Rodrigo A. Vicencio, Mario I. Molina, Yuri S. Kivshar
We suggest an effective method for controlling nonlinear switching in arrays of weakly coupled optical waveguides. We demonstrate the digitized switching of a narrow input beam for up to eleven waveguides in the engineered waveguide arrays.
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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…
We demonstrate ultrafast all-optical deflection of spatial solitons in an AlGaAs slab waveguide using 190 fs, 1550 nm pulses which are used to generate and deflect the spatial soliton. The steering beam is focused onto the top of the waveguide near the soliton pathway and the soliton is steered due to refractive index changes induced by optical Kerr, or free carrier (Drude) effects. Angular deflections up to 8 mR are observed.
Optical soliton pulses offer many applications within optical communication systems, but by definition a soliton is only subjected to second-order anomalous group-velocity-dispersion; an understanding of higher-order dispersion is necessary for practical implementation of soliton pulses. A numerical model of a waveguide was developed using the Nonlinear Schrodinger Equation, with parameters set to ensure the input pulse energy would be equal to the fundamental soliton energy. Higher-order group-velocity-dispersion was gradually increased, for various temporal widths and waveguide dispersions. …
We investigate numerically light propagation in a single spiral waveguide formed in a nonlinear photorefractive medium for a low spatial frequency of the waveguide rotation. We present the general procedure for finding solitonic solutions in spiral waveguiding structures, as well as the variational approach to calculate soliton parameters analytically. Solitons supported by the spiral waveguide perform robust stable rotational oscillatory motion, with the period predicted by their static characteristics, without any signatures of wave radiation or soliton decay over many rotation periods and d…
We present a design and protocol to add binary numbers using discrete solitons in waveguide arrays. We show that the nonlinear interaction between discrete solitons in waveguide arrays can be exploited to design half and full adders. By modulating the separation between waveguides and introducing control solitons, we achieve the performance of an XOR gate. We construct the half and full adders using the XOR gate together with the previously-designed OR and AND gates. To facilitate the experimental realization, we calculate the profile of separations between the waveguides that will lead to the…
We demonstrate soliton-effect pulse compression in mm-long photonic crystal waveguides resulting from strong anomalous dispersion and self-phase modulation. Compression from 3ps to 580fs, at low pulse energies(~10pJ), is measured via autocorrelation.
An effort was conducted to numerically determine, using the Nonlinear Schrodinger Split-Step Fourier method, if using cross phase modulation could cause temporal soliton pulse propagation in a silicon slow-light photonic crystal waveguide shorter than a millimeter. The simulations demonstrated that due to the higher powers and shorter scales of photonic crystals, two-photon absorption would cause an optical soliton pulse to be extremely dissipative. The model demonstrated, however, that by utilizing cross-phase modulation, it is possible to sustain a compressed soliton pulse within a silicon p…
We propose a novel method based on the so-called shortcut to adiabatic passage techniques to achieve fast compression of temporal solitons in a nonlinear waveguide. We demonstrate that soliton compression could be achieved, in principle, at an arbitrarily small distance by inverse engineering the pulse width and the nonlinearity of the medium. The proposed scheme could possibly be exploited for various short-distance communication protocols and may be even in nonlinear guided wave-optics devices and generation of ultrashort soliton pulses.
We construct families of optical semi-discrete composite solitons (SDCSs), with one or two independent propagation constants, supported by a planar slab waveguide, XPM-coupled to a periodic array of stripes. Both structures feature the cubic nonlinearity and support intrinsic modes with mutually orthogonal polarizations. We report three species of SDCSs, odd, even, and twisted ones, the first type being stable. Transverse motion of phase-tilted solitons, with potential applications to beam steering, is considered too.
Supercontinuum generation in Kerr media has become a staple of nonlinear optics. It has been celebrated for advancing the understanding of soliton propagation as well as its many applications in a broad range of fields. Coherent spectral broadening of laser light is now commonly performed in laboratories and used in commercial white light sources. The prospect of miniaturizing the technology is currently driving experiments in different integrated platforms such as semiconductor on insulator waveguides. Central to the spectral broadening is the concept of higher-order soliton fission. While wi…
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…
We theoretically investigate light propagation in two periodically modulated nonlinear waveguides with certain propagation constant detuning between two guides. By slowly varying the amplitude of modulation, we can steer the light to the desired output waveguide when equal amounts of lights are launched into each waveguide. We also reveal that the light propagation dynamics depends sensitively on the detuning between two guides. Our findings can be explained qualitatively by means of adiabatic navigation of the extended nonlinear Floquet states.
