In optical second harmonic generation with normal dispersion, the virtually infinite bandwidth of the unbounded, hyperbolic, modulational instability leads to quenching of spatial multi-soliton formation and to the occurrence of a catastrophic spatio-temporal break-up when an extended beam is let to interact with an extremely weak external noise with coherence time much shorter than that of the pump.
We derive analytical expressions for the coherence in the onset of modulation instability, in excellent agreement with thorough numerical simulations. As usual, we start by a linear perturbation analysis, where broadband noise is added to a continuous wave (CW) pump; then, we investigate the effect of adding a deterministic seed to the CW pump, a case of singular interest as it is commonly encountered in parametric amplification schemes. Results for the dependence of coherence on parameters such as fiber type, pump power, propagated distance, seed signal-to-noise ratio are presented. Finally, …
The spectroscopic techniques for time-resolved fine analysis of matter require coherent X-ray radiation with femtosecond duration and high average brightness. Seeded free-electron lasers (FELs), which use the frequency up-conversion of an external seed laser to improve temporal coherence, are ideal for providing fully coherent soft X-ray pulses. However, it is difficult to operate seeded FELs at a high repetition rate due to the limitations of present state-of-the-art laser systems. Here, we report the novel self-modulation method for enhancing laser-induced energy modulation, thereby signific…
Recently, the self-modulation scheme of a weakly pre-bunched electron beam has been proposed [Yan et al., Physical Review Letters 126, 084801 (2021)], which is of great promise for high-repetition-rate seeded free-electron lasers (FELs), such as high-gain harmonic generation (HGHG). In this paper, the self-modulation scheme is systematically analyzed and optimized, and further experiments in which the self-modulator is resonant at the second harmonic of the seed laser are conducted. The three-dimensional numerical simulations show that the required seed laser intensity in the self-modulation s…
We experimentaly investigate higher-order seeded modulation instability in an optical fiber experiment. The recirculating loop configuration with round-trip losses compensation enables the observation in single-shot of the spatio-temporal evolution of an initially modulated continuous field revealing intricate yet deterministic dynamics. By tuning the modulation period, a continuous transition between perfectly coherent and purely noise-driven dynamics is observed that we characterise by means of a statistical study.
Generation of free-space laser-like emissions of high spatiotemporal coherence and narrow bandwidth in atmosphere opens promising opportunities for remote spectroscopic sensing. Here, we report on generation of such laser-like emissions, which results from the combined contributions of perturbative and non-perturbative nonlinear optical effects in nitrogen molecules exposed to intense mid-infrared laser fields. We systematically investigate the dependence of the generated free-space laser spectrum on wavelength and power of the driver laser. It is revealed that the free-space laser is produced…
In $χ^{(2)}$ three-wave mixing, the noise-seeded spatio--temporal modulational instability has a dramatic impact on the spatial-soliton dynamics, leading to the counterintuitive observation of a soliton with no apparent participation of the high-frequency field in the process.
We present detailed experimental study on noise-seeded intermodal modulation instability (IM-MI) in normal dispersion region of a conventional step-index fiber. The sharp refractive index contrast between core and cladding leads to large group velocity mismatch between the spatial modes, coaxing to efficient IM-MI and generation of multiple spectral peaks along with Raman peaks. Evolution of the spectrum with pump powers and fiber lengths are observed. Experimental findings are well supported with the theoretical framework based on bimodal-MI model considering the distinct dispersion parameter…
Numerical simulations are used to study how fiber supercontinuum generation seeded by picosecond pulses can be actively controlled through the use of input pulse modulation. By carrying out multiple simulations in the presence of noise, we show how tailored supercontinuum Spectra with increased bandwidth and improved stability can be generated using an input envelope modulation of appropriate frequency and depth. The results are discussed in terms of the non-linear propagation dynamics and pump depletion.
