arXiv subjects

Vladimir V. Konotop

Publications and source records attributed to Vladimir V. Konotop.

At least 55 records · Page 3Linked to original sources

arXiv2020

Asymmetric perfect absorption and lasing of nonlinear waves by a complex $δ$-potential

Spectral singularities and the coherent perfect absorption are two interrelated concepts that have originally been introduced and studied for linear waves interacting with complex potentials. In the meantime, the distinctive asymptotic behavior of perfectly absorbed waves suggests considering possible generalizations of these phenomena for nonlinear waves. Here we address perfect absorption of nonlinear waves by an idealized infinitely narrow dissipative potential modeled by a Dirac $δ$-function with an imaginary amplitude. Our main result is the existence of perfectly absorbed flows whose spatial amplitude distributions are asymmetric with respect to the position of the absorber. These asymmetric states do not have a linear counterpart. Their linear stability is verified numerically. The nonlinear waveguide also supports symmetric and constant-amplitude perfectly absorbed flows. The stability of solutions of the latter type can be confirmed analytically.

nlin.PS↗

arXiv2020

Localization and delocalization of light in photonic moire lattices

Moire lattices consist of two identical periodic structures overlaid with a relative rotation angle. Present even in everyday life, moire lattices have been also produced, e.g., with coupled graphene-hexagonal boron nitride monolayers, graphene-graphene layers, and layers on a silicon carbide surface.A fundamental question that remains unexplored is the evolution of waves in the potentials defined by the moire lattices. Here we experimentally create two-dimensional photonic moire lattices, which, unlike their material predecessors, have readily controllable parameters and symmetry allowing to explore transitions between structures with fundamentally different geometries: periodic, general aperiodic and quasi-crystal ones. Equipped with such realization, we observe localization of light in deterministic linear lattices. Such localization is based on at band physics, in contrast to previous schemes based on light difusion in optical quasicrystals,where disorder is required for the onset of Anderson localization. Using commensurable and incommensurable moire patterns, we report the first experimental demonstration of two-dimensional localization-delocalization-transition (LDT) of light. Moire lattices may feature almost arbitrary geometry that is consistent with the crystallographic symmetry groups of the sublattices, and therefore afford a powerful tool to control the properties of light patterns, to explore the physics of transitions between periodic and aperiodic phases, and two-dimensional wavepacket phenomena relevant to several areas of science.

physics.optics↗

arXiv2020

Four-wave mixing in spin-orbit coupled Bose-Einstein condensates

We describe possibilities of spontaneous, degenerate four-wave mixing (FWM) processes in spin-orbit coupled Bose-Einstein condensates. Phase matching conditions (i.e., energy and momentum conservation laws) in such systems allow one to identify four different configurations characterized by involvement of distinct spinor states in which such a process can take place. We derived these conditions from first principles and then illustrated dynamics with direct numerical simulations. We found, among others, the unique configuration, where both probe waves have smaller group velocity than pump wave and proved numerically that it can be observed experimentally under proper choice of the parameters. We also reported the case when two different FWM processes can occur simultaneously. The described resonant interactions of matter waves is expected to play important role in the experiments of BEC with artificial gauge fields. Beams created by FWM processes are important source of correlated particles and can be used the experiments testing quantum properties of atomic ensembles.

quant-ph↗

arXiv2020

Stable nonlinear modes sustained by gauge fields

We reveal the universal effect of gauge fields on the existence, evolution, and stability of solitons in the spinor multidimensional nonlinear Schrödinger equation. Focusing on the two-dimensional case, we show that when gauge field can be split in a pure gauge and a \rtext{non-pure gauge} generating \rtext{effective potential}, the roles of these components in soliton dynamics are different: the \btext{localization characteristics} of emerging states are determined by the curvature, while pure gauge affects the stability of the modes. Respectively the solutions can be exactly represented as the envelopes independent of the pure gauge, modulating stationary carrier-mode states, which are independent of the curvature. Our central finding is that nonzero curvature can lead to the existence of unusual modes, in particular, enabling stable localized self-trapped fundamental and vortex-carrying states in media with constant repulsive interactions without additional external confining potentials and even in the expulsive external traps.