We have studied harmonic oscillations in an elliptical optical waveguide array in which the coupling between neighboring waveguides is varied in accord with a Kac matrix so that the propagation constant eigenvalues can take equally spaced values. As a result, long-living Bloch oscillation (BO) and dipole oscillation (DO) are obtained when a linear gradient in the propagation constant is applied. Moreover, we achieve a switching from DO to BO or vice versa by ramping up the gradient profile. The various optical oscillations as well as their switching are investigated by field evolution analysis…
Switching of a single photon interacting with two Λ-type three-level quantum dots embedded in cavities coupled to one-dimensional waveguide is investigated theoretically via the real-space approach. We demonstrated that switching of a single photon can be achieved by tuning the classic driving field on or off, and by controlling the QD-cavity coupling strength, Rabi frequency and the cavity-waveguide coupling rate. The transmission properties of a single photon by such a nanosystem discussed here could find the applications in the design of next-generation quantum devices and quantum informati…
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 study propagation of light in nonlinear diffraction-managed photonic lattices created with arrays of periodically-curved coupled optical waveguides which were fabricated using femtosecond laser writing in silica glass, and titanium indiffusion in LiNbO3 crystals. We identify different regimes of the nonlinear propagation of light beams depending on the input power, and present the first experimental observation of diffraction-managed solitons, which are formed as a result of the interplay between the engineered beam diffraction and nonlinear self-focusing or defocusing. We observe that in s…
We demonstrate the potential of birefringence-based, all-optical, ultrafast conversion between the transverse modes in integrated optical waveguides by modelling the conversion process by numerically solving the multi-mode coupled nonlinear Schroedinger equations. The observed conversion is induced by a control beam and due to the Kerr effect, resulting in a transient index grating which coherently scatters probe light from one transverse waveguide mode into another. We introduce birefringent phase matching to enable efficient all-optically induced mode conversion at different wavelengths of t…
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.
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 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…
Achieving ultrafast all-optical switching in a silicon waveguide geometry is a key milestone on the way to an integrated platform capable of handling the increasing demands for higher speed and higher capacity for information transfer. Given the weak electro-optic and thermo-optic effects in silicon, there has been intense interest in hybrid structures in which that switching could be accomplished by integrating another material into the waveguide, including the phase-changing material, vanadium dioxide (VO2). It has long been known that the phase transition in VO2 can be triggered by ultrafas…
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 analyze the resonant linear and nonlinear transmission through a photonic crystal waveguide side-coupled to a Kerr-nonlinear photonic crystal resonator. Firstly, we extend the standard coupled-mode theory analysis to photonic crystal structures and obtain explicit analytical expressions for the bistability thresholds and transmission coefficients which provide the basis for a detailed understanding of the possibilities associated with these structures. Next, we discuss limitations of standard coupled-mode theory and present an alternative analytical approach based on the effective discrete …
We study the quantum properties of light propagating through an array of coupled nonlinear waveguides and forming a discrete soliton. We demonstrate that it is possible to use certain types of quasi-solitons to form continuous variables entanglement between the certain pair of waveguides. This entanglement generation process occurs even with a very large number of photons in the laser field used, so it does not require a special material with an extremely high nonlinearity coefficient. Also absorption in the waveguide media does not influence it too much.
Dissipative Kerr solitons (DKSs) in the high-Q micro-resonator corresponds to self-organized short pulse in time domain via double balance between dispersion and Kerr nonlinearity, as well as cavity loss and parametric gain. In this paper, we first experimentally demonstrate deterministic generation and switching of DKSs in a thermally controlled micro-ring resonator based on high-index doped silica glass platform. In our scheme, an auxiliary laser is introduced to timely balance the intra-cavity heat fluctuation. By decreasing the operating temperature through a thermo-electric cooler, solito…
Generation of strongly localized skin solitons in non-Hermitian waveguide arrays with the Kerr effect
研究非互易耦合的非线性光学波导阵列中两种孤子传播问题，发现非厄米皮肤效应加速宽孤子向边界传播并导致强局域化，同时识别了非线性体模和近边皮肤孤子。
The dispersion relations for surface plasmon-polaritons propagating in the Voigt geometry in a metal-insulator-metal waveguide with a magneto-optically active dielectric medium are derived. The symmetry between the upper and lower interfaces is broken by the introduction of the magnetic field; the balance between the field distributions on the two interfaces can be controlled by the applied field. This control is illustrated by finite-element method numerical simulations of the field distributions around a point dipole placed in the centre of the short waveguide; it is shown that both the tota…
We study the coupling between photonic molecules and waveguides in photonic crystal slab structures using finite-difference time-domain method and coupled mode theory. In a photonic molecule with two cavities, the coupling of cavity modes results in two super-modes with symmetric and anti-symmetric field distributions. When two super-modes are excited simultaneously, the energy of electric field oscillates between the two cavities. To excite and probe the energy oscillation, we integrate photonic molecule with two photonic crystal waveguides. In coupled structure, we find that the quality fact…
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 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.
