Spatial photonics in nonlinear waveguide arrays

Fleischer, Jason W.; Bartal, Guy; Cohen, Oren; Schwartz, Tal; Manela, Ofer; Freedman, Barak; Segev, Mordechai; Buljan, Hrvoje; Efremidis, Nikolaos K.

doi:10.1364/opex.13.001780

Cited by 191 publications

(154 citation statements)

References 77 publications

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“…In BEC, it describes an external potential applied to the condensate. The potential can be localized (e.g., a single waveguide in nonlinear optics [39,32]), parabolic (e.g., a magnetic trap in BEC [1,31]) or periodic (e.g., a waveguide array or photonic crystal lattice in nonlinear optics [42]). …”

Section: Introductionmentioning

confidence: 99%

Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential

Coz

Fukuizumi

Fibich

et al. 2008

Physica D: Nonlinear Phenomena

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We study analytically and numerically the stability of the standing waves for a nonlinear Schrödinger equation with a point defect and a power type nonlinearity. A major difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves. This is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing-wave solution is stable in H 1 rad (R) and unstable in H 1 (R) under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercritical nonlinear interaction, we prove the instability by blowup in the repulsive case by showing a virial theorem and using a minimization method involving two constraints. In the subcritical radial case, unstable bound states cannot collapse, but rather narrow down until they reach the stable regime (a finite-width instability). In the nonradial repulsive case, all bound states are unstable, and the instability is manifested by a lateral drift away from the defect, sometimes in combination with a finite-width instability or a blowup instability.

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Section: Introductionmentioning

confidence: 99%

Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential

Coz

Fukuizumi

Fibich

et al. 2008

Physica D: Nonlinear Phenomena

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“…tunnelling through adjacent potential wells, and nonlinearity, leading to a large variety of nonlinear effects that have no analogue in bulk media. This increasing interest may be at least partially attributed to recent progress in the investigation of nonlinear wave propagation in optical periodic media, where the ability to engineer optical band structures and diffraction as well as a rather easy experimental observation of nonlinear effects has led to the discovery of many new fundamental features [5][6][7][8][9][10].…”

mentioning

confidence: 99%

Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays

et al. 2006

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We report on the formation of dark discrete solitons in a nonlinear periodic system consisting of evanescently-coupled channel waveguides that are fabricated in defocusing lithium niobate. Localized nonlinear dark modes displaying a phase jump in the center that is located either on-channel (mode A) or in-between channels (mode B) are formed, which is to our knowledge the first experimental observation of mode B. By numerical simulations we find that the saturable nature of the nonlinearity is responsible for the improved stability of mode B. The ability of the induced refractive index structures to guide light of a low-power probe beam is demonstrated.

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“…With the suggestion [5] and the experimental realization of optically induced photonic lattices, both in one [6] and two [7] spatial dimensions, novel excitations such as vortices [8,9] (that cannot occur in 1D) were discovered and explored. One-and two-dimensional photonic lattices discussed here [1,2] are also referred to as waveguide arrays, because they are continuous along another dimension (second or third) along which the light propagates. Photonic crystals provide the opportunity to study versatile linear (e.g., see [10]) and nonlinear phenomena [11] in three spatial dimensions.…”

mentioning

confidence: 99%

“…Throughout the paper we use the following normalization: α |ψ α | 2 = 1. This model was succesfully used to describe dynamics of light in 1D and 2D photonic lattices (waveguide arrays) [1,2]. It is applicable when the lattice wells are sufficiently deep, such that each well has a well defined resonance, and the coupling between different lattice sites is weak.…”

mentioning

confidence: 99%

Four-dimensional photonic lattices and discrete tesseract solitons

Jukić

Buljan

2013

Phys. Rev. A

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We theoretically study discrete photonic lattices in more than three dimensions and point out that such systems can exist in continuous three-dimensional (3D) space. We study discrete diffraction in the linear regime, and predict the existence of four-dimensional (4D) tesseract solitons in nonlinear 4D periodic photonic lattices. Finally, we propose a design towards a potential realization of such periodic 4D lattices in experiments.

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Spatial photonics in nonlinear waveguide arrays

Cited by 191 publications

References 77 publications

Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential

Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential

Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays

Four-dimensional photonic lattices and discrete tesseract solitons

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