Yaroslav V. Kartashov, Boris A. Malomed, Victor A. Vysloukh, Lluis Torner
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.
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We are reporting that the Lugiato-Lefever equation describing the frequency comb generation in ring resonators with the localized pump and loss terms also describes the simultaneous nonlinear resonances leading to the multistability of nonlinear modes and coexisting solitons that are associated with the spectrally distinct frequency combs.
Vortex clusters bifurcating from multipoles and second-order ring solitons
研究立方-五次介质中多极孤子和涡旋簇，通过线性稳定性分析和数值模拟，发现特定条件下涡旋簇可从多极子或二阶环形孤子分叉，揭示了N=2和4的上支涡旋簇的稳定特性及形成机制。
Soliton crystals are periodic patterns of multi-spot optical fields formed from either time or space entanglements of equally separated identical high-intensity pulses. These specific nonlinear optical structures have gained interest in recent years with the advent and progress in nonlinear optical fibers and fiber lasers, photonic crystals, wave-guided wave systems and most recently optical ring microresonator devices. In this work an extensive analysis of characteristic features of soliton crystals is carried out, with emphasis on their one-to-one correspondance with Elliptic solitons. In th…
We study nonlinear wave phenomena in coupled ring resonator optical waveguides in the tight coupling regime. A discrete model for the system dynamics is put forward and its steady state nonlinear Bloch modes are derived. The switching behavior of the transmission system is addressed numerically and the results are explained in the light of this analytical result. We also present a numerical study on the spontaneous generation of Bragg solitons from a continuous-wave input.
We study the propagation of quasi-discrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split ring resonators. By considering the relevant transmission line analogue, we derive a nonlinear lattice model which is studied analytically by means of a quasi-discrete approximation. We derive a nonlinear Schr{ö}dinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the p…
$π$-solitons on a ring of waveguides
研究了周期性振荡波导环上$π$-孤子的存在性与稳定性，揭示了Floquet结构中反常拓扑$π$-模的强耦合机制及其对拓扑孤子性质的影响。
We study solitons of the two-dimensional nonlinear Dirac equation with asymmetric cubic nonlinearity. We show that, with the nonlinearity parameters specifically tuned, a high degree of localization of both spinor components is enabled on a ring of certain radius. Such ring Dirac soliton can be viewed as a self-induced nonlinear domain wall and can be implemented in nonlinear photonic graphene lattice with Kerr-like nonlinearities. Our model could be instructive for understanding localization mechanisms in nonlinear topological systems.
Stable higher-charge vortex solitons in the cubic-quintic medium with a ring potential
本研究提出带环形折射率调制的三次-五次非线性介质模型，可捕获高拓扑荷稳定光学涡旋孤子，上支孤子完全稳定且满足反Vakhitov-Kolokolov判据，为低功率高涡量窄涡旋孤子制备提供可能。
Azimuthal modulation instability, breathers and solitons in ring-core optical fibers
本研究通过数值模拟探究环形芯涡旋光纤中的方位角调制不稳定性，发现其非线性阶段可用非线性薛定谔方程的解析呼吸子解描述，还揭示了方位角孤子动力学等特性，为光纤横向非线性波研究及轨道角动量态操控提供新方向。
We introduce solitons supported by Bessel photonic lattices in cubic nonlinear media. We show that the cylindrical geometry of the lattice, with several concentric rings, affords unique soliton properties and dynamics. In particular, besides the lowest-order solitons trapped in the center of the lattice, we find soliton families trapped at different lattice rings. Such solitons can be set into controlled rotation inside each ring, thus featuring novel types of in-ring and inter-ring soliton interactions.
