A. Szameit, Yaroslav V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, V. A. Vysloukh, L. Torner
We report the observation of surface solitons in chirped semi-infinite waveguide arrays whose waveguides exhibit exponentially decreasing refractive indices. We show that the power threshold for surface wave formation decreases with an increase of the array chirp and that for sufficiently large chirp values linear surface modes are supported.
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We address soliton formation at the edge of chirped optical lattices imprinted in Kerr-type nonlinear media. We find families of power thresholdless surface waves that do not exist at other types of lattice interfaces. Such solitons form due to combined action of internal reflection at the interface, distributed Bragg-type reflection, and focusing nonlinearity. Remarkably, we discover that surfaces of chirped lattices are soliton attractors: Below an energy threshold, solitons launched well within the lattice self-bend toward the interface, and then stick to it.
Approximate analytical chirped solitary pulse (chirped dissipative soliton) solutions of the one-dimensional complex cubic-quintic nonlinear Ginzburg-Landau equation are obtained. These solutions are stable and highly-accurate under condition of domination of a normal dispersion over a spectral dissipation. The parametric space of the solitons is three-dimensional, that makes theirs to be easily traceable within a whole range of the equation parameters. Scaling properties of the chirped dissipative solitons are highly interesting for applications in the field of high-energy ultrafast laser phy…
We study optical solitons in chirped periodic optical lattices whose amplitude or frequency changes in the transverse direction. We discover that soliton propagation in such lattices can be accompanied by the progressive self-bending of the soliton trajectory, and we show that the soliton bending rate and output position can be controlled by varying the lattice depth, as well as the chirp amplitude and frequency modulation rate. This effect has potential applications for controllable soliton steering and routing.
Temporal solitons in driven microresonator, fiber-resonator, and bulk enhancement cavities enable attractive optical sources for spectroscopy, communications, and metrology. Here we present theoretical and experimental observations of a new class of temporal optical soliton characterized by pulses with large and positive chirp in normal dispersion resonators with strong spectral filtering. Numerical simulations reveal stable waveforms over a wide new range of parameters including highly chirped pulses at large drive powers. Chirped temporal solitons matching predictions are observed in experim…
We propose a method to efficiently pump an excited mode of a multimode optical waveguide starting from a fundamental-mode input by combining Stark-Chirped Rapid Adiabatic Passage (SCRAP) and Supersymmetry (SUSY) transformations. In a two-waveguide set, we implement SCRAP by modulating the core refractive index of one waveguide, which is evanescently coupled to its SUSY partner. SCRAP provides an efficient transfer of light intensity between the modes of different waveguides, while SUSY allows to control which modes are supported. Using both techniques allows to achieve fidelities above 99% for…
The analytical theory of chirped dissipative soliton solutions of nonlinear complex Ginzburg-Landau equation is exposed. Obtained approximate solutions are easily traceable within an extremely broad range of the equation parameters and allow a clear physical interpretation as a representation of the strongly chirped pulses in mode-locked both solid-state and fiber oscillators. Scaling properties of such pulses demonstrate a feasibility of sub-mJ pulse generation in the continuous-wave mode-locking regime directly from an oscillator operating at the MHz repetition rate.
We present a series of chirp-free and chirped analytical nonautonomous soliton solutions to the generalized nonlinear Schrodinger equation (NLSE) with distributed coefficients by Darboux transformation from a trivial seed. For chirpfree nonautonomous soliton, the dispersion management term can change the motion of nonautonomous soliton and do not affect its shape at all. Especially,the classical optical soliton can be presented with variable dispersion term and nonlinearity when there is no gain. For chirped nonautonomous soliton, dispersion management can affect the shape and motion of nonaut…
