Nonlinear symmetry breaking induced by third-order dispersion in optical fiber cavities

Impact of third-order dispersion on the dynamics of dissipative solitons in an ultrafast fiber laser

Dissipative solitons (DSs), due to the complex interplay among dispersion, nonlinear, gain and loss, illustrate abundant nonlinear dynamics behaviors. Especially, dispersion plays an important role in the research of DS dynamics in ultrafast fiber lasers. Previous studies have mainly focused on the effect of even-order dispersion, i.e., group velocity dispersion (GVD) and fourth-order dispersion. In fact, odd-order dispersions, such as third-order dispersion (TOD), also significantly influences the dynamics of DSs. However, due to the lack of dispersion engineering tools, few experimental researches in this domain have been reported. In this work, by employing a pulse shaper in ultrafast fiber laser, an in-depth exploration of the DS dynamics influenced by TOD was conducted. With the increase of TOD value, the stable single DS undergoes a splitting into two solitons and then enters explosion state, and ultimately evolves into a chaotic state. The laser operation state is correlated to dispersion profile, which could be controlled by TOD. Here, the positive dispersion at long-wavelength side will be gradually shifted to negative dispersion by increasing the TOD, where soliton effect will drive the transitions. These findings offer valuable insights into the nonlinear dynamics of ultrafast lasers and may also foster applications involving higher-order dispersion.

Multi-frequency radiation of dissipative solitons in optical fiber cavities

New resonant emission of dispersive waves by oscillating solitary structures in optical fiber cavities is considered analytically and numerically. The pulse propagation is described in the framework of the Lugiato-Lefever equation when a Hopf-bifurcation can result in the formation of oscillating dissipative solitons. The resonance condition for the radiation of the dissipative oscillating solitons is derived and it is demonstrated that the predicted resonances match the spectral lines observed in numerical simulations perfectly. The complex recoil of the radiation on the soliton dynamics is discussed. The reported effect can have importance for the generation of frequency combs in nonlinear microring resonators.

Gain-through-filtering enables tuneable frequency comb generation in passive optical resonators

Optical frequency combs (OFCs), consisting of a set of phase-locked, equally spaced laser frequency lines, have enabled a great leap in precision spectroscopy and metrology since seminal works of Hänsch et al. Nowadays, OFCs are cornerstones of a wealth of further applications ranging from chemistry and biology to astrophysics and including molecular fingerprinting and light detection and ranging (LIDAR) systems, among others. Driven passive optical resonators constitute the ideal platform for OFC generation in terms of compactness and low energy footprint. We propose here a technique for the generation of OFCs with a tuneable repetition rate in externally driven optical resonators based on the gain-through-filtering process, a simple and elegant method, due to asymmetric spectral filtering on one side of the pump wave. We demonstrate a proof-of-concept experimental result in a fibre resonator, pioneering a new technique that does not require specific engineering of the resonator dispersion to generate frequency-agile OFCs.

Third Order Dispersion in Time-Delayed Systems

Time-delayed dynamical systems materialize in situations where distant, pointwise, nonlinear nodes exchange information that propagates at a finite speed. However, they are considered devoid of dispersive effects, which are known to play a leading role in pattern formation and wave dynamics. We show how dispersion may appear naturally in delayed systems and we exemplify our result by studying theoretically and experimentally the influence of third order dispersion in a system composed of coupled optical microcavities. Dispersion-induced pulse satellites emerge asymmetrically and destabilize the mode-locking regime.

Influences of high-order dispersion on temporal and spectral properties of microcavity solitons

We theoretically and numerically investigate the effects of high-order dispersion (HOD) on microcavity solitons, both in time and frequency domain with an extended normalized Lugiato-Lefever equation (LLE). The observed temporal drift of bright and dark solitons is shown to originate from high-odd-order dispersion, while the sign determines the direction of soliton movement and the amplitude decides the drift speed. HOD can also be introduced to stabilize the breathing bright and dark cavity solitons. In spectral domain, the nonlinear symmetry breaking is mainly introduced by third-order dispersion, whereas both third- and fourth-order dispersion can introduce dispersive wave accompanied by soliton tail oscillation. This work could give insight for exploring detailed intracavity pulse dynamics and spectral characteristics of Kerr combs influenced by HOD, as well as provide a viable route to delicate control of Kerr comb generation through tailoring the dispersion parameters.

Modulation instability in the weak normal dispersion region of passive fiber ring cavities

We report the experimental observation of modulation instability in the weak normal dispersion region of a passive fiber ring cavity. We show that the fourth-order dispersion strongly modifies the dynamics of the cavity through the generation of new instability bands. Experimental results are in excellent agreement with theoretical predictions and numerical simulations.

