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W. Krolikowski

Publications and source records attributed to W. Krolikowski.

At least 19 recordsLinked to original sources
arXiv2017

Topological monopoles and currents in electromagnetic waves

Singularities, i.e. places of discontinuities of parameters are extremely general objects appearing in electromagnetic waves and thus are the key to understanding fundamental wave processes. These structures commonly occur in purely coherent, highly directional waves, such as laser beams, determining additional spatial or "`topological"' properties of the wave fields independently of their propagational dynamics. For instance, topologies of wave fronts, called phase singularities, add orbital degrees of freedom to electromagnetic waves. These singularities are common to all types of scalar waves described only by their intensity and phase distributions. As the electromagnetic wave is a vector wave, its topological properties generally depend on all field components leading to complex field patterns in space and time. These patterns may contain singular points of undefined instantaneous orientation of the vector field, i.e. the instantaneous field (IF) singularities. In zero-order paraxial approximation of purely transverse electromagnetic waves, some instantaneous field distributions may carry apparent topological monopoles, when the originally source-free wave exhibits spatial structure associated with the 2D "virtual" sources of electromagnetic fields. Here we present systematic description of topological singularities in both electric and magnetic field of the electromagnetic waves in a paraxial approximation. We also consider the important types of paraxial electromagnetic waves with complex transverse field structures containing instantaneous field singularities.

physics.optics↗
arXiv2016

Self-organization of light in optical media with competing nonlinearities

We study the propagation of light beams through optical media with competing nonlocal nonlinearities. We demonstrate that the nonlocality of competing focusing and defocusing nonlinearities gives rise to self-organization and stationary states with stable hexagonal intensity patterns, akin to transverse crystals of light filaments. Signatures of this long-range ordering are shown to be observable in the propagation of light in optical waveguides and even in free space. We consider a specific form of the nonlinear response that arises in atomic vapor upon proper light coupling. Yet, the general phenomenon of self-organization is a generic consequence of competing nonlocal nonlinearities, and may, hence, also be observed in other settings.

nlin.PS↗
arXiv2014

Optical vault: reconfigurable bottle beam by conically refracted light

We employ conical refraction of light in a biaxial crystal to create an optical bottle for trapping and manipulation of particles. We show that by just varying the polarization of the input light the bottle can be opened and closed at will. We experimentally demonstrate stable photophoretic trapping and controllable loading and unloading of light absorbing particles in the trap.

physics.optics↗
arXiv2013

Quasiperiodic oscillations and homoclinic orbits in the nonlinear nonlocal Schrödinger equation

Quasiperiodic oscillations and shape-transformations of higher-order bright solitons in nonlinear nonlocal media have been frequently observed in recent years, however, the origin of these phenomena was never completely elucidated. In this paper, we perform a linear stability analysis of these higher-order solitons by solving the Bogoliubov-de Gennes equations. This enables us to understand the emergence of a new oscillatory state as a growing unstable mode of a higher-order soliton. Using dynamically important states as a basis, we provide low-dimensional visualizations of the dynamics and identify quasiperiodic and homoclinic orbits, linking the latter to shape-transformations.

nlin.PS↗
arXiv2012

Stability of solitary waves in random nonlocal nonlinear media

We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schrödinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the nonlocality-induced finite correlation length of the noise in the transverse plane, by means of both numerical simulations and analytical estimates. In fact, solitons are practically insensitive to noise when the correlation length of the noise becomes comparable to the extent of the wave packet. We characterize soliton stability using two different criteria based on the evolution of the Hamiltonian of the soliton and its power. The first criterion allows us to estimate a time (or distance) over which the soliton preserves its form. The second criterion gives the life-time of the solitary wave packet in terms of its radiative power losses. We derive a simplified mean field approach which allows us to calculate the power loss analytically in the physically relevant case of weakly correlated noise, which in turn serves as a lower estimate of the life-time for correlated noise in general case.

nlin.PS↗
arXiv2011

Collapse in the nonlocal nonlinear Schrödinger equation

We discuss spatial dynamics and collapse scenarios of localized waves governed by the nonlinear Schrödinger equation with nonlocal nonlinearity. Firstly, we prove that for arbitrary nonsingular attractive nonlocal nonlinear interaction in arbitrary dimension collapse does not occur. Then we study in detail the effect of singular nonlocal kernels in arbitrary dimension using both, Lyapunoff's method and virial identities. We find that for for a one-dimensional case, i.e. for $n=1$, collapse cannot happen for nonlocal nonlinearity. On the other hand, for spatial dimension $n\geq2$ and singular kernel $\sim 1/r^α$, no collapse takes place if $α<2$, whereas collapse is possible if $α\ge2$. Self-similar solutions allow us to find an expression for the critical distance (or time) at which collapse should occur in the particular case of $\sim 1/r^2$ kernels. Moreover, different evolution scenarios for the three dimensional physically relevant case of Bose Einstein condensate are studied numerically for both, the ground state and a higher order toroidal state with and without an additional local repulsive nonlinear interaction. In particular, we show that presence of an additional local repulsive term can prevent collapse in those cases.

nlin.PS↗
arXiv2010

Analytical theory of dark nonlocal solitons

We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe the dark solitons, for the first time, in the whole range of degree of nonlocality.

nlin.PS↗
arXiv2009

Rotating three-dimensional solitons in Bose Einstein condensates with gravity-like attractive nonlocal interaction

