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.

Generation of high-dimensional caustic beams via phase holograms using angular spectral representation.

Using angular spectral representation, we demonstrate a generalized approach for generating high-dimensional elliptic umbilic and hyperbolic umbilic caustics by phase holograms. The wavefronts of such umbilic beams are investigated via the diffraction catastrophe theory determined by the potential function, which depends on the state and control parameters. We find that the hyperbolic umbilic beams degenerate into classical Airy beams when the two control parameters are simultaneously equal to zero, and elliptic umbilic beams possess an intriguing autofocusing property. Numerical results demonstrate that such beams exhibit clear umbilics in 3D caustic, which link the two separated parts. The dynamical evolutions verify that they both possess prominent self-healing properties. Moreover, we demonstrate that hyperbolic umbilic beams follow along a curve trajectory during propagation. As the numerical calculation of diffraction integral is relatively complex, we have developed an effective approach for successfully generating such beams by using phase hologram represented by angular spectrum. Our experimental results are in good agreement with the simulations. Such beams with intriguing properties are likely to be applied in emerging fields such as particle manipulation and optical micromachining.

Customizing non-diffracting structured beams.

We demonstrate a universal approach to designing and generating non-diffracting structured light beams with arbitrary shapes. Such light beams can be tailored by predefining suitable spectral phases that match the corresponding beam shapes in the transverse plane. We develop a practical spectral superposition algorithm to discuss the non-diffracting properties and experimentally confirm our numerical results. Our proposed approach differs from that of classical non-diffracting beams, which are always constructed from wave equation solutions. The various non-diffracting structured beams could help manipulate particles following arbitrary transverse shapes and are likely to give rise to new applications in optical micromachining.

Swallowtail-type diffraction catastrophe beams.

We demonstrate a universal approach for generating high-order diffraction catastrophe beams, specifically for Swallowtail-type beams (abbreviated as Swallowtail beams), using diffraction catastrophe theory that was defined by potential functions depending on the control and state parameters. The three-dimensional curved caustic surfaces of these Swallowtail catastrophe beams are derived by the potential functions. Such beams are generated by mapping the cross sections of the high-order control parameter space to the corresponding transverse plane. Owing to the flexibility of the high-order diffraction catastrophe, these Swallowtail beams can be tuned to a diverse range of optical light structures. Owing to the similarity in their frequency spectra, we found that the Swallowtail beams change into low-order Pearcey beams under given conditions during propagation. Our experimental results are in close agreement with our simulated results. Such fantastic catastrophe beams that can propagate along curved trajectories are likely to give rise to new applications in micromachining and optical manipulation, furthermore, these diverse caustic beams will pave the way for the tailoring of arbitrarily accelerating caustic beams.

Generation of perfect helical Mathieu vortex beams.

We introduced a kind of novel perfect optical vortex beam, which we termed herein as perfect helical Mathieu vortex (PHMV) beams. The theoretical mechanism regarding the construction of PHMV beams was divided into two parts: generation of helical Mathieu (HM) beams using the stationary phase method and then Fourier transform of HM beams into the PHMV beams. Accordingly, the experimental system for generating PHMV beams was built as follows. Based on the complex amplitude modulation method, HM beams of different orders and ellipticity were generated using an amplitude-type spatial light modulator (SLM) and a radial-helical phase mask. Subsequently, an achromatic Fourier transform lens was illuminated using the HM beams, and the PHMV beams were presented on the focal plane after the Fourier transform lens. The experimental results were consistent with theoretical predictions. Compared with the classical perfect optical vortex (POV) beams, the PHMV beams still retained the property of ring radius independent of topological charge values. The distribution pattern of the PHMV beams can be controlled by the topological charges and elliptical parameters. Furthermore, two important optical properties of the PHMV beams were theoretically elucidated. First, we proved that the PHMV beams carry a fractional order orbital angular momentum (OAM). Second, we found that the complex amplitudes of any two PHMV beams with the same elliptical parameter but different order numbers are orthogonal to each other.

Abruptly autofocusing circular swallowtail beams.

In this Letter, to the best of our knowledge, we report the first experimental demonstration of a new family of autofocusing beams, circular swallowtail beams (CSBs), based on the high-order swallowtail catastrophe, which were determined by potential functions depending on the state and control parameters. The dynamics of the CSBs is discussed here. These types of CSBs tend to automatically focus without external components. Numerical results showed the focal intensity increased significantly, and it was as much as 110 times in the initial plane when the radius of the main ring was 40. Additionally, in contrast to previous circular Pearcey and Airy beams, these CSBs appeared to have more diversity and tunability due to having more propagation trajectories and intensity distribution structures due to high-order diffraction catastrophe. The numerical simulations were verified by our experimental results. These diverse CSBs could have new applications in flexible optical manipulation. These various CSBs could be beneficial for potential applications in optical trapping, medical treatment, or micromachining.

Experimental visualization of various cross sections through a butterfly caustic.

Optical caustics and wavefronts of butterfly beams (BBs) derived by using a catastrophe theory determined by potential functions depending on the state and control variables are reported. Due to the high dimensionality for the control variables, BBs can be manipulated into various optical light structures. It is also demonstrated that these curious beams have relatively simple Fourier spectra that can be described as polynomials, and another way to generate BBs from the Fourier spectrum's perspective is provided. The dynamics for BBs are investigated by potential functions. Our experimental results agree well with the theoretical predictions. In addition to micro-manipulation and machining, these novel, to the best of our knowledge, caustic beams will pave the way for creating waveguide structures since they display high-intensity formations that evolve along curved trajectories.

Annular arrayed-Airy beams carrying vortex arrays.