Characteristic features of soliton-comb structures in optical microresonators are investigated in normal and anomalous dispersion regimes, when the detuning parameter is varied over a broad range of values. The study rests on the assumption that soliton combs are self-organized ensemble of co-propagating coherently entangled states of light, and depending on the group-velocity dispersion they can result from space-division multiplexing of single-bright and single-dark solitons. Their analytical and numerical reconstruction schemes are discussed, while a linear-stability analysis leads to a $2\…
We analyze the salient features of vortex-ring solitons supported by cylindrically symmetric media with nonlocal thermal nonlinearity. We discover the existence of a maximum allowed topological charge for such vortex solitons to be stable on propagation: Only vortex-ring solitons with topological charge m<=2 are found to be stable. This remarkable result holds independently of the radius of the sample.
We reveal the existence of dynamically stable composite topological solitons in Bessel photonic lattices imprinted in focusing Kerr-type nonlinear media. The new stable composite solitons are made of a vortex-ring with unit topological charge incoherently coupled to a fundamental soliton. The stabilization of the otherwise highly azimuthally unstable vortex-rings is provided under suitable conditions, which we study in detail, by cross-phase-modulation coupling with the fundamental soliton companion.
Multi-ring necklace vortex solitons in Kerr nonlinear media with azimuthally modulated Bessel potentials
在Kerr非线性介质中，通过方位调制贝塞尔势实现多环涡旋项链孤子的稳定生成，为复杂光场操控提供新途径。
We propose a system of coupled microring resonators for the generation frequency combs and dissipative Kerr solitons in silicon at telecommunication frequencies. By taking advantage of structural slow-light, the effective non-linearity of the material is enhanced, thus relaxing the requirement of ultra-high quality factors that currently poses a major obstacle to the realization of silicon comb devices. We demonstrate a variety of frequency comb solutions characterized by threshold power in the 10-milliwatt range and a small footprint of $0.1$ mm$^2$, and study their robustness to structural d…
Ring dark and anti-dark solitons in nonlocal media are found. These structures have, respectively, the form of annular dips or humps on top of a stable continuous-wave background, and exist in a weak or strong nonlocality regime, defined by the sign of a characteristic parameter. It is demonstrated analytically that these solitons satisfy an effective cylindrical Kadomtsev-Petviashvilli (aka Johnson's) equation and, as such, can be written explicitly in closed form. Numerical simulations show that they propagate undistorted and undergo quasi-elastic collisions, attesting to their stability pro…
We report on the experimental observation of temporal cavity soliton destabilization via spatiotemporal chaos in a coherently-driven optical fiber ring resonator. Numerical simulations and theoretical analyses are in good agreement with experimental observations.
We study basic properties of quiescent and rotating multipole-mode solitons supported by axially symmetric Bessel lattices in a medium with defocusing cubic nonlinearity. The solitons can be found in different rings of the lattice and are stable when the propagation constant exceeds the critical value, provided that the lattice is deep enough. In a high-power limit the multipole-mode solitons feature a multi-ring structure.
Nozaki-Bekki optical solitons
本文将半导体激光器与Kerr微谐振器技术融合于环形半导体激光器，实验并理论证明可通过偏置调谐自发生成结构稳定的Nozaki-Bekki暗孤子及多孤子态。
Stable ring vortex solitons, featuring a bright-shape, appear to be very rare in nature. However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice. We find the families of vortex lattice solitons and reveal their salient properties, including the conditions required for their stability. We show that the higher the soliton topological charge, the deeper the lattice modulation necessary for stabilization.
We demonstrate the first fully controlled generation of immobile and slow spatial gap solitons in nonlinear periodic systems with band-gap spectra, and reveal the key features of gap solitons which distinguish them from conventional counterparts, including a dynamical transformation of gap solitons due to nonlinear inter-band coupling. We also predict theoretically and confirm experimentally the effect of anomalous steering of gap solitons in optically-induced photonic lattices.
We elucidate the properties of mixed-gap vector surface solitons supported by the interface between a uniform medium and an optical lattice imprinted in a Kerr-type nonlinear media. The components of such mixed-gap solitons emerge from different gaps of lattice spectrum and their mutual trapping results in the formation of stable vector states. The unstable soliton component is stabilized by the cross-coupling with the stable component. We show that vector mixed-gap surface solitons exhibit a new combination of properties of vectorial surface waves and gap solitons.
