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Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate two-soliton which also leads to high amplitude maxima. In this study, we report several observations of such multi-soliton with doubly-localized peaks in a water wave flume. The data collected in this experiment confirm the distinctive attainment of wave amplification by a factor of two in good agreement with the dynamics of the nonlinear Schr\"odinger equation solution. Advanced numerical simulations solving the problem of nonlinear free water surface boundary conditions of an ideal fluid quantify the physical limitations of the degenerate two-soliton in hydrodynamics.

Mutual interaction of localized nonlinear waves, e.g. solitons and modulation instability patterns, is a fascinating and intensively-studied topic of nonlinear science. In this research report, we report on the observation of a novel type of breather interaction in telecommunication optical fibers, in which two identical breathers propagate with opposite group velocities. Under certain conditions, neither amplification nor annihilation occur at the collision point and most interestingly, its amplitude is almost equal to another maximum of either oscillating breather. This ghost-like breather interaction dynamics can be fully described by the N-breather solution of the nonlinear Schr\"odinger equation.

We report on the experimental and numerical observation of polarization modulation instability (PMI) in a nonlinear fiber Kerr resonator. This phenomenon is phased-matched through the relative phase detuning between the intracavity fields associated with the two principal polarization modes of the cavity. Our experimental investigation is based on a 12-m long fiber ring resonator in which a polarization controller is inserted to finely control the level of intra-cavity birefringence. Depending on the amount of birefringence, the temporal patterns generated via PMI are found to be either stationary or to exhibit a period-doubled dynamics. Experimental results are in good agreement with numerical simulations based on an Ikeda map for the two orthogonally polarized modes. Our study provides new insights into the control of modulation instability in multimode Kerr resonators. Modulation instability (MI) is a nonlinear phenomenon characterized by the exponential growth and evolution of periodic perturbations on top of an intense continuous-wave (cw) laser beam [1, 2]. Underpinned by a nonlinearly phase-matched parametric process, it is associated with a transfer of energy from a narrow pump frequency component to a pair of sidebands arranged symmetrically around the pump. In single-pass optical fiber propagation, MI can be naturally phase-matched through a balance between anomalous group-velocity dispersion and Kerr nonlinearity [1, 2]. In contrast, more general phase-matching conditions are possible in the context of passive Kerr resonators, such as fiber ring cavities, because of the crucial role played by the systems' boundary conditions [3-5]. Various configurations of MI have been investigated in that context, including MI in the normal dispersion regime, MI via bichromatic or incoherent driving, as well as competition between MI and Faraday or period-doubled (P2) instabilities [6--12]. Moreover, at variance with single-pass propagation, MI in Kerr resonators can lead to the emergence of stationary periodic (Turing) patterns; such patterns are now understood to be intimately related to temporal cavity solitons and microresonator optical frequency combs [13--16]. Birefringence, and nonlinear coupling between the polarization components of light, is also known to contribute to the phase-matching of parametric processes. This leads to polarization MI (PMI) and the emergence of vector temporal patterns [17-19]. In driven resonators, PMI has only been investigated theoretically so far [20-22], but recent demonstrations of orthogonally-polarized dual comb generation in microresonators are sparking a renewed interest in this process [23]. In this Letter, we report on the direct experimental observation of PMI in a passive Kerr resonator. Our experimental test-bed is based on a normally dispersive fiber ring cavity that incorporates a polarization controller for adjustment of the intra-cavity birefringence. This localized birefringence gives rise to a relative phase detuning between the two orthogonal polarization modes of the cavity, which in turn affects the frequency shift of the PMI sidebands. We also find that birefringence can lead to period-doubled (P2) dynamics, characterized by a two round-trip cycle. Our experimental results are in good agreement with theoretical predictions and numerical simulations based on an iterative two-component Ikeda map. The experimental setup is displayed in Fig. 1(a). It consists of a L = 12-m long passive fiber ring cavity with a finesse F of about 27, mainly built out of spun fiber. To avoid competition with scalar MI [2], we have built a cavity with normal group-velocity dispersion estimated to 2 = 47 ps 2 /km, a value large enough to neglect third-order dispersion. Also, the use of a spun fiber (nearly isotropic) avoids group-velocity mismatch between the polarization components. Additionally, to prevent any additional source of bending-induced birefringence, the fiber was carefully off-spooled and wound directly on our experimental board with a large 50-cm diameter. We estimate that this causes a birefringence $\Delta$n no greater than 10 --8 [24], which can be neglected in our study.

