Temporal Dissipative Solitons Research Articles

Discovery of dissipative microwave photonic soliton molecules in dual-bandpass optoelectronic oscillator

Optoelectronic oscillators (OEOs), which have attracted extensive studies in the past decades, are high quality-factor optoelectronic feedback loops for generating various ultra-pure microwave signals. In essence, OEOs are also dissipative nonlinear systems with multiple timescale characteristics and abundant nonlinearities, which open the possibilities for exploring localized dissipative solitary waves. In this paper, we demonstrate a new-class temporal dissipative soliton, i.e., dissipative microwave photonic soliton molecule (DMPSM), in a dual-bandpass OEO. Both the numerical simulation and experiment are conducted to reveal the physical mechanism of DMPSM generation and to evaluate the characteristics of the generated DMPSM sequences. Unlike optical soliton molecules in mode-locked lasers, the formation of DMPSMs arises from the combined action of multiple timescale coupling, nonlinear bistability, and time-delayed feedback in the OEO cavity, where the soliton interval and number in a DMPSM can be well-controlled through varying the multiple timescale variables in the OEO cavity, and the repetition frequency of the DMPSMs can be tuned through changing that of the initially injected perturbation signal. Meanwhile, the generated DMPSM sequence performs with high stability and excellent coherence, which shows enormous application potentials in pulse radar detection, dense microwave comb generation, and neuromorphology.

Intrinsic polarization conversion and avoided-mode crossing in X-cut lithium niobate microrings

Compared with well-developed free space polarization converters, polarization conversion between TE and TM modes in the waveguide is generally considered to be caused by shape birefringence, like curvature, morphology of waveguide cross section and scattering. Here, we study the polarization conversion mechanism in 1-THz-FSR X-cut lithium niobate microrings with multiple-resonance condition, that is the conversion can be implemented by birefringence of waveguides, which will also introduce an avoided-mode crossing. In the experiment, we find that this mode crossing results in severe suppression of one sideband in local nondegenerate four-wave mixing and disrupts the cascaded four-wave mixing on this side. Simultaneously, we propose one two-dimensional method to simulate the eigenmodes (TE and TM) in X-cut microrings, and the mode crossing point. This work will provide one approach to the design of polarization converters and simulation for monolithic photonics integrated circuits, and may be helpful to the studies of missed temporal dissipative soliton formation in X-cut lithium niobate rings.

Dissipative soliton molecules in active random metamaterials

Self-organization of radiation in random media is a key to controlling the optical energy flow and constitutes the basis of innovative cavity-free laser designs. Here, we theoretically demonstrate the existence of robust temporal dissipative soliton molecules in a graphene-based active disordered metamaterial. We observe that localized pulses with single and multiple peaks can coexist inside this metamaterial for a wide range of gain parameters, thereby exhibiting optical bistability. We further investigate the stability of such bound states under perturbation by analyzing their interaction force, finding stable tri-soliton molecule states with a periodically oscillating relative phase and a stable bi-soliton molecule. Our results offer a paradigm for mode-locking in active random metamaterials and pave the way for versatile applications such as multilevel encoding in optical communications, future designs of low-cost cavity-free lasers, and optical amplifiers.

Universal dynamics and deterministic motion control of decoherently seeded temporal dissipative solitons via spectral filtering effect

Temporal dissipative solitons have been widely studied in optical systems, which exhibit various localized structures and rich dynamics, and have shown great potential in applications including optical encoding and sensing. Yet, most of the soliton states, as well as the switching dynamics amongst, were fractionally captured or via self-evolution of the system, lacking of control on the soliton motion. While soliton motion control has been widely investigated in coherently seeded optical cavities, such as microresonator-based dissipative solitons, its implementation in decoherently seeded systems, typically the soliton mode-locked lasers, remains an outstanding challenge. Here, we report the universal dynamics and deterministic motion control of temporal dissipative solitons in a mode-locked fibre laser by introducing a scanned spectral filtering effect. We investigate rich switching dynamics corresponding to both the assembly and the disassembly of solitons, revealing a complete and reversible motion from chaotic states to soliton and soliton-molecule states. Significant hysteresis has been recognized in between the redshift and blueshift scan of the motorized optical filter, unveiling the nature of having state bifurcations in dissipative and nonlinear systems. The active soliton motion control enabled by filter scanning highlights the potential prospects of encoding and sensing using soliton molecules.

