We investigate dissipative nonlinear dynamics in graphene-based active metamaterials composed of randomly dispersed graphene nano-flakes embedded within an externally pumped gain medium. We observe that graphene saturable nonlinearity produces a sub-critical bifurcation of nonlinear modes, enabling self-organization of the emitted radiation into several dissipative soliton structures with distinct topological charges. We systematically investigate the existence domains of such nonlinear waves and their spatio-temporal dynamics, finding that soliton vortices are unstable, thus enabling self-organization into single dissipative structures with vanishing topological charge, independently of the shape of the graphene nano-flakes. Our results shed light on self-organization of coherent radiation structures in disordered systems and are relevant for future cavity-free lasers and amplifier designs.
We predict that nonlinear left-handed metamaterials can support both TE- and TM-polarized self-trapped localized beams, spatial electromagnetic solitons. Such solitons appear as single- and multi-hump beams, being either symmetric or antisymmetric, and they can exist due to the hysteresis-type magnetic nonlinearity and the effective domains of negative magnetic permeability.
Second harmonic generation is considered in lossy negative-index metamaterials. It is shown that energy transfer from fundamental to harmonic takes place in the entire sample for the range of phase mismatch values. Note that in conventional case this range collapses to the point (ideal phase matching). The dependance of the boundary of this range as function of dissipation values is obtained using computer simulations.
Electromagnetic localization and existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band - where the magnetic permeability $μ(ω)$ is positive and the dielectric permittivity $ε(ω)$ is negative - is described by a nonlinear Klein-Gordon equation with a dispersive nonlinear term. A family of standing and moving localized waves for both electric and magnetic fields is found, and the rol…
We analytically investigate transverse magnetic (TM) spatial bright solitons, as exact solutions of Maxwell's equations, propagating through nonlinear metamaterials whose linear dielectric permittivity is very close to zero and whose effective nonlinear Kerr parameters can be tailored to achieve values not available in standard materials. Exploiting the fact that, in the considered medium, linear and nonlinear polarization can be comparable at feasible and realistic optical intensities, we identify two novel self-trapping mechanisms able to support two-peaked and flat-top solitons, respectivel…
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.
We present a stability analysis of a modified nonlinear Schroedinger equation describing the propagation of ultra-short pulses in negative refractive index media. Moreover, using methods of quantum statistics, we derive a kinetic equation for the pulses, making it possible to analyze and describe partial coherence in metamaterials. It is shown that a novel short pulse soliton, which is found analytically, can propagate in the medium.
Stable dissipative solitons are perfect carries of optical information due to remarkable stability of their waveforms that allows the signal transmission with extremely dense soliton packing without loosing the encoded information. Apart of unaffected passing of solitons through a communication network, controllable transformations of soliton waveforms are needed to perform all-optical information processing. In this paper we employ the basic model of dissipative optical solitons in the form of the complex Ginzburg-Landau equation with a potential term to study the interactions between two sta…
Anisotropic homogeneous metamaterials that are neither wholly dissipative nor wholly active at a specific frequency are permitted by classical electromagnetic theory. Well-established homogenization formalisms indicate that such a metamaterial may be realized quite simply as a random mixture of electrically small (possibly nanoscale) spheroidal particles of at least two different isotropic dielectric materials, one of which must be dissipative but the other active. The dielectric properties of this metamaterial are influenced by the volume fraction, spatial distribution, particle shape and siz…