cond-mat.quant-gas↗

arXiv2020

A universal form of arrays with spectral singularities

An array of non-Hermitian optical waveguides can operate as a laser or as a coherent perfect absorber, which corresponds to a spectral singularity of the underlying discrete complex potential. We show that all lattice potentials with spectral singularities are characterized by the universal form of the gain-and-loss distribution. Using this result we systematically construct potentials characterized by several spectral singularities at arbitrary wavelengths, as well as potentials with second-order spectral singularities in their spectra. Higher-order spectral singularities demonstrate a greatly enhanced response to incident beams resulting in the excitation of high-intensity lasing modes.

physics.optics↗

arXiv2020

Construction of potentials with multiple spectral singularities

We develop an approach for designing complex potentials with two or three coexisting spectral singularities in the spectra of the respective Schrödinger operators. The approach is illustrated with several examples. In addition, we offer a simple recipe to create a second-order spectral singularity by intentionally colliding two simple ones.

math-ph↗

arXiv2020

Bragg solitons in topological Floquet insulators

We consider a topological Floquet insulator consisting of two honeycomb arrays of identical waveguides having opposite helicities. The interface between the arrays supports two distinct topological edge states, which can be resonantly coupled by additional weak longitudinal refractive index modulation with a period larger than the helix period. In the presence of Kerr nonlinearity, such coupled edge states enable topological Bragg solitons. Theory and examples of such solitons are presented.

physics.optics↗

arXiv2020

Edge Solitons in Lieb Topological Floquet Insulators

We describe topological edge solitons in a continuous dislocated Lieb array of helical waveguides. The linear Floquet spectrum of this structure is characterized by the presence of two topological gaps with edge states residing in them. A focusing nonlinearity enables families of topological edge solitons bifurcating from the linear edge states. Such solitons are localized both along and across the edge of the array. Due to the non-monotonic dependence of the propagation constant of the edge states on the Bloch momentum, one can construct topological edge solitons that either propagate in different directions along the same boundary or do not move. This allows us to study collisions of edge solitons moving in the opposite directions. Such solitons always interpenetrate each other without noticeable radiative losses; however, they exhibit a spatial shift that depends on the initial phase difference.

physics.optics↗

arXiv2020

Vector Topological Edge Solitons in Floquet Insulators

We introduce topological vector edge solitons in a Floquet insulator, consisting of two honeycomb arrays of helical waveguides with opposite directions of rotation in a focusing nonlinear optical medium. Zigzag edges of two arrays placed in contact create a zigzag-zigzag interface between two structures with different topology. A characteristic feature of such a photonic insulator is that, in the linear limit, it simultaneously supports two topologically protected chiral edge states at the interface between the two arrays. In the presence of nonlinearity, either bright or dark scalar Floquet edge soliton can bifurcate from a linear topological edge state. Such solitons are unidirectional and are localized in both directions, along the interface due to nonlinear self-action, and across the interface as being an edge state. The presence of two edge states with equal averaged group velocities enables the existence of stable topological vector edge solitons. In our case, these are nonlinearly coupled bright and dark solitons bifurcating from different branches of the topological Floquet edge states. Here we put forward a new mathematical description of scalar and vector small-amplitude Floquet envelope solitons in the above-mentioned continuous system. Importantly for the design of future photonic devices based on Floquet edge solitons, we find that the latter can be described by nonlinear Schrodinger equations for the mode envelopes obtained by averaging over one rotation period in the evolution coordinate.

