We investigate Airy-soliton interactions in self-defocusing media with PT potentials in one transverse dimension. We discuss different potentials in which the interacting beams with different phases are launched into the media at different separation distances. During interactions, there exist a primary collision region and a relaxation region accompanied by continuous interaction with the dispersed Airy tail. In the relaxation region, the beams exist soliton-like and breathers-like propagation. The beam width and mean power are influenced by initial separation, phase shift and modulation depth of PT potentials. Especially, the collision distance decreases with the spatial beam separation and the mean power possesses sinusoidal dependence on the phase shift.
It is studied the bright spatial solitons in nonlocal defocusing Kerr media with parity-time (PT) symmetric potentials. We find that these solitons can exist and be stable over a different range of potential parameters. The influence of the degree of nonlocality on the solitons and the transverse energy flow within the stable solitons are also examined.
We study the interaction of a co-propagating finite energy Airy pulse and a soliton in a Kerr medium under third order dispersion. It is observed that a strong radiation appears when selfaccelerating Airy pulse collides with a delayed soliton in time domain. We confirm both analytically and numerically that this radiation can only be initiated in the environment of third order dispersion (TOD). The radiation frequency is red or blue shifted depending on the numeric sign of TOD parameter. We adopt a simple Si-based waveguide to validate the normalised parameter that we use for the analysis. We …
We develop one numerical method to compute the optical vortex soliton with self-defocusing Kerr-type nonlocal nonlinearity. With the numerical simulation method, the propagation and interaction properties of such optical vortex solitons are investigated.
We address the dynamics of two-dimensional (2D) truncated Airy waves and three-component solitons in the system of two fundamental-frequency and second-harmonic fields, coupled by quadratic (chi^(2)) terms. The system models second-harmonic-generating optical media and atomic-molecular mixtures in Bose-Einstein condensates. In addition to stable solitons, the system maintains truncated-Airy-waves states in either one of the fundamental-frequency components, represented by exact solutions, which are stable, unlike the Airy waves in the degenerate (two-component) chi^(2) system. It is also possi…
We observe experimentally higher-order solitons in waveguide arrays with defocusing saturable nonlinearity. Such solitons can comprise several in-phase bright spots and are stable above a critical power threshold. We elucidate the impact of the nonlinearity saturation on the domains of existence and stability of the observed complex soliton states.
We predict that a photonic crystal fiber whose strands are filled with a defocusing nonlinear medium can support stable bright and also vortex solitons if the strength of the defocusing nonlinearity grows toward the periphery of the fiber. The domains of soliton existence depend on the transverse growth rate of the filling nonlinearity and nonlinearity of the core. Remarkably, solitons exist even when the core material is linear.
Generating energetic femtosecond mid-IR pulses is crucial for ultrafast spectroscopy, and currently relies on parametric processes that, while efficient, are also complex. Here we experimentally show a simple alternative that uses a single pump wavelength without any pump synchronization and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO$_3$ cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband ($\sim 1,000$ cm$^{-1}$) mid-IR pulses around $3.0~μ\rm m$ are generated with excellent spati…
We show that an inhomogeneous defocusing nonlinearity that grows toward the periphery in the positive and negative transverse directions at different rates can support strongly asymmetric fundamental and multipole bright solitons, which are stable in wide parameter regions. In the limiting case when nonlinearity is uniform in one direction, solitons transform into stable domain walls (fronts), with constant or oscillating intensity in the homogeneous region, attached to a tail rapidly decaying in the direction of growing nonlinearity.
We show that bimodal systems with a spatially nonuniform defocusing cubic nonlinearity, whose strength grows toward the periphery, can support stable two-component solitons. For a sufficiently strong XPM interaction, vector solitons with overlapping components become unstable, while stable families of solitons with spatially separated components emerge. Stable complexes with separated components may be composed not only of fundamental solitons, but of multipoles too.
We investigate numerically soliton-plasma interaction in a noble-gas-filled silica hollow-core anti-resonant fiber pumped in the mid-IR at 3.0 μm. We observe multiple soliton self-compression stages due to distinct stages where either the self-focusing or the self-defocusing nonlinearity dominates. Specifically, the parameters may be tuned so the competing plasma self-defocusing nonlinearity only dominates over the Kerr self-focusing nonlinearity around the soliton self-compression stage, where the increasing peak intensity on the leading pulse edge initiates a competing self-defocusing plasma…
We demonstrate that spatially inhomogeneous defocusing nonlinear landscapes with the nonlinearity coefficient growing toward the periphery as [1+abs(r)]**a support one- and two-dimensional fundamental and higher-order bright solitons, as well as vortex solitons, with algebraically decaying tails. The energy flow of the solitons converges as long as nonlinearity growth rate exceeds the dimensionality, i.e., a>D. Fundamental solitons are always stable, while multipoles and vortices are stable if the nonlinearity growth rate is large enough.