Multimode optical fibers has emerged as the platform that will bridge the gap between nonlinear optics in bulk media and in single-mode fibers. However, the understanding of the transition between these two research fields still remains incomplete despite numerous investigations of intermodal nonlinear phenomena and spatiotemporal coupling. Some of the striking phenomena observed in bulk media with ultrashort and ultra-intense pulses (i.e., conical emission, harmonic generation and light bullets) require a deeper insight to be possibly unveiled in multimode fibers. Here we generalize the concept of conical waves described in bulk media towards structured media, such as multimode optical fibers, in which only a discrete and finite number of modes can propagate. The modal distribution of optical fibers provides a quantization of conical emission (e.g., quantized X-waves) through phase-matched resonant radiations (i.e., dispersive waves) seeded by optical shocks or ultrashort wave structures during spatiotemporal compression stages. Such quantized dispersion- and diffraction-free waves are generated when a rather intense short pulse propagates nonlinearly in a multimode waveguide, whatever the dispersion regime and waveguide geometry. Future nonlinear experiments in commercially-available multimode fibers could reveal different forms of conical emission and an easy control of supercontinuum light bullets., Comment: 6 pages, 3 figures

We report on the experimental observation of a simultaneous threefold wavelength and spatial conversion process at telecommunication wavelengths taking place in a 6-LP-mode graded-index few-mode fiber. The physical mechanism is based on parallel and phase-matched frequency-degenerated intermodal four-wave mixing (FD-IFWM) phenomena occurring between the fundamental mode and higher-order spatial modes. More precisely, a single high-power frequency-degenerated pump wave is simultaneously injected in the four spatial modes LP01, LP11, LP02 and LP31 of a 1.8-km long graded-index few-mode fiber together with three independent signals in the fundamental mode. By means of three parallel phase-matched FD-IFWM interactions, these initial signals are then simultaneously spatially and frequency converted from the fundamental mode to specific high-order modes. The influence of the differential modal group delay is also investigated and shows that the walk-off between the spatially multiplexed signals significantly limits the bandwidth of the conversion process for telecom applications.

We present both theoretical description and experimental observation of the modulation instability process and related rogue breathers in the case of stationary periodic background waves, namely cnoidal and dnoidal envelopes. Despite being well-known solutions of the nonlinear Schrodinger equation, the stability of such background waves has remained unexplored experimentally until now, unlike the fundamental plane wave. By means of two experimental setups, namely, in nonlinear optics and hydrodynamics, we report on quantitative measurements of spontaneous modulation instability gain seeded by input random noise, as well as the formation of rogue breather solutions induced by a coherent perturbation. Our results confirm the generalization of modulation instability when more complex background waves are involved.

The clinical need for vascular grafts is associated with cardiovascular diseases frequently leading to fatal outcomes. Artificial vessels based on bioresorbable polymers can replace the damaged vascular tissue or create a bypass path for blood flow while stimulating regeneration of a blood vessel in situ. However, the problem of proper conditions for the cells to grow on the vascular graft from the adventitia while maintaining its mechanical integrity of the luminal surface remains a challenge. In this work, we propose a two-stage technology for processing electrospun vascular graft from polycaprolactone, which consists of plasma treatment and subsequent immobilization of hyaluronic acid on its surface producing thin double-sided graft with one hydrophilic and one hydrophobic side. Plasma modification activates the polymer surfaces and produces a thin layer for linker-free immobilization of bioactive molecules, thereby producing materials with unique properties. The proposed modification does not affect the morphology or mechanical properties of the graft and improves cell adhesion. The proposed approach can potentially be used for various biodegradable polymers such as polylactic acid, polyglycolide, and their copolymers and blends, with a hydrophilic inner surface and a hydrophobic outer surface.

