Demonstration of flat-band image transmission in optically induced Lieb photonic lattices

Xia, Shiqiang; Hu, Yi; Song, Daohong; Zong, Yuanyuan; Tang, Liqin; Chen, Zhigang

doi:10.1364/ol.41.001435

Cited by 138 publications

(140 citation statements)

References 27 publications

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“…For example, in femtosecond written waveguide arrays [21,34], the coupling interaction strongly depends on the elliptical profile of written waveguides (although the Silica buffer is essentially isotropic). On the other hand, photonic lattices induced in SBN photorefractive crystals [20,25] also presents a strong anisotropy, but caused by the crystal itself (induced waveguides have a symmetrical profile). This consideration effectively implies that, for a fixed distance, the coupling also changes depending on their orientation (V x = V y ) [31].…”

Section: Anisotropymentioning

confidence: 99%

“…The special geometry of FB systems generates consecutive phase cancellations that, effectively, reduces the excited region to a mini-array of a given lattice. The linear combination of these localized states is thought to be important for applications in all-optical imaging transmission [24,25], as a secure and compact mechanism of transporting information at a very low level of power.…”

Section: Introductionmentioning

confidence: 99%

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Simple method to construct flat-band lattices

Morales‐Inostroza

Vicencio

2016

Phys. Rev. A

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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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Section: Anisotropymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simple method to construct flat-band lattices

Morales‐Inostroza

Vicencio

2016

Phys. Rev. A

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“…Results on theoretical predictions and experimental confirmation of light propagation without spreading have been published in Refs. [30][31][32][33]. However, the presence of Kerr nonlinearity in the system may exhibit conical diffraction at the Dirac cone [30,34].…”

Section: Introductionmentioning

confidence: 99%

“…The fundamental flat band eigenmode in this model can be chosen as a four-site closed ring with staggered phase relation between neighboring sites in the ring. In general, it has been shown theoretically and demonstrated experimentally that linear compact localized modes of the ring type can be formed within Lieb systems [30][31][32][33].…”

Section: Introductionmentioning

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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“…Flat band networks have been proposed in one, two, and three dimensions and various flat band generators were identified [3][4][5][6]. Experimental observations of flat bands and CLS are reported in photonic waveguide networks [7][8][9][10][11][12][13][14][15], exciton-polariton condensates [16][17][18], and ultracold atomic condensates [19,20]. The tight binding network equations correspond to an eigenvalue problem EΨ l = − m t lm Ψ m .…”

mentioning

confidence: 99%

Topological flat Wannier-Stark bands

2018

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We analyze the spectrum and eigenstates of a quantum particle in a bipartite two-dimensional tight-binding dice network with short range hopping under the action of a dc bias. We find that the energy spectrum consists of a periodic repetition of one-dimensional energy band multiplets, with one member in the multiplet being strictly flat. The corresponding macroscopic degeneracy invokes eigenstates localized exponentially perpendicular to the dc field direction, and super-exponentially along the dc field direction. We also show that the band multiplet is characterized by a topological winding number (Zak phase), which changes abruptly if we vary the dc field strength. These changes are induced by gap closings between the flat and dispersive bands, and reflect the number of these closings.Recently much attention has been paid to flat bands in one-, two-and three-dimensional lattices with short range hoppings and non-trivial geometry [1]. Flat bands with finite range hoppings exist due to destructive interference leading to a macroscopic number of degenerate compact localized eigenstates (CLS) which have strictly zero amplitudes outside a finite region of the lattice [2]. Flat band networks have been proposed in one, two, and three dimensions and various flat band generators were identified [3][4][5][6]. Experimental observations of flat bands and CLS are reported in photonic waveguide networks [7][8][9][10][11][12][13][14][15], exciton-polariton condensates [16][17][18], and ultracold atomic condensates [19,20]. The tight binding network equations correspond to an eigenvalue problem EΨ l = − m t lm Ψ m . For bipartite lattices, the existence of flat bands and CLS is ensured through a proper usage of the protecting chiral symmetry [6]. For example, for the dice lattice shown in Fig. 1(a) and t lm = 1 the CLS consists of an empty C site which is surrounded by six excited A and B sites with alternating amplitudes ±1/ √ 6.When a dc field is added, quantum particles start to experience well studied Bloch oscillations (see e.g. [21,22]). Our results are therefore applicable for ultracold atoms in optical lattices where the electric field is substituted by a tilt of the lattice in the gravitational field [23] or accelerating the whole lattice [24]. The same type of perturbations can be arranged in optical waveguide arrays where the electric field is modeled by a curved geometry of the waveguides [25].In the present letter we report on a new family of flat bands which exist in dc biased bipartite lattices and which are not supported by CLS, despite of the short range hopping. We consider the dice lattice in the presence of a dc field oriented along the y-direction (Fig.1(a)). The absence of CLS indicates nontrivial topology. We compute winding numbers (Zak phase) which indeed show abrupt changes through conical intersection point degeneracies upon variations of the dc field strength. We also generalize to different orientations of the field F and other lattice geometries.

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Demonstration of flat-band image transmission in optically induced Lieb photonic lattices

Cited by 138 publications

References 27 publications

Simple method to construct flat-band lattices

Simple method to construct flat-band lattices

Localized gap modes in nonlinear dimerized Lieb lattices

Topological flat Wannier-Stark bands

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