Investigation of internal polarization dynamics of vector dissipative-soliton-resonance (DSR) pulses in a mode-locked fiber laser is presented. Stable vector DSR pulses are experimentally ob- served. Using a waveplate-analyzer configuration, we find that polarization is not uniform across a resonant dissipative soliton. Specifically, although the central plane wave of the resonant dissi- pative soliton acquires nearly a fixed polarization, the fronts feature polarization states that are different and spatially varying. This distinct polarizaiton distribution is maintained while the whole solit…
Vector soliton operation of erbium-doped fiber lasers mode locked with atomic layer graphene was experimentally investigated. Either the polarization rotation or polarization locked vector dissipative solitons were experimentally obtained in a dispersion-managed cavity fiber laser with large net cavity dispersion, while in the anomalous dispersion cavity fiber laser, the phase locked NLSE solitons and induced NLSE soliton were experimentally observed. The vector soliton operation of the fiber lasers unambiguously confirms the polarization insensitive saturable absorption of the atomic layer gr…
This chapter describes the discovery and stable generation of temporal dissipative Kerr solitons in continuous-wave (CW) laser driven optical microresonators. The experimental signatures as well as the temporal and spectral characteristics of this class of bright solitons are discussed. Moreover, analytical and numerical descriptions are presented that do not only reproduce qualitative features but can also be used to accurately model and predict the characteristics of experimental systems. Particular emphasis lies on temporal dissipative Kerr solitons with regard to optical frequency comb gen…
Dissipative solitons are localized solutions in non-integrable and non-conservative nonlinear system, due to a balance of nonlinearity, dispersion, filtering, and loss/gain. Different from conventional soliton, they exhibit extremely complex and striking dynamics, and are more universal in the far-from-equilibrium natural system. Taking advantage of dispersive Fourier transform and time lens, the spatio-temporal transient dynamics of dissipative solitons have been characterized with both amplitude and phase. Yet, a full avenue of the buildup process of dissipative soliton is full of debris for…
Application of stable localized dissipative solitons as basic carriers of information promises the significant progress in the development of new optical communication networks. The success development of such systems requires getting the full control over soliton waveforms. In this paper we use the fundamental model of dissipative solitons in the form of the complex Ginzburg-Landau equation with a potential term to demonstrate controllable transitions between different types of coexisted waveforms of stationary and moving dissipative solitons. Namely, we consider mutual transitions between so…
A theory of self-induced transparency of surface TM-mode propagating along a interface separating conventional and left-handed metamaterials is developed. A transition layer sandwiched between connected media is described using a model of a two-dimensional gas of quantum dots. Explicit analytical expressions for a surface optical soliton in the presence of single and biexciton transitions, depending on the magnetic permeability of the left-handed medium, are obtained with realistic parameters which can be reached in current experiments. It is shown that the sign of the total energy flow the su…
Quantum Thermodynamic Transformation Optics: A Unified Framework for Energy and Entropy with Application to the Casimir Force in Dissipative Metamaterials
We demonstrate an experimental approach to create dissipative solitons in a microcavity laser. In particular, we shape the spatial gain profile of a quasi-one-dimensional microcavity laser with a nonresonant, pulsed optical pump to create spatially localised structures, called gain-pinned dissipative solitons that exist due to the balance of gain and nonlinear losses and are confined to a diffraction-limited volume. The ultrafast formation dynamics and decay of the gain-pinned solitons are probed directly, showing that they are created on a picosecond timescale, orders of magnitude faster than…
We report the existence of stable symmetric vortex-type solutions for two-dimensional nonlinear discrete dissipative systems governed by a cubic-quintic complex Ginzburg-Landau equation. We construct a whole family of vortex solitons with a topological charge S = 1. Surprisingly, the dynamical evolution of unstable solutions of this family does not alter significantly their profile, instead their phase distribution completely changes. They transform into two-charges swirl-vortex solitons. We dynamically excite this novel structure showing its experimental feasibility.
