Temporal Solitons Research Articles

Evolution characteristics of generalized Hermite-cosine-Gaussian solitons in optical nonlinear medium with spatial nonlocality

The evolution characteristics of Hermite-cosine-Gaussian beams in optical nonlinear medium with spatial nonlocality are investigated theoretically in detail. We obtain a series of analytical expressions to describe the evolution characteristics of Hermite-cosine-Gaussian beams in nonlocal medium, such as the expressions of the evolutionary propagation, the beam spot size, the statistical wavefront curvature, the critical energy etc. The results show that the statistical spot size of Hermite-cosine-Gaussian beam can remain unchanged or change periodically according to different initial incident energy. However, the transverse intensity mode of Hermite-cosine-Gaussian beam always presents periodic transformation. This is consistent with high-order temporal solitons, so the evolution of Hermite-cosine-Gaussian beams can also be called generalized solitons or breathers. The influences of initial incident energy and cosine parameters on the evolution characteristics of Hermite-cosine-Gaussian beams are analyzed in detail. Through numerical simulation, some typical evolution characteristics are shown graphically.

Conservative Solitons and Reversibility in Time Delayed Systems.

Time delayed dynamical systems have proven to be a fertile framework for the study of physical phenomena. In natural sciences, their uses have been limited to the study of dissipative dynamics. In this Letter, we demonstrate the existence of nonlinear reversible conservative time delayed systems. We consider the example of a dispersive microcavity containing a Kerr medium coupled to a distant external mirror. At low energies and in the long delay limit, a multiscale analysis shows the equivalence with the nonlinear Schrödinger equation. We unveil some of the symmetries and conserved quantities, as well as bright temporal solitons. While elastic collisions occur for shallow wave packets, we observe the lack of integrability at higher energies. We recover the Lugiato-Lefever equation in the weakly dissipative regime.

Efficiency of pulse pumped soliton microcombs

Temporal soliton mode locking in coherently pumped microcavities is a promising route towards miniaturized frequency comb systems. However, the power efficiency of the resulting microcombs is usually quite low. Soliton generation by pulse pumping provides a way to increase conversion efficiency (so far, as high as 8%). Here, we study conversion efficiency and report a single-soliton conversion efficiency as high as 54% using a scanning laser, as well as a steady-state single-soliton conversion efficiency as high as 34%. We use the Lagrangian approach to develop analytical expressions for efficiency and soliton temporal placement within the pumping pulse, and our measurements reveal features in the tuning dependence of soliton power and efficiency not seen in continuous pumping. Our experimentally confirmed expressions for efficiency will be useful in understanding advantages and limitations of pulse pumped systems.

Optical Solitons with Tilted Wavefronts

The propagation of nonresonant solitons with phase and group wavefronts tilted with respect to each other is studied. It is shown that the tilt of fronts leads to the redefinition of the group velocity dispersion, introducing an additional anomalous contribution to it. As a result, light temporal and spatiotemporal solitons can be formed at the normal dispersion of the group velocity and focusing nonlinearity, including the cases of absence of this dispersion. A spatiotemporal soliton is a structure that is extended along group fronts normally to the plane of polarization and is localized in all directions perpendicular to the direction of extension of the soliton.

Temporal cavity solitons and frequency combs via quantum interference

Temporal cavity solitons in ring microresonators provide broad and controllable generation of frequency combs with applications in frequency standards and precise atomic clocks. Three level media in the {\Lambda} configuration inside microresonators displaying electromagnetically induced transparency can be used for the generation of temporal cavity solitons and frequency combs in the presence of anomalous dispersion and two external driving fields close to resonance. Here, domain walls separating regions of two dark states due to quantum interference correspond to realizations of stimulated Raman adiabatic passage without input pulses. With no need of modulational instabilities, bright temporal cavity solitons and frequency combs are formed when these domain walls lock with each other. Wide stability ranges, close to resonance operation and optimal shape of the cavity solitons due to three-level quantum interference can make them preferable to those in two-level media.

Observations of existence and instability dynamics of near-zero-dispersion temporal Kerr cavity solitons

Dissipative Kerr cavity solitons (CSs) are persisting pulses of light that manifest themselves in driven optical resonators and that have attracted significant attention over the last decade. Whilst the vast majority of studies have revolved around conditions where the resonator exhibits strong anomalous dispersion, recent studies have shown that solitons with unique characteristics and dynamics can arise under conditions of near-zero-dispersion driving. Here, we report on experimental studies of the existence and stability dynamics of Kerr CSs under such conditions. In particular, we experimentally probe the solitons' range of existence and examine how their breathing instabilities are modified when group-velocity dispersion is close to zero, such that higher-order dispersion terms play a significant role. On the one hand, our experiments directly confirm earlier theoretical works that predict (i) breathing near-zero-dispersion solitons to emit polychromatic dispersive radiation, and (ii) that higher-order dispersion can extend the range over which the solitons are stable. On the other hand, our experiments also reveal a novel cross-over scenario, whereby the influence of higher-order dispersion changes from stabilising to destabilising. Our comprehensive experiments sample soliton dynamics both in the normal and anomalous dispersion regimes, and our results are in good agreement with numerical simulations and theoretical predictions.

