Auto-focusing and self-healing of Pearcey beams

Abstract

We present a new solution of the paraxial equation based on the Pearcey function, which is related to the Airy function and describes diffraction about a cusp caustic. The Pearcey beam displays properties similar not only to Airy beams but also Gaussian and Bessel beams. These properties include an inherent auto-focusing effect, as well as form-invariance on propagation and self-healing. We describe the theory of propagating Pearcey beams and present experimental verification of their auto-focusing and self-healing behaviour.

Conical refraction: fundamentals and applications

“…Recently, there has been a great interest in the study of the self-healing effect appearing in Bessel beams [149,150] and other diffraction-free beams including Airy beams [151,152] and Pearcey beams [153], or other exotic beams such as helico-conical beams [154] as well as Mathieu and Webber beams [155]. The major advantage of self-healing beams is that they can be used through turbulent media [152] and that they are ideal candidates for particle manipulation at different planes [156,157] and in microscopy [158].…”

Caustics, catastrophes, and symmetries in curved beams

“…Its caustic field was tied to the Pearcey function having a quartic power in the generating function [1][2][3]19,20]. In spite of this, a beam exhibiting a cusplike structure was recently generated from a phase having a cubic power but with an even symmetry [21][22][23][24].…”

Helico-conical optical beams self-heal

“…© 2013 Optical Society of America OCIS codes: 140.3300, 260.6042, 260.0260, 070.2580. The study of the self-healing properties of beams is of great interest in optics [1][2][3][4][5][6]. An optical beam is said to be self-healing when, after propagation, its transverse intensity profile is hardly affected by a small perturbation-a block-that has been placed in its path [1][2][3][4][5].…”

“…The study of the self-healing properties of beams is of great interest in optics [1][2][3][4][5][6]. An optical beam is said to be self-healing when, after propagation, its transverse intensity profile is hardly affected by a small perturbation-a block-that has been placed in its path [1][2][3][4][5]. The surge of interest in self-healing beams is bouyed mainly by its range of applications; self-healing can be advantageous, for instance, in beam propagation through scattering and turbulent media, and in optical manipulation [7,8].…”

“…In the case of the BBs and Airy beams, self-healing happens at a relatively small propagation distance, while LG beams self-heal at a distance of the order of the Rayleigh length [2,3]. Self-healing is independent of the diffracting nature of the beams, as shown by caustic [4] and LG beams [3].…”