Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays

Molina, Mario I.; Vicencio, Rodrigo A.; Kivshar, Yuri S.

doi:10.1364/ol.31.001693

Cited by 121 publications

(124 citation statements)

References 9 publications

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“…Using the same numerical approach and starting from the anti-continuum limit, we find several other families of two-color localized modes located at the interface. These modes provide a generalization of the surface modes known for truncated one-dimensional lattices located at different distances from the edge, and corresponding to a crossover between the interface and bulk discrete solitons as discussed earlier [19]. In addition, we find novel classes of the so-called interface twisted modes, and an example of such mode is shown in Figs.…”

Section: Discrete Modelsupporting

confidence: 58%

Multipole-mode interface solitons in quadratic nonlinear photonic lattices

Xu¹,

Molina²,

Kivshar³

2009

Phys. Rev. A

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We study the properties of two-color nonlinear localized modes which may exist at the interfaces separating two different periodic photonic lattices in quadratic media, focussing on the impact of phase mismatch of the photonic lattices on the properties, stability, and threshold power requirements for the generation of interface localized modes. We employ both an effective discrete model and continuum model with periodic potential and find good qualitative agreement between both models. Dynamics excitation of interface modes shows that, a two-color interface twisted mode splits into two beams with different escaping angles and carrying different energies when entering a uniform medium from the quadratic photonic lattice. The output position and energy contents of each two-color interface solitons can be controlled by judicious tuning of the lattice parameters.

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Section: Discrete Modelsupporting

confidence: 58%

Multipole-mode interface solitons in quadratic nonlinear photonic lattices

Xu¹,

Molina²,

Kivshar³

2009

Phys. Rev. A

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“…The interest in studying surface waves has been renewed recently because the interplay of discreteness and nonlinearity can facilitate the formation of discrete surface solitons [2,3] at the edge of the waveguide array. That can be understood as the localization of a discrete optical soliton near the surface [4] for powers exceeding a certain threshold value, for which the repulsive effect of the surface is balanced. A similar effect of light localization near the edge of the waveguide array and the formation of surface gap solitons have been predicted and observed for defocusing nonlinear media [5,6].…”

Section: Pacs Numbersmentioning

confidence: 99%

“…For α < ∼ 0.3, the minimum P th will be located outside of the array boundaries, and intermediate localized states (located between the center and the surfaces of the array) will be the easier states to excite. For 1D semi-infinite arrays [4], it was shown that the power threshold for surface modes decreases as the mode moves away from the surface [see also Fig. 2(c)].…”

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confidence: 99%

Discrete surface solitons in two-dimensional anisotropic photonic lattices

et al. 2007

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We study nonlinear surface modes in two-dimensional anisotropic periodic photonic lattices and demonstrate that, in a sharp contrast to one-dimensional discrete surface solitons, the mode threshold power is lower at the surface, and two-dimensional discrete solitons can be generated easier near the lattice corners and edges. We analyze the crossover between effectively one-and two-dimensional regimes of the surface-mediated beam localization in the lattice. PACS numbers:Surface modes have been studied in different branches of physics; in guided wave optics surface states were predicted to exist at interfaces separating periodic and homogeneous dielectric media [1]. The interest in studying surface waves has been renewed recently because the interplay of discreteness and nonlinearity can facilitate the formation of discrete surface solitons [2,3] at the edge of the waveguide array. That can be understood as the localization of a discrete optical soliton near the surface [4] for powers exceeding a certain threshold value, for which the repulsive effect of the surface is balanced. A similar effect of light localization near the edge of the waveguide array and the formation of surface gap solitons have been predicted and observed for defocusing nonlinear media [5,6].It is important to analyze how the properties of nonlinear surface waves are modified by the lattice dimensionality, and the first studies of different types of discrete surface solitons in two-dimensional lattices [7,8,9,10] revealed, in particular, that the presence of a surface increases the stability region for two-dimensional (2D) discrete solitons [10] and the threshold power for the edge surface state is slightly higher than that for the corner soliton [9].In this Letter we consider anisotropic semi-infinite twodimensional photonic lattices and study the crossover between one-and two-dimensional surface solitons emphasizing the crucial effect of the lattice dimensionality on the formation of surface solitons.We consider a semi-infinite 2D lattice [shown schematically in Fig.2(a) below], described by the system of coupled-mode equations for the normalized amplitudes u n,m [11,12],where ξ is the normalized propagation distance. We de- fine the lattice coupling as follows:where α characterizes the lattice anisotropy.Linear lattice waves of the form u n,m (ξ) = u 0 sin(kn) sin(qm) exp(iβξ) satisfy the dispersion relation β kq = 2(cos k + α cos q). In the nonlinear case, we look for localized stationary solutions of the form u n,m (ξ) = u n,m exp(iλξ), where the amplitudes u n,m are real, and λ is the nonlinear propagation constant. For a given λ, localized solutions are found in a 15 × 15 lattice by using the Newton-Raphson method.We calculate the power threshold P th that characterizes the discrete solitons in 2D lattices [13]. We study three different modes: corner [ Fig. 1(a)], edge surface [ Fig. 1(b,c)] and central [ Fig. 1(d)] localized modes. The corner and edge modes represent 2D surface localized

