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

Abstract

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.

Tailoring accelerating beams in phase space

“…(6) and (7) are consistent with previous caustic methods either in real space [27,28] or in Fourier space [29,30], which shows, on one hand, the reliability of our approach and, on the other hand, the inner connection between the two previous caustic methods from the perspective of the WDF. Apart from this, our analysis also gives the initial amplitude distribution, which relates to the intensity variation along the caustic [39].…”

“…Moreover, for the same caustic trajectory, the beams shaped in real space and in Fourier space always behave similarly on the whole. This, on one hand, unifies the previous works' results obtained either in real space or in Fourier space [27][28][29][30] and, on the other hand, provides more than one experimental generation scheme for the same caustic trajectory, including light fields shaped in real space, Fourier space (realized by a Fourier lens), and even their combination.…”

“…One strategy is to keep on finding other rare analytical solutions of the wave equation, while a more efficient way is based on the caustic method, which associates the desired trajectory with an optical caustic, the envelope of a family of light rays [24][25][26]. This method was first implemented in real space [27,28] and successfully realized arbitrary convex propagating trajectories for two-dimensional (2D) light fields, while the caustic method in Fourier space was also proposed subsequently [29][30][31]. Therefore, for one predesigned trajectory, accelerating beams can be constructed by caustic methods either in real space or in Fourier space, but the relationship between them is not clear * chenyj69@mail.sysu.edu.cn yet.…”

Caustics, catastrophes, and symmetries in curved beams

“…Since the observation of the first curved caustic beam, the Airy beam, in 2007 [10,11], the basic and applied research on caustic laser beams grew quickly, not only in its original rectangular coordinate frame [12][13][14][15], but also in a cylindrical frame with the appearance of the circular Airy beam [16][17][18]. A significant advance had a place through the design of curved beams propagating along arbitrary convex trajectories [13,14].…”

“…A significant advance had a place through the design of curved beams propagating along arbitrary convex trajectories [13,14]. All of these beams were properly tied to a fold catastrophe.…”