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...
Mode sorting is an essential function for optical multiplexing systems that exploit the orthogonality of the orbital angular momentum mode space. The familiar log-polar optical transformation provides a simple yet efficient approach whose resolution is, however, restricted by a considerable overlap between adjacent modes resulting from the limited excursion of the phase along a complete circle around the optical vortex axis. We propose and experimentally verify a new optical transformation that maps spirals (instead of concentric circles) to parallel lines. As the phase excursion along a spiral in the wave front of an optical vortex is theoretically unlimited, this new optical transformation can separate orbital angular momentum modes with superior resolution while maintaining unity efficiency.
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.
For decades, singular beams carrying angular momentum have been a topic of considerable interest. Their intriguing applications are ubiquitous in a variety of fields, ranging from optical manipulation to photon entanglement, and from microscopy and coronagraphy to free-space communications, detection of rotating black holes, and even relativistic electrons and strong-field physics. In most applications, however, singular beams travel naturally along a straight line, expanding during linear propagation or breaking up in nonlinear media. Here, we design and demonstrate diffraction-resisting singular beams that travel along arbitrary trajectories in space. These curved beams not only maintain an invariant dark “hole” in the center but also preserve their angular momentum, exhibiting combined features of optical vortex, Bessel, and Airy beams. Furthermore, we observe three-dimensional spiraling of microparticles driven by such fine-shaped dynamical beams. Our findings may open up new avenues for shaped light in various applications.
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