Dissipative solitons are self-localised structures that can persist indefinitely in "open" systems characterised by continual exchange of energy and/or matter with the environment. They play a key role in photonics, underpinning technologies from mode-locked lasers to microresonator optical frequency combs. Here we report on the first experimental observations of spontaneous symmetry breaking of dissipative optical solitons. Our experiments are performed in a passive, coherently driven nonlinear optical ring resonator, where dissipative solitons arise in the form of persisting pulses of light …
The process of soliton Cherenkov radiation (also known as dispersive wave emission) in microresonator frequency combs plays a critical role in generating broadband and coherent microcomb spectra. Here, we report the observation of symmetry breaking in the group velocity of counter-propagating dissipative Kerr solitons, induced by polychromatic soliton Cherenkov radiation. Results show that in the presence of higher-order dispersion, the temporal arrangement of a multi-soliton state affects its group velocity, an effect which originates from the interference between multiple radiative tails emi…
We adopt a variational technique to study the dynamics of perturbed dissipative solitons, whose evolution is governed by a Ginzburg--Landau equation (GLE). As a specific example of such solitons, we consider a silicon-based active waveguide in which free carriers are generated through two-photon absorption. In this case, dissipative solitons are perturbed by physical processes such as third-order dispersion, intrapulse Raman scattering, self-steepening, and free-carrier generation. To solve the variational problem, we adopt the Pereira--Stenflo soliton as an ansatz since this soliton is the ex…
We demonstrate polarization multiplexed dissipative Kerr solitons in an on-chip silicon nitride micro-resonator. In our experiment, TE- and TM-polarized soliton can be individually generated and controlled, thanks to their weak mutual interaction as the result of sufficiently different repetition rates and orthogonal polarization states. Furthermore, we find that TE- and TM-polarized solitons usually exhibit uncorrelated time jitters, therefore the frequency and phase coherence between the polarization multiplexed soliton microcombs change dramatically as a function of pump laser parameters, b…
We propose an electrically tunable graphene-based metamaterial showing a large nonlinear optical response at THz frequencies, which we calculate analytically for the first time to our knowledge and arises from the intraband current. The structure sustains a novel type of stable two-dimensional spatial solitary wave, a relativistic version of the Townes soliton. These results can be also applied to any material exhibiting a conical dispersion with massless Dirac fermions.
We show that the nonlinear polarization dynamics of a vertical-cavity surface-emitting laser placed into an external cavity leads to the formation of temporal vectorial dissipative solitons. These solitons arise as cycles in the polarization orientation, leaving the total intensity constant. When the cavity round-trip is much longer than their duration, several independent solitons as well as bound states (molecules) may be hosted in the cavity. All these solutions coexist together and with the background solution, i.e. the solution with zero soliton. The theoretical proof of localization is g…
Real-time access to the internal ultrafast dynamics of complex dissipative optical systems opens new explorations of pulse-pulse interactions and dynamic patterns. We present the first direct experimental evidence of the internal motion of a dissipative optical soliton molecule generated in a passively modelocked erbium-doped fiber laser. We map the internal motions of a soliton pair molecule by using a dispersive Fourier-transform imaging technique, revealing different categories of internal pulsations, including vibration-like and phase drifting dynamics. Our experiments agree well with nume…
We experimentally observe soliton self-organization and pulsation in a passively mode-locked fiber laser. The optomechanical interaction in the optical fiber is key to the formation of equidistant soliton bunches. These solitons simultaneously undergo a pulsation process with a period corresponding to tens of the cavity round trip time. Using the dispersive Fourier transformation technique, we find that the Kelly sidebands in the shot-to-shot spectra appear periodically, synchronizing with the pulsation.
We predict the existence of a novel class of multidimensional light localizations in out-of-equilibrium ferroelectric crystals. In two dimensions, the non-diffracting beams form at arbitrary low power level and propagate even when their width is well below the optical wavelength. In three dimensions, a novel form of subwavelength light bullets is found. The effects emerge when compositionally disordered crystals are brought to their metastable glassy state, and can have a profound impact on super-resolved imaging and ultra-dense optical storage, while resembling many features of the so-called …
Dissipative structures are the result of spontaneous symmetry breaking in a dynamic open system, which is induced by either the nonlinear effect or loss fluctuations. While optical temporal dissipative solitons in nonlinear Kerr cavities has been widely studied, they are operated in a red-detuned regime that is non-trivial to access. Here, we demonstrate an emergent dissipative soliton state in optical cavities in the presence of loss fluctuations, which is accessible by self-evolution of the system and is operated in resonance. We numerically investigate both the effect of loss modulation and…