We analyse the temporal properties of the optical pulse wave that is obtained by applying a set of spectral $\pi/2$ phase shifts to continuous-wave light that is phase-modulated by a temporal sinusoidal wave. We develop an analytical model to describe this new optical waveform that we name 'besselon'. We also discuss the reduction of sidelobes in the wave intensity profile by means of an additional spectral $\pi$ phase shift, and show that the resulting pulses can be efficiently time-interleaved. The various predicted properties of the besselon are confirmed by experiments demonstrating the generation of low-duty cycle, high-quality pulses at repetition rates up to 28 GHz.

Material characteristics and input-field specifics limit the controllability of nonlinear electromagnetic-field interactions. As these nonlinear interactions could be exploited to create strongly localized bright and dark waves, such as nonlinear surface polaritons, ameliorating this limitation is important. We present our approach to amelioration, which is based on a surface-polaritonic waveguide reconfiguration that enables excitation, propagation and coherent control of coupled dark rogue waves having orthogonal polarizations. Our control mechanism is achieved by finely tuning laser-field intensities and their respective detuning at the interface between the atomic medium and the metamaterial layer. In particular, we utilize controllable electromagnetically induced transparency (EIT) windows commensurate with surface-polaritonic polarization-modulation instability to create symmetric and asymmetric polaritonic frequency combs associated with dark localized waves. Our method takes advantage of an atomic self-defocusing nonlinearity and dark rogue-wave propagation to obtain a sufficient condition for generating phase singularities. Underpinning this method is our theory which incorporates dissipation and dispersion due to the atomic medium being coupled to nonlinear surface-polaritonic waves~(SPWs). Consequently, our waveguide configuration acts as a bimodal polaritonic frequency-comb generator and a high-speed phase rotator, thereby opening prospects for phase singularities in nanophotonic and quantum communication devices.

We investigate in detail the qualitative similarities between the pulse localization characteristics observed using sinusoidal phase modulation during linear propagation and those seen during the evolution of Akhmediev breathers during propagation in a system governed by the nonlinear Schr{\"o}dinger equation. The profiles obtained at the point of maximum focusing indeed present very close temporal and spectral features. If the respective linear and nonlinear longitudinal evolutions of those profiles are similar in the vicinity of the point of maximum focusing, they may diverge significantly for longer propagation distance. Our analysis and numerical simulations are confirmed by experiments performed in optical fiber.

We theoretically and experimentally demonstrate a new electro-optic linear approach to generate high repetition-rate picosecond pulse trains. This simple cavity-free method is based on a temporal sinusoidal phase modulation combined with a triangular spectral phase processing. Experimental results validate the concept at repetition rates ranging from 10 GHz up to 40 GHz with the generation of background-free pulse trains made of nearly Gaussian Fourier-transform limited pulses.

Spontaneous emergence of self-organized patterns and their bifurcations towards a regime of complex dynamics in non-equilibrium dissipative systems is a paradigm of phase transition. Indeed, the behavior of these patterns in the highly nonlinear regime remains less explored, even in recent high-quality-factor resonators such as Kerr-nonlinear optical ones. Here, we investigate theoretically and experimentally the alteration of the resulting Kerr frequency combs from the weakly to the highly nonlinear regime, in the frameworks of spatiotemporal chaos, and dissipative phase transitions. We reveal the existence of a striking and easily accessible scenario of spatiotemporal chaos, free of cavity solitons, in a monostable operating regime, wherein a transition to amplitude turbulence via spatiotemporal intermittency is evidenced. Moreover, statistics of the light bursts in the resulting turbulent regime unveils the existence of rogue waves as extreme events characterized by long-tail statistics.

