Recent observations show that the probability of encountering an extremely large rogue wave in the open ocean is much larger than expected from ordinary wave-amplitude statistics. Although considerable effort has been directed towards understanding the physics behind these mysterious and potentially destructive events, the complete picture remains uncertain. Furthermore, rogue waves have not yet been observed in other physical systems. Here, we introduce the concept of optical rogue waves, a counterpart of the infamous rare water waves. Using a new real-time detection technique, we study a system that exposes extremely steep, large waves as rare outcomes from an almost identically prepared initial population of waves. Specifically, we report the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation--a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input. We model the generation of these rogue waves using the generalized nonlinear Schrödinger equation and demonstrate that they arise infrequently from initially smooth pulses owing to power transfer seeded by a small noise perturbation.

Strong-field physics, an extreme limit of light-matter interaction, is expanding into the realm of surfaces and nanostructures from its origin in atomic and molecular science. The attraction of nanostructures lies in two intimately connected features: local intensity enhancement and sub-wavelength confinement of optical fields. Local intensity enhancement facilitates access to the strong-field regime and has already sparked various applications, whereas spatial localization has the potential to generate strong-field dynamics exclusive to nanostructures. However, the observation of features unattainable in gaseous media is challenged by many-body effects and material damage, which arise under intense illumination of dense systems. Here, we non-destructively access this regime in the solid state by employing single plasmonic nanotips and few-cycle mid-infrared pulses, making use of the wavelength-dependence of the interaction, that is, the ponderomotive energy. We investigate strong-field photoelectron emission and acceleration from single nanostructures over a broad spectral range, and find kinetic energies of hundreds of electronvolts. We observe the transition to a new regime in strong-field dynamics, in which the electrons escape the nanolocalized field within a fraction of an optical half-cycle. The transition into this regime, characterized by a spatial adiabaticity parameter, would require relativistic electrons in the absence of nanostructures. These results establish new degrees of freedom for the manipulation and control of electron dynamics on femtosecond and attosecond timescales, combining optical near-fields and nanoscopic sources.

Coherent manipulation of quantum systems with light is expected to be a cornerstone of future information and communication technology, including quantum computation and cryptography. The transfer of an optical phase onto a quantum wavefunction is a defining aspect of coherent interactions and forms the basis of quantum state preparation, synchronization and metrology. Light-phase-modulated electron states near atoms and molecules are essential for the techniques of attosecond science, including the generation of extreme-ultraviolet pulses and orbital tomography. In contrast, the quantum-coherent phase-modulation of energetic free-electron beams has not been demonstrated, although it promises direct access to ultrafast imaging and spectroscopy with tailored electron pulses on the attosecond scale. Here we demonstrate the coherent quantum state manipulation of free-electron populations in an electron microscope beam. We employ the interaction of ultrashort electron pulses with optical near-fields to induce Rabi oscillations in the populations of electron momentum states, observed as a function of the optical driving field. Excellent agreement with the scaling of an equal-Rabi multilevel quantum ladder is obtained, representing the observation of a light-driven 'quantum walk' coherently reshaping electron density in momentum space. We note that, after the interaction, the optically generated superposition of momentum states evolves into a train of attosecond electron pulses. Our results reveal the potential of quantum control for the precision structuring of electron densities, with possible applications ranging from ultrafast electron spectroscopy and microscopy to accelerator science and free-electron lasers.

Nonequilibrium carrier dynamics in single exfoliated graphene layers on muscovite substrates are studied by ultrafast optical pump-probe spectroscopy and compared with microscopic theory. The very high 10-fs-time resolution allows for mapping the ultrafast carrier equilibration into a quasi-Fermi distribution and the subsequent slower relaxation stages. Coulomb-mediated carrier-carrier and carrier-optical phonon scattering are essential for forming hot separate Fermi distributions of electrons and holes which cool by intraband optical phonon emission. Carrier cooling and recombination are influenced by hot phonon effects.