An all optical soliton diode (AOSD) is proposed based on a sandwich nonlinear Bragg-grating structure: a linearly chirped Bragg-grating linked to a uniform Bragg-grating and again to a chirped Bragg-grating. The nonreciprocity is achieved by introducing two spatially asymmetric chirped Bragg-gratings with optical nonlinearity. High transmission ratio up to 150 is obtained when launching a picosecond Gaussian pulse into the setting. We find that such pulses in a form of solitons propagate at a rather small velocity ($<0.03c$) when pulse wavelength is selected in the vicinity of photonic bandgap…
A comprehensive study on beam dynamics inside symmetrically chirped waveguide array mimicking the graded index media
本文研究对称啁啾波导阵列中的束流动力学，提出实用结构，通过半解析变分方法分析，发现其类似梯度折射率介质，高斯光束呈振荡轨迹，非线性下形成离散孤子。
We theoretically and numerically investigate the evolution of discrete soliton in a 1D linearly chirped nonlinear waveguide array (WA). The discrete soliton is self-accelerated inside the transversely chirped WA and emits a \textit{dynamic diffractive resonant radiation} (DifRR). The radiation appears when soliton wave-number matched with linear radiation wave. Unlike uniform WA, the DifRR can be excited even for zero wave-number of input soliton when the waveguide channels are chirped. The transverse modulation due to chirp conceptually imposes a linear potential which acts as a perturbation …
We show that chirped metal-dielectric waveguide arrays with focusing cubic nonlinearity can support plasmonic lattice solitons that undergo self-deflection in the transverse plane. Such lattice solitons are deeply-subwavelength self-sustained excitations, although they cover several periods of the array. Upon propagation,the excitations accelerate in the transverse plane and follow trajectories curved in the direction in which the separation between neighboring metallic layers decreases, a phenomenon that yields considerable deflection angles. The deflection angle can be controlled by varying …
We demonstrate protected single-soliton formation and operation in a Kerr microresonator using a phase-modulated pump laser. Phase modulation gives rise to spatially varying effective loss and detuning parameters, which in turn lead to an operation regime in which multi-soliton degeneracy is lifted and a single soliton is the only observable behavior. Direct excitation of single solitons is indicated by observed reversal of the characteristic 'soliton step.' Phase modulation also enables precise control of the soliton pulse train's properties, and measured dynamics agree closely with simulatio…
Chirped pulse waveguide amplifier
本文提出一种单模Cr:ZnS晶体波导超快放大器，利用超快激光写入的凹陷包层波导实现5.5 dB/cm增益和2.35 W平均输出功率，并通过解析模型优化设计，在CPA装置中验证了宽带高增益放大性能。
Segment-chirped periodically poled lithium niobate waveguides for broadband supercontinuum generation
本文提出分段啁啾周期性极化铌酸锂纳米光子波导，通过离散化啁啾极化分布实现高保真铁电畴反转和宽带准相位匹配，实验上产生了覆盖三个光学倍频程（320-2600 nm）的光谱平坦超连续谱。
Strongly chirped dissipative solitons in normal and anomalous dispersion regimes
研究立方-五次复Ginzburg-Landau方程在正常和异常色散中的强啁啾耗散孤子，通过稳态相位近似推导出解析谱并构建主图，揭示控制参数比与缩放孤子能量的关系，发现正常色散中耗散孤子共振受可接受性约束，而异常色散中需强饱和五次自相位调制。
Adiabatic Theory Data on Strongly Chirped Dissipative Solitons of the Cubic-Quintic Nonlinear Ginzburg-Landau Equation
该数据文章提供复现强啁啾耗散孤子主图、谱、相干性和稳定性图所需的数据集、推导和脚本，涵盖正常与反常色散区。
We observe clamping of the output spatial light distribution of a waveguide array. Using a chirped pulse amplifier we reach peak intensities in the waveguides of ~24 GW/cm2. At this level, three photon absorption in the AlGaAs material clamps the discrete spatial soliton to a set distribution. Further increase in intensity does not change the distribution.
Broadband Quantum Photon Source in Step-Chirped Periodically Poled Lithium Niobate Waveguide
本文设计制备6.82 mm阶梯啁啾CPPLN波导，利用宽带准相位匹配实现高效SHG与带宽达99 THz的SPDC宽带光子对产生。
The nonlinear pulse propagation in an optical fibers with varying parameters is investigated. The capture of moving in the frequency domain femtosecond colored soliton by a dispersive trap formed in an amplifying fiber makes it possible to accumulate an additional energy and to reduce significantly the soliton pulse duration. Nonlinear dynamics of the chirped soliton pulses in the dispersion managed systems is also investigated. The methodology developed does provide a systematic way to generate infinite ``ocean'' of the chirped soliton solutions of the nonlinear Schrödinger equation (NSE) wit…
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.
The perturbations of chirped dissipative solitons are analyzed in the spectral domain. It is shown, that the structure of the perturbed chirped dissipative soliton is highly nontrivial and has a tendency to an enhancement of the spectral perturbations especially at the spectrum edges, where the irregularities develop. Even spectrally localized perturbations spread over a whole soliton spectrum. As a result of spectral irregularity, the chaotic dynamics develops due to the spectral loss action. In particular, the dissipative soliton can become fragmented though remains localized.