Spatial cage solitons—taming light bullets

Multimode nonlinear optics is used to overcome a long-standing limitation of fiber optics, tightly phase locking several spatial modes and enabling the coherent transport of a wave packet through a multimode fiber. A similar problem is encountered in the temporal compression of multimillijoule pulses to few-cycle duration in hollow gas-filled fibers. Scaling the fiber length to up to 6 m, hollow fibers have recently reached 1 TW of peak power. Despite the remarkable utility of the hollow fiber compressor and its widespread application, however, no analytical model exists to enable insight into the scaling behavior of maximum compressibility and peak power. Here we extend a recently introduced formalism for describing mode locking to the analog scenario of locking spatial fiber modes together. Our formalism unveils the coexistence of two soliton branches for anomalous modal dispersion and indicates the formation of stable spatiotemporal light bullets that would be unstable in free space, similar to the temporal cage solitons in mode-locking theory. Our model enables deeper understanding of the physical processes behind the formation of such light bullets and predicts the existence of multimode solitons in a much wider range of fiber types than previously considered possible.

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator.

Temporal solitons have attracted great interest in the past decades for their behavior in a steady state, where the dispersion is balanced by the nonlinearity in a propagation Kerr medium. The development of dissipative Kerr solitons (DKSs) in high-Q microcavities drives a novel, compact, chip-scale soliton source. When DKSs serve as femtosecond pulses, the repetition rate fluctuation can be applied to ultrahigh precision metrology, high-speed optical sampling, and optical clocks, etc. In this paper, the rapid repetition rate fluctuation of soliton crystals (SCs), a special state of DKSs where particle-like solitons are tightly packed and fully occupy a resonator, is measured based on the well-known delayed self-heterodyne method. The SCs are generated using a thermal-controlled method. The pump is a frequency fixed laser with a linewidth of 100 Hz. The integral time in frequency fluctuation measurements is controlled by the length of the delay fiber. For a SC with a single vacancy, the repetition rate fluctuations are ~53.24 Hz within 10 µs and ~509.32 Hz within 125 µs, respectively.

Discrete solitons in nonlinear optomechanical array

The detection of the solitons whose the propagation is spatially localized on the array is an interesting feature for experimental purposes. Here, we investigate the effect of position-modulated self-Kerr nonlinearity on discrete soliton propagating in an optomechanical array. The optomechanical cells are coupled to their neighbors by optical channels, and each cell supports the self-Kerr nonlinear term. Modulational Instability (MI) together with numerical simulations are carried out to characterize the behavior of the solitonic waves. It results that the nonlinear term shortens the transient regime of the temporal solitonic waves, which allows the wave propagation to be confined along specific cells. As the nonlinear term increases, the pulsed shape of soliton waves get sharped and highly peaked. For a strong enough value of the nonlinear term, the waves feature chaos-like motion. Owing to these results, the position-modulated self-Kerr nonlinear term manifests itself as being an energy source for the solitonic waves, allowing to the generated solitons to propagate during a long time while acquiring energy. These results shed light on the fact that nonlinear optomechanical platforms could be used to generate long-lived temporal localized solitons and even chaotic solitonic waves, which are good prerequisites for information processing purposes.

Space-Quasiperiodic and Time-Chaotic Parametric Patterns in a Magnonic Quasicrystal Active Ring Resonator

We demonstrate the dissipative spatiotemporal patterns that are generated by an active ring resonator based on a magnonic quasicrystal (MQC) with Fibonacci-type structure. The dissipative patterns are formed through the magnetostatic surface spin-wave (MSSW) parametric decay into exchange spin waves (SWs), temporal dispersion of the ring resonator and amplification. In the spatial domain, the MSSW and SW parametric patterns measured with the help of Brillouin light spectroscopy have the quasiperiodic spatial localization in crests and grooves of the MQC, respectively. In contrast to the optical quasiperiodic parametric spatial conservative solitons, the amplitude profiles of the magnonic quasiperiodic parametric spatial dissipative patterns correspond to the profiles of the crests and grooves of the MQC. In the time domain, the packets of the chaotic parametric pulses, which are analogs of temporal solitons, are generated at each point of the spatial patterns. The chaotic nature of such pulses is confirmed by an estimate of a highest Lyapunov exponent from the experimental time series. The pulse packets are formed through the time-filtering technique using the external microwave (MW) pulses to control a ring gain. It is shown that at a certain duty factor of the external MW pulses, the parametric MSSW pulses have the amplitude and phase profiles corresponding to the profiles of a conservative bright envelope soliton.

