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1.
Phys Rev Lett ; 108(7): 070401, 2012 Feb 17.
Artículo en Inglés | MEDLINE | ID: mdl-22401179

RESUMEN

We introduce a novel concept of surface bound states in the continuum, i.e., surface modes embedded into the linear spectral band of a discrete lattice. We suggest an efficient method for creating such surface modes and the local bounded potential necessary to support the embedded modes. We demonstrate that the surface embedded modes are structurally stable, and the position of their eigenvalues inside the spectral band can be tuned continuously by adding weak nonlinearity.

2.
Opt Lett ; 35(17): 2895-7, 2010 Sep 01.
Artículo en Inglés | MEDLINE | ID: mdl-20808361

RESUMEN

We analyze localization of light in honeycomb photonic lattices restricted in one dimension, which can be regarded as an optical analog of graphene nanoribbons. We discuss the effect of lattice topology on the properties of discrete solitons excited inside the lattice and at its edges. We discuss a type of soliton bistability, geometry-induced bistability, in the lattices of a finite extent.

3.
Opt Lett ; 33(23): 2761-3, 2008 Dec 01.
Artículo en Inglés | MEDLINE | ID: mdl-19037418

RESUMEN

We analyze localization of light at the interfaces separating square and hexagonal photonic lattices, as recently realized experimentally for two-dimensional laser-written waveguides in silica glass with self-focusing nonlinearity [Opt. Lett.33, 663 (2008)]. We find the conditions for the existence of linear and nonlinear surface states substantially influenced by the lattice topology, and study the effect of different symmetries and couplings on the stability of two-dimensional interface solitons.

4.
Opt Express ; 16(18): 14076-94, 2008 Sep 01.
Artículo en Inglés | MEDLINE | ID: mdl-18773018

RESUMEN

We study, analytically and numerically, the dynamics of interband transitions in two-dimensional hexagonal periodic photonic lattices. We develop an analytical approach employing the Bragg resonances of different types and derive the effective multi-level models of the Landau-Zener-Majorana type. For two-dimensional periodic potentials without a tilt, we demonstrate the possibility of the Rabi oscillations between the resonant Fourier amplitudes. In a biased lattice, i.e., for a two-dimensional periodic potential with an additional linear tilt, we identify three basic types of the interband transitions or Zener tunnelling. First, this is a quasi-one-dimensional tunnelling that involves only two Bloch bands and occurs when the Bloch index crosses the Bragg planes away from one of the high-symmetry points. In contrast, at the high-symmetry points (i.e., at the M and Gamma points), the Zener tunnelling is essentially two-dimensional, and it involves either three or six Bloch bands being described by the corresponding multi-level Landau-Zener-Majorana systems. We verify our analytical results by numerical simulations and observe an excellent agreement. Finally, we show that phase dislocations, or optical vortices, can tunnel between the spectral bands preserving their topological charge. Our theory describes the propagation of light beams in fabricated or optically-induced two-dimensional photonic lattices, but it can also be applied to the physics of cold atoms and Bose-Einstein condensates tunnelling in tilted two-dimensional optical potentials and other types of resonant wave propagation in periodic media.


Asunto(s)
Modelos Teóricos , Oscilometría/métodos , Refractometría/métodos , Simulación por Computador , Luz , Dispersión de Radiación
5.
Opt Lett ; 33(9): 917-9, 2008 May 01.
Artículo en Inglés | MEDLINE | ID: mdl-18451938

RESUMEN

We study light localization at a phase-slip defect created by two semi-infinite mismatched identical arrays of coupled optical waveguides. We demonstrate that the nonlinear defect modes possess the specific properties of both nonlinear surface modes and discrete solitons. We analyze the stability of the localized modes and their generation in both linear and nonlinear regimes.

6.
Opt Lett ; 32(18): 2668-70, 2007 Sep 15.
Artículo en Inglés | MEDLINE | ID: mdl-17873929

RESUMEN

We study surface modes at the edge of a semi-infinite chirped photonic lattice in the framework of an effective discrete nonlinear model. We demonstrate that the lattice chirp can change dramatically the conditions for the mode localization near the surface, and we find numerically the families of discrete surface solitons in this case. Such solitons do not require any minimum power to exist provided the chirp parameter exceeds some critical value. We also analyze how the chirp modifies the interaction of a soliton with the lattice edge.

7.
Opt Lett ; 31(15): 2332-4, 2006 Aug 01.
Artículo en Inglés | MEDLINE | ID: mdl-16832476

RESUMEN

We analyze discrete surface modes in semi-infinite binary waveguide arrays, which can support simultaneously two types of discrete solitons. We demonstrate that the analysis of linear surface states in such arrays provides important information about the existence of nonlinear surface modes and their properties. We find numerically the families of both discrete surface solitons and nonlinear Tamm (gap) states and study their stability properties.