Energy Scalability Limits of Dissipative Solitons
本研究通过热力学方法揭示了耗散孤子能量缩放的主要限制，识别了耗散孤子共振的三个特征，并将破裂归因于相关尺度解耦、熵增和负温度相变，理论与实验吻合，为优化高能飞秒脉冲产生提供指导。
We demonstrate that an array of discrete waveguides on a slab substrate, both featuring the $χ^{2}$ nonlinearity, supports stable solitons composed of discrete and continuous components. Two classes of fundamental composite solitons are identified: ones consisting of a discrete fundamental-frequency (FF) component in the waveguide array, coupled to a continuous second-harmonic (SH) component in the slab waveguide, and solitons with an inverted FF/SH structure. Twisted bound states of the fundamental solitons are found too. In contrast with usual systems, the \emph{intersite-centered} fundament…
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 study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to a…
We consider light pulses in a circular array of $2N$ coupled nonlinear optical waveguides. The waveguides are either hermitian or alternate gain and loss in a $\mathcal{PT}$-symmetric fashion. Simple patterns in the array include a ring of $2N$ pulses travelling abreast, and a breather -- a string of pulses where all even and all odd waveguides flash in turn. In addition, the structure displays solitons gyrating around the necklace by switching from one waveguide to the next. Some of the gyrating solitons are stable while other ones are weakly unstable and evolve into gyrating multiflash strin…
We address surface soliton complexes formed at the edge of annular guiding structures containing several concentric rings. Such soliton complexes feature a -phase difference between neighboring spots. It is shown that the multipole-mode solitons can rotate steadily upon propagation, and the existence domain is strongly affected by the rotation frequency. The rotation may enhance the stabilization of surface multipole-mode solitons.
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.
We reveal and observe experimentally significant modifications undertaken by discrete solitons in waveguide lattices upon the continuous transformation of the lattice structure from one-dimensional to two-dimensional. Light evolution and soliton excitation in arrays with a gradually increasing number of rows are investigated, yielding solitons with an effective reduced dimensionality residing at the edge and in the bulk of the lattice.
Conservation equations for the mass, linear momentum and energy densities of solitons propagating in finite, infinite and periodic, nonlinear, planar waveguides and governed by the nonlinear Schrödinger equation are derived. These conservation equations are used to determine classical force densities which are compared with those derived by drawing a quantum mechanics analogy between the propagation of solitons and the motion of a quantum particle in a nonlinear potential well.
We analyze the dynamics of dissipative solitons in silicon on insulator waveguides embedded in a gain medium. The optical propagation is modeled through a cubic Ginzburg-Landau equation for the field envelope coupled with an ordinary differential equation accounting for the generation of free carriers owing to two-photon absorption. Our numerical simulations clearly indicate that dissipative solitons accelerate due to the carrier-induced index change and experience a considerable blue-shift, which is mainly hampered by the gain dispersion of the active material. Numerical results are fully exp…
Stable high-charge vortex dissipative solitons in azimuthally modulated waveguide arrays with localized gain
研究发现，在具有局部增益的 azimuthally 调制波导阵列中，高电荷涡旋孤子可通过低功率阈值稳定存在，且传播稳定性优于低电荷状态。
We explore the possibility to excite the so-called embedded solitons in specially designed slot waveguides based on silicon and silica or silicon nanocrystals. This requires the excitation of the structure with quasi-TM polarized pulses -- for which Raman effect is absent -- and at a specific infrared wavelength for which only the second- and fourth-order group velocity coefficients are non-vanishing. Pulses launched in these conditions will generate a spectrally localized continuum, associated to a frequency comb coming from the spectral interference of many embedded solitons.
The forces acting on and the energies of solitons governed by the nonlinear Schrödinger equation in finite, planar waveguides with periodic and with homogeneous Dirichlet, Neumann and Robin boundary conditions are determined by means of a quantum analogy. It is shown that these densities have S-shape profiles and increase as the hardness of the boundary conditions is increased.
