Temporal Solitons Research Articles

Non-autonomous solitons in inhomogeneous nonlinear media with distributed dispersion

We show that the methodology based on the powerful method of the so-called hidden symmetry reductions (HSR) provides a systematic way to analytically derive non-autonomous temporal soliton solutions of a one-dimensional inhomogeneous nonlinear Schrodinger equation with a linear gain or loss, a linear density profile, and distributed dispersion. The fundamental innovation of our approach is to notice that the ansatz used in the powerful method of the HSR contains a free parameter that can be used to control the wave propagations related to both the rogue and the symmetric cnoidal solitons raising the possibility of relative experiments and potential applications in nonlinear optics and Bose–Einstein condensates (BECs). We show that for BECs with the time-dependent s-wave scattering length in linear potential when the loss or the gain of atoms is taken into consideration our algorithm is a useful tool to control non-autonomous bright rogue and symmetric cnoidal solitons of BECs. Our results show that the nonlinearity and the linear trapping potential play important roles in the evolutional characteristics such as amplitude, width, trajectory, linear chirp phase, phase offset, and phase shift. Our analysis might have the applications in the theory of nonlinear transmission networks for achieving pulse compression.

Super-efficient temporal solitons in mutually coupled optical cavities

A coherently driven Kerr optical cavity is able to convert a continuous-wave laser to a sequence of ultrashort soliton pulses, enabling the generation of broadband and mode-locked frequency combs. Kerr cavity solitons are balanced through an energy exchange with the driving pump field. Improving the energy conversion efficiency from the pump to the soliton is of great significance for practical applications, but remains an outstanding challenge due to a limited temporal overlap between the soliton and the pump. Here, we report the discovery of temporal Kerr solitons in mutually coupled cavities instead of a traditional single cavity. We propose a strategy for breaking the limitation of pump-to-soliton energy conversion, and connect the underlying mechanism to impedance matching in radiofrequency electronic circuits. With macro optical fiber ring cavities which share the same physical model as miniature optical microresonators, we demonstrate nearly one-order improvement of the efficiency. The results pave the way towards super-efficient soliton microcombs based on optical microresonators with ultra-high quality factors.

Digital signal processing in coupled photonic crystal waveguides and its application to an all-optical AND logic gate

The realization of all-optical AND logic gates for pulsed signal operation based on the photonic bandgap transmission phenomenon is proposed. We are using realistic planar air-hole type coupled photonic crystal waveguides (C-PCWs) with Kerr-type nonlinear background medium. The novelty of our analysis is that the proposed AND logic gate operates with the temporal solitons, which maintain a stable envelope propagating in the nonlinear C-PCWs, enabling true ultrafast full-optical digital signal processing in the time-domain. The bandgap transmission takes place when the operating frequency is chosen at the very edge of the dispersion curve of one of the supermodes in the C-PCWs. In this regard, our original fast and accurate method is used to efficiently calculate the supermodes of the C-PCW system. The underlying semi-analytical full-wave modal analysis is based on the evaluation of the lattice sums for complex wavenumbers using the transition-matrix method in combination with the generalized reflection-matrix approach. As a proof of concept successful pulse operation of the all-optical AND logic gate is demonstrated in the framework of extensive full-wave finite-difference time-domain electromagnetics analysis.

Efficient, broadband third-harmonic generation in silicon nanophotonic waveguides spectrally shaped by nonlinear propagation.

Optical emission from silicon is most practically accessible through nonlinear optical wave mixing, due to the indirect bandgap of the material. Although silicon is a material that absorbs visible light, third-harmonic generation driven by infrared signals can be used to generate visible light in silicon structures. In this work, we present a comprehensive investigation into third-harmonic generation in silicon-on-insulator waveguides. We demonstrate that few-micrometer length waveguides can be used to up-convert ultrafast 1550nm laser pulses to their third-harmonic with efficiencies up to ηTHG=2.8×10-5, the highest third-harmonic generation conversion efficiency reported to date in a silicon-based structure. Nonlinear propagation through 200μm long waveguides produces self-compressing temporal solitons, which dramatically broaden and blue shift the observed third-harmonic spectrum. Such devices are envisioned to provide a method for generating coherent visible signals within an integrated, CMOS compatible platform.

