Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrodinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.

http://www.physics.sfsu.edu/~laser/pdf/rop347172p20.pdf

Optical spatial solitons: historical overview and recent advances

Over the last dozen years, the area of accelerating waves has made considerable advances not only in terms of fundamentals and experimental demonstrations, but also in connection to a wide range of applications. Starting from the prototypical Airy beam that was proposed and observed in 2007, new families of accelerating waves have been identified in the paraxial and nonparaxial domains in space and/or time, with different methods developed to control at will their trajectory, amplitude, and beam width. Accelerating optical waves exhibit a number of highly desirable attributes. They move along a curved or accelerating trajectory while being resilient to perturbations (self-healing) and are diffraction-free. It is because of these particular features that accelerating waves have been utilized in a variety of applications in the areas of filamentation, beam focusing, particle manipulation, biomedical imaging, plasmons, and material processing, among others.

Airy beams and accelerating waves: an overview of recent advances

We report femtosecond laser micromachining of micron-size curved structures using tailored accelerating beams. We report surface curvatures as small as 70 μm in both diamond and silicon, which demonstrates the wide applicability of the technique to materials that are optically transparent or opaque at the pump laser wavelength. We also report the machining of curved trenches in silicon. Our results are consistent with an ablation-threshold model based on calculated local beam intensity, and we also observe asymmetric debris deposition which is interpreted in terms of the optical properties of the incident accelerating beam.

/pdf/micromachining-along-a-curve-femtosecond-laser-1lxqlctwe3.pdf

Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams

Acoustic metamaterials provide tailored beams for a range of purposes, but are limited to environments where the material structures can be deployed. By careful choice of phases for a speaker array, Zhang et al. show that bottle or bent beams can be created in air, without the use of metamaterials.

/pdf/generation-of-acoustic-self-bending-and-bottle-beams-by-122c93zqvi.pdf

Generation of acoustic self-bending and bottle beams by phase engineering

Electric breakdown in air occurs for electric fields exceeding 34 kV/cm and results in a large current surge that propagates along unpredictable trajectories. Guiding such currents across specific paths in a controllable manner could allow protection against lightning strikes and high-voltage capacitor discharges. Such capabilities can be used for delivering charge to specific targets, for electronic jamming, or for applications associated with electric welding and machining. We show that judiciously shaped laser radiation can be effectively used to manipulate the discharge along a complex path and to produce electric discharges that unfold along a predefined trajectory. Remarkably, such laser-induced arcing can even circumvent an object that completely occludes the line of sight.

/pdf/laser-assisted-guiding-of-electric-discharges-around-objects-3sigjj8o6n.pdf

Laser-assisted guiding of electric discharges around objects.

We use caustic beam shaping on 100 fs pulses to experimentally generate non-paraxial accelerating beams along a 60 degree circular arc, moving laterally by 14 \mum over a 28 \mum 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 non-paraxial diffraction-free beam profile which also preserves the femtosecond temporal structure in the vicinity of the caustic.

/pdf/sending-femtosecond-pulses-in-circles-highly-non-paraxial-2xs10k4eda.pdf

Sending femtosecond pulses in circles: highly non-paraxial accelerating beams

We report the observation of arbitrary accelerating beams designed using a non-paraxial 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 degrees of arc. Applying a complementary binary mask also allows the generation of periodic accelerating beams taking the forms of snake-like trajectories, and the application of a rotation to the caustic allows the first experimental synthesis of optical accelerating beams upon the surface of a sphere in three dimensions.

Arbitrary non-paraxial accelerating periodic beams and spherical shaping of light

We report on filamentation of nondiffracting beams and show that the intense light-matter interaction regime achieved on long distances allows for an enhanced control on ultrashort laser deep ablation.

https://hal.archives-ouvertes.fr/hal-00939278/document

Filamentation of high-angle nondiffracting beams and applications to ultrafast laser processing

Although versatile and widely used, femtosecond laser micro-nanomachining faces a challenge for the fabrication of high aspect ratio or deep structures. The control of the profile along the longitudinal dimension is extremely difficult. In this context, our approach is based on controlling the direction of light rather than shaping the intensity pattern in one plane. Here we review our recent work in this field using Bessel beams and accelerating beams. In Bessel beams, light propagates along the generatrix of a cone, with a fixed radial wavevector. Contrary to Gaussian beams, the femtosecond filamentation regime of Bessel beams can be stationary, and can generate extended plasma tracks in dielectrics. This allowed us to generate nanochannels in glass with aspect ratio up to 100:1 [1]. Numerical simulations of the nonlinear propagation in this regime show the importance of the conical structure in generating extremely dense plasmas [2]. Airy beams and more generally accelerating beams constitute another family of beams that possess quasi-nondiffracting behaviour and their nonlinear propagation can also be stationary. Their primary intensity lobe propagates along a curved trajectory that can be arbitrarily shaped even in the nonparaxial regime. Since this lobe is adjacent to a region where no light propagates, accelerating beams can be used for direct curved edge profiling and trench processing in transparent and opaque materials [3,4]. Our results show that controlling the linear and nonlinear propagation of ultrashort femtosecond laser pulses by nondiffracting beams is a key new technological approach for laser processing.

https://hal.archives-ouvertes.fr/hal-00938936/document

Femtosecond laser material processing with nondiffracting light

Summary form only given. Femtosecond laser micro and nano-processing is a versatile material processing tool which has opened up a broad range of technologies and applications. However, in the particular context of the fabrication of deep trenches and channels, precise control of profile of the ablated structure is extremely challenging. We have recently developed a novel approach to fabricate controlled high aspect structures using novel Bessel and Airy beams, and this contribution will review our recent work in this field.

A. Mathis

Papers

Sending femtosecond pulses in circles: highly non-paraxial accelerating beams

Arbitrary non-paraxial accelerating periodic beams and spherical shaping of light

Filamentation of high-angle nondiffracting beams and applications to ultrafast laser processing

Femtosecond laser material processing with nondiffracting light

Femtosecond laser micro and nano processing with nondiffracting Bessel and accelerating Airy beams