Modern nanotechnology allows one to scale down various important devices (sensors, chips, fibers, etc.) and thus opens up new horizons for their applications. The efficiency of most of them is based on fundamental physical phenomena, such as transport of wave excitations and resonances. Short propagation distances make phase-coherent processes of waves important. Often the scattering of waves involves propagation along different paths and, as a consequence, results in interference phenomena, where constructive interference corresponds to resonant enhancement and destructive interference to resonant suppression of the transmission. Recently, a variety of experimental and theoretical work has revealed such patterns in different physical settings. The purpose of this review is to relate resonant scattering to Fano resonances, known from atomic physics. One of the main features of the Fano resonance is its asymmetric line profile. The asymmetry originates from a close coexistence of resonant transmission and resonant reflection and can be reduced to the interaction of a discrete (localized) state with a continuum of propagation modes. The basic concepts of Fano resonances are introduced, their geometrical and/or dynamical origin are explained, and theoretical and experimental studies of light propagation in photonic devices, charge transport through quantum dots, plasmon scattering in Josephson-junction networks, and matter-wave scattering in ultracold atom systems, among others are reviewed.

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Fano resonances in nanoscale structures

Dark optical solitons: physics and applications

Discrete Solitons in Optics

Spatial solitons, beams that do not spread owing to diffraction when they propagate, have been demonstrated to exist by virtue of a variety of nonlinear self-trapping mechanisms. Despite the diversity of these mechanisms, many of the features of soliton interactions and collisions are universal. Spatial solitons exhibit a richness of phenomena not found with temporal solitons in fibers, including effects such as fusion, fission, annihilation, and stable orbiting in three dimensions. Here the current state of knowledge on spatial soliton interactions is reviewed.

https://science.sciencemag.org/content/sci/286/5444/1518.full.pdf

Optical Spatial Solitons and Their Interactions: Universality and Diversity.

In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic–cubic or cubic–quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose–Einstein condensates supported by full or low-dimensional optical lattices.

https://iopscience.iop.org/article/10.1088/1464-4266/7/5/R02/pdf

Spatiotemporal optical solitons

Solitary waves in materials with a cascaded χ(2):χ(2) nonlinearity are investigated, and the implications of the robustness hypothesis for these solitary waves are discussed. Both temporal and spatial solitary waves are studied. First, the basic equations that describe the χ(2):χ(2) nonlinearity in the presence of dispersion or diffraction are derived in the plane-wave approximation, and we show that these equations reduce to the nonlinear Schrodinger equation in the limit of large phase mismatch and can be considered a Hamiltonian deformation of the nonlinear Schrodinger equation. We then proceed to a comprehensive description of all the solitary-wave solutions of the basic equations that can be expressed as a simple sum of a constant term, a term proportional to a power of the hyperbolic secant, and a term proportional to a power of the hyperbolic secant multiplied by the hyperbolic tangent. This formulation includes all the previously known solitary-wave solutions and some exotic new ones as well. Our solutions are derived in the presence of an arbitrary group-velocity difference between the two harmonics, but a transformation that relates our solutions to zero-velocity solutions is derived. We find that all the solitary-wave solutions are zero-parameter and one-parameter families, as opposed to nonlinear-Schrodinger-equation solitons, which are a two-parameter family of solutions. Finally, we discuss the prediction of the robustness hypothesis that there should be a two-parameter family of solutions with solitonlike behavior, and we discuss the experimental requirements for observation of solitonlike behavior.

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Solitary waves due to χ (2) :χ (2) cascading

We report an experimental observation of one-dimensional spatial solitary waves due to cascaded second-order optical nonlinearities.

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One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides

Discrete solitons with two frequency components mutually locked by a quadratic nonlinearity have been observed for the first time. Optical experiments have been performed in arrays of coupled channel waveguides with tunable cascaded quadratic nonlinearity. The tunability was the prerequisite that soliton species with different topology could be identified in the same array. Moreover, soliton stability has been experimentally probed. Good agreement with theoretical predictions was found.

Observation of discrete quadratic solitons.

In crystals that lack a center of inversion, in addition to the third-order nonlinearity a cascaded χ(2):χ(2) second-order nonlinearity contributes to the nonlinear refraction. A coupled-mode theory in the frequency domain is used to investigate theoretically the application of this new nonlinear index of refraction for realizing intensity-dependent temporal and spatial light-field evolution in waveguide structures. The significant modification and the immense enhancement of the effects of purely third-order optical nonlinearity by second-order down-mixing of the driven second-harmonic field with the incoming light at the fundamental are discussed.

Nonlinear refraction caused by cascaded second-order nonlinearity in optical waveguide structures

We report the first observation of discrete quadratic surface solitons in self-focusing and defocusing periodically poled lithium niobate waveguide arrays. By operating on either side of the phase-matching condition and using the cascading nonlinearity, both in-phase and staggered discrete surface solitons were observed. This represents the first experimental demonstration of staggered/gap surface solitons at the interface of a semi-infinite nonlinear lattice. The experimental results were found to be in good agreement with theory.

Roland Schiek

Papers

Solitary waves due to χ (2) :χ (2) cascading

One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in planar waveguides

Observation of discrete quadratic solitons.

Nonlinear refraction caused by cascaded second-order nonlinearity in optical waveguide structures

Observation of discrete quadratic surface solitons