The aim of the present paper is twofold. First, to give the main ideas behind quantum computingand quantum information, a field based on quantum-mechanical phenomena. Therefore, a shortreview is devoted to (i) quantum bits or qubits (and more generally qudits), the analogues of theusual bits 0 and 1 of the classical information theory, and to (ii) two characteristics of quantummechanics, namely, linearity (which manifests itself through the superposition of qubits and theaction of unitary operators on qubits) and entanglement of certain multi-qubit states (a resourcethat is specific to quantum mechanics). Second, to focus on some mathematical problems relatedto the so-called mutually unbiased bases used in quantum computing and quantum informationprocessing. In this direction, the construction of mutually unbiased bases is presented via twodistinct approaches: one based on the group SU(2) and the other on Galois fields and Galois rings.

We present a detailed study of the phase properties of rational breather waves observed in the hydrodynamic and optical domains, namely the Peregrine soliton and related second-order solution. At the point of maximum compression, our experimental results recorded in a wave tank or using an optical fiber platform reveal a characteristic phase shift that is multiple of $\pi$ between the central part of the pulse and the continuous background, in agreement with analytical and numerical predictions. We also stress the existence of a large longitudinal phase shift across the point of maximum compression.

The data recorded in optical fiber [1] and in hydrodynamic [2] experiments reported the pioneering observation of nonlinear waves with spatiotemporal localization similar to the Peregrine soliton are examined by using nonlinear spectral analysis. Our approach is based on the integrable nature of the one-dimensional focusing nonlinear Schrodinger equation (1D-NLSE) that governs at leading order the propagation of the optical and hydrodynamic waves in the two experiments. Nonlinear spectral analysis provides certain spectral portraits of the analyzed structures that are composed of bands lying in the complex plane. The spectral portraits can be interpreted within the framework of the so-called finite gap theory (or periodic inverse scattering transform). In particular, the number N of bands composing the nonlinear spectrum determines the genus g = N - 1 of the solution that can be viewed as a measure of complexity of the space-time evolution of the considered solution. Within this setting the ideal, rational Peregrine soliton represents a special, degenerate genus 2 solution. While the fitting procedures employed in [1] and [2] show that the experimentally observed structures are quite well approximated by the Peregrine solitons, nonlinear spectral analysis of the breathers observed both in the optical fiber and in the water tank experiments reveals that they exhibit spectral portraits associated with more general, genus 4 finite-gap NLSE solutions. Moreover, the nonlinear spectral analysis shows that the nonlinear spectrum of the breathers observed in the experiments slowly changes with the propagation distance, thus confirming the influence of unavoidable perturbative higher order effects or dissipation in the experiments.

A relation is established in the present paper between Dicke states in a d-dimensional space and vectors in the representation space of a generalized Weyl-Heisenberg algebra of finite dimension d. This provides a natural way to deal with the separable and entangled states of a system of N = d-1 symmetric qubit states. Using the decomposition property of Dicke states, it is shown that the separable states coincide with the Perelomov coherent states associated with the generalized Weyl-Heisenberg algebra considered in this paper. In the so-called Majorana scheme, the qudit (d-level) states are represented by N points on the Bloch sphere; roughly speaking, it can be said that a qudit (in a d-dimensional space) is describable by a N-qubit vector (in a N-dimensional space). In such a scheme, the permanent of the matrix describing the overlap between the N qubits makes it possible to measure the entanglement between the N qubits forming the qudit. This is confirmed by a Fubini-Study metric analysis. A new parameter, proportional to the permanent and called perma-concurrence, is introduced for characterizing the entanglement of a symmetric qudit arising from N qubits. For d=3 (i.e., N = 2), this parameter constitutes an alternative to the concurrence for two qubits. Other examples are given for d=4 and 5. A connection between Majorana stars and zeros of a Bargmmann function for qudits closes this article., Comment: to be published in Entropy (special issue: Entropy and Information in the Foundation of Quantum Physics)