Optical pump-probe spectroscopy with 7-fs pump pulses and a probe spectrum wider than 0.7 eV reveals the ultrafast carrier dynamics in freestanding thin graphite films. We discern for the first time a rapid intraband carrier equilibration within 30 fs, leaving the system with separated electron and hole chemical potentials. Phonon-mediated intraband cooling of electrons and holes occurs on a 100 fs time scale. The kinetics are in agreement with simulations based on Boltzmann equations.

Intense multiphoton electron emission is observed from sharp (approximately 20 nm radius) metallic tips illuminated with weak 100-pJ, 7-fs light pulses. Local field enhancement, evidenced by concurrent nonlinear light generation, confines the emission to the tip apex. Electrons are emitted from a highly excited nonequilibrium carrier distribution, resulting in a marked change of the absolute electron flux and its dependence on optical power with the tip bias voltage. The strong optical nonlinearity of the electron emission allows us to image the local optical field near a metallic nanostructure with a spatial resolution of a few tens of nanometers in a novel tip-enhanced electron emission microscope.

We describe and demonstrate a new nanometer-scale broadband light source. It is based on the grating-coupled excitation of surface plasmon polaritons (SPPs) on the shaft of a sharp conical metal taper with a tip radius of few tens of nanometers. Far-field excitation of linear nanoslit gratings results in the resonant generation of SPPs traveling over more than 10 mum to the tip apex and converging to an intense radiative local light spot. Such nanofabricated tips are expected to find various applications in nanospectroscopy, overcoming problems with background illumination in apertureless microscopy.

We introduce a framework for the preparation, coherent manipulation and characterization of free-electron quantum states, experimentally demonstrating attosecond pulse trains for electron microscopy. Specifically, we employ phaselocked single-color and two-color optical fields to coherently control the electron wave function along the beam direction. We establish a new variant of quantum state tomography -"SQUIRRELS" -to reconstruct the density matrices of freeelectron ensembles and their attosecond temporal structure. The ability to tailor and quantitatively map electron quantum states will promote the nanoscale study of electron-matter entanglement and the development of new forms of ultrafast electron microscopy and spectroscopy down to the attosecond regime.Optical, electron and x-ray microscopy and spectroscopy reveal specimen properties via spatial and spectral signatures imprinted onto a beam of radiation or electrons. Leaving behind the traditional paradigm of idealized, simple probe beams, advanced optical techniques increasingly harness tailored probes, or even their quantum properties and probe-sample entanglement. The rise of structured illumination microscopy 1 , pulse shaping 2 , and multidimensional 3 and quantum-optical spectroscopy 4 exemplify this development. Similarly, electron microscopy explores the use of shaped electron beams exhibiting particular spatial symmetries 5 or angular momentum 6,7 , and novel measurement schemes involving quantum aspects of electron probes have been proposed 8,9 . Ultrafast imaging and spectroscopy with electrons and x-rays are the basis for an ongoing revolution in the understanding of dynamical processes in matter on atomic scales [10][11][12][13] . The underlying technology heavily rests on laser science for the 2 generation and characterization of ever-shorter femtosecond electron 10,14 and xray [15][16][17] probe pulses, with examples in optical pulse compression 18 and streaking spectroscopy [19][20][21] . The temporal structuring of electron probe beams is facilitated by time-dependent fields in the radio-frequency [22][23][24] , terahertz 18,25 or optical domains. Promising a further leap in temporal resolution, recent findings suggest that ultrafast electron diffraction and microscopy with optically phasecontrolled and sub-cycle, attosecond-structured wave functions may be feasible 8,[26][27][28][29][30] . Specifically, light-field control may translate the temporal resolution of ultrafast transmission electron microscopy (UTEM) 31,32 and electron diffraction (UED) 10,33 , currently at about 200 fs 34 and 20 fs 14,23 , respectively, to the range of attoseconds 26,27,35 . However, such future technologies call for means to both prepare and fully analyze the corresponding quantum states of free electrons.Here, we demonstrate the coherent control and attosecond density modulation of free-electron quantum states using multiple phase-locked optical interactions. Moreover, we introduce quantum state tomography for free electrons, providing crucial e...