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“…Despite being approximate, the discrete model can be employed to reveal an important physical mechanism of the nonlinearity-induced surface mode stabilization. To this end we follow earlier studies [17,18] and calculate the effective energy of the mode,…”

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Observation of Surface Gap Solitons in Semi-Infinite Waveguide Arrays

et al. 2006

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We report on the first observation of surface gap solitons, recently predicted to exist at the interface between uniform and periodic dielectric media with defocusing nonlinearity [Ya. V. Kartashov et al., Phys. Rev. Lett. 96, 073901 (2006)]. We demonstrate strong self-trapping at the edge of a LiNbO3 waveguide array and the formation of staggered surface solitons with propagation constant inside the first photonic band gap. We study the crossover between linear repulsion and nonlinear attraction at the surface, revealing the mechanism of nonlinearity-mediated stabilization of the surface gap modes.PACS numbers: 42.65. Tg, 42.65.Sf5, 42.65.Wi Interfaces between different physical media can support a special class of localized waves known as surface waves or surface modes. In periodic systems, staggered surface modes are often referred to as Tamm states [1], first identified as localized electronic states at the edge of a truncated periodic potential. Because of the difficulties in observing this type of surface waves in natural materials such as crystals, successful efforts were made to demonstrate their existence in nano-engineered periodic structures or superlattices [2]. An optical analog of linear Tamm states has been described theoretically and demonstrated experimentally for an interface separating periodic and homogeneous dielectric media [3,4].Nonlinear surface waves have been studied in different fields of physics and most extensively in optics where surface TE and TM modes were predicted and analyzed for the interfaces between two different homogeneous nonlinear dielectric media [5,6,7]. In addition, nonlinear effects have been shown to stabilize surface waves in discrete systems, generating different types of modes localized at and near the surface [8]. Self-trapping of light near the boundary of a self-focusing photonic lattice has recently been predicted theoretically [9] and demonstrated in experiment [10] through the formation of discrete surface solitons at the edge of a waveguide array.Recently, Kartashov et al. [11] predicted theoretically the existence of surface gap solitons at the interface between a uniform medium and a photonic lattice with defocusing nonlinearity. In such systems, light localization occurs inside a photonic bandgap in the form of staggered surface modes. This enables us to draw an analogy with the localized electronic Tamm states and extend it to the nonlinear regime, so that the surface gap solitons can be termed as nonlinear Tamm states. They posses a unique combination of properties related to both electronic and optical surface waves and discrete optical gap solitons. The ability to generate such surface gap solitons could provide novel and effective experimental tools for the study of nonlinear effects near surfaces with possible applications in optical sensing and switching.In this Letter we study experimentally self-action of a narrow beam propagating near the edge of a LiNbO 3 waveguide array with defocusing nonlinearity. For the first time to our knowledge, ...

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Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays

Cited by 121 publications

References 9 publications

Multipole-mode interface solitons in quadratic nonlinear photonic lattices

Multipole-mode interface solitons in quadratic nonlinear photonic lattices

Discrete surface solitons in two-dimensional anisotropic photonic lattices

Observation of Surface Gap Solitons in Semi-Infinite Waveguide Arrays

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