Soliton molecules, bound states composed of interacting fundamental solitons, exhibit remarkable resemblance with chemical compounds and phenomena in quantum mechanics. Whereas optical molecules composed of two or more temporally locked solitons have been observed in a variety of platforms, soliton molecules formed by bound solitons at different frequencies have only recently been theoretically proposed. Here, we report the observation of polychromatic soliton molecules within a mode-locked laser cavity, achieving the desired dispersion by implementing a spectral pulse-shaper. This system supports two or more coincident solitons with different frequencies, but common group velocities. Our results open new directions of exploration in nonlinear dynamics within systems with complex dispersion and offer a convenient platform for optical analogies to mutual trapping and spectral tunneling in quantum mechanics.
We study dynamical reshaping of polychromatic beams due to collective nonlinear self-action of multiple-frequency components in periodic photonic lattices and predict the formation of polychromatic discrete solitons facilitated by localization of light in spectral gaps. We show that the self-trapping efficiency and structure of emerging polychromatic gap solitons depends on the spectrum of input beams due to the lattice-enhanced dispersion, including the effect of crossover from localization to diffraction in media with defocusing nonlinearity.
We study resonant radiation generated by bound solitons in a twin-core fiber near zero-dispersion wavelength, in the presence of higher order dispersion terms. We propose a theoretical description of dispersive wave generation mechanism and derive resonance conditions. The presence of third order dispersion term leads to generation of polychromatic dispersive radiation and transition from the regime of center of mass oscillations to the regime of amplitude oscillations. Such a transition is not reproduced in the case of symmetric fourth order dispersion.
When a laser cavity supports the propagation of several ultrashort pulses, these pulses interact and can form compact bound states called soliton molecules. Soliton molecules are fascinating objects of nonlinear science, which present striking analogies with their matter molecules counterparts. The soliton pair, composed of two identical pulses, constitutes the chief soliton molecule of fundamental interest. The relative timing and phase between the two propagating pulses are the most salient internal degrees of freedom of the soliton molecule. These two internal degrees of freedom allow self-…
Optical soliton molecules in ultrafast lasers present striking analogies with their matter molecule counterparts, such as internal vibrations. However, the vibrations of soliton molecules are nonlinear, with frequencies that are sensitive to the system parameters, thus presenting an opportunity of control. Here, we experimentally demonstrate the synchronization of the internal vibrations of self-excited vibrating soliton molecules through a modulated optical injection. We show efficient sub-harmonic, fundamental and super-harmonic synchronization, forming a pattern of Arnold tongues with respe…
We implement a super-localization method in the time domain that allows the observation of the external motion of soliton molecules in a fiber ring cavity laser with unprecedented accuracy. In particular, we demonstrate the synchronization of two oscillating soliton molecules separated by several nanoseconds, with inter-molecules oscillations following the same pattern as the intramolecular motion of the individual molecules. These experimental findings indicate an interplay between the different interaction mechanisms that coexist inside the laser cavity, despite their very different characte…
The emergence of confined structures and pattern formation are exceptional manifestations of concurring nonlinear interactions found in a variety of physical, chemical and biological systems[1]. Optical solitons are a hallmark of extreme spatial or temporal confinement enabled by a variety of nonlinearities. Such particle-like structures can assemble in complex stable arrangements, forming "soliton molecules"[2,3]. Recent works revealed oscillatory internal motions of these bound states, akin to molecular vibrations[4-8]. These observations beg the question as to how far the "molecular" analog…
Optical soliton molecules are bound states of solitons that arise from the balance between attractive and repulsive effects. Having been observed in systems ranging from optical fibers to mode-locked lasers, they provide insights into the fundamental interactions between solitons and the underlying dynamics of the nonlinear systems. Here, we enter the multistability regime of a Kerr microresonator to generate superpositions of distinct soliton states that are pumped at the same optical resonance, and report the discovery of heteronuclear dissipative Kerr soliton molecules. Ultrafast electroopt…
Many physical systems display quantized energy states. In optics, interacting resonant cavities show a transmission spectrum with split eigenfrequencies, similar to the split energy levels that result from interacting states in bonded multi-atomic, i.e. molecular, systems. Here, we study the nonlinear dynamics of photonic diatomic molecules in linearly coupled microresonators and demonstrate that the system supports the formation of self-enforcing solitary waves when a laser is tuned across a split energy level. The output corresponds to a frequency comb (microcomb) whose characteristics in te…