We have experimentally investigated the soliton interaction in a passively mode-locked fiber ring laser and revealed the existence of three types of strong soliton interaction: a global type of soliton interaction caused by the existence of unstable CW components; a local type of soliton interaction mediated through the radiative dispersive waves; and the direct soliton interaction. We found that the appearance of the various soliton operation modes observed in the passively mode locked fiber soliton lasers are the direct consequences of these three types of soliton interaction. The soliton in…
We demonstrate that, in a two-dimensional dissipative medium described by the cubic-quintic (CQ) complex Ginzburg-Landau (CGL) equation with the viscous (spectral-filtering) term, necklace rings carrying a mixed radial-azimuthal phase modulation can evolve into polygonal or quasi-polygonal stable soliton clusters, and into stable fundamental solitons. The outcome of the evolution is controlled by the depth and azimuthal anharmonicity of the phase-modulation profile, or by the radius and number of "beads" in the initial necklace ring. Threshold characteristics of the evolution of the patterns a…
We analyze nonlinear collective effects near surfaces of semi-infinite periodic systems with multi-gap transmission spectra and introduce a novel concept of multi-gap surface solitons as mutually trapped surface states with the components associated with different spectral gaps. We find numerically discrete surface modes in semi-infinite binary waveguide arrays which can support simultaneously two types of discrete solitons, and analyze different multi-gap states including the soliton-induced waveguides with the guided modes from different gaps and composite vector solitons.
Soliton microcombs are helping to advance the miniaturization of a range of comb systems. These combs mode lock through the formation of short temporal pulses in anomalous dispersion resonators. Here, a new microcomb is demonstrated that mode locks through the formation of pulse pairs in normal-dispersion coupled-ring resonators. Unlike conventional microcombs, pulses in this system cannot exist alone, and instead must phase lock in pairs to form a bright soliton comb. Also, the pulses can form at recurring spectral windows and the pulses in each pair feature different optical spectra. This pa…
We report on the experimental observation of a new type of dark soliton in a fiber laser made of all normal group velocity dispersion fibers. It was shown that the soliton is formed due to the cross coupling between two different wavelength laser beams and has the characteristic of separating the two different wavelength laser emissions. Moreover, we show experimentally that the dual-wavelength dark solitons have a much lower pump threshold than that of the nonlinear Schrödinger equation dark solitons formed in the same laser.
We suggest a novel concept of diffraction management in waveguide arrays and predict the existence of discrete gap solitons that possess the properties of both conventional discrete and Bragg grating solitons. We demonstrate that both the soliton velocity and propagation direction can be controlled by varying the input light intensity.
We demonstrate self-started mode-locking in an Erbium-doped fiber ring laser by using the nonlinear polarization rotation mode-locking technique but without an isolator in cavity. We show that due to the intrinsic effective nonlinearity discrimination of the mode-locked pulse propagating along different cavity directions, the soliton operation of the laser is always unidirectional, and its features have no difference to that of the unidirectional lasers with an isolator in cavity.
We have investigated mixed-gap vector solitons involving incoherently coupled fundamental and dipole components in a parity-time (PT) symmetric lattice with saturable nonlinearity. For the focusing case, vector solitons emerge from the semi-infinite and the first finite gaps, while for the defocusing case, vector solitons emerge from the first finite and the second finite gaps. For both cases, we find that stronger saturable nonlinearity is relative to sharper increase/decrease of soliton power with propagation constant and to narrower existence domain of vector solitons. This finding is helpf…
We study the formation of gap solitons in the presence of parametric pump. It is shown that parametric pump can stabilize stationary solitons continuously emitting dispersive waves. The resonant interactions of the radiation and the solitons are studied and it is shown that the solitons can be effectively controlled by the radiation. In particular it is shown that the solitons can collide or to get pinned to inhomogeneities due to the interactions mediated by the resonant radiation.