Revealing the behavior of soliton buildup in a mode-locked laser

Real-time spectroscopy based on an emerging time-stretch technique can map the spectral information of optical waves into the time domain, opening several fascinating explorations of nonlinear dynamics in mode-locked lasers. However, the self-starting process of mode-locked lasers is quite sensitive to environmental perturbation, which causes the transient behaviors of lasers to deviate from the true buildup process of solitons. We optimize the laser system to improve its stability, which suppresses the Q-switched lasing induced by environmental perturbation. We, therefore, demonstrate the first observation of the entire buildup process of solitons in a mode-locked laser, revealing two possible pathways to generate the temporal solitons. One pathway includes the dynamics of raised relaxation oscillation, quasimode-locking stage, spectral beating behavior, and finally the stable single-soliton mode-locking. The other pathway contains, however, an extra transient bound-state stage before the final single-pulse mode-locking operation. Moreover, we propose a theoretical model to predict the buildup time of solitons, which agrees well with the experimental results. Our findings can bring real-time insights into ultrafast fiber laser design and optimization, as well as promote the application of fiber laser.

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.

A Convolution-Free Mixed Finite-Element Time-Domain Method for General Nonlinear Dispersive Media

In this paper, a mixed finite-element time-domain (FETD) method is presented for the simulation of electrically complex materials, including general combinations of linear dispersion, instantaneous nonlinearity, and dispersive nonlinearity. Using both edge and face elements, the presented method offers greater geometric flexibility than existing finite-difference time-domain (FDTD) implementations, and in contrast to existing nonlinear FETD methods, also incorporates both linear and nonlinear material dispersions. Dielectric nonlinearity is incorporated into the Crank–Nicolson mixed FETD formulation via a straightforward Newton–Raphson approach, for which the associated Jacobian is derived. Moreover, the dispersion is modeled via the Mobius $z$ transform method, yielding a simpler more general algorithm. The method’s accuracy and convergence are verified, and its capability demonstrated via the simulation of several nonlinear phenomena, including temporal and spatial solitons in two spatial dimensions.

A microphotonic astrocomb

Earth-like planets, dark energy and variability of fundamental physical constants can be discovered by observing wavelength shifts in the optical spectra of astronomical objects1–5. These wavelength shifts are so tiny that exquisitely accurate and precise wavelength calibration of astronomical spectrometers is required. Laser frequency combs, broadband spectra of laser lines with absolutely known optical frequencies, are uniquely suited for this purpose6–13, provided their lines are resolved by the spectrometer. Generating such astronomical laser frequency combs (‘astrocombs’) remains challenging. Here, a microphotonic astrocomb is demonstrated via temporal dissipative Kerr solitons14–16 in photonic-chip-based silicon nitride microresonators17, directly providing a spurious-free spectrum of resolvable calibration lines. Sub-harmonically driven by temporally structured light18, the astrocomb is stabilized to a frequency standard, resulting in absolute calibration with a precision of 25 cm s–1 (radial velocity equivalent), relevant for Earth-like planet detection and cosmological research. The microphotonic technology can be extended in spectral span17,19–24, further boosting the calibration precision. A microphotonic astrocomb is demonstrated via temporal dissipative Kerr solitons in photonic-chip-based silicon nitride microresonators with a precision of 25 cm s–1 (radial velocity equivalent), useful for Earth-like planet detection and cosmological research.

Invited Article: Emission of intense resonant radiation by dispersion-managed Kerr cavity solitons

We report on an experimental and numerical study of temporal Kerr cavity soliton dynamics in dispersion-managed fiber ring resonators. We find that dispersion management can significantly magnify the Kelly-like resonant radiation sidebands emitted by the solitons. Because of the underlying phase-matching conditions, the sideband amplitudes tend to increase with increasing pump-cavity detuning, ultimately limiting the range of detunings over which the solitons can exist. Our experimental findings show excellent agreement with numerical simulations.

From the Lugiato-Lefever equation to microresonator-based soliton Kerr frequency combs.

The model, that is usually called the Lugiato-Lefever equation (LLE), was introduced in 1987 with the aim of providing a paradigm for dissipative structure and pattern formation in nonlinear optics. This model, describing a driven, detuned and damped nonlinear Schroedinger equation, gives rise to dissipative spatial and temporal solitons. Recently, the rather idealized conditions, assumed in the LLE, have materialized in the form of continuous wave driven optical microresonators, with the discovery of temporal dissipative Kerr solitons (DKS). These experiments have revealed that the LLE is a perfect and exact description of Kerr frequency combs-first observed in 2007, i.e. 20 years after the original formulation of the LLE-and in particular describe soliton states. Observed to spontaneously form in Kerr frequency combs in crystalline microresonators in 2013, such DKS are preferred state of operation, offering coherent and broadband optical frequency combs, whose bandwidth can be extended exploiting soliton-induced broadening phenomena. Combined with the ability to miniaturize and integrate on-chip, microresonator-based soliton Kerr frequency combs have already found applications in self-referenced frequency combs, dual-comb spectroscopy, frequency synthesis, low noise microwave generation, laser frequency ranging, and astrophysical spectrometer calibration, and have the potential to make comb technology ubiquitous. As such, pattern formation in driven, dissipative nonlinear optical systems is becoming the central Physics of soliton micro-comb technology.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Robust, Synchronous Optical Buffer, and Logic Operation in Dual-Pump Kerr Micro-Resonator