Physics phenomena of multi-soliton complexes have enriched the life of dissipative solitons in fiber lasers. By developing a birefringence-enhanced fiber laser, we report the first experimental observation of group-velocity-locked vector soliton (GVLVS) molecules. The birefringence-enhanced fiber laser facilitates the generation of GVLVSs, where the two orthogonally polarized components are coupled together to form a multi-soliton complex. Moreover, the interaction of repulsive and attractive forces between multiple pulses binds the particle-like GVLVSs together in time domain to further form …
We show a new class of bound soliton molecule that exists in a parametrically driven nonlinear optical cavity with appropriate dispersion characteristics. The composed solitons exhibit distinctive colors but coincide in time and share a common phase, bound together via strong inter-soliton four-wave mixing and Cherenkov radiation. The multicolor bound soliton molecule shows intriguing spectral locking characteristics and remarkable capability of spectrum management to tailor soliton frequencies, which may open up a great avenue towards versatile generation and manipulation of multi-octave span…
Soliton molecules are the manifestation of attractive and repulsive interaction between optical pulses mediated by a nonlinear medium. However, the formation and breakup of soliton molecules are difficult to observe due to the transient nature of the process. Using the time stretch technique, we have been able to track the real-time evolution of the bound state formation in a femtosecond fiber laser and unveil different evolution paths towards a stable bound state. A non-stationary Q-switched mode-locking regime consisting of various transient solitons is observed in this transition period. We…
Stable (2+1)-dimensional soliton and breather molecules in a cold Rydberg atomic gas
Henan Normal University（河南师范大学）；Hubei University of Automotive Technology（湖北汽车工业学院）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Tel Aviv University（特拉维夫大学）；Universidad de Tarapacá（塔拉帕卡大学）
Mode-locked lasers have been widely used to explore interactions between optical solitons, including bound-soliton states that may be regarded as "photonic molecules". Conventional mode-locked lasers can however host at most only a few solitons, which means that stochastic behaviour involving large numbers of solitons cannot easily be studied under controlled experimental conditions. Here we report the use of an optoacoustically mode-locked fibre laser to create hundreds of temporal traps or "reactors" within which multiple solitons can be isolated and controlled both globally and individually…
Recently, in addition to exploring the application of new saturable absorber devices in fiber lasers, soliton dynamics has also become a focus of current research. In this article, we report an ultrashort pulse fiber laser based on VSe2/GO nanocomposite and verify the formation process of soliton and soliton molecules by the numerical simulation. The prepared VSe2/GO-based device shows excellent saturable absorption characteristics with a modulation depth of 14.3% and a saturation absorption intensity of 0.93MW/cm2. The conventional soliton is obtained with pulse width of 573fs, which is curre…
Analysis of Dispersive Fourier Transform dataset using Dynamic Mode Decomposition: evidence of multiple vibrational modes, and their interplay in a three-soliton molecule
Soliton molecules (SMs) are fundamentally important modes in nonlinear optical systems. It is a challenge to experimentally produce SMs with a required temporal separation in mode-locked fiber lasers. Here, we propose and realize an experimental scenario for harnessing SM dynamics in a laser setup. In particular, we tailor SMs in a mode-locked laser controlled by second-order group-velocity dispersion and dispersion losses: the real part of dispersion maintains the balance between the dispersion and nonlinearity, while the dispersion loss determines the balance of gain and losses. The experime…
In recent years, beta gallium oxide (beta-\ce{Ga2O3}) has become the most investigated isomorph of gallium oxide polymorphs, due to the great potential it represents for applications in optoelectronics and photonics for solar technology, particularly in blind ultraviolet photodetector solar cells (SBUV) designs. To optimize its use in these applications, and to identify possible new features, knowledge of its fundamental properties is relevant. In this respect, optical, thermal and electronic properties of beta-\ce{Ga2O3} have been studied expriementally, providing evidence of a wide-band inor…
Investigation on the relative phase evolution between two bounded optical solitons is essential for its potential applications in development of larger telecommunication capacity of optical fiber transmission lines, resolution improvement in advancing ultrafast characterization approaches and development of all-optical information storage. Here we characterized relative comb-line phase jitter power spectral density (PSD) of a soliton molecule pair generated from a passively mode-locked Er:fiber laser. Through tracking the intensity difference between two selected wavelengths in one certain spe…
Bound states of solitons, alias soliton molecules (SMs), are well known in one-dimensional (1D) systems, while making stable bound states of multidimensional solitons is a challenging problem because of the underlying instabilities. Here we propose a scheme for the creation of stable (2+1)D and (3+1)D optical SMs in a gas of cold Rydberg atoms, in which electromagnetically induced transparency (EIT) is induced by a control laser field. We show that, through the interplay of the EIT and the strong long-range interaction between the Rydberg atoms, the system gives rise to giant nonlocal Kerr non…
For waveguides with two separate regions of anomalous dispersion, it is possible to create a quasi-stable two-color solitary wave. In this paper we consider how those waves interact with dispersive radiation, both generation of Cherenkov radiation and scattering of incident dispersive waves. We derive the analytic resonance conditions and verify them through numeric experiments. We also report incident radiation driving the internal oscillations of the soliton during the scattering process in case of an intense incident radiation. We generalize the resonance conditions for the case of an oscil…