physics.optics↗

arXiv2019

A universal form of complex potentials with spectral singularities

We establish necessary and sufficient conditions for complex potentials in the Schrödinger equation to enable spectral singularities (SSs) and show that such potentials have the universal form $U(x) = -w^2(x) - iw_x(x) + k_0^2$, where $w(x)$ is a differentiable function, such that $\lim_{x\to \pm \infty}w(x)=\mp k_0$, and $k_0$ is a nonzero real. We also find that when $k_0$ is a complex number, then the eigenvalue of the corresponding Shrödinger operator has an exact solution which, depending on $k_0$, represents a coherent perfect absorber (CPA), laser, a localized bound state, a quasi bound state in the continuum (a quasi-BIC), or an exceptional point (the latter requiring additional conditions). Thus, $k_0$ is a bifurcation parameter that describes transformations among all those solutions. Additionally, in a more specific case of a real-valued function $w(x)$ the resulting potential, although not being $PT$ symmetric, can feature a self-dual spectral singularity associated with the CPA-laser operation. In the space of the system parameters, the transition through each self-dual spectral singularity corresponds to a bifurcation of a pair of complex-conjugate propagation constants from the continuum. The bifurcation of a first complex-conjugate pair corresponds to the phase transition from purely real to complex spectrum.

nlin.PS↗

arXiv2019

Route to chaos in a coupled microresonator system with gain and loss

We consider chaotic dynamics of a system of two coupled ring resonators with a linear gain and a nonlinear absorption. Such a structure can be implemented in various settings including microresonator nanostructures, polariton condensates, optical waveguides or atomic Bose-Einstein condensates of ultra-cold atoms placed in a circular-shaped trap. From the theoretical point of view this system is attractive due to its modulational instability and rich structure, including various types of spontaneous symmetry breaking, period doubling bifurcations, eventually leading to chaotic regime. It is described by set of partial differential equations but we show that the so called Galerkin approximation can explain most of the system characteristics mapping it on the dynamics of few coupled oscillator modes. The main goal of present study is to investigate various routes to chaos in our non-hermitian system and to show the correspondence between the continuous operator problem and its discrete representation.

physics.optics↗

arXiv2019

Designing lasing and perfectly absorbing potentials

Existence of a spectral singularity (SS) in the spectrum of {a Schrödinger operator with} a non-Hermitian potential requires exact matching of parameters of the potential. We provide a necessary and sufficient condition for a potential to have a SS at a given wavelength. It is shown that potentials with SSs at prescribed wavelengths can be obtained by a simple and effective procedure. In particular, the developed approach allows one to obtain potentials with several SSs and with SSs of the second order, as well as potentials obeying a given symmetry, say, $\PT-$symmetric potentials. Also, the problem can be solved when it is required to obtain a potential obeying a given symmetry, say, $\PT-$symmetric potential. We illustrate all these opportunities with examples. We also describe splitting of a second-order SSs under change of the potential parameters, and discuss possibilities of experimental observation of SSs of different orders.

physics.optics↗

arXiv2019

Spectral singularities of a potential created by two coupled microring resonators

Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, coupling for each microring resonator yields two counter-propagating modes with equal frequencies. We show that such a system enables implementation of many types of scattering peculiarities, which are either the second or fourth order. The spectral singularities separate parameter regions where the spectrum is either pure real or else comprises complex eigenvalues; hence, they represent the points of the phase transition. By modifying the gain-loss relation for the resonators such an optical scatterer can act as a laser, as a coherent perfect absorber, be unidirectionally reflectionless or transparent, and support bound states either growing or decaying in time. These characteristics are observed for a discrete series of the incident-radiation wavelengths.