We consider linear and nonlinear modes pinned to a grating-free (gapless) layer placed between two symmetric or asymmetric semi-infinite Bragg gratings (BGs), with a possible phase shift between them, in a medium with the uniform Kerr nonlinearity. The asymmetry is defined by a difference between bandgap widths in the two BGs. In the linear system, exact defect modes (DMs) are found. Composite gap solitons pinned to the central layer are found too, in analytical and numerical forms, in the nonlinear model. In the asymmetric system, existence boundaries for the DMs and gap solitons, due to the …
Backscattering-Induced Dissipative Solitons in Ring Quantum Cascade Lasers
本研究针对环形量子级联激光器的孤子稳定机制，采用自洽Maxwell-Bloch模型，证实分布背散射引发的反向波微小有限耦合是孤子稳定的核心，且与实验数据高度一致，为中红外、太赫兹集成光谱仪发展提供支撑。
We report on the first experimental observation of discrete gap solitons in binary arrays of optical waveguides. We observe the soliton generation when the inclination angle of an input beam is slightly above the Bragg angle, and show that the propagation direction of the emerging gap soliton depends on the input power as a result of an inter-band momentum exchange.
A ring dark soliton is a dark soltion occurring in higher dimensions. It is still unknown in microcavity-polariton condensates due to its instability. We find that a stable RDS cannot exist in a MPC without a defect. We then propose a way to create a stable RDS in a MPC by adding a defect with a ring structure to the system. A RDS pinned by the defect potential becomes stable. For various pump powers, we also investigate the stable regime of the RDS by tuning the strength and width of the defect potential. We conclude that the stable RDSs can be obtained.
Dissipative Kerr solitons are self-organized optical waves arising from the interplay between Kerr effect and dispersion. They can form spontaneously in nonlinear microresonators pumped with an external continuous-wave laser, which provides the parametric gain for the proliferation of an ultrastable frequency comb. These miniaturized and battery driven microcombs have become a disruptive technology for precision metrology, broadband telecommunication and ultrafast optical ranging. In this work, we report on the first experimental observation of dissipative Kerr solitons generated in a ring cav…
We show that gap-acoustic solitons, i.e., optical gap solitons with electrostrictive coupling to sound modes, can be produced with velocities down to less than 2.5% of the speed of light using a fiber Bragg grating that is linearly coupled to a non-Bragg fiber over a finite domain. Forward- and backward-moving light pulses in the non-Bragg fiber that reach the coupling region simultaneously couple into the Bragg fiber and form a moving soliton, which then propagates beyond the coupling region.
We experimentally demonstrate the formation and stable propagation of various types of discrete temporal solitons in an optical fiber system. Pulses interacting with a time-periodic potential and defocusing nonlinearity are shown to form gap solitons and nonlinear truncated Bloch waves. Multi-pulse solitons with defects, as well as novel structures composed of a strong soliton riding on a weaker truncated nonlinear Bloch wave are shown to propagate over up to eleven coupling lengths. The nonlinear dynamics of all pulse structures is monitored over the full propagation distance which provides d…
Nonlinear dynamics of soliton molecules in a Kerr micro-ring
本研究探讨Kerr微环中TE和TM模式分别产生明暗孤子并结合成孤子分子对的非线性动力学，揭示失谐区间对孤子态的影响，为光通信、高精度测量和全光控制提供新方案。
The existence and stability of defect solitons in parity-time (PT) symmetric optical lattices with nonlocal nonlinearity are reported. It is found that nonlocality can expand the stability region of defect solitons. For positive or zero defects, fundamental and dipole solitons can exist stably in the semi-infinite gap and the first gap, respectively. For negative defects, fundamental solitons can be stable in both the semi-infinite gap and the first gap, whereas dipole solitons are unstable in the first gap. There exist a maximum degree of nonlocal nonlinearity, above which the fundamental sol…
We demonstrate numerically that partially incoherent light can be trapped in the spectral band gaps of a photonic lattice, creating partially incoherent multi-component spatial optical solitons in a self-defocusing nonlinear periodic medium. We find numerically such incoherent multi-gap optical solitons and discuss how to generate them in experiment by interfering incoherent light beams at the input of a nonlinear periodic medium.