We report that defocusing cubic media with spatially inhomogeneous nonlinearity, whose strength increases rapidly enough toward the periphery, can support stable bright localized modes. Such nonlinearity landscapes give rise to a variety of stable solitons in all three dimensions, including 1D fundamental and multihump states, 2D vortex solitons with arbitrarily high topological charges, and fundamental solitons in 3D. Solitons maintain their coherence in the state of motion, oscillating in the nonlinear potential as robust quasi-particles and colliding elastically. In addition to numerically …
We present a numerical investigation of the propagation dynamics of a truncated Airy pulse in a highly dispersive and nonlinear medium by employing the split-step Fourier transform method and look, in particular, into the effects of fourth order dispersion (FOD) and cubic-quintic-septic nonlinearity on pulse evolution. Presence of FOD cancels the Airy pulse self-acceleration along with eclipsing the oscillatory tail during propagation in the linear regime. Further, we observe soliton shedding at low input pulse power in the presence of cubic and quintic nonlinearity and negative FOD. The emerg…
We experimentally observe long-wavelength dispersive waves generation in a BBO crystal. A soliton was formed in normal GVD regime of the crystal by a self-defocusing and negative nonlinearity through phase-mismatched quatradic interaction. Strong temporal pulse compression confirmed the formation of soliton during the pulse propagation inside the crystal. Significant dispersive wave radiation was measured in the anomalous GVD regime of the BBO crystal. With the pump wavelengths from 1.24 to 1.4 $μ$m, tunable dispersive waves are generated around 1.9 to 2.2 $μ$m. The observed dispersive wave ge…
We investigate numerically interactions between two in-phase or out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media in one transverse dimension. We discuss different cases in which the beams with different intensities are launched into the medium, but accelerate in opposite directions. Since both the Airy beams and nonlinear accelerating beams possess infinite oscillating tails, we discuss interactions between truncated beams, with finite energies. During interactions we see solitons and soliton pairs generated that are not accelerating. In general, t…
We employ the generic three-wave system, with the $χ^{(2)}$ interaction between two components of the fundamental-frequency (FF) wave and second-harmonic (SH) one, to consider collisions of truncated Airy waves (TAWs) and three-wave solitons in a setting which is not available in other nonlinear systems. The advantage is that the single-wave TAWs, carried by either one of the FF component, are not distorted by the nonlinearity and are stable, three-wave solitons being stable too in the same system. The collision between mutually symmetric TAWs, carried by the different FF components, transform…
We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time(PT )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave propagation in graded-index optical waveguides with balanced gain and loss. We find both fundamental and multipole solitons for both focusing and defocusing signs of the saturable nonlinearity in such PT -symmetric waveguides. The dependence of the propagation constant on the soliton's power is presented for different strengths of the nonlinearity saturation, S. …
We consider bright solitons supported by a symmetric inhomogeneous defocusing nonlinearity growing rapidly enough toward the periphery of the medium, combined with an antisymmetric gain-loss profile. Despite the absence of any symmetric modulation of the linear refractive index, which is usually required to establish a PT-symmetry in the form of a purely real spectrum of modes, we show that the PT-symmetry is never broken in the present system, and that the system always supports stable bright solitons, fundamental and multi-pole ones. Such phenomenon is connected to non-linearizability of the…
We investigate numerically the interactions of two in-phase and out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media, in one transverse dimension. We find that bound and unbound soliton pairs, as well as single solitons, can form in such interactions. If the interval between two incident beams is large relative to the width of their first lobes, the generated soliton pairs just propagate individually and do not interact. However, if the interval is comparable to the widths of the maximum lobes, the pairs interact and display varied behavior. In the in-…
In this paper, we propose a complex short pulse equation of both focusing and defocusing types, which governs the propagation of ultra-short pulses in nonlinear optical fibers. It can be viewed as an analogue of the nonlinear Schrödinger (NLS) equation in the ultra-short pulse regime. Furthermore, we construct the multi-dark soliton solution for the defocusing complex short pulse equation through the Darboux transformation and reciprocal (hodograph) transformation. One- and two-dark soliton solutions are given explicitly, whose properties and dynamics are analyzed and illustrated.