physics.optics↗

arXiv2018

Spectral singularities of odd-$PT$-symmetric potential

We describe one-dimensional stationary scattering of a two-component wave field by a non-Hermitian matrix potential which features odd-$PT$ symmetry, i.e., symmetry with $(PT)^2=-1$. The scattering is characterized by a $4\times 4$ transfer matrix. The main attention is focused on spectral singularities which are classified into two types. Weak spectral singularities are characterized by zero determinant of a diagonal $2\times 2$ block of the transfer matrix. This situation corresponds to the lasing or coherent perfect absorption of pairs of oppositely polarized modes. Strong spectral singularities are characterized by zero diagonal block of the transfer matrix. We show that in odd-$PT$-symmetric systems any spectral singularity is self-dual, i.e., lasing and coherent perfect absorption occur simultaneously. Detailed analysis is performed for a case example of a $PT$-symmetric coupler consisting of two waveguides, one with localized gain and another with localized absorption, which are coupled by a localized antisymmetric medium. For this coupler, we discuss weak self-dual spectral singularities and their splitting into complex-conjugate eigenvalues which represent bound states characterized by propagation constants with real parts lying in the continuum. A rather counterintuitive restoration of the unbroken odd-$PT$-symmetric phase subject to the increase of the gain-and-loss strength is also revealed. The comparison between odd- and even-$PT-$symmetric couplers, the latter characterized by $(PT)^2=1$, is also presented.

physics.optics↗

arXiv2018

Coherent perfect absorber and laser for nonlinear waves in optical waveguide arrays

A localized non-Hermitian potential can operate as a coherent perfect absorber or as a laser for nonlinear waves. The effect is illustrated for an array of optical waveguides, with the central waveguide being either active or absorbing. The arrays situated to the left and to the right from the center can have different characteristics. The result is generalized to setups with the central waveguide carrying additional nonlinear dissipation or gain and to the two-dimensional arrays with embedded one-dimensional absorbing or lasing sub-arrays.

physics.optics↗

arXiv2018

Coherent perfect absorption of nonlinear matter waves

Coherent perfect absorption is the complete extinction of incoming radiation by a complex potential in a physical system supporting wave propagation. The concept was proven for linear waves in variety of systems including light interacting with absorbing scatterers, plasmonic metasurfaces and graphene films, as well as sound waves. We extend the paradigm to coherent perfect absorption of nonlinear waves and experimentally demonstrate it for matter waves in an atomic Bose-Einstein condensate. Coherent absorption of nonlinear matter waves is achieved easier than its linear analogs because the strength of two-body interactions offers additional freedom for control. Implementation of the coherent perfect absorber of Bose-Einstein condensates paves the way towards broad exploitation of the phenomenon in nonlinear optics, exciton-polariton condensates, acoustics, and other areas of nonlinear physics. It also opens perspectives for designing atomic laser.

cond-mat.quant-gas↗

arXiv2018

Linear and nonlinear coherent perfect absorbers on simple layers

We consider linear and nonlinear coherent perfect absorbers (CPAs) in multidimensional geometries and construct explicitly the respective perfectly absorbed solutions. The multidimensional CPAs have a structure of the so-called simple layers which represent the generalization of the point $δ$ function potential to higher dimensions. The considered examples include broadband CPAs confined to a straight line (in a two-dimensional setting) and to a plane (in the three-dimensional space); CPAs for topological vortices on an absorbing circle; as well as axially-symmetric CPAs on a sphere. Additionally, it is shown that a paraxial beam propagating along a surface nonlinear CPA embedded in the three-dimensional space can be stable against perturbations. The results are interpreted in applications to optical and acoustic systems.

physics.optics↗

arXiv2018

Vortex creation without stirring in coupled ring resonators with gain and loss

We present study of the dynamics of two ring waveguide structure with space dependent coupling, linear gain and nonlinear absorption - the system that can be implemented in polariton condensates, optical waveguides, and nanocavities. We show that by turning on and off local coupling between rings one can selectively generate permanent vortex in one of the rings. We find that due to the modulation instability it is also possible to observe several complex nonlinear phenomena, including spontaneous symmetry breaking, stable inhomogeneous states with interesting structure of currents flowing between rings, generation of stable symmetric and asymmetric circular flows with various vorticities, etc. The latter can be created in pairs (for relatively narrow coupling length) or as single vortex in one of the channels, that is later alternating between channels.

nlin.PS↗