Temporal cavity solitons (CSs) have been proposed to store the information in the form of optical bits in a single-pump Kerr micro-resonator. However, such optical buffers (OBs) realized using a single-pump are essentially asynchronous in nature. In this paper, we show that dual-pump scheme can lead to both synchronous and robust OB. Numerical simulations reveal the resilience in the performance of the OB against the writing jitters and third-order dispersion induced temporal drift. The impact of nonideal operating conditions, such as unequal pump amplitudes and pump detuning mismatch on the performance of the synchronous OB, are evaluated and the robustness of the OB with respect to these aspects are explored both analytically and numerically. As an interesting application of the proposed dual-pump scheme, we have demonstrated the capability to perform simultaneous logic operations (AND, OR) of the proposed device. All the conclusions are supported by analytical and semi-analytical approaches.

Three coupled slow temporal vector optical solitons in a cold seven-level atomic system

A theoretical scheme is proposed to investigate the formation of three coupled slow temporal vector optical solitons in a lifetime-broadened seven-state atomic medium. We demonstrate that the three polarized components of a low intensity linear-polarized pulsed probe field can evolve into three coupled slow temporal vector optical solitons due to the fact that group-velocity dispersion can be well compensated by the self- and cross-phase-modulation effects. Moreover, this atomic system could support the existence of various types of three coupled slow temporal vector solitons, such as bright–bright–bright, bright–dark–bright, dark–dark–dark, and bright–dark–dark vector solitons.

The effect of relative phase on the stability of temporal dark soliton in $${{\mathcal {PT}}}$$ PT -symmetric nonlinear directional fiber coupler

In this paper, we numerically investigate the effect of relative phase on the stability of dark solitons in $${\mathcal {PT}}$$ -Symmetric nonlinear directional coupler (NLDC), by considering gain in the bar and loss in the cross in the range of $$\theta =0^\circ$$ to $$180^\circ$$ . The $${\mathcal {PT}}$$ -Symmetric perturbed eigenfunctions are used to study the soliton stability. The results of simulations are shown that in the first half region of the relative phase the soliton is unstable while in the second one, is stable. In the stable region gain and loss cancel each other and also the perturbed eigenfunctions have no effect on solitons while in the unstable region solitons are amplified in the bar and attenuated in the cross except for some small intervals which the roles are changed. The behavior of such perturbation can be interpreted as self all-optical phase soliton switching and optical logic gates.

Unstable and stable regimes of polariton condensation

Modulational instabilities play a key role in a wide range of nonlinear optical phenomena, leading e.g. to the formation of spatial and temporal solitons, rogue waves and chaotic dynamics. Here we experimentally demonstrate the existence of a modulational instability in condensates of cavity polaritons, arising from the strong coupling of cavity photons with quantum well excitons. For this purpose we investigate the spatiotemporal coherence properties of polariton condensates in GaAs-based microcavities under continuous-wave pumping. The chaotic behavior of the instability results in a strongly reduced spatial and temporal coherence and a significantly inhomogeneous density. Additionally we show how the instability can be tamed by introducing a periodic potential so that condensation occurs into negative mass states, leading to largely improved coherence and homogeneity. These results pave the way to the exploration of long-range order in dissipative quantum fluids of light within a controlled platform.

The Nth-order Darboux transformation, vector dark solitons and breathers for the coupled defocusing Hirota system in a birefringent nonlinear fiber

Under investigation in this paper is the coupled defocusing Hirota system, which describes the propagation of ultra-short pulses in a birefringent nonlinear fiber. With respect to the amplitudes of the pulse envelopes, we construct the Nth-order Darboux transformation, which is different from those in the existing literatures, where N is a positive integer. The first- and second-order solutions are obtained via the Darboux transformation. Pulse envelopes including the gray-gray/antidark-gray/dark-bright solitons, vector Akhmediev breathers, temporal cavity solitons and (time, space)-periodic breathers are acquired. As the relative width of the spectrum that arises due to the quasi monochromocity decreases, we find that: the velocity and width of the dark-bright solitons increase; the width of the temporal cavity soliton decreases; the temporal period of the vector (time, space)-periodic breather becomes longer while its spacial period becomes shorter. Relative width of the spectrum that arises due to the quasi monochromocity does not affect the amplitudes of the pulse envelopes obtained. Elastic interactions between the breathers and solitons, and inelastic interactions between the two gray-gray solitons are obtained.