We show numerically that ultrashort self-defocusing temporal solitons colliding with a weak pulsed probe in the near-IR can convert the probe to the mid-IR. A near-perfect conversion efficiency is possible for a high effective soliton order. The near-IR self-defocusing soliton can form in a quadratic nonlinear crystal (beta-barium borate) in the normal dispersion regime due to cascaded (phase-mismatched) second-harmonic generation, and the mid-IR converted wave is formed in the anomalous dispersion regime between $λ=2.2-2.4~μ\rm m$ as a resonant dispersive wave. This process relies on non-dege…
We investigate interactions by means of direct numerical simulations between two finite Airy-Gaussian (AiG) beams in different media with the defected photonic lattices in one transverse dimension. We discuss different lattice structures in which the beams with different intensities and phases are launched into the medium, but accelerate in opposite directions. During interactions we see the interference fringe, breathers and soliton pairs generated that are not accelerating. In the linear media, the initial deflection direction of the accelerated beams is changed by adjusting the phase shift …
We present a unified theoretical study of the bright solitons governed by self-focusing and defocusing nonlinear Schrodinger (NLS) equations with generalized parity-time (PT)-symmetric Scarff II potentials. Particularly, a PT-symmetric k-wavenumber Scarff II potential and a multi-well Scarff II potential are considered, respectively. For the k-wavenumber Scarff II potential, the parameter space can be divided into different regions, corresponding to unbroken and broken PT-symmetry and the bright solitons for self-focusing and defocusing Kerr nonlinearities. For the multi-well Scarff II potenti…
We predict the existence of surface dark solitons at the interface between a self-defocusing nonlocal nonlinear medium and a linear medium. The fundamental and higher-order surface dark solitons can exist when the linear refractive index of the self-defocusing media is much larger than that of the linear media. The fundamental solitons are stable and the stabilities of higher-order solitons depend on both nonlocality degree and propagation constant.
We construct families of discrete solitons (DSs) in an array of self-defocusing waveguides with an embedded $\mathcal{PT}$ (parity-time)-symmetric dimer, which is represented by a pair of waveguides carrying mutually balanced gain and loss. Four types of states attached to the embedded defect are found, namely, staggered and unstaggered bright localized modes and gray or anti-gray DSs. Their existence and stability regions expand with the increase of the strength of the coupling between the dimer-forming sites. The existence of the gray and staggered bright DSs is qualitatively explained by di…
In the present work, we examine "binary" waveguide arrays, where the coupling between adjacent sites alternates between two distinct values $C_1$ and $C_2$ and a saturable nonlinearity is present on each site. Motivated by experimental investigations of this type of system in fabricated LiNbO$_3$ arrays, we proceed to analyze the nonlinear wave excitations arising in the self-defocusing nonlinear regime, examining, in particular, dark solitons and bubbles. We find that such solutions may, in fact, possess a reasonably wide, experimentally relevant parametric interval of stability, while they m…
Photon-conserving Raman soliton attractors in focusing and defocusing Kerr media
State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications（北京邮电大学信息光子学与光通信国家重点实验室）；Laboratory of Infrared Materials and Devices, The Research Institute of Advanced Technologies, Ningbo University（宁波大学先进技术研究研究院红外材料与器件实验室）；Ultrafast Laser Laboratory, Key Laboratory of Optoelectronic Information Science and Technology of the Ministry of Education, School of Precision Instruments and Opto-electronics Engineering, Tianjin University（天津大学精密仪器与光电子工程学院教育部光电信息科技重点实验室超快激光实验室）；Institut für Physik, Humboldt-Universität zu Berlin（柏林洪堡大学物理研究所）；Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy（马克斯·玻恩非线性光学和短脉冲光谱研究所）；Department of Physics, School of Physical Science and Technology, Ningbo University（宁波大学物理科学与技术学院物理学系）
The defocusing nonlinear Schrödinger (NLS) equation has no the modulational instability, and was not found to possess the rogue wave (RW) phenomenon up to now. In this paper, we firstly investigate some novel nonlinear wave structures in the defocusing NLS equation with real-valued time-dependent and time-independent potentials such that the stable new RWs and W-shaped solitons are found, respectively. Moreover, the interactions of two or three RWs are explored such that the RWs with higher amplitudes are generated in the defocusing NLS equation with real-valued time-dependent potentials. Fina…
We address the existence and properties of one-dimensional solitons maintained by localized parameter gain in focusing and defocusing lossy nonlinear media. Localized parametric gain supports both fundamental and multipole solitons. We found that the family of fundamental solitons is partly stable in focusing nonlinear medium, and completely stable in defocusing medium, while all higher-order solitons are unstable. In addition to numerical results, the existence threshold for the solitons, and a particular stable exact solution are obtained in an exact analytical form.