Detuning regulation of temporal solitons in a CaF2 microcavity

Detuning regulation based on the scanning pump wavelength plays an important role in the generation of temporal solitons in an optical microcavity. Field evolution inside a CaF2 microcavity during the detuning regulation process is demonstrated. It is found that a stable single soliton can be excited when modulation instability dominates in the microcavity during frequency tuning with an appropriate scanning speed and operational parameters. However, due to the excessive loss caused by tuning, the soliton eventually evolves into a DC distribution. The influence of different parameters on the light field after formation of the soliton is also studied. Other different parameters lead to different distributional forms of soliton evolution. For maintenance of the single soliton, the appropriate detuning parameter and pump power are changed suddenly after the soliton is generated, causing the soliton to remain stable. Moreover, in the single soliton region, a path within the parameter space of detuning and pump power is planned in order to compress the pulse width of the soliton, and the comb spectrum is broadened. The results of theoretical analysis are important for studying field and spectral characteristics during frequency detuning and for maintaining the temporal soliton in the microcavity.

Absence of Galilean invariance for pure-quartic solitons

Optical temporal solitons, arising from self-phase modulation and negative quadratic (${\ensuremath{\beta}}_{2}$) dispersion, are Galilean invariant, and therefore their properties do not depend on their group velocity. This is no longer true for pure-quartic soliton pulses arising from quartic (${\ensuremath{\beta}}_{4}$) dispersion, for which a change in group velocity necessarily leads to nonzero quadratic and cubic (${\ensuremath{\beta}}_{3}$) dispersion. Analyzing the generalized nonlinear Schr\"odinger equation for such dispersion relations analytically and numerically, we find that pure-quartic solitons are members of a larger family traveling at other speeds. These solitons, which appear to be stable, have a complex phase structure and have an asymmetric spectrum. Our results extend the understanding of solitons arising from high orders of dispersion.

Soliton molecules in femtosecond fiber lasers: universal binding mechanism and direct electronic control

Sequences of ultrashort pulses form the basis of extremely precise laser applications ranging from femtosecond spectroscopy, to material microprocessing, to biomedical imaging. Dynamic patterns of temporal solitons—termed “soliton molecules”—inside mode-locked cavities provide yet unexplored means for generating reconfigurable arrangements of ultrashort pulses. Here, we demonstrate the external control of solitonic bound states in widespread erbium-doped fiber lasers via direct electronic modulation of the semiconductor pump source. This straightforward approach allows for switching between discrete soliton doublet states of picosecond separations, employing and relying on laser-intrinsic soliton interactions. We analyze the externally induced dynamics based on real-time switching data acquired by time-stretch dispersive Fourier transform spectroscopy and identify a universal bound-state formation mechanism different from broadly considered models. Owing to the ease of implementation and its intrinsic tunability, our control scheme is readily applicable to various laser platforms enabling, e.g., rapid multipulse measurements and tailored nonlinear light–matter interactions.

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.

Parametrically driven Kerr cavity solitons

Temporal cavity solitons are optical pulses that propagate indefinitely in nonlinear resonators. They are currently attracting a lot of attention, both for their many potential applications and for their connection to other fields of science. Cavity solitons are phase locked to a driving laser. This is what distinguishes them from laser dissipative solitons and the main reason why they are excellent candidates for precision applications such as optical atomic clocks. To date, the focus has been on driving Kerr solitons close to their carrier frequency, in which case a single stable localised solution exists for fixed parameters. Here we experimentally demonstrate, for the first time, Kerr cavity solitons excitation around twice their carrier frequency. In that configuration, called parametric driving, two solitons of opposite phase may coexist. We use a fibre resonator that incorporates a quadratically nonlinear section and excite stable solitons by scanning the driving frequency. Our experimental results are in excellent agreement with a seminal amplitude equation, highlighting connections to hydrodynamic and mechanical systems, amongst others. Furthermore, we experimentally confirm that two different phase-locked solitons may be simultaneously excited and harness this multiplicity to generate a string of random bits, thereby extending the pool of applications of Kerr resonators to random number generators and Ising machines.

