Pre-engineered abruptly autofocusing beams

Abstract

We introduce a new family of ð2 þ 1ÞD light beams with pre-engineered abruptly autofocusing properties. These beams have a circularly symmetric input profile that develops outward of a dark disk and oscillates radially as a sublinear-chirp signal, creating a series of concentric intensity rings with gradually decreasing width. The light rays involved in this process form a caustic surface of revolution that bends toward the beam axis at an acceleration rate that is determined by the radial chirp itself. The collapse of the caustic on the axis leads to a large intensity buildup right before the intended focus. This ray-optics interpretation provides valuable insight into the dynamics of abruptly autofocusing waves. © 2011 Optical Society of America OCIS codes: 050.1940, 260.2030 Recently, a new class of light beams has been revealed with abruptly autofocusing (AAF) properties [1]. As opposed to self-focusing effects mediated by Kerr nonlinearities, this autofocusing behavior is purely linear in origin and is a result of the optical field structure itself. During propagation, these AAF fields can maintain a relatively low intensity profile while suddenly releasing all their energy right before a target. The first AAF beam proposed [1] exhibited a ð2 þ 1ÞD circularly symmetric field that involved the salient diffraction-resisting and selfbending features of a finite-energy ð1 þ 1ÞD Airy beam [2,3]. As the Airy radial profile is accelerated toward the center, a paraboloid caustic surface is formed that "collapses" on axis-thus leading to a large intensity buildup right before the intended focus. The intensity contrast reached at the focus compared to the maximum input intensity was shown to reach several orders of magnitude. Moreover, due to the diffraction-free character of ð1 þ 1ÞD Airy beams, the maximum intensity of the wave over the transverse plane remains almost constant along the entire propagation path until the focus is reached. As indicated in [1], AAF waves may prove advantageous in medical laser treatments and in other nonlinear optical settings over standard Gaussian beams obeying a more gradual Lorentzian focusing law. In this Letter, we report on a new family of AAF beams. These are circularly symmetric waves whose input amplitude develops outward of a dark disk and oscillates radially as a sublinear chirp signal. During propagation, these wavefronts form inward-bending caustic surfaces of revolution with an acceleration that is directly related to their chirp rate. We hereby extend the family of circular Airy beams [1], the rays of which are known to form paraboloids as a result of the quadratic inward radial shift of the Airy rings. This new flexibility comes at the cost of losing the unique diffraction-resisting properties of the Airy waveform, which is, however, here traded for greater transverse accelerations, enhanced focusing abruptness, and larger intensity contrasts.We begin with the scaled paraxial equation of light in cylindrical coordinates ðr; φ; zÞwhere the radial distance r is normali...

Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories

“…9. A closely related example is using abruptly autofocusing beams (a cylindrical superposition of Airy beams) for multiphoton microscopy 34,35 . In such cases, where the losses stem from multiphoton absorption, proper design of the input beam can support an accelerating beam propagating for very large distances with its main lobe maintaining its structure and peak intensity in spite of the nonlinear losses.…”

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].…”

Guided Self-Accelerating Airy Beams—A Mini-Review

“…The beam possesses a ring-shaped initial transverse Airy amplitude pattern, and accelerates in either inward or outward direction, determined by the Airy wave function tail [36]. During propagation, the AAF beam can keep low intensity profile initially, and then abruptly converge to a focal point where the intensity grows by orders of magnitude [35,[37][38][39][40][41]. This abruptly autofocusing property of an AAF beam avoids possible interaction of the beam with the transmission medium before focusing.…”