Reduced-Symmetry Two-Dimensional Solitons in Photonic Lattices

Fischer, Robert; Träger, Denis; Neshev, Dragomir N.; Sukhorukov, Andrey A.; Królikowski, Wiesław; Denz, Cornélia; Kivshar, Yuri S.

doi:10.1103/physrevlett.96.023905

Cited by 76 publications

(45 citation statements)

References 25 publications

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“…Such state represents the theoretically predicted gap solitons in photonic crystals [17,18]. It has a reduced symmetry with respect to the lattice and it is formed by the combined action of Bragg reflection in x-direction and total internal reflection in y-direction [36]. The experimental data are in excellent agreement with the numerical simulations [ Fig.…”

Section: -Pointsupporting

confidence: 80%

Nonlinear Bloch modes in two-dimensional photonic lattices

Träger¹,

Fischer²,

Neshev³

et al. 2006

Opt. Express

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Abstract:We generate experimentally different types of two-dimensional Bloch waves of a square photonic lattice by employing the phase imprinting technique. We probe the local dispersion of the Bloch modes in the photonic lattice by analyzing the linear diffraction of beams associated with the highsymmetry points of the Brillouin zone, and also distinguish the regimes of normal, anomalous, and anisotropic diffraction through observations of nonlinear self-action effects.

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Section: -Pointsupporting

confidence: 80%

Nonlinear Bloch modes in two-dimensional photonic lattices

Träger¹,

Fischer²,

Neshev³

et al. 2006

Opt. Express

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“…These results suggest that although the m=1 vortex can evolve into a gap vortex soliton, it does not bifurcate from the edge of the first Bloch band, quite different from all previously observed fundamental, dipole or quadrupole-like gap solitons in self-defocusing lattices [6,12,21]. It is also significantly different from the second-band gap vortex solitons [17] or the reduced-symmetry gap solitons [26] in self-focusing lattices, which all bifurcate from the edge of the second band. On the other hand, the m=2 vortex can evolve into a quadrupole-like localized state, which does seem to bifurcate from the edge of the first Bloch band as confirmed by numerical analysis below.…”

mentioning

confidence: 42%

Self-trapping of optical vortices in waveguide lattices with a self-defocusing nonlinearity

Song¹,

Lou²,

Tang³

et al. 2008

Opt. Express

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“…This indicates that the saddle solitons must consist of modes from the interior X points of the first band, although far away from the soliton center staggered phase characteristic to band edge M point modes is evident. These 2D saddle solitons differ from previously observed quasi-1D embedded or gap solitons (also from first-band X points), which are localized only in one direction [6,9], and from the reduced symmetry solitons created solely by self-focusing nonlinearity (but from second-band X points) [11]. Their stable long-distance propagation [Figs.…”

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confidence: 46%

Saddle solitons: a balance between bi-diffraction and hybrid nonlinearity

Lou

Zhang

et al. 2009

Opt. Lett.

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We demonstrate self-trapping of light by simultaneously compensating normal and anomalous (saddleshaped) diffractions with self-focusing and self-defocusing hybrid nonlinearity in optically induced ionic-type photonic lattices. Innovative two-dimensional gap solitons, named "saddle solitons," are established, whose phase and spectrum characteristics are different from all previously observed spatial solitons. © 2009 Optical Society of America OCIS codes: 190.6135, 190.5330, 350.4238. Despite the discovery of a variety of soliton entities in discrete systems [1], to our knowledge, it has not been possible to demonstrate a two-dimensional (2D) spatial soliton in a physical arrangement where an optical beam exhibits simultaneously normal and anomalous diffractions in different transverse directions. First, natural materials typically are not endowed with a saddle-shaped bi-diffractive property; second, it remains a challenge to find a nonlinear material that can support hybrid self-focusing and selfdefocusing nonlinearities without changing experimental conditions. Previous work on nonlinear X waves and light bullets was aimed toward balancing of beam diffraction and pulse dispersion simultaneously, but in spatial domain alone compensation of normal and anomalous diffractions in the same experimental setting has not been realized. Man-made periodic structures have shown many intriguing optical properties. In an optically induced 2D square lattice [2][3][4], for example, the highsymmetry X point in the first Bloch band is akin to a saddle point in diffraction spectrum [see Fig. 1(c)], where normal and anomalous diffractions coexist along orthogonal directions [5]. At this X point, a quasi-1D soliton train can be excited provided that an appropriate type of nonlinearity is used to balance beam diffraction in one particular direction, whereas in the orthogonal direction it is an extended plane wave [6]. The propagation constant of such a 1D soliton train could reside within the first Bloch band, thus named "in-band" or "embedded" solitons [7]. However, to simultaneously balance normal and anomalous diffractions for self-trapping of a 2D-localized optical beam, one needs orientationdependent hybrid nonlinearity. Fortunately, such nonlinearity was found in our recent work with photorefractive nonlinear crystals under nonconventional bias (NCB) condition [8][9][10], in which coexistence of self-focusing and self-defocusing nonlinearities at two orthogonal directions has led to observation of controlled 1D soliton transition from different band edges or subband edges.In this Letter, we employ the hybrid nonlinearity to demonstrate a type of spatial gap solitons, namely, "saddle solitons," by balancing the saddle-shaped diffraction in an optically induced 2D ionic-type lattice [10]. Such solitons have propagation constant residing in the Bragg reflection gap, but they differ from all previously observed solitons supported by a single self-focusing or self-defocusing nonlinearity. In addition, quasi-localized 2D in-band...

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Reduced-Symmetry Two-Dimensional Solitons in Photonic Lattices

Cited by 76 publications

References 25 publications

Nonlinear Bloch modes in two-dimensional photonic lattices

Nonlinear Bloch modes in two-dimensional photonic lattices

Self-trapping of optical vortices in waveguide lattices with a self-defocusing nonlinearity

Saddle solitons: a balance between bi-diffraction and hybrid nonlinearity

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