Kerr frequency combs and triangular spectra

Nonlinear externally driven optical cavities are known to generate periodic patterns. They grow from the linearly unstable background states due to modulation instability. These periodic solutions are also known as Kerr frequency combs, which have a variety of applications in metrology. The stationary state of periodic wave trains can be explained theoretically only in weakly nonlinear regimes near the onset of the instability using the order parameter description. However, in both weakly and strongly nonlinear dissipative regimes, only numerical solutions can be found. No analytic solutions are known so far except for the homogeneous continuous wave solution. Here, we derive an analytical expression for the intracavity fully nonlinear dissipative periodic wave train profiles that provides good agreement with the results of numerical simulations. Our approach is based on empirical knowledge of the triangular shape of the frequency comb spectrum.

Modulation instability in the weak dispersion regime of a dispersion modulated passive fiber-ring cavity

We present a theoretical and experimental study of the modulation instability process in a dispersion oscillating passive fiber-ring resonator in the low dispersion region. Generally, the modulation of the dispersion along the cavity length is responsible for the emergence of a regime characterised by multiple parametric resonances (or Faraday instabilities). We show that, under weak dispersion conditions, a huge number of Faraday sidebands can grow under the influence of fourth order dispersion. We specifically designed a piecewise uniform fiber-ring cavity and report on experiments that confirm our theoretical predictions. We recorded the dynamics of this system revealing strong interactions between the different sidebands in agreement with numerical simulations.

Coherent and incoherent seeding of dissipative modulation instability in a nonlinear fiber ring cavity

We investigate the coherent or incoherent seeding of dissipative modulation instability (MI) in a nonlinear fiber ring cavity. By varying wavelength and degree of coherence of the seed signal across the MI gain band, we observe a strong sensitivity of the resulting MI sidebands in terms of bandwidth and amplification. Both spectral and temporal characterizations are performed to reveal intensity coherence properties (over a single round-trip) of the generated temporal patterns. Experimental observations are well confirmed by numerical simulations. Our results provide new insights into the control of dissipative MI through a specific seeding in optical resonators with a moderate free-spectral range. In particular, a large tunability of the subsequent Kerr comb spacing is achieved by means of the early transient stage of seeded MI growth.

Parametric instabilities in modulated fiber ring cavities

We investigate modulational instability in inhomogeneous passive cavities modeled by the Ikeda map. The cavity boundary conditions and the modulation of the fiber dispersion force the system to develop parametric instabilities, which lead to the generation of simple, as well as period-doubled, temporal patterns. The analytical results obtained by means of the Floquet theory are validated through numerical solution of the Ikeda map, and the limitations of the mean-field Lugiato-Lefever model are highlighted.

Competing Turing and Faraday Instabilities in Longitudinally Modulated Passive Resonators

We experimentally investigate the interplay of Turing (modulational) and Faraday (parametric) instabilities in a bistable passive nonlinear resonator. The Faraday branch is induced via parametric resonance owing to a periodic modulation of the resonator dispersion. We show that the bistable switching dynamics is dramatically affected by the competition between the two instability mechanisms, which dictates two completely novel scenarios. At low detunings from resonance, switching occurs between the stable stationary lower branch and the Faraday-unstable upper branch, whereas at high detunings we observe the crossover between the Turing and Faraday periodic structures. The results are well explained in terms of the universal Lugiato-Lefever model.

Dynamics of Localized Structures in Systems with Broken Parity Symmetry

A great variety of nonlinear dissipative systems are known to host structures having a correlation range much shorter than the size of the system. The dynamics of these localized structures (LSs) has been investigated so far in situations featuring parity symmetry. In this Letter we extend this analysis to systems lacking this property. We show that the LS drifting speed in a parameter varying landscape is not simply proportional to the parameter gradient, as found in parity preserving situations. The symmetry breaking implies a new contribution to the velocity field which is a function of the parameter value, thus leading to a new paradigm for LSs manipulation. We illustrate this general concept by studying the trajectories of the LSs found in a passively mode-locked laser operated in the localization regime. Moreover, the lack of parity affects significantly LSs interactions which are governed by asymmetrical repulsive forces.

