Multisoliton complexes in a sea of radiation modes

We derive exact analytical solutions describing multi-soliton complexes and their interactions on top of a multi-component background in media with self-focusing or self-defocusing Kerr-like nonlinearities. These results are illustrated by numerical examples which demonstrate soliton collisions and field decomposition between localized and radiation modes.Comment: 7 pages, 7 figure

Relation between the autocorrelation and Wigner functions

We show a simple mechanism to measure the Wigner function of a harmonic oscillator. For this system we also show that autocorrelation and Wigner functions are equivalent.Comment: Modified title and slightly modified version from the one publishe

Supersymmetry-generated complex optical potentials with real spectra

We show that the formalism of supersymmetry (SUSY), when applied to parity-time (PT) symmetric optical potentials, can give rise to novel refractive index landscapes with altogether non-trivial properties. In particular, we find that the presence of gain and loss allows for arbitrarily removing bound states from the spectrum of a structure. This is in stark contrast to the Hermitian case, where the SUSY formalism can only address the fundamental mode of a potential. Subsequently we investigate isospectral families of complex potentials that exhibit entirely real spectra, despite the fact that their shapes violate PT-symmetry. Finally, the role of SUSY transformations in the regime of spontaneously broken PT symmetry is investigated.Comment: 6 pages, 4 figure

Exact bidirectional X-wave solutions in fiber Bragg gratings

We find exact solutions describing bidirectional pulses propagating in fiber Bragg gratings. They are derived by solving the coupled-mode theory equations and are expressed in terms of products of modified Bessel functions with algebraic functions. Depending on the values of the two free parameters the general bidirectional X-wave solution can also take the form of a unidirectional pulse. We analyze the symmetries and the asymptotic properties of the solutions and also discuss about additional waveforms that are obtained by interference of more than one solutions. Depending on their parameters such pulses can create a sharp focus with high contrast

Quantum Correlations in Two-Particle Anderson Localization

We predict the quantum correlations between non-interacting particles evolving simultaneously in a disordered medium. While the particle density follows the single-particle dynamics and exhibits Anderson localization, the two-particle correlation develops unique features that depend on the quantum statistics of the particles and their initial separation. On short time scales, the localization of one particle becomes dependent on whether the other particle is localized or not. On long time scales, the localized particles show oscillatory correlations within the localization length. These effects can be observed in Anderson localization of non-classical light and ultra-cold atoms.Comment: 4 pages, 4 figures, comments welcom

Bessel-like optical beams with arbitrary trajectories

A method is proposed for generating Bessel-like optical beams with arbitrary trajectories in free space. The method involves phase-modulating an optical wavefront so that conical bundles of rays are formed whose apexes write a continuous focal curve with prespecified shape. These ray cones have circular bases on the input plane, thus their interference results in a Bessel-like transverse field profile that propagates along the specified trajectory with a remarkably invariant main lobe. Such beams can be useful as hybrids between nonaccelerating and accelerating optical waves that share diffraction-resisting and self-healing properties

Scattering in PT\cal PT and RT\cal RT Symmetric Multimode Waveguides: Generalized Conservation Laws and Spontaneous Symmetry Breaking beyond One Dimension

We extend the generalize conservation law of light propagating in a one-dimensional $\cal PT$-symmetric system, i.e., $|T-1|=\sqrt{R_LR_R}$ for the transmittance $T$ and the reflectance $R_{L,R}$ from the left and right, to a multimode waveguide with either $\cal PT$ or $\cal RT$ symmetry, in which higher dimensional investigations are necessary. These conservation laws exist not only in a matrix form for the transmission and reflection matrices; they also exist in a scalar form for real-valued quantities by defining generalized transmittance and reflectance. We then discuss, for the first time, how a multimode $\cal PT$-symmetric waveguide can be used to observe spontaneous symmetry breaking of the scattering matrix, which typically requires tuning the non-hermiticity of the system (i.e. the strength of gain and loss). Here the advantage of using a multimode waveguide is the elimination of tuning any system parameters: the transverse mode order $m$ plays the role of the symmetry breaking parameter, and one observes the symmetry breaking by simply performing scattering experiment in each waveguide channel at a single frequency and fixed strength of gain and loss.Comment: 8 pages, 6 figure

Advanced trajectory engineering of diffraction-resisting laser beams

We introduce an analytical technique for engineering the trajectory of diffraction-resisting laser beams. The generated beams have a Bessel-like transverse field distribution and can be navigated along rather arbitrary curved paths in free space, thus being an advanced hybrid between accelerating and non-accelerating diffraction-free optical waves. The method involves phase-modulating the wavefront of a Gaussian laser beam to create a continuum of conical ray bundles whose apexes define a prespecified focal curve, along which a nearly perfect circular intensity lobe propagates without diffracting. Through extensive numerical simulations, we demonstrate the great flexibility in the design of a gamut of different beam trajectories. Propagation around obstructions and self-healing scenarios are also investigated. The proposed wave entities can be used extensively for light trajectory control in applications such as laser microfabrication, optical tweezers and curved plasma filamentation spectroscopy

Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices

We investigate the interaction between a light beam and a two-dimensional photonic lattice that is photo-induced in a photorefractive crystal using partially coherent light. We demonstrate that this interaction process is associated with a host of new phenomena including lattice dislocation, lattice deformation, and creation of structures akin to optical polarons. In addition, two-dimensional discrete solitons are realized in such partially coherent photonic lattices.Comment: 12 pages, 4 figures (revised). accepted by Phys. Rev. Let