Bound states of solitons (molecules) occur in various settings, playing an important role in the operation of fiber lasers, optical emulations, encoding, and communications. Soliton interactions are generally related to breathing dynamics in nonlinear dissipative systems, maintaining potential applications in spectroscopy. In the present work, dichromatic breather molecules (DBMs) are created in a synchronized mode-locked fiber laser. Real-time delay-shifting interference spectra are measured to display the temporal evolution of the DBMs, that cannot be observed by means of the usual real-time…
Breathing solitons are nonlinear waves in which the energy concentrates in a localized and oscillatory fashion. Similarly to stationary solitons, breathers in dissipative systems can form stable bound states displaying molecule-like dynamics, which are frequently called breather molecules. So far, the experimental observation of optical breather molecules and the real-time detection of their dynamics have been limited to diatomic molecules, that is, bound states of only two breathers. In this work, we report on the observation of different types of breather complexes in a mode-locked fibre las…
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…
Controlling the coherence between light and matter has enabled the radiation of electromagnetic waves with spectral purity and stability that defines the Système International (SI) second. While transitions between hyperfine levels in atoms are accessible in the microwave and optical domains, faithfully transferring such stability to other frequency ranges of interest is not trivial. Such stability is specifically sought after for the terahertz domain to improve the resolution in very long baseline interferometry and molecular spectroscopy, and advance the technological development of high-spe…
We demonstrate experimentally that the interactions between a pair of nonlocal spatial optical solitons in a nematic liquid crystal (NLC) can be controlled by the degree of nonlocality. For a given beam width, the degree of nonlocality can be modulated by varying the pretilt angle of NLC molecules via the change of the bias. When the pretilt angle is smaller than pi/4, the nonlocality is strong enough to guarantee the independence of the interactions on the phase difference of the solitons. As the pretilt angle increases, the degree of nonlocality decreases. When the degree is below its critic…
The strongly-constrained physics-informed neural network (SCPINN) is proposed by adding the information of compound derivative embedded into the soft-constraint of physics-informed neural network(PINN). It is used to predict nonlinear dynamics and the formation process of bright and dark picosecond optical solitons, and femtosecond soliton molecule in the single-mode fiber, and reveal the variation of physical quantities including the energy, amplitude, spectrum and phase of pulses during the soliton transmission. The adaptive weight is introduced to accelerate the convergence of loss function…
Based on conservation laws as one of the important integrable properties of nonlinear physical models, we design a modified physics-informed neural network method based on the conservation law constraint. From a global perspective, this method imposes physical constraints on the solution of nonlinear physical models by introducing the conservation law into the mean square error of the loss function to train the neural network. Using this method, we mainly study the standard nonlinear Schrödinger equation and predict various data-driven optical soliton solutions, including one-soliton, soliton …
Binding of particles through weak (non-covalent) interactions plays a central role in multiple modern disciplines, from Cooper pairing of electrons in superconductivity to formation of supramolecules in biochemistry. Optical solitons, which are analogous in many ways to particles, arise from a balance between nonlinearity and dispersion and have only been known to be able to form molecule-like, localized structures through covalent interactions due to direct overlapping. Non-covalent binding of optical solitons that based on long-rang interactions have, however, so far escaped experimental obs…
We present a stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs in whispering gallery mode resonators pumped in the anomalous dispersion regime. This article is the second part of a research work whose first part was devoted to the regime of normal dispersion, and was presented in ref. \cite{Part_I}. The case of anomalous dispersion is indeed the most interesting from the theoretical point of view, because of the considerable variety of dynamical behaviors that can be observed. From a technological point of view, it is also the most relevant because it corresponds…
We propose to use a quantized version of coherent two-color photoassociation to realize a hybrid device for quantum control of light. The dynamical features of this system are exhibited, including the slowing down or storage of light and the molecular matter-wave solitons. This may indicate a hybrid atom-molecule quantum device for storage and retrieve of optical information.
Optical nonlinearity in a strongly interacting Rydberg atom ensemble
Henan Normal University（河南师范大学）；Hubei University of Automotive Technology（湖北汽车工业学院）；East China Normal University（华东师范大学）；University of Nottingham（诺丁汉大学）；Fuyao University of Science and Technology（福耀科技大学）；NYU-ECNU Institute of Physics, New York University Shanghai（纽约大学-华东师范大学物理研究所，上海纽约大学）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