Topological frequency combs and nested temporal solitons

Recent advances in realizing optical frequency combs using nonlinear parametric processes in integrated photonic resonators have revolutionized on-chip optical clocks, spectroscopy, and multi-channel optical communications. At the same time, the introduction of topological physics in photonic systems has provided a new paradigm to engineer the flow of photons, and thereby, design photonic devices with novel functionalities and inherent robustness against fabrication disorders. Here, we use topological design principles to theoretically propose the generation of optical frequency combs and temporal Kerr solitons in a two-dimensional array of coupled ring resonators that creates a synthetic magnetic field for photons and exhibits topological edge states. We show that these topological edge states constitute a traveling-wave super-ring resonator that leads to the generation of coherent nested optical frequency combs, and self-formation of nested temporal solitons and Turing rolls that are remarkably phase-locked over >40 rings. In the nested soliton regime, our system operates as a pulsed optical frequency comb and achieves a mode efficiency of >50%, an order of magnitude higher than single ring frequency combs that are theoretically limited to only ~5%. Furthermore, we show that the topological nested solitons are robust against defects in the lattice. This topological frequency comb works in a parameter regime that can be readily accessed using existing low loss integrated photonic platforms like silicon-nitride. Our results could pave the way for efficient on-chip optical frequency combs, and investigations of various other soliton solutions in conjunction with synthetic gauge fields and topological phenomena in large arrays of coupled resonators.

A shower of mid-infrared Raman solitons at designed wavelength of ∼3 μm from a tapered fluorotellurite fiber

Optical temporal soliton generation in optical fibers and resonators has achieved great breakthroughs and found significant applications in many fields. Despite recent advances on optical soliton generation in optical fibers, it remains challenging to realize a shower of Raman solitons at a certain wavelength in optical fibers, i.e. put all the generated Raman solitons at a same wavelength on demand. Here we propose and experimentally demonstrate a shower of mid-infrared Raman solitons at designed wavelength of 3 μm from a tapered fluorotellurite fiber pumped by a 1960 nm picosecond fiber laser. Tapered fluorotellurite fibers have an untapered region length of ∼49 cm and a tapered transition region length of ∼1 cm. The fiber segment at the end of the tapered region has a 2nd zero-dispersion wavelength of ∼3 μm. Firstly, multiple Raman solitons with different wavelengths are generated in the untapered region pumped by the 1960 nm picosecond laser. Then, as Raman solitons propagate into the tapered region, the redshift of all the generated Raman solitons with different wavelengths are accelerated due to the dramatic increase of the nonlinear coefficient. Finally, as Raman solitons move out from the tapered region, all the accelerated Raman solitons are stopped around 3 μm owing to the occurrence of soliton self-frequency shift cancellation, causing the generation of a shower of mid-infrared Raman solitons around 3 μm. This phenomenon may find applications in super-efficient nonlinear light generation and signal processing.

Perfect Soliton Crystals in the High-Q Microrod Resonator

The coherent temporal soliton in optical microresonators has attracted great attention recently. Here, we have fabricated the microrod resonator with Q factor as high as 2×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> and demonstrated the dissipative Kerr soliton generation in such a microresonator, by utilizing an auxiliary-laser-assisted thermal response control. In addition, we have changed the pump laser and observed the perfect soliton crystals. With the simulation, we found that the perfect soliton crystals are generated based on the avoided mode crossing, which is affected by the pump resonance and pump power.

Giant anomalous self-steepening and temporal soliton compression in silicon photonic crystal waveguides

Self-steepening (SS) is enhanced by slow-light effects in photonic crystal waveguides (PhCWs), with coefficients as large as hundreds of femtoseconds, and it plays an important role in temporally compressed solitons with narrow widths. Here, we investigate the soliton evolution in silicon PhCWs through experiments and numerical simulations; the simulated results agree well with the experimental measurements and help in revealing the physical mechanism of high-order soliton evolution. The dual opposite effects of giant anomalous SS on temporal soliton compression are demonstrated for the first time, i.e., the SS weakens or improves the compression competing with the effects of third-order dispersion (TOD) through two different physical mechanisms. It is also found that SS flattens or steepens the pulse leading edge depending on the strength of the positive TOD perturbation. These results promote the understanding of high-order solitons and can help with the design of suitable dispersion engineered silicon waveguides for superior on-chip temporal pulse compression for optical interconnects, data processing, and microwave photonics.

Temporal Boundary Solitons and Extreme Superthermal Light Statistics.

We discover the formation of a temporal boundary soliton (TBS) in close proximity of a temporal boundary, moving in a nonlinear optical medium, upon high-intensity pulse collision with the boundary. We show that the emergent TBS is unstable to perturbations caused by the cross-phase modulation between the TBS and the other soliton products of the collision and that such instability triggers colossal intensity fluctuations of the reflected pulse ensemble with unprecedented magnitudes of the normalized autocorrelation function for an even weakly fluctuating input pulse.