8.
Opt Lett ; 31(11): 1693-5, 2006 Jun 01.
Artículo en Inglés | MEDLINE | ID: mdl-16688264

RESUMEN

We discuss the formation of self-trapped localized states near the edge of a semi-infinite array of nonlinear optical waveguides. We study a crossover from nonlinear surface states to discrete solitons by analyzing the families of odd and even modes centered at finite distances from the surface and reveal the physical mechanism of the nonlinearity-induced stabilization of surface modes.

9.
Phys Rev E Stat Nonlin Soft Matter Phys ; 74(5 Pt 2): 056602, 2006 Nov.
Artículo en Inglés | MEDLINE | ID: mdl-17280001

RESUMEN

We discuss the interband light tunneling in a two-dimensional periodic photonic structure, as studied recently in experiments for optically induced photonic lattices [Trompeter, Phys. Rev. Lett. 96, 053903 (2006)]. We identify the Zener tunneling regime at the crossing of two Bloch bands, which occurs in the generic case of a Bragg reflection when the Bloch index crosses the edge of the irreducible Brillouin zone. Similarly, higher-order Zener tunneling involves four Bloch bands when the Bloch index passes through a high-symmetry point on the edge of the Brillouin zone. We derive simple analytical models that describe the tunneling effect, and calculate the corresponding tunneling probabilities.

10.
Phys Rev E Stat Nonlin Soft Matter Phys ; 72(3 Pt 2): 036622, 2005 Sep.
Artículo en Inglés | MEDLINE | ID: mdl-16241607

RESUMEN

We analyze the properties and stability of two-color discrete localized modes in arrays of channel waveguides where tunable quadratic nonlinearity is introduced as a nonlinear defect by periodic poling of a single waveguide in the array. We show that, depending on the value of the phase mismatch and the input power, such two-color defect modes can be realized in three different localized states. We also study resonant light scattering in the arrays with the defect waveguide.

11.
Phys Rev E Stat Nonlin Soft Matter Phys ; 71(5 Pt 2): 056613, 2005 May.
Artículo en Inglés | MEDLINE | ID: mdl-16089674

RESUMEN

We study the dynamics of discrete vector solitons in arrays of weakly coupled birefringent optical waveguides with cubic nonlinear response. We start with a modulational instability analysis, followed by approximate analytical solutions in the form of strongly localized modes. Next, we compute the effective Peierls-Nabarro potential for these modes and obtain the spatial average of the power transfer between both polarizations modes as a function of their relative phase. Finally, we combine the concepts of polarization mode instability with discreteness-induced beam trapping by the array, and demonstrate numerically the amplification of a weak signal by a strong pump of the other polarization, combined with simultaneous discretized all-optical switching.

12.
Phys Rev E Stat Nonlin Soft Matter Phys ; 70(2 Pt 2): 026602, 2004 Aug.
Artículo en Inglés | MEDLINE | ID: mdl-15447605

RESUMEN

We demonstrate a simple concept for controlling nonlinear switching of discrete solitons in arrays of weakly coupled optical waveguides, for both cubic and quadratic nonlinear response. Based on the effective discrete nonlinear equations describing light propagation in the waveguide arrays in the tight-binding approximation, we demonstrate the key ideas of the array engineering by means of a steplike variation of the waveguide coupling. We demonstrate the digitized switching of a narrow input beam for up to 11 neighboring waveguides, in the case of the cubic nonlinearity, and up to 10 waveguides, in the case of the quadratic nonlinearity. We discuss our predictions in terms of the physics of the engineered Peierls-Nabarro (PN) potential experienced by strongly localized nonlinear modes in a lattice, and calculate the PN potential for the quadratic nonlinear array for the first time.

13.
Opt Lett ; 29(24): 2905-7, 2004 Dec 15.
Artículo en Inglés | MEDLINE | ID: mdl-15645819

RESUMEN

We study all-optical switching based on the dynamic properties of discrete vector solitons in waveguide arrays. We employ the concept of polarization mode instability and demonstrate simultaneous switching and amplification of a weak signal by a strong pump of the opposite polarization.

14.
Opt Lett ; 28(20): 1942-4, 2003 Oct 15.
Artículo en Inglés | MEDLINE | ID: mdl-14587783

RESUMEN

We suggest an effective method for controlling nonlinear switching in arrays of weakly coupled optical waveguides. We demonstrate digitized switching of a narrow input beam for as many as 11 waveguides in the engineered waveguide arrays.

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