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…
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…
High-Q silicon nitride (SiN) microresonators enable optical Kerr frequency comb generation on a photonic chip and have recently been shown to support fully coherent combs based on temporal dissipative Kerr soliton formation. For bright soliton formation it is necessary to operate SiN waveguides in the multimode regime so as to produce anomalous group velocity dispersion. This can lead to local disturbances of the dispersion due to avoided crossings caused by coupling between different mode families, and therefore prevent the soliton formation. Here we demonstrate that a single mode "filtering"…
Temporal-dissipative Kerr solitons are self-localized light pulses sustained in driven nonlinear optical resonators. Their realization in microresonators has enabled compact sources of coherent optical frequency combs as well as the study of dissipative solitons. A key parameter of their dynamics is the effective-detuning of the pump laser to the thermally- and Kerr-shifted cavity resonance. Together with the free spectral range and dispersion, it governs the soliton-pulse duration, as predicted by an approximate analytical solution of the Lugiato-Lefever equation. Yet, a precise experimental …
Dissipative solitons are self-localized structures resulting from a double balance between dispersion and nonlinearity as well as dissipation and a driving force. They occur in a wide variety of fields ranging from optics, hydrodynamics to chemistry and biology. Recently, significant interest has focused on their temporal realization in driven optical microresonators, known as dissipative Kerr solitons. They provide access to coherent, chip-scale optical frequency combs, which have already been employed in optical metrology, data communication and spectroscopy. Such Kerr resonator systems can …
Starting from the Maxwell equations, we used the reductive perturbation method to derive a system of two coupled nonlinear Schrödinger (NLS) equations for the two Beltrami components of the electromagnetic field propagating along a fixed direction in an isotropic nonlinear chiral metamaterial. With single-resonance Lorentz models for the permittivity and permeability and a Condon model for the chirality parameter, in certain spectral regimes, one of the two Beltrami components exhibits a negative real refractive index when nonlinearity is ignored and the chirality parameter is sufficiently lar…
We study the propagation of few-cycle pulses in two-component medium consisting of nonlinear amplifying and absorbing two-level centers embedded into a linear and conductive host material. First we present a linear theory of propagation of short pulses in a purely conductive material, and demonstrate the diffusive behavior for the evolution of the low-frequency components of the magnetic field in the case of relatively strong conductivity. Then, numerical simulations carried out in the frame of the full nonlinear theory involving the Maxwell-Drude-Bloch model reveal the stable creation and pro…
We demonstrate self-started unidirectional dissipative soliton operation and noise-like pulse operation in an all-normal-dispersion bidirectional Yb-doped fiber laser mode-locked by nonlinear polarization rotation. The laser works unidirectional once mode locking was achieved due to the cavity directional nonlinearity asymmetry along with the nonlinear polarization rotation mode locking mechanism.
Dissipative Kerr solitons have recently been generated in optical microresonators, enabling ultrashort optical pulses at microwave repetition rates, that constitute coherent and numerically predictable Kerr frequency combs. However, the seeding and excitation of the temporal solitons is associated with changes in the intracavity power, that can lead to large thermal resonance shifts during the excitation process and render the soliton states in most commonly used resonator platforms short lived. Here we describe a "power kicking" method to overcome this instability by modulating the power of t…
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…
Dissipative Kerr cavity solitons are pulses of light that can persist in coherently driven nonlinear optical resonators. They have attracted significant attention over the past decade due to their rich nonlinear dynamics and key role in the generation of coherent microresonator optical frequency combs. Whilst the vast majority of implementations have relied on \emph{homogeneous} continuous wave driving, the soliton's "plasticity" combined with \emph{inhomogeneous} driving offers attractive advantages for a host of applications. Here we review recent studies into the dynamics and applications o…
Evolution of dissipative-soliton-resonance (DSR) pulses in an all-normal-dispersion fiber laser with pump power under various operation conditions are experimentally studied. The fiber laser is mode-locked by using a nonlinear fiber loop mirror. Apart from the typical pulse broadening due to the peak power clamping effect, pulse breaking was observed. In addition, pulse narrowing with pump power increasing was observed. All the incompatible evolution of DSR pulses could be attributed to the multiple parameters change due to pump power increasing under specific operation conditions.