We report the existence, and study mobility and interactions of gap polariton solitons in a microcavity with a periodic potential, where the light field is strongly coupled to excitons. Gap solitons are formed due to the interplay between the repulsive exciton-exciton interaction and cavity dispersion. The analysis is carried out in an analytical form, using the coupled-mode (CM) approximation, and also by means of numerical methods.
We introduce a novel type of surface waves that form at the edge of guiding structures consisting of several concentric rings. Such surface waves rotate steadily upon propagation and, in contrast to nonrotating waves, for high rotation frequencies they do not exhibit power thresholds for their existence. There exists an upper limit for the surface wave ro-tation frequency, which depends on the radius of the outer guiding ring and on its depth.
The propagation properties of optical fields in linear and nonlinear parity-time symmetric microring coupled resonator optical waveguides are studied. The effects described include the existence of symmetry breaking thresholds, the propagation of gap solitons in nonlinear transmission lines and the existence of quasi stable propagation regimes outside the broken symmetry regions.
We report results of the investigation of gap solitons (GSs) in the generic model of a periodically modulated Bragg grating (BG), which includes periodic modulation of the BG chirp or local refractive index, and periodic variation of the local reflectivity. We demonstrate that, while the previously studied reflectivity modulation strongly destabilizes all solitons, the periodic chirp modulation, which is a novel feature, stabilizes a new family of double-peak fundamental BGs in the side bandgap at negative frequencies (gap No. -1), and keeps solitons stable in the central bandgap (No. 0). The …
Modulation instability with subsideband generation induced by periodic power variation in soliton fiber ring lasers is reported. We found that different wavelength shifts of subsideband generation are related to different periodic power variation. The period of power variation and wavelength shifts of subsideband can be changed by altering the linear cavity phase delay. It is also found that the periodic power variation is caused by the interaction between the nonuniform polarization state of the circulating light and the polarizer in the laser cavity.
We analyze the existence, stability, and mobility of gap solitons (GSs) in a periodic photonic structure built into a nonlocal self-defocusing medium. Counter-intuitively, the GSs are supported even by a highly nonlocal nonlinearity, which makes the system quasi-linear. Unlike local models, the variational approximation (VA) predicts the GSs in a good agreement with numerical findings, due to the suppression of undulating tails of the solitons.
We report on the first observation of surface gap solitons, recently predicted to exist at the interface between uniform and periodic dielectric media with defocusing nonlinearity [Ya.V. Kartashov et al., Phys. Rev. Lett. 96, 073901 (2006). We demonstrate strong self-trapping at the edge of a LiNbO_3 waveguide array and the formation of staggered surface solitons with propagation constant inside the first photonic band gap. We study the crossover between linear repulsion and nonlinear attraction at the surface, revealing the mechanism of nonlinearity-mediated stabilization of the surface gap m…
We consider the generation and propagation of (2+1)-dimensional beams in a nonlinear waveguide with the linear gain. Simple self-similar evolution of the beams is achieved at the asymptotic stage, if the input beams represent the fundamental mode. On the contrary, if they carry vorticity or amplitude nodes (or phase slips), vortex tori and ring dark solitons (RDSs) are generated, featuring another type of the self-similar evolution, with an exponentially shrinking vortex core or notch of the RDS. Numerical and analytical considerations reveal that these self-similar structures are robust entit…
Self-organization of cavity solitons in Brillouin-Kerr ring resonators
研究揭示了在双共振环形谐振器中，受激布里渊散射与时间腔soliton的相互作用如何自发形成稳定的晶格结构，推动了混合布里渊-凯尔光学频率梳的理解。
Superluminal k-gap solitons in nonlinear photonic time-crystals
本文提出非线性光子时间晶体中动量间隙内的超光速孤子，其源于无限群速度模式，并通过截断种子验证其超光速传播不违反爱因斯坦因果性。
We design a plasmonic fiber waveguide (PFW) composed of coaxial cylindrical metal-dielectric multilayers in nanoscale, and constitute the corresponding dynamical equations describing the modes of propagation in the PFW with the Kerr nonlinearity in the dielectric layers. The physics is connected to the discrete matrix nonlinear Schrödinger equations, from which the highly confined ring-like solitons in scale of subwavelength are found both for the visible light and the near-infrared light in the self-defocusing condition. Moreover, the confinement could be further improved when increasing the …
We introduce novel optical solitons that consist of a periodic and a spatially localized components coupled nonlinearly via cross-phase modulation. The spatially localized optical field can be treated as a gap soliton supported by the optically-induced nonlinear grating. We find different types of these band-gap composite solitons and demonstrate their dynamical stability.
