We study nonparaxial autofocusing beams with pre-engineered trajectories. We consider the case of linearly polarized electric optical beams and examine their focusing properties such as contrast, beam width, and numerical aperture. Such beams are associated with larger intensity contrasts, can focus at smaller distances, and have smaller spot sizes as compared to the paraxial regime.Since 2007 when exponentially truncated diffractionfree Airy beams have been predicted and observed [1,2] the study of curved and accelerating beams has attracted a lot of attention. Due to their unique properties such beams are associated with a variety of potential applications in areas including imaging [3,4], filamentation [5, 6], particle manipulation [7,8], and plasmon generation [9] (see also the review [10]).

In this Letter, we propose a general real-space method for the generation of nonparaxial accelerating beams with arbitrary predefined convex trajectories. Our results lead to closed-form expressions for the required phase at the input plane. We present such closed-form results for a variety of caustic curves: beside circular, elliptic, and parabolic, we find for the first time general power-law and exponential trajectories. Furthermore, by changing the initial amplitude, we can design different intensity profiles along the caustic.

We show that it is possible to generate non-paraxial optical beams with pre-engineered trajectories and designed maximum amplitude along these trajectories. The independent control of these two degrees of freedom is made possible by engineering both the amplitude and the phase of the optical wave on the input plane. Furthermore, we come to the elegant conclusion that the beam width depends solely on the local curvature of the trajectory. Thus, we can generate beams with pre-defined amplitude and beam-width by appropriately selecting the local curvature. Our theoretical results are in excellent agreement with numerical simulations. We discuss about methods that can be utilized to experimentally generate such beam. Our work might be useful in applications where precise beam control is important such as particle manipulation, filamentation, and micromachining.

We predict and experimentally observe three-dimensional microscale nonparaxial optical bottle beams based on the generation of a caustic surface under revolution. Such bottle beams exhibit high contrast between the surrounding surface and the effectively void interior. Via caustic engineering, we can precisely control the functional form of the high-intensity surface to achieve microscale bottle beams with longitudinal and transverse dimensions of the same order of magnitude. Although, in general, the phase profile at the input plane can be computed numerically, we find closed-form expressions for bottle beams with various types of surfaces both in the real and in the Fourier space.