This work models the propagation of an optical pulse in a 4-level atomic system in the electromagnetic induced transparency regime. By demonstrating that linear and nonlinear optical properties can be externally controlled and tailored by a continuous-wave control laser beam and an assisting incoherent pump field, it is shown how these media can provide an excellent framework to experimentally explore pulse dynamics in the presence of non-conservative terms, either gain or loss. Furthermore, we explore the existence of stable dissipative soliton solutions, testing the analytical results with c…
We demonstrate stable microresonator Kerr soliton frequency combs in a III-V platform (AlGaAs on SiO$_2$) through quenching of thermorefractive effects by cryogenic cooling to temperatures between 4~K and 20~K. This cooling reduces the resonator's thermorefractive coefficient, whose room-temperature value is an order of magnitude larger than that of other microcomb platforms like Si$_3$N$_4$, SiO$_2$, and AlN, by more than two orders of magnitude, and makes soliton states adiabatically accessible. Realizing such phase-stable soliton operation is critical for applications that fully exploit the…
Dissipative temporal Kerr solitons in optical microresonators enable to convert a continuous wave laser into a train of femtosecond pulses. Of particular interest are single soliton states, whose $\mathrm{sech}^{2}$ spectral envelope provides a spectrally smooth and low noise optical frequency comb, and that recently have been generated in crystalline, silica, and silicon-nitride resonators. Here, we study the dynamics of multiple soliton states containing ${N}$ solitons and report the discovery of a novel, yet simple mechanism which makes it possible to reduce deterministically the number of …
We report results of the study of solitons in a system of two nonlinear-Schrodinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials(MMs). The same model applies to photonic crystals (PCs), as well as to ordinary optical fibers, close to the zero-dispersion point. A peculiarity of the system is a small positive or negative value of the relative group-velocity dispersion (GVD) coefficient in one equation, assuming that the dispersion is anomalous in the other. In contrast to earlier studied systems of nonlinearly coupled NLS equations…
Optical frequency comb, with precisely controlled spectral lines spanning a broad range, has been the key enabling technology for many scientific breakthroughs. In addition to the traditional implementation based on modelocked lasers, photonic frequency microcombs based on dissipative Kerr and quadratic cavity solitons in high-Q microresonators have become invaluable in applications requiring compact footprint, low cost, good energy efficiency, large comb spacing, and access to nonconventional spectral regions. In this review, we comprehensively examine the recent progress of photonic frequenc…
We explore the dynamical response of dissipative Kerr solitons to changes in pump power and detuning and show how thermal and nonlinear processes couple these parameters to the frequency-comb degrees of freedom. Our experiments are enabled by a Pound-Drever-Hall (PDH) stabilization approach that provides on-demand, radiofrequency control of the frequency comb. PDH locking not only guides Kerr-soliton formation from a cold microresonator, but opens a path to decouple the repetition and carrier-envelope-offset frequencies. In particular, we demonstrate phase stabilization of both Kerr-comb degre…
We present results on the dynamics of split-ring dimers having both gain and loss in one dimensional nonlinear parity-time- (PT-)symmetric magnetic metamaterials. For the longwave (continuum) limit approximation and in the weakly nonlinear limit, we show analytic results on the existence of gap soliton solutions and on symmetry breaking phenomenon at a critical value of the gain/loss term.
Dissipative solitons are non-dispersive localized waves that exhibit intriguing dynamics. In optical systems, the discovery of new soliton dynamics and how to accurately manipulate dissipative solitons are still largely unexplored and challenging in the ultrafast fiber laser community. Herein, we unveil a new type of dissipative soliton behavior in a net-normal-dispersion bidirectional ultrafast fiber laser. That is, the bidirectional dissipative solitons will always reveal similar spectral and temporal characteristics through common gain and loss modulation, even if the transient instability …
We numerically investigate the formation of soliton pairs (bound states) in mode-locked fiber ring lasers. In the distributed model (complex cubic-quintic Ginzburg-Landau equation) we observe a discrete family of soliton pairs with equidistantly increasing peak separation. This family was identified by two alternative numerical schemes and the bound state instability was disclosed by a linear stability analysis. Moreover, similar families of unstable bound state solutions have been found in a more realistic lumped laser model with an idealized saturable absorber (instantaneous response). We sh…
We theoretically study the nature of parametrically driven dissipative Kerr soliton (PD-DKS) in a doubly resonant degenerate micro-optical parametric oscillator (DR-DμOPO) with the cooperation of \c{hi}(2) and \c{hi}(3) nonlinearities. Lifting the assumption of close-to-zero group velocity mismatch (GVM) that requires extensive dispersion engineering, we show that there is a threshold GVM above which single PD-DKS in DR-DμOPO can be generated deterministically. We find that the exact PD-DKS generation dynamics can be divided into two distinctive regimes depending on the phase matching conditio…