Topological solitons in coupled Su-Schrieffer-Heeger waveguide arrays
研究了耦合SSH波导阵列边缘多极拓扑孤子的形成，发现波导间距的独立变化会产生不同对称性的边缘态，并在非线性下形成多极拓扑边缘孤子族，丰富了稳定拓扑孤子的多样性。
Dissipative spatiotemporal soliton in a driven waveguide laser
本文提出通过泵浦光空间整形在波导激光器中产生耗散时空孤子，并利用慢时间调制结合动态增益饱和实现宽参数范围稳定，且该方法可类比推广至弱耗散玻色-爱因斯坦凝聚体的稳定。
We analyse Raman-induced self-frequency shift in two-component solitons supported by both quadratic and cubic nonlinearities. Treating Raman terms as a perturbation, we derive expressions for soliton velocity and frequency shifts of the fundamental frequency and second harmonic soliton components. We find these predictions compare well with simulations of soliton propagation. We also show that Raman shift can cause two-component solitons to approach the boundary of their own existence and subsequently trigger soliton instabilities. In some cases these instabilities are accompanied by an almost…
We study the influences to the discrete soliton (DS) by introducing linearly long-range nonlocal interactions, which give rise to the off-diagonal elements of the linearly coupled matrix in the discrete nonlinear schrodinger equation to be filled by non-zero terms. Theoretical analysis and numerical simulations find that the DS under this circumstance can exhibit strong digital effects: the fundamental DS is a narrow one, which occupies nearly only one waveguide, the dipole and double-monopole solitons, which occupy two waveguides, can be found in self-focusing and -defocusing nonlinearities, …
We develop a method for achieving scalable transmission stabilization and switching of $N$ colliding soliton sequences in optical waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss. We show that dynamics of soliton amplitudes in $N$-sequence transmission is described by a generalized $N$-dimensional predator-prey model. Stability and bifurcation analysis for the predator-prey model are used to obtain simple conditions on the physical parameters for robust transmission stabilization as well as on-off and off-on switching of $M$ out of $N$ soliton sequences. Nume…
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 address the formation of \{chi}(2) topological edge solitons emerging in topologically nontrivial phase in Su-Schrieffer-Heeger (SSH) waveguide arrays. We consider edge solitons, whose fundamental frequency (FF) component belongs to the topological gap, while phase mismatch determines whether second harmonic (SH) component falls into topological or trivial forbidden gaps of the spectrum for SH wave. Two representative types of edge solitons are found, one of which is thresholdless and bifurcates from topological edge state in FF component, while other exists above power threshold and emanat…
We present a design and protocol to achieve an essential feature of an optical transistor, namely the amplification of input signal with the use of discrete solitons in waveguide arrays. We consider the scattering of a discrete soliton by a reflectionless potential in the presence of a control soliton. We show that at the sharp transition region between full reflectance and full transmittance, the intensity of the reflected or transmitted soliton is highly sensitive to the intensity of the control soliton. This suggests a setup of signal amplifier. For realistic purposes, we modulate the param…
A blazed chirped Bragg grating in a planar silica waveguide device was used to create an integrated diffractive element for a spectrometer. The grating diffracts light from a waveguide and creates a wavelength dependent focus in a manner similar to a bulk diffraction grating spectrometer. An external imaging system is used to analyse the light, later device iterations plan to integrate detectors to make a fully integrated spectrometer. Devices were fabricated with grating period chirp rates in excess of 100nm/mm, achieving a focal length of 5.5mm. Correction of coma aberrations resulted in a d…
We report on the experimental observation of two-dimensional surface waves localized at the edge or in the corner of femtosecond laser-written waveguide arrays in fused silica. Increasing the power of the input beam allows one to observe a clear transition from a linear diffraction pattern to localized nonlinear surface states, which can exist at the interface only above a certain power threshold.
We study analytically and numerically a kind of diffractive resonant radiation emitted by spatial solitons, which is generated in waveguide arrays with Kerr nonlinearity. The phase matching condition between soliton and radiation is derived and agrees well with direct pulse propagation simulations. The folded dispersion due to the Brillouin zone leads to a peculiar anomalous soliton recoil that we describe in detail. A linear potential applied across the array generates the analogue of the Raman self-frequency shift in optical fibers, only now applied to the wavenumber. We demonstrate that it …
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…
We report a detailed study on soliton steering dynamics in a parity-time-symmetric directional coupler in the femtosecond domain, which requires incorporation of higher-order perturbative effects such as third-order and fourth-order dispersions, self-steepening, and intrapulse Raman scattering. With a high gain/loss, the combination of all these effects is found to stabilize the soliton pulse evolution in the coupler from the chaotic behavior of unperturbed evolution. This work demonstrates that efficient soliton steering can be achieved at very low critical power and a relatively higher gain/…
We construct dark solitons in the recently introduced model of the nonlinear dual-core coupler with the mutually balanced gain and loss applied to the two cores, which is a realization of parity-time symmetry in nonlinear optics. The main issue is stability of the dark solitons. The modulational stability of the CW (continuous-wave) background, which supports the dark solitons, is studied analytically, and the full stability is investigated in a numerical form, via computation of eigenvalues for modes of small perturbations. Stability regions are thus identified in the parameter space of the s…
We study transmission stabilization against radiation emission in soliton-based nonlinear optical waveguides with weak linear gain-loss, cubic loss, and delayed Raman response. We show by numerical simulations with perturbed nonlinear Schrödinger propagation models that transmission quality in waveguides with frequency independent linear gain and cubic loss is not improved by the presence of delayed Raman response due to the lack of an efficient mechanism for suppression of radiation emission. In contrast, we find that the presence of delayed Raman response leads to significant enhancement of …
We consider the process of low-power light scattering by optical solitons in a slab waveguide with homogeneous and inhomogeneous refractive index core. We observe resonant reflection (Fano resonance) as well as resonant transmission of light by optical solitons at certain incident angles. The resonance position can be controlled experimentally by changing the soliton intensity and the relative frequency detuning between the soliton and the probe light beams.
