Amaury Mathis

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.

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

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.

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.

Caustics and Rogue Waves in an Optical Sea

There are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with particular recent interest in optics. Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes. In this paper, we report a detailed experimental study of linear rogue waves in an optical system, using a spatial light modulator to impose random phase structure on a coherent optical field. After free space propagation, different random intensity patterns are generated, including partially-developed speckle, a broadband caustic network, and an intermediate pattern with characteristics of both speckle and caustic structures. Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra. In addition, the electric field statistics of the intermediate pattern shows properties of an “optical sea” with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed.

Studies and realization of an experimental set-up for micro Airy beams generation

Airy beams are a solution to the paraxial wave equation with nondiffracting properties [1]. These beams were only recently experimentally observed by Siviloglou et al [2]. Airy beams generate a growing interest since they remain focused during the propagation, exhibit properties of self-healing and their trajectory is parabolic along the propagation axis. At present, applications of Airy beams are dedicated to trapping and filamentation. For applications to extreme nonlinear optics and material structuring, nondiffracting beams have key benefits over gaussian beams [3].

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

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.

Nonparaxial circular and weber beams from caustics

Here, we show that using a caustic-based approach and an appropriate modeling of high-numerical aperture microscope objectives with Debye integral, analytical solutions for phase mask design can be also obtained. We report on numerical modeling of high aperture microscope objectives to reproduce our experimental results. This work allows for an enhanced flexibility in designing and modeling experimentally realizable curved beams since deviations from the pure analytical case can be taken into account.

Tailored accelerating beam profiles through a caustic-based approach to wavefront design

Transversally accelerating beams exhibit a curved trajectory of their point of maximum intensity. Although the well-known example of the Airy beam was introduced by Berry and Balazs over 30 years ago [1], it is only recently that they were experimentally observed [2]. This observation, however, has since generated tremendous interest, and important applications : all-optical manipulation, curved nonlinear optics and filamentation are the subject of much current research [3–5].