All-optical Lithography for Spatiotemporal Patterning of High-Modulation Azopolymer Microreliefs
University of Naples Federico II（那不勒斯费德里科二世大学）；Leibniz Institute of Polymer Research Dresden（德累斯顿莱布尼茨聚合物研究所）；Dresden University of Technology（德累斯顿工业大学）
The recent surge of interest in temporal modulation schemes to induce magnet-free non-reciprocity has inspired several exciting opportunities for photonic technology. Here, we investigate a scheme to realize free-space isolators and highly non-reciprocal mirrors with weak modulation imparted by an acoustic wave. Conventional optical mirrors are reciprocal: in a given plane of incidence, reflection is independent of the sign of the angle of incidence, which enables two people to simultaneously look at each other through their reflection. In contrast, we propose a strategy to dramatically break …
Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the manipulation of the modulation instability is of primary importance in controlling and manipulating the character of spatial patterns initiated by that instability. We show that the spatio-temporal periodic modulation of the potential of the spatially extended system results in a modification of its pattern forming instability. Depending on the modulation charac…
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 …
Using the Jacobi Elliptic Functions, an analytical solution is developed for the nonlinear amplitude equation of Surface Plasmon Polaritons (SPPs) in a graphene-dielectric waveguide. It is shown that the field localization of SPPs coupled with TM polarized terahertz light can be enhanced if the nonlinearity is increased. On the side, a numerical solution based on Split Step Beam Propagation Method (SSBPM) suggests that spatial Modulation Instabilty (MI) can be dominant. Accordingly, larger nonlinearity leads to the generation of discrete plasmon solitons rather than the diffracted profile resu…
Various seeding configurations have being proposed for frequency up-conversion of the electron beam density distribution, in which the energy spread, may however hinder the harmonic generation efficiency. In this Letter, a method for cooling the electron beam energy spread by off-resonance seed laser modulation is described, using a transversely dispersed beam and a modulator undulator with proper transverse gradient. With this novel mechanism, it is shown that the frequency up-conversion efficiency can be significantly enhanced. We present theoretical analysis and numerical simulations for se…
Characterizing an isolated attosecond pulse (IAP) is essential for its potential applications. A complete characterization of an IAP ultimately requires the determination of its electric field in both time and space domains. However, previous methods, like the widely-used RABBITT and attosecond streaking, only measure the temporal profile of the attosecond pulse. Here we demonstrate an all-optical method for the measurement of the space-time properties of an IAP. By introducing a non-collinear perturbing pulse to the driving field, the process of IAP generation is modified both spatially and t…
We theoretically investigate the free-carrier induced spatio-temporal dynamics of continuous waves in silicon waveguides embedded in an amplifying medium. Optical propagation is governed by a cubic Ginzburg-Landau equation coupled with an ordinary differential equation accounting for the free-carrier dynamics. We find that, owing to free-carrier dispersion, countinuous waves are modulationally unstable in both anomalous and normal dispersion regimes and chaotically generate unstable accelerating pulses.
We analyze the propagation of electromagnetic waves in media where the dielectric constants undergo rapid temporal periodic modulation. Both spatially homogeneous and periodic media are studied. Fast periodic temporal modulation of the dielectric constant of a homogeneous medium leads to existence of photonic band-gap like phenomena. In the presence of both spatial and tem- poral periodicity the electromagnetic spectrum is described in a four-dimensional cube, defining an effective Brillouin zone. In the case of incommensurability between space and time periodicities, completely dispersed poin…
We introduce an approach to implement full coherent control on nanometer length scales. It is based on spatio-temporal modulation of the surface plasmon polariton (SPP) fields at the thick edge of a nanowedge. The SPP wavepackets propagating toward the sharp edge of this nanowedge are compressed and adiabatically concentrated at a nanofocus, forming an ultrashort pulse of local fields. The one-dimensional spatial profile and temporal waveform of this pulse are completely coherently controlled.
The nonlinear stage of modulational instability in optical fibers induced by a wide and easily accessible class of localized perturbations is studied using the nonlinear Schrodinger equation. It is showed that the development of associated spatio-temporal patterns is strongly affected by the shape and the parameters of the perturbation. Different scenarios are presented that involve an auto-modulation developing in a characteristic wedge, possibly coexisting with breathers which lie inside or outside the wedge.
