Single-shot ultrafast laser processing of high-aspect-ratio nanochannels using elliptical Bessel beams.

Ultrafast lasers have revolutionized material processing, opening a wealth of new applications in many areas of science. A recent technology that allows the cleaving of transparent materials via non-ablative processes is based on focusing and translating a high-intensity laser beam within a material to induce a well-defined internal stress plane. This then enables material separation without debris generation. Here, we use a non-diffracting beam engineered to have a transverse elliptical spatial profile to generate high-aspect-ratio elliptical channels in glass of a dimension 350 nm×710 nm and subsequent cleaved surface uniformity at the sub-micron level.

High aspect ratio micro-explosions in the bulk of sapphire generated by femtosecond Bessel beams.

Femtosecond pulses provide an extreme degree of confinement of light matter-interactions in high-bandgap materials because of the nonlinear nature of ionization. It was recognized very early on that a highly focused single pulse of only nanojoule energy could generate spherical voids in fused silica and sapphire crystal as the nanometric scale plasma generated has energy sufficient to compress the material around it and to generate new material phases. But the volumes of the nanometric void and of the compressed material are extremely small. Here we use single femtosecond pulses shaped into high-angle Bessel beams at microjoule energy, allowing for the creation of very high 100:1 aspect ratio voids in sapphire crystal, which is one of the hardest materials, twice as dense as glass. The void volume is 2 orders of magnitude higher than those created with Gaussian beams. Femtosecond and picosecond illumination regimes yield qualitatively different damage morphologies. These results open novel perspectives for laser processing and new materials synthesis by laser-induced compression.

Hydrodynamics of periodic breathers.

We report the first experimental observation of periodic breathers in water waves. One of them is Kuznetsov-Ma soliton and another one is Akhmediev breather. Each of them is a localized solution of the nonlinear Schrödinger equation (NLS) on a constant background. The difference is in localization which is either in time or in space. The experiments conducted in a water wave flume show results that are in good agreement with the NLS theory. Basic features of the breathers that include the maximal amplitudes and spectra are consistent with the theoretical predictions.

Experimental dynamics of Akhmediev breathers in a dispersion varying optical fiber.

We investigate experimentally the dynamics of Akhmediev breathers in an optical fiber with a longitudinally tailored dispersion that allows to nearly freeze the breather evolution near their point of maximal compression. Our results are in good agreement with numerical simulations.

Spatiotemporal structure of femtosecond Bessel beams from spatial light modulators.

We numerically investigate the spatiotemporal structure of Bessel beams generated with spatial light modulators (SLMs). Grating-like phase masks enable the spatial filtering of undesired diffraction orders produced by SLMs. Pulse front tilt and temporal broadening effects are investigated. In addition, we explore the influence of phase wrapping and show that the spatiotemporal structure of SLM-generated femtosecond Bessel beams is similar to Bessel X-pulses at short propagation distance and to subluminal pulsed Bessel beams at long propagation distance.

Hydrodynamic supercontinuum.

We report the experimental observation of multi-bound-soliton solutions of the nonlinear Schrödinger equation (NLS) in the context of hydrodynamic surface gravity waves. Higher-order N-soliton solutions with N=2, 3 are studied in detail and shown to be associated with self-focusing in the wave group dynamics and the generation of a steep localized carrier wave underneath the group envelope. We also show that for larger input soliton numbers, the wave group experiences irreversible spectral broadening, which we refer to as a hydrodynamic supercontinuum by analogy with optics. This process is shown to be associated with the fission of the initial multisoliton into individual fundamental solitons due to higher-order nonlinear perturbations to the NLS. Numerical simulations using an extended NLS model described by the modified nonlinear Schrödinger equation, show excellent agreement with experiment and highlight the universal role that higher-order nonlinear perturbations to the NLS play in supercontinuum generation.

Real time noise and wavelength correlations in octave-spanning supercontinuum generation.

We use dispersive Fourier transformation to measure shot-to-shot spectral instabilities in femtosecond supercontinuum generation. We study both the onset phase of supercontinuum generation with distinct dispersive wave generation, as well as a highly-unstable supercontinuum regime spanning an octave in bandwidth. Wavelength correlation maps allow interactions between separated spectral components to be identified, even when such interactions are not apparent in shot-to-shot or average measurements. Experimental results are interpreted using numerical simulations. Our results show the clear advantages of dispersive Fourier transformation for studying spectral noise during supercontinuum generation.