Efficient supercontinuum generation (SCG) requires excitation of solitons at the pump laser wavelength. Quadratic nonlinear waveguides may support an effective self-defocusing nonlinearity so solitons can directly be generated at common ultrafast laser wavelengths without any waveguide dispersion engineering. We here experimentally demonstrate efficient SCG in a standard lithium niobate (LN) waveguide without using quasi-phase matching (QPM). By using femtosecond pumps with wavelengths in the $1.25-1.5 μ\rm m$ range, where LN has normal dispersion and thus supports self-defocusing solitons, oc…
We introduce a new species of gap solitons (GSs) supported by an azimuthally modulated guiding ring in defocusing cubic media. The periodicity in the azimuthal direction strongly modifies properties and existence domains of GSs. In addition to the fundamental solitons, we report even and twisted bound states. The former type is found to be stable, while the twisted states are always unstable in defocusing media.
We investigate numerically that a finite Airy-Gaussian (AiG) beam varies its trajectory and shape in the defected photonic lattices. The propagation properties and beam self-bending are controlled with modulation depth and period of the photonic lattices, positive and negative defects, beam distribution factor and nonlinearity change. For positive defects, the pseudo-period oscillation and localization of the AiG beam may be formed under a certain condition, while the beam is diffused for negative defects. Moreover, the solitons may appear during the propagation process when the self-focusing …
It is shown that the pair plasmas with small temperature asymmetry can support existence of localized as well as de-localized optical vortex solitons. Coexistence of such solitons is possible due to peculiar form of saturating nonlinearity which has a focusing-defocusing nature -- for weak amplitudes being focusing becoming defocusing for higher amplitudes. It is shown that delocalized vortex soliton is stable in entire region of its existence while single- and multi-charged localized vortex solitons are unstable for low amplitudes and become stable for relativistic amplitudes.
We address the existence and properties of solitons in layered thermal media made of alternating focusing and defocusing layers. Such structures support robust bright solitons even if the averaged nonlinearity is defocusing. We show that non-oscillating solitons may form in any of the focusing domains, even in those located close to the sample edge, in contrast to uniform thermal media where light beams always oscillate when not launched exactly on the sample center. Stable multipole solitons may include more than four spots in layered media.
The stability of two-dimensional bright vortex solitons in a media with focusing cubic and defocusing quintic nonlinearities is investigated analytically and numerically. It is proved that above some critical beam powers not only one- and two-charged but also multiple-charged stable vortex solitons do exist. A vortex soliton occurs robust with respect to symmetry-breaking modulational instability in the self-defocusing regime provided that its radial profile becomes flattened, so that a self-trapped wave beam gets a pronounced surface. It is demonstrated that the dynamics of a slightly perturb…
It has been recently demonstrated that self-defocusing (SDF) media with the cubic nonlinearity, whose local coefficient grows from the center to periphery fast enough, support stable bright solitons, without the use of any linear potential. Our objective is to test the genericity of this mechanism for other nonlinearities, by applying it to one- and two-dimensional (1D and 2D) quintic SDF media. The models may be implemented in optics (in particular, in colloidal suspensions of nanoparticles), and the 1D model may be applied to the description of the Tonks-Girardeau gas of ultracold bosons. In…
We reveal the relevance between the nonlocality and the focusing/defocusing states in nonlocally nonlinear media, and predict a novel phenomenon that the self-focusing/self-defocusing property of the optical beam in the nonlocally nonlinear medium with a sine-oscillation response function depends on its degree of nonlocality. The transition from the focusing nonlinearity to the defocusing nonlinearity of the nonlinear refractive index will happen when the degree of nonlocality of the system goes cross a critical value, and vise verse. Bright and dark soliton solutions are obtained, respectivel…
Nonlinear Bessel beams in self-defocusing media are found to be the natural, non-diffracting background where vortex solitons can be nested, interact and survive for propagation distances that are one order of magnitude larger than in the usual Gaussian or super-Gaussian backgrounds. The dynamics of the vortex solitons approaches that in the ideal, uniform background, preventing vortex spiraling and decay, which eases vortex steering for applications.