Spatio-temporally modulated impedance surfaces can be good candidates for generation of radiating waves with arbitrary eigenstates by breaking momentum and energy conservations. Here, we present a theoretical framework based on the holographic technique and generalized Floquet-wave expansion to analyze spatio-temporally modulated impedance surfaces. The holographic technique estimates the required impedance distribution to achieve the desired momentum. Injecting temporal modulation deviates the eigenvalues and changes the radiation frequency. Using the proposed analytical model, the eigenvalue…
Shenzhen University（深圳大学）；East China Normal University（华东师范大学）；University of Shanghai for Science and Technology（上海理工大学）；Northwestern Polytechnical University（西北工业大学）
Plane waves in Kerr media spontaneously generate paraxial X-waves (i.e. non-dispersive and non-diffractive pulsed beams) that get amplified along propagation. This effect can be considered a form of conical emission (i.e. spatio-temporal modulational instability), and can be used as a key for the interpretation of the out of axis energy emission in the splitting process of focused pulses in normally dispersive materials. A new class of spatio-temporal localized wave patterns is identified. X-waves instability, and nonlinear X-waves, are also expected in periodical Bose condensed gases.
Measuring the field of visible light with high spatial resolution has been challenging, as many established methods only detect a focus-averaged signal. Here, we introduce a near-field method for optical field sampling that overcomes that limitation by employing the localization of the enhanced near-field of a nanometric needle tip. A probe field perturbs the photoemission from the tip, which is induced by a pump pulse, generating a field-dependent current modulation that can easily be captured with our electronic detection scheme. The approach provides reliable characterization of near-petahe…
Spatio-temporal modulation has shown great promise as a strong time-reversal symmetry breaking mechanism that enables integrated nonreciprocal devices and topological materials at optical frequencies. However, optical modulation has its own constraints in terms of modulation index and frequency, which limit the bandwidth and miniaturization of circulators and isolators, not unlike the magneto-optical schemes that it promises to replace. Here we propose and numerically demonstrate a Floquet circulator that leverages the untapped degrees of freedom unique to time-modulated resonators. Excited by…
We investigate the spontaneous growth of noise that accompanies the nonlinear evolution of seeded modulation instability into Fermi-Pasta-Ulam recurrence. Results from the Floquet linear stability analysis of periodic solutions of the three-wave truncation are compared with full numerical solutions of the nonlinear Schrödinger equation. The predicted initial stage of noise growth is in good agreement with simulations, and is expected to provide further insight in the subsequent dynamics of the field evolution after recurrence breakup.
We report the use of prism-assisted side-coupling to investigate the spatio-temporal dynamics of photoionization in an Ar-filled hollow-core photonic crystal fiber. By launching four different LP core modes we are able to probe temporal and spatial changes in the modal refractive index on timescales from a few hundred picoseconds to several hundred microseconds after the ionization event. We experimentally analyze the underlying gas density waves and find good agreement with quantitative and qualitative hydrodynamic predictions. Moreover, we observe periodic modulations in the MHz-range lastin…
We show that, in the pure-quartic systems, modulation instability (MI) undergoes heteroclinic-structure transitions (HSTs) at two critical frequencies of ω c1 and ω c2 ( ω c2 > ω c1 ), which indicates that there are significantchanges of the spatiotemporal behavior in the system. The complicated heteroclinic structure of instability obtained by the mode truncation method reveals all possible dynamic trajectories of nonlinear waves, which allows us to discover the various types of Fermi-Pasta-Ulam (FPU) recurrences and Akhmediev breathers (ABs). When the modulational frequency satisfies ω < ω c…
A problem of self-organized motions in solid-state nonequilibrium media has been studied experimentally using methods of quantum acoustics. Generalized Poincare cross-sections of microwave power spectra (MPS) have been obtained in an optical-wavelengths acoustic laser (paramagnetic phaser) based on ruby crystal. Considerable narrowing of MPS and their autowave-like superslow motion have been observed under conditions of periodical pump modulation beyond the region of the phaser relaxation resonance. Some preliminar experimental results of this work were published in: Solid State Communications…
Bound states in the continuum in multilayered time-varying metasurfaces
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院理论固体物理研究所）；Institute for Analysis, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院分析学研究所）；Institute of Nanotechnology, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院纳米技术研究所）；Center for Integrated Quantum Science and Technology (IQST), Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院综合量子科学与技术中心）
Dynamic optical metasurfaces with ultrafast temporal response, i.e., spatiotemporal optical metasurfaces, provide attractive solutions and open fascinating perspectives for modern highly integrated optics and photonics. In this work, electro-optically controlled optical metasurfaces operating in reflection and utilizing resonant waveguide mode excitation are demonstrated from the viewpoint of free-space propagating light modulation. The modulation of reflected light power with superior characteristics in comparison with prior research is achieved by identifying a suitable low-loss waveguide mo…
