Enhanced distribution of a wave-packet in lattices with disorder and nonlinearity

Naether, Uta; Rojas-Rojas, Santiago; Martínez, Alejandro J.; Stützer, Simon; Tünnermann, Andreas; Nolte, Stefan; Molina, Mario I.; Vicencio, Rodrigo A.; Szameit, Alexander

doi:10.1364/oe.21.000927

Cited by 18 publications

(28 citation statements)

References 31 publications

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“…For 2D systems, we do not expect to experimentally observe similar results. As a larger disorder is required to observe localization in 2D lattices [12], the whole picture will be scaled up and the different polarizations will essentially show the same. The transition to localization in ID is more abrupt and, therefore, the different polarizations really experience different dynamics.…”

Section: Discussionmentioning

confidence: 99%

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Analytical model for polarization-dependent light propagation in waveguide arrays and applications

et al. 2014

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We study the polarization properties of elliptical femtosecond-laser-written waveguide arrays. An analytical model is presented to explain the asymmetry of the spatial transverse profiles of linearly polarized modes in these waveguides. This asymmetry produces a polarization-dependent coupling coefficient, between adjacent waveguides, which strongly affects the propagation of light in a lattice. Our analysis explains how this effect can be exploited to tune the final intensity distribution of light propagated through the array and links the properties of a polarizing beam splitter in integrated optical circuits to the geometry of the waveguides

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Section: Discussionmentioning

confidence: 99%

“…In fact, the first experim ental dem onstration o f A nderson localization w as perform ed using optical lattices [7,8]. D isordered lattices exhibit a w ealth o f transport phenom ena, such as disorder-induced edge states [9], disorder-enhanced transport [ 10,11 ], and the interplay betw een nonlinearity and disorder [12].…”

Section: Introductionmentioning

confidence: 99%

Analytical model for polarization-dependent light propagation in waveguide arrays and applications

et al. 2014

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“…Randomized on-site energy for the diagonal disorder can be introduced by a controlled variation of the width [16] or the refractive index [45,46] of each waveguide while keeping the tunneling rates between waveguides constant. Randomized tunneling strength can be introduced by a controlled variation of the separation between adjacent waveguides [2,19,47], while keeping the symmetry with respect to the diagonal axis. For this off-diagonal disorder, identical waveguides should be employed except in the diagonal axis where a difference between the refractive indices of the diagonal (n d ) and offdiagonal (n 0 ) waveguides effectively leads to the interaction U ∼ (n 0 − n d ).…”

Section: Figmentioning

confidence: 99%

“…In fact, Anderson himself first noticed the importance of interaction in localization phenomena [8] and launched a theoretical investigation in collaboration with Fleishman [9]. Recently, advances in technology have reinvigorated theoretical [10,11] and experimental [12][13][14][15][16][17][18][19] interest on this subject. For the special case of two interacting particles in a random one-dimensional (1D) potential, Shepelyansky has investigated the interplay of disorder and interaction and concluded that interaction modifies (weakens) localization [20].…”

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confidence: 99%

Probing the effect of interaction in Anderson localization using linear photonic lattices

et al. 2014

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We show how two-dimensional waveguide arrays can be used to probe the effect of on-site interaction on Anderson localization of two interacting bosons in one dimension. It is shown that classical light and linear elements are sufficient to experimentally probe the interplay between interaction and disorder in this setting. For experimental relevance, we evaluate the participation ratio and the intensity correlation function as measures of localization for two types of disorder (diagonal and off-diagonal), for two types of interaction (repulsive and attractive), and for a variety of initial input states. Employing a commonly used set of initial states, we show that the effect of interaction on Anderson localization is strongly dependent on the type of disorder and initial conditions, but is independent of whether the interaction is repulsive or attractive. We then analyze a certain type of entangled input state where the type of interaction is relevant and discuss how it can be naturally implemented in waveguide arrays. We conclude by laying out the details of the two-dimensional photonic lattice implementation including the required parameter regime.Introduction. Anderson localization (AL) [1], one of the most famous manifestations of quantum destructive interference, has been probed and verified in perhaps the most diverse physical platforms such as light propagation in spatially random optical media [2,3], noninteracting Bose-Einstein condensates in random optical potentials [4,5], microwave cavity fields with randomly distributed scatterers [6], and an integrated array of interferometers [7]. Interesting deviations in AL arise when interactions between the particles become significant. In fact, Anderson himself first noticed the importance of interaction in localization phenomena [8] and launched a theoretical investigation in collaboration with Fleishman [9]. Recently, advances in technology have reinvigorated theoretical [10, 11] and experimental [12-19] interest on this subject. For the special case of two interacting particles in a random one-dimensional (1D) potential, Shepelyansky has investigated the interplay of disorder and interaction and concluded that interaction modifies (weakens) localization [20]. However, several studies analyzing the two-particle case further [21][22][23][24][25][26][27][28][29] have shown that the problem of the interplay between disorder and interaction is very complex and the results depend on the details of the system, the localization measure, and the numerical technique employed [3,13,14].

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“…When nonlinearity is introduced, the problem becomes significantly more complicated: on the one hand, nonlinearity can lead to self-trapping and the formation of discrete breathers, thus enhancing localization [3]. On the other hand, nonlinearity can also destroy the phase coherence which is essential for Anderson localization, which can result in chaotic dynamics and enhanced spreading [4], [5], [6], [7]. There is still no complete picture of the different nonlinear dynamical regimes [8].…”

Section: Introductionmentioning

confidence: 99%

Anderson localization and nonlinearity in flat bands

Leykam

Flach

Bahat-Treidel

et al. 2013

2013 IEEE 2nd International Workshop "Nonlinear Photonics" (NLP*2013)

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We explore the interplay between Anderson localization and Kerr nonlinearity in a lattice system containing intersecting flat and dispersive bands. The disordered system supports two distinct types of modes: high energy modes experience conventional Anderson localization. Low energy modes have a much shorter localization length, but are also highly sparse, consisting of multiple, well-separated peaks. Nonlinearity introduces different regimes of wavepacket spreading, determined by which types or modes are strongly coupled together. The spreading of localized excitations can either be massively enhanced, or suppressed, depending on the strength of nonlinearity.

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Enhanced distribution of a wave-packet in lattices with disorder and nonlinearity

Cited by 18 publications

References 31 publications

Analytical model for polarization-dependent light propagation in waveguide arrays and applications

Analytical model for polarization-dependent light propagation in waveguide arrays and applications

Probing the effect of interaction in Anderson localization using linear photonic lattices

Anderson localization and nonlinearity in flat bands

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