Pulse-adding of temporal dissipative solitons: resonant homoclinic points and the orbit flip of case B with delay

We numerically investigate the branching of temporally localised, two-pulse solutions from one-pulse periodic solutions with non-oscillating tails in delay differential equations (DDEs) with large delay. Solutions of this type are commonly referred to as temporal dissipative solitons (TDSs) (Yanchuk et al 2019 Phys. Rev. Lett. 123 53901) in applications, and we adopt this term here. We show by means of a prototypical example that—analogous to travelling pulses in reaction–diffusion partial differential equations (Yanagida 1987 J. Differ. Equ. 66 243–62)—the branching of two-pulse TDSs from one-pulse TDSs with non-oscillating tails is organised by codimension-two homoclinic bifurcation points of a real saddle equilibrium (Homburg and Sandstede 2010 Handbook of Dynamical Systems Elsevier) in a corresponding profile equation. We consider a generalisation of Sandstede’s model (Sandstede 1997 J. Dyn. Differ. Equ. 9 269–88) (a prototypical model for studying codimension-two homoclinic bifurcation points in ordinary differential equations) with an additional time-shift parameter, and use Auto07p (Doedel 1981 Congr. Numer. 30 265–84; Doedel and Oldeman 2010 AUTO-07P: Continuation and Bifurcation Software for Ordinary Differential Equations Concordia University) and DDE-BIFTOOL (Sieber et al 2014 arXiv:1406.7144) to compute numerically the unfolding of these bifurcation points in the resulting DDE. We then interpret this model as the profile equation for TDSs in a DDE with large delay by exploiting the reappearance of periodic solutions in DDEs (Yanchuk and Perlikowski 2009 Phys. Rev. E 79 046221). In doing so, we identify both the non-orientable resonant homoclinic bifurcation and the orbit flip bifurcation of case B as organising centres for the existence of two-pulse TDSs in the DDE with large delay. We study the bifurcation curves emanating from these codimension-two points beyond a local neighbourhood in parameter space. In this way, we are able to discuss how folds of homoclinic bifurcations in an extended system bound the existence region of TDSs in the DDE with large delay. We also discuss the relation between a reduced multivalued-map (in the limit of infinite delay) and the existence of TDSs.

Dissipative solitons characterization in singly resonant optical parametric oscillators: A variational formalism

In this work, the emergence of single-peak temporal dissipative solitons in singly-resonant degenerate optical parametric oscillators is investigated analytically. Applying the Kantarovitch optimization method, through a Lagrangian variational formalism, an approximate analytical soliton solution is computed using a parameter-dependent ansatz. This permits to obtain analytical estimations for the DS energy, peak power, and boundaries of the DS existence region, which are of great value for experimentalist. To confirm the validity of this procedure, these analytical results are compared with a numerical study performed in the context of pure quadratic systems, showing a good agreement.

All-step-index-fiber spatiotemporally mode-locked laser

Spatiotemporal mode-locking (STML) in multi-mode fiber (MMF) lasers has extended the concept of temporal dissipative solitons into spatiotemporal dissipative solitons. To date, all reported STML in MMF lasers has used graded-index (GRIN) MMFs either solely or hybridly with other fibers. Compared to GRIN MMFs, step-index (STIN) MMFs have much larger intermode dispersion on both group and phase velocities. Building all-STIN MMF lasers can provide a new platform to explore the spatiotemporal dissipative soliton dynamics. Here, we report experimental and numerical observation of STML in an all-STIN MMF laser. Distinct from GRIN MMF lasers, the large intermode dispersion in the all-STIN MMF laser cannot be balanced by Kerr nonlinearity, and significant walk-off between mode-resolved pulses was observed experimentally. Simulations suggest that this walk-off is counteracted by spatial coupling in the laser, and a mother–child coupling mechanism is proposed to understand it. This mother–child coupling can enable STML with a single repetition rate with infinitely large intermode dispersion. Our work enriches MMF laser architectures for STML in a parameter regime that has not been considered, to our knowledge.

Temporal dissipative solitons in the Morris-Lecar model with time-delayed feedback.

We study the dynamics and bifurcations of temporal dissipative solitons in an excitable system under time-delayed feedback. As a prototypical model displaying different types of excitability, we use the Morris-Lecar model. In the limit of large delay, soliton like solutions of delay-differential equations can be treated as homoclinic solutions of an equation with an advanced argument. Based on this, we use concepts of classical homoclinic bifurcation theory to study different types of pulse solutions and to explain their dependence on the system parameters. In particular, we show how a homoclinic orbit flip of a single-pulse soliton leads to the destabilization of equidistant multi-pulse solutions and to the emergence of stable pulse packages. It turns out that this transition is induced by a heteroclinic orbit flip in the system without feedback, which is related to the excitability properties of the Morris-Lecar model.

Temporal dissipative structures in optical Kerr resonators with transient loss fluctuation.