We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable nonlinearity. The saturability allows the existence of breathers with high power. Three main regimes are observed: breather fusion, breather reflection and breather creation. The last regime seems to be exclusive of systems with a saturable nonlinearity, and has been previously observed in continuous models. In some cases a ``symmetry breaking'' can be observed, which we show to be an numerical artifact.
$π$-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。
This paper deals with the temporal nonlinear dynamics of plasmon-solitons in a plasmonic waveguide. Duffing equation is recognized as the temporal part of the nonlinear amplitude equation governing the plasmonic waveguide. It is shown that Duffing oscillator waveforms stand for the temporal nonlinear dynamics of plasmon-soliton waves. The exchange of Lorentz-type bright and dark solitons energies gives rise to a Fano resonance. It is thus shown that the interaction of solitons and the formation of plasmon-solitons is inherently nonlinear. It is accordingly indicated that the nonlinear modulati…
By means of a systematic numerical analysis, we demonstrate that hexagonal lattices of parallel linearly-coupled waveguides, with the intrinsic cubic self-focusing nonlinearity, give rise to three species of stable semi-discrete complexes (which are continuous in the longitudinal direction), with embedded vorticity S: triangular modes with S=1, hexagonal ones with S=2, both centered around an empty central core, and compact triangles with S=1, which do not not include the empty site. Collisions between stable triangular vortices are studied too. These waveguiding lattices can be realized in op…
Radiation families emitted by a discrete soliton in parity-time-symmetric waveguide arrays
本研究探究了宇称-时间对称波导阵列中离散孤子的辐射动力学，揭示了多种新型辐射的起源，建立了相位匹配条件，通过线性哈密顿分析确定相变区域，提出的理论与数值结果高度吻合。
We investigate the ultrafast nonlinear dynamics of light emitted in an active plasmonic waveguide composed of a thin film of gold sandwiched by two silicon layers immersed in externally pumped Al$_2$O$_3$:Er$^{3+}$. We model optical propagation in such a dissipative system through a generalized cubic Ginzburg-Landau equation accounting for the amplification of the active medium and the effect of absorption and thermo-modulational nonlinearity of gold. We find that heating heavily affects the propagation of temporal dissipative solitons in such a plasmonic waveguide by producing a soliton self-…
We study transmission stability and dynamics of pulse amplitudes in $N$-channel soliton-based optical waveguide systems, taking into account second-order dispersion, Kerr nonlinearity, delayed Raman response, and frequency dependent linear gain-loss. We carry out numerical simulations with systems of $N$ coupled nonlinear Schrödinger (NLS) equations and compare the results with the predictions of a simplified predator-prey model for Raman-induced amplitude dynamics. Coupled-NLS simulations for single-fiber transmission with $2 \le N \le 4$ frequency channels show stable oscillatory dynamics of…
Dynamics of localized solutions in three core coupled waveguides with quasi-periodic nonlinearity
本文研究具有准周期非线性的三个耦合波导系统中的孤子动力学，分析不同调制参数下孤子的演化与行为，揭示其复杂特性，为非线性光学和光子器件应用奠定基础。
We study light propagation in waveguide arrays made in Kerr nonlinear media with a transverse refractive index gradient, and we find that the presence of the refractive index gradient leads to the appearance of a number of new soliton families. The effective coupling between the solitons and the localized linear eigenmodes of the lattice induces a drastic asymmetry in the soliton shapes and the appearance of long tails at the soliton wings. Such unusual solitons are found to be completely stable under propagation, and we report their experimental observation in fs-laser written waveguide array…
We present a model of soliton propagation in waveguides with quadratic nonlinearity. Criteria for solitons to exist in such waveguides are developed and two example nano-waveguide structures are simulated as proof of concept. Interactions between quadratic solitons and dispersive waves are analysed giving predictions closely matching soliton propagation simulations. The example structures are found to support five different regimes of soliton and quasi-soliton existence. Pulse propagation in these example waveguides has been simulated confirming the possibility of soliton generation at experim…
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