We propose and experimentally demonstrate annular arrayed-Airy beams (AAABs) carrying vortex arrays by combining multiple beams. The propagation dynamics and abrupt autofocusing property are studied. The focal intensity can be greatly increased by two orders of magnitude by increasing vortex array number. Furthermore, the autofocusing property is also enhanced significantly. This tightly autofocusing property would be advantageous for the generation of high intensity laser, optical manipulation, medical treatments, and nonlinear effects.

Generation of spirally accelerating optical beams.

We developed a generalized spectral phase superposition approach for generating accelerating optical beams along arbitrary trajectories. Such beams can be customized by predefining an appropriate superimposed phase pattern that consists of multiple sub-phases. We generated a spirally accelerating beam in a three-dimensional space and developed an algorithm to improve the uniformity of the intensity along the trajectory by introducing phase-shift factors. We also experimentally verified our numerical simulations. The proposed approach breaks the conventional convex trajectory restrictions. These various accelerating beams would pave the way for optically moving particles along a desired trajectory. The generation of such arbitrary accelerating beams is likely to give rise to new applications in flexible optical manipulation, wave front control, and optical transportation and guidance of particles.

Propagation dynamics of generalized and symmetric Airy beams.

We present theoretically and experimentally generalized and symmetric Airy beams, where the two sidelobes are not mutually perpendicular, by introducing two rotary angle factors. The symmetric Airy beam is induced by a binary phase pattern. We demonstrate that the intensity distributions of generalized Airy beams are apparently different from those of normal Airy beams. Moreover, they can propagate along arbitrary trajectories. Numerical results show that the generalized and symmetric Airy beams still have the ability of self-healing and nondiffraction. The experimental results are in complete accord with numerical results. Some possible applications are also discussed, and these interesting properties will also likely have potential applications.

Quasi-Airy beams along tunable propagation trajectories and directions.

We present a theoretical and experimental exhibit that accelerates quasi-Airy beams propagating along arbitrarily appointed parabolic trajectories and directions in free space. We also demonstrate that such quasi-Airy beams can be generated by a tunable phase pattern, where two disturbance factors are introduced. The topological structures of quasi-Airy beams are readily manipulated with tunable phase patterns. Quasi-Airy beams still possess the characteristics of non-diffraction, self-healing to some extent, although they are not the solutions for paraxial wave equation. The experiments show the results are consistent with theoretical predictions. It is believed that the property of propagation along arbitrarily desired parabolic trajectories will provide a broad application in trapping atom and living cell manipulation.

Propagation characteristics of continuously tuning distorted Airy-like beams.

We investigate theoretically and observe experimentally a continuously tuning distorted Airy-like beam, which is generated by introducing a controllable rotation angle into the phase patterns. The beam wavefront can be tuned flexibly by using the introduced angle. The main lobes of beams can be controlled readily to propagate along specified parabolic trajectories. The relevant optical behaviors are discussed and demonstrated in detail. The experimental results are in good agreement with the theoretical analysis. The intriguing characteristics of the continuously tuning Airy-like beams could provide more degrees of freedom in cell and atom manipulation.

Improved approach for ultra-sensitive detection of NO.

An improved approach has been developed for ultra-sensitive detection of the concentration of NO using Faraday Modulation spectrometry (FAMOS) combined with the strong electronic transition. By changing the modulating magnetic field attributing to linear absorption and refraction of gas sample, the polarized laser was rotated and absorbed by the complex refraction index of NO. We confirm the relation between the magnitudes of absorption and the optimum modulation magnetic field. Also, the accuracy and the precision of the technique have been evaluated at different pressures. It is shown that the system is capable of detecting NO concentration down to 0.34 ppb·m.

Real-time image stabilization for arbitrary motion blurred image based on opto-electronic hybrid joint transform correlator.

An efficient approach was put forward to keep real-time image stabilization based on opto-electronic hybrid processing, by which image motion vector can be effectively detected and point spread function (PSF) was accurately modeled instantaneously, it will alleviate greatly the complexity of image restoration algorithm. The approach applies to arbitrary motion blurred images. We have also constructed an image stabilization measurement system. The experimental results show that the proposed method has advantages of real time and preferable effect.

Real-time image deblurring by optoelectronic hybrid processing.

An efficient approach is presented to restore a motion-blurred image in real time by optoelectronic hybrid processing, by which an image motion vector can be effectively detected and an accurate point spread function is constructed rapidly. A simple Wiener filter algorithm is employed to restore the blurred image. It greatly alleviates the complexity of the restoration algorithm. The proposed approach can apply to arbitrary motion-blurred image restoration. An optoelectronic hybrid joint transform correlation is constructed to verify the efficiency. The experimental results show that the proposed method has distinct advantages of preferable effect and good real time.

High-speed and dense three-dimensional surface acquisition using defocused binary patterns for spatially isolated objects.

The three-dimensional (3-D) shape measurement using defocused Ronchi grating is advantageous for the high contrast of fringe. This paper presents a method for measuring spatially isolated objects using defocused binary patterns. Two Ronchi grating with horizontal position difference of one-third of a period and an encoded pattern are adopted. The phase distribution of fringe pattern is obtained by Fourier analysis method. The measurement depth and range is enlarged because the third harmonic component and background illumination is eliminated with proposed method. The fringe order is identified by the encoded pattern. Three gray levels are used and the pattern is converted to binary image with error diffusion algorithm. The tolerance of encoded pattern is large. It is suited for defocused optical system. We also present a measurement system with a modified DLP projector and a high-speed camera. The 3-D surface acquisition speed of 60 frames per second (fps), with resolution of 640 × 480 points and that of 120 fps, with resolution of 320 × 240 points are archived. If the control logic of DMD was modified and a camera with higher speed was employed, the measurement speed would reach thousands fps. This makes it possible to analyze dynamic objects.