The propagation dynamics of two-dimensional (2D) ring-Airy beams is studied in the framework of the fractional Schrödinger equation, which includes saturable or cubic self-focusing or defocusing nonlinearity and Lévy index ((LI) alias for the fractionality) taking values $1\leqα\leq 2$. The model applies to light propagation in a chain of optical cavities emulating fractional diffraction. Management is included by making the diffraction and/or nonlinearity coefficients periodic functions of the propagation distance, $ζ$. The management format with the nonlinearity coefficient decaying as $1/ζ$…
We introduce a system with competing self-focusing (SF) and self-defocusing (SDF) terms, which have the same scaling dimension. In the one-dimensional (1D) system, this setting is provided by a combination of the SF cubic term multiplied by the delta-function, $δ(x)$, and a spatially uniform SDF quintic term. This system gives rise to the most general family of 1D-Townes solitons, the entire family being unstable. However, it is completely stabilized by a finite-width regularization of the $δ$-function. The results are produced by means of numerical and analytical methods. We also consider the…
We show that surface solitons in the one-dimensional nonlinear Schrödinger equation with truncated complex periodic potential can be stabilized by linear homogeneous losses, which are necessary to balance gain in the near-surface channel arising from the imaginary part of potential. Such solitons become stable attractors when the strength of homogeneous losses acquires values from a limited interval and they exist in focusing and defocusing media. The domains of stability of surface solitons shrink with increase of the amplitude of imaginary part of complex potential.
Recent studies have demonstrated that defocusing cubic nonlinearity with local strength growing from the center to the periphery faster than $r^{D}$, in space of dimension $D$ with radial coordinate $r$, supports a vast variety of robust bright solitons. In the framework of the same model, but with a weaker spatial-growth rate, $\sim r^{α}$ with $α\leq D$, we here test the possibility to create stable\textit{\ localized continuous waves} (LCWs) in one- and two-dimensional (1D and 2D) geometries, \textit{% localized dark solitons} (LDSs) in 1D, and \textit{localized dark vortices} (LDVs) in 2D,…
We study the cubic- (focusing-)quintic (defocusing) nonlinear Schrödinger equation in two transverse dimensions. We discuss a family of stationary traveling waves, including rarefaction pulses and vortexantivortex pairs, in a background of critical amplitude. We show that these rarefaction pulses can be generated inside a flattop soliton when a smaller bright soliton collides with it. The fate of the evolution strongly depends on the relative phase of the solitons. Among several possibilities, we find that the dark pulse can reemerge as a bright soliton.
The dynamics of two component coupled Airy beams is investigated. In the linear propagation regime a complete analytic solution describes breather like propagation of the two components featuring non-diffracting self-accelerating Airy behavior. The superposition of two beams with different input properties opens the possibility to design more complex non-diffracting propagation scenarios. In the strongly nonlinear regime the dynamics remains qualitatively robust as is revealed by direct numerical simulations. Due to the Kerr effect the two beams emit solitonic breathers, whose coupling period …
We study the giant Goos-Hanchen shift obtained from an Airy beam impinging on a nonlinear interface. To avoid any angular restriction associated with the paraxial approximation, the analysis is based on the numerical solution of the nonlinear Helmholtz equation. We report the existence of non-standard intermittent and oscillatory regimes for the nonlinear Goos-Hanchen shifts which can be explained in terms of the competition between the critical coupling to a surface mode of the reflected component of the Airy beam and the soliton emission from the refracted beam component.
Vortex solitons (dark solitons) are described in self-defocusing Kerr media whose phase line singularity is not parallel to the propagation direction, but is perpendicular or tilted almost arbitrary angles, depending on the medium linear dispersion. These solitons broaden the so-called spatiotemporal optical vortices recently observed in experiments to the nonlinear realm, opening new perspectives in practical applications of optical vortices.
We reveal the existence of continuous families of guided single-mode solitons in planar waveguides with weakly nonlinear active core and absorbing boundaries. Stable propagation of TE and TM-polarized solitons is accompanied by attenuation of all other modes, i.e. the waveguide features properties of conservative and dissipative systems. If the linear spectrum of the waveguide possesses exceptional points, which occurs in the case of TM-polarization, an originally focusing (defocusing) material nonlinearity may become effectively defocusing (focusing). This occurs due to the geometric phase of…
Criteria for experimental observation of multi-dimensional optical solitons in media with saturable refractive nonlinearities are developed. The criteria are applied to actual material parameters (characterizing the cubic self-focusing and quintic self-defocusing nonlinearities, two-photon loss, and optical-damage threshold) for various glasses. This way, we identify operation windows for soliton formation in these glasses. It is found that two-photon absorption sets stringent limits on the windows. We conclude that, while a well-defined window of parameters exists for two-dimensional solitons…