Arbitrary nonparaxial accelerating periodic beams and spherical shaping of light.

We report the observation of arbitrary accelerating beams (ABs) designed using a nonparaxial description of optical caustics. We use a spatial light modulator-based setup and techniques of Fourier optics to generate circular and Weber beams subtending over 95 deg of arc. Applying a complementary binary mask also allows the generation of periodic ABs taking the forms of snake-like trajectories, and the application of a rotation to the caustic allows the first experimental synthesis of optical ABs upon the surface of a sphere in three dimensions.

Emergence of coherent wave groups in deep-water random sea.

Extreme surface waves in a deep-water long-crested sea are often interpreted as a manifestation in the real world of the so-called breathing solitons of the focusing nonlinear Schrödinger equation. While the spontaneous emergence of such coherent structures from nonlinear wave dynamics was demonstrated to take place in fiber-optics systems, the same point remains far more controversial in the hydrodynamic case. With the aim to shed further light on this matter, the emergence of breatherlike coherent wave groups in a long-crested random sea is investigated here by means of high-resolution spectral simulations of the fully nonlinear two-dimensional Euler equations. The primary focus of our study is to parametrize the structure of random wave fields with respect to the Benjamin-Feir index, which is a nondimensional measure of the energy localization in Fourier space. This choice is motivated by previous results, showing that extreme-wave activity in a long-crested sea is highly sensitive to such a parameter, which is varied here by changing both the characteristic spectral bandwidth and the average wave steepness. It is found that coherent wave groups, closely matching realizations of Kuznetsov-Ma breathers in Euler dynamics, develop within wave fields characterized by sufficiently narrow-banded spectra. The characteristic spatial and temporal scales of wave group dynamics, and the corresponding occurrence of extreme events, are quantified and discussed by means of space-time autocorrelations of the surface elevation envelope and extreme-event statistics.

On Hokusai's Great wave off Kanagawa: localization, linearity and a rogue wave in sub-Antarctic waters.

The Hokusai woodcut entitled The great wave off Kanagawa has been interpreted as an unusually large storm wave, likely to be classed as a rogue wave, and possibly generated from nonlinear wave dynamics (J. H. E. Cartwright and H. Nakamura, Notes Rec. R. Soc.63, 119-135 (2009)). In this paper, we present a complementary discussion of this hypothesis, discussing in particular how linear and nonlinear mechanisms can both contribute to the emergence of rogue wave events. By making reference to the Great wave's simultaneous transverse and longitudinal localization, we show that the purely linear mechanism of directional focusing also predicts characteristics consistent with those of the Great wave. In addition, we discuss the properties of a particular rogue wave photographed on the open ocean in sub-Antarctic waters, which shows two-dimensional localization and breaking dynamics remarkably similar to Hokusai's depiction in the woodcut.

Real-time full bandwidth measurement of spectral noise in supercontinuum generation.

The ability to measure real-time fluctuations of ultrashort pulses propagating in optical fiber has provided significant insights into fundamental dynamical effects such as modulation instability and the formation of frequency-shifting rogue wave solitons. We report here a detailed study of real-time fluctuations across the full bandwidth of a fiber supercontinuum which directly reveals the significant variation in measured noise statistics across the spectrum, and which allows us to study correlations between widely separated spectral components. For two different propagation distances corresponding to the onset phase of spectral broadening and the fully-developed supercontinuum, we measure real time noise across the supercontinuum bandwidth, and we quantify the supercontinuum noise using statistical higher-order moments and a frequency-dependent intensity correlation map. We identify correlated spectral regions within the supercontinuum associated with simultaneous sideband generation, as well as signatures of pump depletion and soliton-like pump dynamics. Experimental results are in excellent agreement with simulations.

Observation of Kuznetsov-Ma soliton dynamics in optical fibre.

The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation.

Sending femtosecond pulses in circles: highly nonparaxial accelerating beams.

We use caustic beam shaping on 100 fs pulses to experimentally generate nonparaxial accelerating beams along a 60° circular arc, moving laterally by 14 µm over a 28 µm propagation length. This is the highest degree of transverse acceleration reported to our knowledge. Using diffraction integral theory and numerical beam propagation simulations, we show that circular acceleration trajectories represent a unique class of nonparaxial diffraction-free beam profile which also preserves the femtosecond temporal structure in the vicinity of the caustic.