Observation of dispersive wave emission by temporal cavity solitons

We examine a coherently-driven, dispersion-managed, passive Kerr fiber ring resonator and report, to the best of our knowledge, the first direct experimental observation of dispersive wave emission by temporal cavity solitons (CSs). Our observations are in excellent agreement with analytical predictions and they are fully corroborated by numerical simulations. These results lead to a better understanding of the behavior of temporal CSs under conditions where higher-order dispersion plays a significant role. Significantly, since temporal CSs manifest themselves in monolithic microresonators, our results are likely to explain the origins of spectral features observed in broadband Kerr frequency combs.

Dispersive radiation induced by shock waves in passive resonators

We show that passive Kerr resonators pumped close to zero dispersion wavelengths on the normal dispersion side can develop the resonant generation of linear waves driven by cavity (mixed dispersive-dissipative) shock waves. The resonance mechanism can be successfully described in the framework of the generalized Lugiato-Lefever equation with higher-order dispersive terms. Substantial differences with radiation from cavity solitons and purely dispersive shock waves dispersion are highlighted.

Modulational instability in dispersion oscillating fiber ring cavities

We show that the use of a dispersion oscillating fiber in passive cavities significantly extends the modulational instability to novel high-frequency bands, which also destabilizes the branches of the steady response that are stable with homogeneous dispersion. By means of Floquet theory, we obtain the exact explicit expression for the sideband gain, and a simple analytical estimate for the frequencies of the maximum gain. Numerical simulations show that stable stationary trains of pulses can be excited in the cavity.

Experimental observation of the spontaneous breaking of the time-reversal symmetry in a synchronously pumped passive Kerr resonator

We experimentally observe a spontaneous temporal symmetry breaking instability in a coherently driven passive optical Kerr resonator. Using a time-symmetric configuration, we report output pulses with strongly asymmetric temporal and spectral intensity profiles, with up to 71% of the energy on the same side of the pump center frequency. The instability occurs above a certain pump power threshold but remarkably vanishes above a second threshold, in excellent agreement with theory. We also observe a generalized bistability in which an asymmetric output state coexists with a symmetric one in the same pumping conditions.

Third-order chromatic dispersion stabilizes Kerr frequency combs

Using numerical simulations of an extended Lugiato-Lefever equation we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber resonators, taking into account third-order dispersion effects. We show that cavity solitons underlying Kerr frequency combs, normally sensitive to oscillatory and chaotic instabilities, are stabilized in a wide range of parameter space by third-order dispersion. Moreover, we demonstrate how the snaking structure organizing compound states of multiple cavity solitons is qualitatively changed by third-order dispersion, promoting an increased stability of Kerr combs underlined by a single cavity soliton.

Dispersive wave-breaking in coherently driven passive cavities

We show that the intracavity field evolving in an externally driven passive Kerr resonator subject to weak normal dispersion undergoes wave-breaking, thus forming dispersive shock waves. At variance with the cavity-less propagation, such dispersive wave-breaking turns out to be strongly favored by cavity bistability and coexisting modulational instability.

Multistability and spontaneous breaking in pulse-shape symmetry in fiber ring cavities

We describe the spatio-temporal evolution of ultrashort pulses propagating in a fiber ring cavity using an extension of the Lugiato-Lefever model. The model predicts the appearance of multistability and spontaneous symmetry breaking in temporal pulse shape. We also use a hydrodynamical approach to explain the stability of the observed regimes of asymmetry.

Soliton families and resonant radiation in a micro-ring resonator near zero group-velocity dispersion

We report theoretical and numerical study of the dynamical and spectral properties of the conservative and dissipative solitons in micro-ring resonators pumped in a proximity of the zero of the group velocity dispersion. We discuss frequency and velocity locking of the conservative solitons, when dissipation is accounted for. We present theory of the dispersive radiation emitted by such solitons, report their Hopf instability and radiation enhancement by multiple solitons.

Coherence properties of Kerr frequency combs

We use numerical simulations based on an extended Lugiato-Lefever equation (LLE) to investigate the stability properties of Kerr frequency combs generated in microresonators. In particular, we show that an ensemble average calculated over sequences of output fields separated by a fixed number of resonator roundtrips allows the coherence of Kerr combs to be quantified in terms of the complex degree of first-order coherence. We identify different regimes of comb coherence, linked to the solutions of the LLE. Our approach provides a practical and unambiguous way of assessing the stability of Kerr combs that is directly connected to an accessible experimental quantity.

Universal scaling laws of Kerr frequency combs

Using the known solutions of the Lugiato-Lefever equation, we derive universal trends of Kerr frequency combs. In particular, normalized properties of temporal cavity soliton solutions lead us to a simple analytic estimate of the maximum attainable bandwidth for given pump resonator parameters. The result is validated via comparison with past experiments encompassing a diverse range of resonator configurations and parameters.