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, their operation is limited to the red-detuned regime. Here, we demonstrate an emergent dissipative soliton state in optical nonlinear cavities in the presence of loss fluctuations, which is accessible by self-evolution of the system on resonance. Based on a modified dissipative and Kerr-nonlinear cavity model, we numerically investigate the effect of the loss modulation on the intracavity field pattern, and in transmission observe a single and bright soliton pulse state at the zero detuning. The effect of the optical saturable absorption is also numerically investigated, which is recognized as an effective approach to the transient loss fluctuation in the cavity. The estimated power efficiency of the resonant bright soliton can be higher than that of the conventional dissipative Kerr soliton, which is determined by the loss modulation depth and the pump intensity. The self-starting soliton state on system's resonance is potentially of wide interest, which physically contributes to insights of the temporal structure formation in dissipative cavities. On application aspect, it may constitute a way to the generation of ultra-fast soliton pulse trains as well as the generation of soliton micro-combs.

The limits of sustained self-excitation and stable periodic pulse trains in the Yamada model with delayed optical feedback.

We consider the Yamada model for an excitable or self-pulsating laser with saturable absorber and study the effects of delayed optical self-feedback in the excitable case. More specifically, we are concerned with the generation of stable periodic pulse trains via repeated self-excitation after passage through the delayed feedback loop and their bifurcations. We show that onset and termination of such pulse trains correspond to the simultaneous bifurcation of countably many fold periodic orbits with infinite period in this delay differential equation. We employ numerical continuation and the concept of reappearance of periodic solutions to show that these bifurcations coincide with codimension-two points along families of connecting orbits and fold periodic orbits in a related advanced differential equation. These points include heteroclinic connections between steady states and homoclinic bifurcations with non-hyperbolic equilibria. Tracking these codimension-two points in parameter space reveals the critical parameter values for the existence of periodic pulse trains. We use the recently developed theory of temporal dissipative solitons to infer necessary conditions for the stability of such pulse trains.

Temporal Dissipative Solitons in Time-Delay Feedback Systems.

Localized states are a universal phenomenon observed in spatially distributed dissipative nonlinear systems. Known as dissipative solitons, autosolitons, and spot or pulse solutions, these states play an important role in data transmission using optical pulses, neural signal propagation, and other processes. While this phenomenon was thoroughly studied in spatially extended systems, temporally localized states are gaining attention only recently, driven primarily by applications from fiber or semiconductor lasers. Here we present a theory for temporal dissipative solitons (TDS) in systems with time-delayed feedback. In particular, we derive a system with an advanced argument, which determines the profile of the TDS. We also provide a complete classification of the spectrum of TDS into interface and pseudocontinuous spectrum. We illustrate our theory with two examples: a generic delayed phase oscillator, which is a reduced model for an injected laser with feedback, and the FitzHugh-Nagumo neuron with delayed feedback. Finally, we discuss possible destabilization mechanisms of TDS and show an example where the TDS delocalizes and its pseudocontinuous spectrum develops a modulational instability.

Heat-induced soliton self-frequency redshift in the ultrafast nonlinear dynamics of active plasmonic waveguides

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-frequency redshift accompanied by soliton deceleration in the time domain. By adopting a semi-analytical variational approach, we evaluate the dependence of the self-induced redshift by deriving a set of coupled differential equations for the pulse parameters. These equations provide physical insight into the complex nonlinear dynamics through simple approximate analytic expressions for temporal and frequency shifts. Such analytical predictions are found in excellent agreement with direct numerical simulations of the generalized cubic Ginzburg-Landau equation. Our results provide a general understanding of ultrafast nonlinear dynamics in gold-based active plasmonic waveguides, as in particular the spectral shaping properties of propagating optical pulses.

Temporal solitons in free-space femtosecond enhancement cavities

Temporal dissipative solitons in nonlinear optical resonators are self-compressed, self-stabilizing and indefinitely circulating wave packets. Owing to these properties, they have been harnessed for the generation of ultrashort pulses and frequency combs in active and passive laser architectures, including mode-locked lasers1–4, passive fibre resonators5 and microresonators6–11. Here, we demonstrate the formation of temporal dissipative solitons in a free-space enhancement cavity with a Kerr nonlinearity and a spectrally tailored finesse. By locking a 100-MHz-repetition-rate train of 350-fs, 1,035-nm pulses to this cavity-soliton state, we generate a 37-fs sech²-shaped pulse with a peak-power enhancement of 3,200, which exhibits low-frequency intensity-noise suppression. The power scalability unique to free-space cavities, the unprecedented combination of peak-power enhancement and temporal compression, and the cavity-soliton-specific noise filtering attest to the vast potential of this platform of optical solitons for applications including spatiotemporal filtering and compression of ultrashort pulses and cavity-enhanced nonlinear frequency conversion. Temporal dissipative soliton formation in a free-space femtosecond enhancement cavity with a thin Kerr medium is reported. Locking a 350-fs, 1,035-nm pulse train with a repetition rate of 100 MHz to this cavity-soliton state generates a 37-fs sech2-shaped pulse with a peak-power enhancement of 3,200.

