact localized modes of ring type exist in many two-dimensional lattices with a flat linear band, such as the Lieb lattice. The uniform Lieb lattice is gapless, but gaps surrounding the flat band can be induced by various types of bond alternations (dimerizations) without destroying the compact linear eigenmodes. Here, we investigate the conditions under which such diffractionless modes can be formed and propagated also in the presence of a cubic on-site (Kerr) nonlinearity. For the simplest type of dimerization with a three-site unit cell, nonlinearity destroys the exact compactness, but strongly localized modes with frequencies inside the gap are still found to propagate stably for certain regimes of system parameters. By contrast, introducing a dimerization with a 12-site unit cell, compact (diffractionless) gap modes are found to exist as exact nonlinear solutions in continuation of flat band linear eigenmodes. These modes appear to be generally weakly unstable, but dynamical simulations show parameter regimes where localization would persist for propagation lengths much larger than the size of typical experimental waveguide array configurations. Our findings represent an attempt to realize conditions for full control of light propagation in photonic environments.

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Section: Discussionmentioning

confidence: 99%

Localized gap modes in nonlinear dimerized Lieb lattices

et al. 2017

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“…In recent years, such effects have been experimentally observed in photonic systems. Localization effects due to the presence of disorder [9,10], analogous external fields [11,12] and nonlinearity [13] have been observed. Recently, a novel type of localization due to a non-dispersive band in the energy spectrum was demonstrated in a photonic Lieb lattice [14,15].…”

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confidence: 89%

Observation of localized flat-band modes in a quasi-one-dimensional photonic rhombic lattice

2015

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We experimentally demonstrate the photonic realization of a dispersionless flat-band in a quasione-dimensional photonic lattice fabricated by ultrafast laser inscription. In the nearest neighbor tight binding approximation, the lattice supports two dispersive and a non-dispersive (flat) band. We experimentally excite superpositions of flat-band eigen modes at the input of the photonic lattice and show the diffractionless propagation of the input states due to their infinite effective mass. In the future, the use of photonic rhombic lattices, together with the successful implementation of a synthetic gauge field, will enable the observation of AharonovBohm photonic caging.Introduction The dynamics of electrons in a crystal reveals many interesting phenomena that depend on the lattice geometry, external fields, presence of disorders and inter-particle interactions. The propagation of light waves across a photonic lattice, a periodic array of coupled optical waveguides, mimics the time evolution of the electronic wavefunction in a periodic potential. Due to this mapping, the photonic analogue of various solidstate-phenomena [1][2][3][4][5] can be realized in the system of engineered waveguide-arrays. As with cold atoms in optical lattices [6][7][8], this artificial system allows us to engineer and access a desired Hamiltonian, and hence acts as a powerful platform for the study of various complex quantum mechanical effects in a clean environment. Indeed photonic lattices are ideal systems to study various effects in the absence of undesired excitations such as phonons in a real solid.

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“…In this case, the energy is trapped due to consecutive destructive interference from randomly distributed scatters (sites or waveguides). Before this very fundamental observation, localization resulting as a balance between discreteness (diffraction) and nonlinearity (self-focusing) was observed in 1D [6][7][8] and 2D [9,10] lattices. Nonlinear localized modes of this nature are known as Discrete Solitons or Intrinsic Localized Modes [11], and the conditions for existence and stability, in diverse contexts, are nowadays well understood [12].…”

Section: Introductionmentioning

confidence: 96%

Simple method to construct flat-band lattices

2016

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We develop a simple and general method to construct arbitrary Flat Band lattices. We identify the basic ingredients behind zero-dispersion bands and develop a method to construct extended lattices based on a consecutive repetition of a given mini-array. The number of degenerated localized states is defined by the number of connected mini-arrays times the number of modes preserving the symmetry at a given connector site. In this way, we create one or more (depending on the lattice geometry) complete degenerated Flat Bands for quasi-one and two-dimensional systems. We probe our method by studying several examples, and discuss the effect of additional interactions like anisotropy or nonlinearity. At the end, we test our method by studying numerically a ribbon lattice using a continuous description.

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Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica

Cited by 174 publications

References 16 publications

Localized gap modes in nonlinear dimerized Lieb lattices

Localized gap modes in nonlinear dimerized Lieb lattices

Observation of localized flat-band modes in a quasi-one-dimensional photonic rhombic lattice

Simple method to construct flat-band lattices

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