We address the impact of asymmetric nonlocal diffusion nonlinearity on the properties of gap solitons supported by photorefractive crystal with an imprinted optical lattice. We reveal how the asymmetric nonlocal response alters the domains of existence and the stability of solitons originating from different gaps. We find that in such media gap solitons cease to exist above a threshold of the nonlocality degree. We discuss how the interplay between nonlocality and lattice strength modifies the gap soliton mobility.
Frequency combs have become a prominent research area in optics. Of particular interest as integrated comb technology are chip-scale sources, such as semiconductor lasers and microresonators, which consist of resonators embedding a nonlinear medium either with or without population inversion. Such active and passive cavities were so far treated distinctly. Here we propose a formal unification by introducing a general equation that describes both types of cavities. The equation also captures the physics of a hybrid device - a semiconductor ring laser with an external optical drive - in which we…
Nonlinear Kerr micro-resonators have enabled fundamental breakthroughs in the understanding of dissipative solitons, as well as in their application to optical frequency comb generation. However, the conversion efficiency of the pump power into a soliton frequency comb typically remains below a few percent. We introduce a hybrid Mach-Zehnder ring resonator geometry, consisting of a micro-ring resonator embedded in an additional cavity with twice the optical path length of the ring. The resulting interferometric back coupling enables to achieve an unprecedented control of the pump depletion: pu…
We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic systems described by the nonlinear Schrodinger equation with a sinusoidal potential, such as photonic crystals, waveguide arrays, optically-induced photonic lattices, and Bose-Einstein condensates loaded onto an optical lattice. We study bifurcations of gap solitons from the band edges of the Floquet-Bloch spectrum, and show that gap solitons can appear near all lower or upper band edges of the spectrum, for focusing or defocusing nonlinearity, respectively. We show that, in general, two types of gap …
Langevin model for soliton molecules in ultrafast fiber ring laser cavity: investigating experimentally the interplay between noise and inertia
提出一种由实验数据构建的简约 Langevin 模型，用于刻画超快光纤环形激光腔中孤子分子演化的确定性、随机特性及噪声与惯性作用。
Quantum Cascade Lasers (QCL) constitute an intriguing opportunity for the production of on-chip optical Dissipative Kerr Solitons (DKS): self-organized optical waves which can travel while preserving their shape thanks to the interplay between Kerr effect and dispersion. Originally demonstrated in passive microresonators, DKS were recently observed in mid-IR ring QCL paving the way for their achievement even at longer wavelengths. To this end we realized defect-less THz ring QCLs featuring anomalous dispersion leveraging on a technological platform based on waveguide planarization. A concentri…
We numerically study the nonlocal gap solitons in parity-time (PT) symmetric optical lattices built into a nonlocal self-focusing medium. We state the existence, stability, and propagation dynamics of such PT gap solitons in detail. Simulated results show that there exist stable gap soltions. The influences of the degree of nonlocality on the soliton power, the energy flow density and the stable region of the PT gap solitons are also examined.
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