Fourier-space generation of abruptly autofocusing beams and optical bottle beams

Abstract

We demonstrate analytically and experimentally that a circular abruptly autofocusing (AAF) Airy beam can be generated by Fourier-transforming an appropriately apodized Bessel beam whose radial oscillations are chirped by a cubic phase term. Depending on the relation between the chirp rate and the focal distance of the Fourier-transforming lens, it is possible to generate AAF beams with one or two foci, the latter case leading to the formation of an elegant paraboloid optical bottle.

Symmetric Airy beams

“…But at ξ ξ f the peak intensity is higher for SAB. For a 1D case, the ratio is I On the other hand, the only Airy-like beam with autofocusing properties experimentally demonstrated was the CAB [9,10], that only exists for two transverse dimensions because of its circular-cylindrical symmetry. One of the main characteristics of CABs is that the ratio autofocus/initial peak intensity can reach several orders of magnitude [6][7][8], while such a ratio is about one order of magnitude for a 2D SAB, as shown in Fig.…”

“…The Airy function has no defined symmetry in rectangular coordinates, but if extended to cylindrical ones, it results in a beam having circular symmetry with an Airy radial profile, called abruptly autofocusing beam or circular Airy beam (CAB) [6][7][8]. These beams were experimentally demonstrated [9,10] and possess an unusual feature. As they propagate the profile is accelerated toward the center of symmetry yielding a parabolic caustic surface of revolution.…”

Guided Self-Accelerating Airy Beams—A Mini-Review

“…In a 2D parabolic potential, the wave exhibits all the properties of 1D Airy beams: periodic inversion, phase transition, and anharmonic oscillation. For the cases that cannot be treated with the variable separation method, e.g., when the initial beam is a superposition of AAF beams carrying orbital angular momentum [13,36,37,40,73], in the radially symmetric case one can switch to the polar coordinates. Then, the input can be written as:…”

“…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.…”

Light capsules shaped by curvilinear meta-surfaces

“…Alternatively, wave fields exhibiting a peak intensity of curvilinear trajectory that additionally constitutes the closed boundary of a geometrical shadow, instead of a null point, have been proposed to be used as optical bottles 6,7 . A well-known example of this kind of wave fields are the so-called Airy beams.…”