Propagation of Airy-related beams

Abstract

New types of finite energy Airy beams are proposed. We consider two different types of beams, namely, beams that are obtained as blocked and exponentially attenuated versions of Airy functions Ai and Bi, and beams of finite width but having the Airy functions typical phase. All of them show very interesting properties, such as parabolic trajectories for longer propagation distances, profile evolution exhibiting less diffraction, or better definiteness of the main peak, when compared with other finite energy Airy beams studied before.

Analytic description of Airy-type beams when truncated by finite apertures

“…In the last five years, a new nondiffracting wave has called attention: the Airy Beam [1][2][3][4]. Solution of the wave equation under paraxial approximation, the Airy Beam has slightly different properties.…”

“…Until now, to the best of our knowledge, no one has ever studied propagation characteristics of truncated Airy-Type beams using any kind of analytic method once that all results reported in literature were done numerically [2] or experimentally [3]. In this paper we will present the first effort to this direction, describing the propagation of truncated Airy-Type beams in a homogeneous medium through an analytic approach.…”

Incomplete Airy beams: finite energy from a sharp spectral cutoff

“…Alternatively, finite-energy can be enforced by modulating the Airy function with a wide Gaussian profile [6], or even by a sharp truncation [7][8][9]. These beams display good approximations of the transverse acceleration of infinite-energy Airy beams over an appreciable propagation distance.…”

“…However, finiteness of energy can also be enforced by limiting the beam's spectrum [8][9][10][11][12], which is more practical as the simple Airy spectrum is easy to generate and manipulate [10,11] experimentally. In the laboratory, this is done by illuminating a cubic phase mask (or spatial light modulator) with a Gaussian beam [5,11], or using a finite-sized cubic element or hard aperture [8][9][10].…”

“…In the laboratory, this is done by illuminating a cubic phase mask (or spatial light modulator) with a Gaussian beam [5,11], or using a finite-sized cubic element or hard aperture [8][9][10].…”