Construction, characteristics, and constraints of accelerating beams based on caustic design

Adjustable focusing property of circular Airyprime beam through Fourier space modulation

Airyprime beams are known for their powerful autofocusing property, which are further enhanced by the introduction of a circular structure-circular Airyprime beam (CAPB). We derive an asymptotic expression of the CAPB in Fourier space (FS) and verify its accuracy by the numerical Fourier transform (FT) method. Through FS modulation on it, adjustable control of autofocusing property of the FS-modulated CAPB can be achieved, whose lower and upper limits can reach 8.7% reduction and 2.6 times enhancement compared to the unmodulated one. The experimental results agree well with the numerical analyses. Our findings offer promising possibilities for efficient particle trapping and enhancing free-space optical communication capabilities.

Sidelobe suppression for accelerating beams

Although the control of trajectory, amplitude and beam-width in accelerating beams have been extensively investigated, sidelobes manipulation of such beams, which is required in many applications, has been surprisingly under-researched. This paper presents an approach for the generating of accelerating beams with significantly reduced sidelobes. The proposed method encompasses a two-step angular spectrum design, including employing a general model to establish the phase distribution and applying a stochastic parallel gradient descent (SPGD) algorithm to optimize the binary amplitude modulation. Experimental results confirm that the sidelobe intensity of accelerating beams can be reduced by over 50% with our method, thereby enhancing their applicability in many fields, such as micro-machining, particle manipulation, and optical communication.

Generation for high-dimensional caustics and artificially tailored structured caustic beams

We theoretically propose and demonstrate topological parabolic umbilic beams (PUBs) with high-dimensional caustic by mapping catastrophe theory into optics. The PUBs are first experimentally observed via dimensionality reduction. Due to the high-dimensionality, such light beams exhibit rich caustic structures characterized by optical singularities where the high-intensity gradient appears. Further, we propose an improved caustic approach to artificially tailored structured beams which exhibit significant intensity gradient and phase gradient. The properties can trap and drive particles to move along the predesigned trajectory, respectively. The advantages for structured caustic beams likely enable new applications in flexible particle manipulation, light-sheet microscopy, and micromachining.

Space-time wave packets with both arbitrary transverse and longitudinal accelerations

The group velocity in the free space of space-time wave packets (STWPs) and light bullets can be flexibly regulated by many advanced strategies; however, these regulations are restricted to only the longitudinal group velocity. In this work, a computational model based on catastrophe theory is proposed, to devise STWPs with both arbitrary transverse and longitudinal accelerations. In particular, we investigate the attenuation-free Pearcey-Gauss STWP, which enriches the family of non-diffracting STWPs. This work may advance the development of space-time structured light fields.

Terahertz Airy beam generated by Pancharatnam-Berry phases in guided wave-driven metasurfaces

Metasurface antennas scatter traveling guided waves into spatial waves, which act as extendable subsources to overcome the size limitation on emission sources. With the use of a Pancharatnam-Berry phase metasurface stimulated by a circularly polarized wave in a waveguide, the local phase distributions of scattered spatial waves can be made consistent with those of an Airy beam, thereby allowing the generation of high-quality Airy beams. In a slab waveguide, circularly polarized waves are synthesized through superposition of in-plane transverse electric modes. Simulations demonstrate that a 20 mm × 20 mm footprint all-dielectric guided wave-driven metasurface generates a 2D Airy beam at a frequency of 0.6 THz. Furthermore, we employ a metasurface deposited on a strip waveguide to generate a 1D Airy beam under direct stimulation by the fundamental transverse electric mode. Our work not only provides a large-scale emitter, but it also suggests promising potential applications in on-chip imaging and holography.

Manipulation of curved beams using beam-domain optimization

An efficient scheme for the design of aperture fields (distributed sources) that radiate arbitrary trajectory curved (accelerating) beams, with enhanced controllability of various beam features, is presented. The scheme utilizes a frame-based phase-space representation of aperture fields to overcome the main hurdles in the design for large apertures: First, it uses the a-priory localization of caustic beams to significantly reduce the optimization problem's variable space, to that of few Gaussian window coefficients accurately capturing those beams. Then, the optimization problem is solved in the reduced (local) spectral domain. We adopt a linearization approach that enables the solution by sequential application of conventional convex optimization tools, which are naturally compatible with the proposed phase-space representation. The localized nature of the Gaussian windows' radiation is used also for fast field evaluation at a greatly reduced number of optimization constraint points. The significant enhancement in the controllability over the various beam parameters is demonstrated through a range of examples.

Generation of multi-focus abruptly autofocusing beams with adjustable focus characteristics

This work introduces and demonstrates a method for tailoring multi-focus abruptly autofocusing beams (MFAABs) in free space. Since MFAABs are formed by superposing the wavefronts of abruptly autofocusing beams (AABs), the number, positions, and relative intensity of foci are directly and independently adjusted during the pre-design of AABs. Also, we show that the size of the light field involves the characteristics of focus, such as peak intensity, focal size, and subsequent oscillations. We apply the double-phase hologram method to generate the required complex field with a phase-only spatial light modulator in experiments. With flexible control on foci characteristics, this work may broaden potential applications of autofocusing beams.

Shaping caustics into propagation-invariant light

Structured light has revolutionized optical particle manipulation, nano-scaled material processing, and high-resolution imaging. In particular, propagation-invariant light fields such as Bessel, Airy, or Mathieu beams show high robustness and have a self-healing nature. To generalize such beneficial features, these light fields can be understood in terms of caustics. However, only simple caustics have found applications in material processing, optical trapping, or cell microscopy. Thus, these technologies would greatly benefit from methods to engineer arbitrary intensity shapes well beyond the standard families of caustics. We introduce a general approach to arbitrarily shape propagation-invariant beams by smart beam design based on caustics. We develop two complementary methods, and demonstrate various propagation-invariant beams experimentally, ranging from simple geometric shapes to complex image configurations such as words. Our approach generalizes caustic light from the currently known small subset to a complete set of tailored propagation-invariant caustics with intensities concentrated around any desired curve.

Manipulation and control of 3-D caustic beams over an arbitrary trajectory

We present an algorithm for manipulating and controlling 3-D field patterns, with energy confined to the narrow vicinity of predefined 3-D trajectories in free-space, which are of arbitrary curvature and torsion. This is done by setting the aperture field's phase to form smooth caustic surfaces that include the desired trajectory. The aperture amplitude distribution is constructed to manipulate both the on-axis intensity profile and the off-axis beam-width, and is updated iteratively. Once the aperture distribution is calculated, the radiation from a finite sampled aperture is computed numerically using a Fast Fourier Transform-based scheme. This allows for both verification of the design and examination of its sensitivity to parameters of realistic discrete implementation. The algorithm is demonstrated for the cases of an Airy beam of a planar trajectory, as well as for helical and conical-helical trajectory beams.