We study formation of rotating three-dimensional high-order solitons (azimuthons) in Bose Einstein condensate with attractive nonlocal nonlinear interaction. In particular, we demonstrate formation of toroidal rotating solitons and investigate their stability. We show that variational methods allow a very good approximation of such solutions and predict accurately the soliton rotation frequency. We also find that these rotating localized structures are very robust and persist even if the initial condensate conditions are rather far from the exact soliton solutions. Furthermore, the presence of repulsive contact interaction does not prevent the existence of those solutions, but allows to control their rotation. We conjecture that self-trapped azimuthons are generic for condensates with attractive nonlocal interaction.

cond-mat.quant-gas↗
arXiv2009

Tracking azimuthons in nonlocal nonlinear media

We study the formation of azimuthons, i.e., rotating spatial solitons, in media with nonlocal focusing nonlinearity. We show that whole families of these solutions can be found by considering internal modes of classical non-rotating stationary solutions, namely vortex solitons. This offers an exhaustive method to identify azimuthons in a given nonlocal medium. We demonstrate formation of azimuthons of different vorticities and explain their properties by considering the strongly nonlocal limit of accessible solitons.

nlin.PS↗
arXiv2008

Rotating soliton solutions in nonlocal nonlinear media

We discuss generic properties of rotating nonlinear wave solutions, the so called azimuthons, in nonlocal media. Variational methods allow us to derive approximative values for the rotating frequency, which is shown to depend crucially on the nonlocal response function. Further on, we link families of azimuthons to internal modes of classical non-rotating stationary solutions, namely vortex and multipole solitons. This offers an exhaustive method to identify azimuthons in a given nonlocal medium.

nlin.PS↗
arXiv2008

Limits to compression with cascaded quadratic soliton compressors

We study cascaded quadratic soliton compressors and address the physical mechanisms that limit the compression. A nonlocal model is derived, and the nonlocal response is shown to have an additional oscillatory component in the nonstationary regime when the group-velocity mismatch (GVM) is strong. This inhibits efficient compression. Raman-like perturbations from the cascaded nonlinearity, competing cubic nonlinearities, higher-order dispersion, and soliton energy may also limit compression, and through realistic numerical simulations we point out when each factor becomes important. We find that it is theoretically possible to reach the single-cycle regime by compressing high-energy fs pulses for wavelengths $λ=1.0-1.3 μ{\rm m}$ in a $β$-barium-borate crystal, and it requires that the system is in the stationary regime, where the phase mismatch is large enough to overcome the detrimental GVM effects. However, the simulations show that reaching single-cycle duration is ultimately inhibited by competing cubic nonlinearities as well as dispersive waves, that only show up when taking higher-order dispersion into account.

physics.optics↗
arXiv2006

Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor

We show that ballistic transport of optically excited atoms in an atomic vapor provides a nonlocal nonlinearity which stabilizes the propagation of vortex beams and higher order modes in the presence of a self-focusing nonlinearity. Numerical experiments demonstrate stable propagation of lowest and higher order vortices over a hundred diffraction lengths, before dissipation leads to decay of these structures.

physics.optics↗
arXiv2006

Stability of two-dimensional spatial solitons in nonlocal nonlinear media

We discuss existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose Einstein condensates, may support a variety of stationary localized structures - including rotating spatial solitons. We also demonstrate that the stability of these structures critically depends on the spatial profile of the nonlocal response function.

nlin.PS↗
arXiv2004

Guesswork for Dirac and Majorana neutrino mass matrices

In the framework of seesaw mechanism with three neutrino flavors, we propose tentatively an efficient parametrization for the spectra of Dirac and righthanded Majorana neutrino mass matrices in terms of three free parameters. Two of them are related to (and determined by) the corresponding parameters introduced previously for the mass spectra of charged leptons and up and down quarks. The third is determined from the experimental estimate of solar $Δm^2_{21}$. Then, the atmospheric $Δm^2_{32}$ is {\it predicted} close to its experimental estimation. With the use of these three parameters all light active-neutrino masses $ m_1 < m_2 < m_3$ and heavy sterile-neutrino masses $ M_1 < M_2 < M_3$ are readily evaluated. The latter turn out much more {\it hierarchical} than the former. The lightest heavy mass $ M_1$ comes out to be of the order $O(10^6 {\rm GeV})$ so, it is too light to imply that the mechanism of baryogenesis through thermal leptogenesis might work.

hep-ph↗
arXiv2003

Is there a dynamical group structure behind the bilarge form of neutrino mixing matrix?

We observe that the {\it invariance} of neutrino mixing matrix under the simultaneous discrete transformations $ν_1, ν_2, ν_3 \to -ν_1, -ν_2, ν_3 $ and $ν_e, ν_μ, ν_τ\to -ν_e, ν_τ, ν_μ$ (neutrino "horizontal conjugation") {\it characterizes} (as a sufficient condition for it) the familiar bilarge form of neutrino mixing matrix, favored experimentally at present. Thus, the mass neutrinos $ν_1, ν_2, ν_3 $ get a new quantum number, {\it covariant} with respect to their mixings into the flavor neutrinos $ν_e, ν_μ, ν_τ$ (neutrino "horizontal parity" equal to -1, -1,1, respectively). The "horizontal parity" turns out to be embedded in a group structure consisting of some Hermitian and real $3\times 3$ matrices $μ_1, μ_2, μ_3 $ and $ϕ_1, ϕ_2, ϕ_3 $, forming pairs interconnected through neutrino mixings. They generate some discrete transformations of mass and flavor neutrinos, respectively, in such a way that the group relations $μ_1 μ_2 = μ_3 $ (cyclic) and $ϕ_1 ϕ_2 = ϕ_3 $ (cyclic) hold, while $μ_a μ_b = μ_b μ_a $ and $ϕ_a ϕ_b = ϕ_b ϕ_a $. Then, for instance, the $μ_3$ matrix may be chosen equal to the "horizontal parity".

hep-ph↗