Spatiotemporal solitary modes in a twisted cylinder waveguide shell with the self-focusing Kerr nonlinearity

We study the spatiotemporal solitary modes that propagate in a hollow twisted cylinder waveguide pipe with a self-focusing Kerr nonlinearity. Three generic solitary modes, one belonging to the zero-harmonic (0H) and the other two belonging to the first-harmonic (1H), are found in the first rotational Brillouin zone. The 0H solitary modes can be termed as a quasi-1D (one-dimensional) temporal soliton. Their characteristics depend only on the energy flow. The 1H solitary mode can be termed a quasi-2D (two-dimensional) bullet, whose width is much narrower than the angular domain of the waveguide. In contrast to the 0H mode, the characteristics of the 1H solitary mode depend on both their energy flow and the rotating speed of the waveguide. We demonstrate numerically that the 1H solitary modes are stable when their energy flow is smaller than the threshold norm of the Townes soliton. The boundaries of the bistable area for these two types of solitary modes are predicted by the analyses via two-mode approximation. This prediction is in accordance with the numerical findings. We also demonstrate analytically that the 1H solitary mode of this system can be applied to emulate the nonlinear dynamics of solitary modes with 1D Rashba spin-orbit (SO) coupling by optics. Two degenerated states of the 1H solitary mode, semi-dipole and mixed mode, are found from this setting via the mechanism of SO coupling. Collisions between the pair of these two types of solitary modes are also discussed in the paper. The pair of the 0H solitary mode features only the elastic collision, whereas the pair of 1H solitary modes can feature both elastic and inelastic collision when the total energy flow of the two modes are smaller or close to the threshold norm of the Townes soliton.

Experimental observations of breathing Kerr temporal cavity solitons at large detunings.

It was recently predicted that, due to stimulated Raman scattering, temporal Kerr cavity solitons may exhibit oscillatory instabilities at large cavity detunings [Phys. Rev. Lett.120, 053902 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.053902]. Here, we report experimental observations of this behavior. To access the appropriate oscillatory regime, we construct a macroscopic fiber ring resonator with a high finesse of F≈240. By synchronously driving the resonator with flat-top nanosecond pulses, we can reach very large intracavity power levels, where Raman-induced soliton oscillations can be observed. We also surprisingly find that, in the limit of large cavity driving strengths, new soliton instability regimes that are not accounted for in the known bifurcation structure of driven Kerr resonators can emerge even in the absence of Raman effects. Our experimental results are in good agreement with numerical simulations.

Realization of true all-optical AND logic gate based on nonlinear coupled air-hole type photonic crystal waveguides

In this manuscript we propose an easily scalable true all-optical AND logic gate for pulsed signal operation based on band-gap transmission within nonlinear realistic air-hole type coupled photonic crystal waveguides (C-PCW). We call it "true" all-optical AND logic gate, because all AND gate topologies operate with temporal solitons that maintain a stable pulse envelope during the optical signal processing along the different C-PCW modules yielding ultrafast full-optical digital signal processing. We directly use the registered (output) signal pulse as new input signal between multiple concatenated nonlinear C-PCW modules (i.e. AND gates) to setup a multiple-input true all-optical AND logic gate. Extensive full-wave computational electromagnetic analysis proves the correctness of our theoretical studies and the proposed operation principle of the multiple-input AND logic gate is vividly demonstrated for realistic C-PCWs.

Excitation and propagation of surface polaritonic rogue waves and breathers

Excitation and propagation of the surface polaritonic rogue waves and breathers are investigated by proposing a coupler free optical waveguide that consists of a transparent layer, middle negative index metamaterial layer, and bottom layer of the cold four level atomic medium. In this planar optical waveguide, a giant controllable Kerr nonlinearity is achieved by sufficient field concentration and a proper set of intensities and detunings of the driven laser fields. As a result, various kinds of temporal surface polaritonic solitons, rogue waves, and breathers can be propagated in the narrow window for electromagnetically induced transparency. We find that the giant intensity and extreme concentration of surface polaritons with low generation power can be achieved by excitation of the first- and second-order peregrine rogue waves. Furthermore, the first- and higher-order surface polaritonic Akhmediev breathers can be propagated at the slow light level due to modulation instability in the proposed optical waveguide. We demonstrate that surface-polariton propagation length can be significantly enhanced by Kuznetsov-Ma breather dynamics.

Addressing temporal Kerr cavity solitons with a single pulse of intensity modulation.

We experimentally and numerically study the use of intensity modulation for the controlled addressing of temporal Kerr cavity solitons (CSs). Using a coherently driven fiber ring resonator, we demonstrate that a single temporally broad intensity modulation pulse applied on the cavity driving field permits systematic and efficient writing and erasing of ultrashort cavity solitons. We use numerical simulations based on the mean-field Lugiato-Lefever model to investigate the addressing dynamics, and present a simple physical description of the underlying physics.