Cascaded phase matching and nonlinear symmetry breaking in fiber frequency combs.

We report theoretical, numerical, and experimental studies of cascaded phase matching in fiber frequency combs and show how this mechanism is directly connected to the dynamics of supercontinuum generation. In particular, linking cascaded four-wave mixing with direct higher-order nonlinear processes allows us to derive a simple phase matching condition that governs nonlinear symmetry breaking in the presence of higher-order dispersion. We discuss how this mechanism provides a physical interpretation of soliton-induced Cherenkov radiation and associated spectral recoil in terms of phase-matched frequency mixing pumped by bichromatic pump pairs in the soliton spectrum. Theoretical and numerical predictions are confirmed via experiments using both quasicontinuous wave and picosecond pulse excitation.

Arbitrary accelerating micron-scale caustic beams in two and three dimensions.

We generate arbitrary convex accelerating beams by direct application of an appropriate spatial phase profile on an incident Gaussian beam. The spatial phase calculation exploits the geometrical properties of optical caustics and the Legendre transform. Using this technique, accelerating sheet caustic beams with parabolic profiles (i.e. Airy beams), as well as quartic and logarithmic profiles are experimentally synthesized from an incident Gaussian beam, and we show compatibility with material processing applications using an imaging system to reduce the main intensity lobe at the caustic to sub-10 micron transverse dimension. By applying additional and rotational spatial phase, we generate caustic-bounded sheet and volume beams, which both show evidence of the recently predicted effect of abrupt autofocussing. In addition, an engineered accelerating profile with femtosecond pulses is applied to generate a curved zone of refractive index modification in glass. These latter results provide proof of principle demonstration of how this technique may yield new degrees of freedom in both nonlinear optics and femtosecond micromachining.

Spectral dynamics of modulation instability described using Akhmediev breather theory.

The Akhmediev breather formalism of modulation instability is extended to describe the spectral dynamics of induced multiple sideband generation from a modulated continuous wave field. Exact theoretical results describing the frequency domain evolution are compared with experiments performed using single mode fiber around 1550 nm. The spectral theory is shown to reproduce the depletion dynamics of an injected modulated continuous wave pump and to describe the Fermi-Pasta-Ulam recurrence and recovery towards the initial state. Realistic simulations including higher-order dispersion, loss, and Raman scattering are used to identify that the primary physical factors that preclude perfect recurrence are related to imperfect initial conditions.

Giant dispersive wave generation through soliton collision.

We numerically study long pulse supercontinuum generation in a photonic crystal fiber with two zero-dispersion wavelengths, reporting a dynamical effect where soliton collisions excite dispersive waves with 1 order of magnitude greater peak power than that arising from single-soliton generation. The dispersive wave peak power exhibits extreme-value "rogue" characteristics, with the long tail of the distribution populated by collision-related events.

High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams.

We present a systematic study of femtosecond laser microchannel machining in glass using nondiffracting Bessel beams. In particular, our results identify a source and focusing parameter working window where high aspect ratio taper-free microchannels can be reproducibly produced without sample translation. With appropriate source parameters, we machine channels of 2 microm diameter and with aspect ratios up to 40. We propose the filamentation stability of the Bessel beam propagation as the critical factor underlying the controlled and reproducible results that have been obtained.

Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation.

Numerical simulations of the onset phase of continuous wave supercontinuum generation from modulation instability show that the structure of the field as it develops can be interpreted in terms of the properties of Akhmediev Breathers. Numerical and analytical results are compared with experimental measurements of spectral broadening in photonic crystal fiber using nanosecond pulses.

Surface nanoprocessing with nondiffracting femtosecond Bessel beams.

We demonstrate the application of nondiffracting Bessel beams for reproducible nanometric-scale feature patterning in glass. A femtosecond pulse zero-order Bessel beam with a central spot radius of 360 nm was used to write 500 nm radius nanocraters over a longitudinal positioning range exceeding 20 microm, with a variation in radius of less than 10%. The use of Bessel beams significantly reduces constraints on critical sample positioning in the nanoscale writing regime, enabling the use of femtosecond pulses for fast inscription of nanometer-scale features over large sample areas.