Erratum: Temporal dissipative solitons in a three-level atomic medium confined in a photonic-band-gap fiber [Phys. Rev. A91, 013828 (2015)

Received 14 October 2015DOI:https://doi.org/10.1103/PhysRevA.92.049902©2015 American Physical Society

Generation of dissipative temporal solitons in ring self-oscillating systems with amplifier klystrons

Theoretical and experimental results are presented that show the possibility of forming periodic pulsed signal sequences with a profile similar to that of bright solitons in a ring self-oscillating system with an amplifier klystron. The generated pulse sequences are dissipative temporal solitons formed in the ring due to the establishment of balance both between gain and loss and between time dispersion and cubic nonlinearity of the klystron. Analytical solutions have been obtained for a generator model with a two-cavity amplifier klystron and an additional cavity resonator, which confirm the possibility of forming these dissipative structures.

Publisher's Note: Temporal dissipative solitons in a three-level atomic medium confined in a photonic-band-gap fiber [Phys. Rev. A91, 013828 (2015)

Received 22 January 2015DOI:https://doi.org/10.1103/PhysRevA.91.019902©2015 American Physical Society

Temporal dissipative solitons in a three-level atomic medium confined in a photonic-band-gap fiber

We obtained a propagation equation for an optical pulse at an electromagnetically induced transparency window guided on a gas-filled hollow-core photonic crystal fiber. This equation admits dissipative solitons whose analytical expression was also obtained. Depending on the parameter region, they may be stable or unstable. We simulated a typical experimental arrangement and found some cases for which the equation parameters are such that it admits stable solitons.

Mode Spectrum and Temporal Soliton Formation in Optical Microresonators

The formation of temporal dissipative solitons in optical microresonators enables compact, high-repetition rate sources of ultrashort pulses as well as low noise, broadband optical frequency combs with smooth spectral envelopes. Here we study the influence of the microresonator mode spectrum on temporal soliton formation in a crystalline MgF2 microresonator. While an overall anomalous group velocity dispersion is required, it is found that higher order dispersion can be tolerated as long as it does not dominate the resonator's mode structure. Avoided mode crossings induced by linear mode coupling in the resonator mode spectrum are found to prevent soliton formation when affecting resonator modes close to the pump laser frequency. The experimental observations are in excellent agreement with numerical simulations based on the nonlinear coupled mode equations. The presented results provide for the first time design criteria for the generation of temporal solitons in optical microresonators.

Temporal solitons in optical microresonators

Dissipative solitons can emerge in a wide variety of dissipative nonlinear systems throughout the fields of optics, medicine or biology. Dissipative solitons can also exist in Kerr-nonlinear optical resonators and rely on the double balance between parametric gain and resonator loss on the one hand and nonlinearity and diffraction or dispersion on the other hand. Mathematically these solitons are solution to the Lugiato-Lefever equation and exist on top of a continuous wave (cw) background. Here we report the observation of temporal dissipative solitons in a high-Q optical microresonator. The solitons are spontaneously generated when the pump laser is tuned through the effective zero detuning point of a high-Q resonance, leading to an effective red-detuned pumping. Red-detuned pumping marks a fundamentally new operating regime in nonlinear microresonators. While usually unstablethis regime acquires unique stability in the presence of solitons without any active feedback on the system. The number of solitons in the resonator can be controlled via the pump laser detuning and transitions to and between soliton states are associated with discontinuous steps in the resonator transmission. Beyond enabling to study soliton physics such as soliton crystals our observations open the route towards compact, high repetition-rate femto-second sources, where the operating wavelength is not bound to the availability of broadband laser gain media. The single soliton states correspond in the frequency domain to low-noise optical frequency combs with smooth spectral envelopes, critical to applications in broadband spectroscopy, telecommunications, astronomy and low phase-noise microwave generation.

Dissipative solitons in normal-dispersion fiber lasers

Mode-locked fiber lasers in which pulse shaping is based on filtering of a frequency-chirped pulse are analyzed with the cubic-quintic Ginzburg-Landau equation. An exact analytical solution produces a variety of temporal and spectral shapes, which have not been observed in any experimental setting to our knowledge. Experiments agree with the theory over a wide range of parameters. The observed pulses balance gain and loss as well as phase modulations, and thus constitute dissipative temporal solitons. The normal-dispersion fiber laser allows systematic exploration of this class of solitons.