We propose a type of all-optical switch which consists of two periodically curved nonlinear optical waveguides placed in parallel. Compared to the all-optical switch based on the traditional nonlinear directional coupler with straight waveguides, this all-optical switch has much lower switching threshold power and sharper switching width.
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.
We use the generalized Lugiato-Lefever model to investigate the phenomenon of Kerr optical frequency comb generation when group-velocity dispersion is null. In that case, the first dispersion term that plays a leading role is third-order dispersion. We show that this term is sufficient to allow for the existence of both bright and dark solitons. We identify the areas in the parameter space where both kind of solitons can be excited inside the resonator. We also unveil a phenomenon of hysteretic switching between these two types of solitons when the power of the pump laser is cyclically varied.
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 present a two-waveguide coupler which, realizes complete achromatic all-optical switching. The coupling of the waveguides has a hyperbolic-secant shape while the phase mismatch has a sign flip at the maximum of the coupling. We derive an analytic solution for the electric field propagation using coupled mode theory and show that the light switching is robust again small-to-moderate variations in the coupling and phase mismatch. Thus, we realize an achromatic light switching between the two waveguides. We further consider the extended case of three coupled waveguides in an array and pay spec…
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…
Nonlinear optical switching in hybrid plasmonic waveguides
研究基于ITO在ENZ状态下巨大非线性的HPWG全光开关机制，数值求解非线性Maxwell方程并对比电门控，发现光泵浦更高效且透射率与相位呈阶跃式变化。
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 address azimuthally modulated Bessel optical lattices imprinted in focusing cubic Kerr-type nonlinear media, and reveal that such lattices support different types of stable solitons, whose complexity increases with growth of lattice order. We reveal that the azimuthally modulated lattices cause single solitons launched tangentially to the guiding rings to jump along consecutive sites of the optical lattice. The position of the output channel can be varied by small changes of the launching angle.
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.
We investigate the exceptional points (EPs) in a non-Hermitian system composed of a pair of graphene sheets with different losses. There are two surface plasmon polaritons (SPP) modes in the graphene waveguide. By varying the distance between two graphene sheets and chemical potential of graphene, the EPs appear as the eigenvalues, that is, the wave vectors of the two modes coalesce. The cross conversion of eigenmodes and variation of geometric phase can be observed by encircling the EP in the parametric space formed by the geometric parameters and chemical potential of graphene. At the same t…
We introduce a new coupled mode theory to model nonlinear Schrödinger equations for contra- propagating Bloch modes that include disorder-induced multiple scattering effects on nonlinear soliton propagation in photonic crystal waveguides. We also derive sub unit-cell coupling coefficients and use these to introduce a generalized length scale associated with each coupling effect. In particular, we define a multiple-scattering length scale that quantifies the spatial extent of a disorder- induced cavity mode. Our numerical simulations of nonlinear pulse propagation are in excellent qualitative a…
The Ginzburg-Landau (GL) equation is in general not integrable by the inverse scattering method and support solitary-wave solution, called dissipative soliton (DS). We numerically demonstrate that, a DS can radiate dispersive waves (DWs) in presence of third-order dispersion (TOD). We propose a silicon-based active waveguide that excites stable DSs. Energy can be transferred from these stable DS to linear DWs when a resonance condition is achieved. The dynamics of the DS is governed by the complex GL equation which we solve numerically for different operational parameters. Numerical solution o…
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 experimentally investigate a nonlinear switching mechanism in a dual-core highly nonlinear optical fiber. We focus the input beam of femtosecond pulses on one core only, to identify transitions between inter-core oscillations, self-trapping in the cross core, and self-trapping of the pulse in the straight core. A model based in the system of coupled nonlinear Schrodinger equations provides surprisingly good agreement with the experimental findings.
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 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 develop a method for transmission stabilization and robust dynamic switching for colliding optical soliton sequences in broadband waveguide systems with nonlinear gain and loss. The method is based on employing hybrid waveguides, consisting of spans with linear gain and cubic loss, and spans with linear loss, cubic gain, and quintic loss. We show that amplitude dynamics is described by a hybrid Lotka-Volterra (LV) model, and use the model to determine the physical parameter values required for enhanced transmission stabilization and switching. Numerical simulations with the coupled nonlinea…
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…
Switching of a single plasmon interacting with equally spaced quantum dots coupled to one-dimensional surface plasmonic waveguide is investigated theoretically via the real-space approach. We showed that the transmission and reflection of a single plasmon can be switched on or off by dynamically tuning and changing the number of the equal transition frequencies of the quantum dots.
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…
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