Airy-Gaussian vector beam and its application in generating flexible optical chains.

In recent years, the manipulation of structured optical beam has become an attractive and promising area. The Gaussian beam is the most common beam as the output beam of the laser, and the Airy beam is recently proposed with fascinating properties and applications. In this paper, for the first time to our knowledge, the polarization is used as a tool to design a new kind of Airy-Gaussian vector beam by connecting the Gaussian and Airy functions, which opens a new avenue in designing new beams based on the existed beams. We realize the Airy-Gaussian vector beam with space-variant polarization distribution in theory and experiment, and find that the vector beam can autofocus twice during propagation. The optical chains with flexible intensity peaks are achieved with the Airy-Gaussian vector beam, which can be applied in trapping and delivering particles including biological cells and Rydberg atoms. Such optical chains can significantly improve the trapping efficiency, reduce the heat accumulation, and sweep away the impurity particles.

Sinusoidal-amplitude binary phase mask and its application in achieving an ultra-long optical needle.

Optical needle has become a hot research topic in recent years, due to the excellent properties and potential applications. To achieve a sub-diffraction optical needle, there are three common methods including planar diffractive lenses, reflective mirrors or axicons, and high-NA objective lenses with the designed phase or amplitude elements. Here, we propose a new kind of designed phase and amplitude element called the sinusoidal-amplitude binary phase mask (SA-BPM), which modulates the amplitude and phase distributions of the incident vector optical fields (VOFs) simultaneously. Based on Richards-Wolf vector diffraction integral, the corresponding parameters of SA-BPM and the optimal optical needle length are calculated by exhaustive method and genetic algorithm. We further upgrade the SA-BPM by adding a Gaussian function in the amplitude modulation, and design the Gaussian SA-BPM (GSA-BPM). We find that the ultra-long optical needles are achieved with the SA-BPM and GSA-BPM, and the depth of focus of the optical needles are improved by 30%-70% compared with the case of binary phase mask. Such SA-BPM and GSA-BPM we proposed have great potential for manipulation and utilization of the ultra-long optical needles.

Flexibly modulated Poincaré sphere vector optical field in input and focal planes.

We theoretically design and experimentally generate the flexibly modulated Poincaré sphere vector optical field (PS-VOF), which can be constructed by flattening the Poincaré sphere surface. This new kind of PS-VOF provides additional degrees of freedom to modulate the spatial structure of polarization based on Poincaré sphere. The focal property of the PS-VOF is further studied, and we focus on studying the polarization coverage of the Poincaré sphere in the focal plane. In focusing process, the conversion and annihilation of spin angular momentum are presented. In addition, when the proportion of right-handed polarizations from the northern hemisphere of the Poincaré sphere satisfies Golden ratio (0.618) in the input plane, a full PS-VOF with high quality can be achieved in the focal plane. We hope this study of PS-VOF in both input and focal planes can enrich the family of VOFs, provide a new avenue in studying VOFs based on the Poincaré sphere, and can be potentially applied in the regions with sensitivity to polarizations.

Multifractal vector optical fields.

We introduce the concept of multifractal into vector optical fields (VOFs). We propose, design and generate new fractal VOFs-multifractal VOFs (MF-VOFs), in which multifractal structure and VOF act as the lattice and the base, respectively. We generate two kinds of MF-VOFs experimentally and explore their focusing behaviors. We also investigate the self-healing and information recovering abilities of MF-VOFs, comparing with those of single-fractal VOFs (SF-VOFs) when their lattices are composed of the same hierarchy of fractal geometries. The results show that MF-VOFs have better self-healing and information recovering abilities than that of traditional SF-VOFs, meaning that MF-VOFs have better ability to resist the information loss during the focusing and imaging processes. These properties may find potential applications in information transmission, optical communication, and so on.

Pseudo-topological property of Julia fractal vector optical fields.

Polarization singularities have topological properties, because they can maintain their features invariably during propagation. The topological property can be destroyed by shifting the polarization singularities away from the central axis, and this destruction originates from the space separation of spin angular momentum components. We find that paired centrosymmetric off-axis polarization singularities can recover the topological property in the Fourier plane (reciprocal space), which belongs to the pseudo-topological property. We reveal that the pseudo-topological property is related to the invisible redistribution of both spin and orbital angular momentum states. We experimentally generate a series of Julia fractal vector optical fields with the pseudo-topological property. They may have potential applications in optical encryption and quantum information.

Energy transfer of the tightly focused hybridly polarized vector optical fields with elliptic symmetry in free space.

We theoretically and experimentally present hybridly polarized vector optical fields (HP-VOFs) with elliptic symmetry in an elliptic coordinate system. Compared with the traditional cylindrical HP-VOFs, there is an additional degree of freedom for this new kind of vector optical field, which is the interval between the two foci in the elliptic coordinate system. Except for discussing the singularities of the HP-VOFs, we concentrate on studying the energy transfer of the tightly focused HP-VOFs with elliptic symmetry in free space. We summarize the rules of the energy transfer and introduce a reference optical field to explain them. We hope these results can provide a new way to flexibly modulate tightly focused fields, which may be applied in realms such as optical machining, optical trapping, and information transmission.

Diffraction properties and applications of spatially structured optical fields with fractal amplitude masks.

With fractal amplitude masks of the Sierpinski carpet and Sierpinski triangle, we theoretically and experimentally present the diffraction properties and applications of spatially structured optical fields, including the vector optical field, vortex optical field, and vortex vector optical field. The diffraction patterns of the vector optical fields exhibit self-similarity, and the characteristics of the vector optical fields are maintained in every diffraction peak. The diffraction patterns of the vortex optical fields and vortex vector optical fields exhibit triangular lattice arrays, and the vortex topological charge can be determined by the number of peak spots in the triangular lattice array. We hope these diffraction properties with fractal amplitude masks can be applied not only in detecting topological charges of spatially structured optical fields, but also in generating flexibly controlled diffraction patterns and lattice arrays, which may be useful in optical machining, optical trapping, and information transmission.

Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.

We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.

Inverse method to engineer uniform-intensity focal fields with arbitrary shape.

We present an inverse method to engineer uniform-intensity focal fields with arbitrary shape. Amplitude, phase, and polarization states, as adjustable parameters, are used to seek the desired focal fields in the non-iterative computational procedure. Our method can be applied to the cases with low and moderate numerical aperture (NA), in which case the feasibility and validity of our approach have been demonstrated in theory, simulation and experiment, respectively. For the case of higher NA, simulated results based on the Richards-Wolf diffraction integral are shown. We also made some discussions on the experiments with the higher NA. Our method should have wide applications in optical micro machining, optical trapping and so on.

High-efficiency and flexible generation of vector vortex optical fields by a reflective phase-only spatial light modulator.

The scheme for generating vector optical fields should have not only high efficiency but also flexibility for satisfying the requirements of various applications. However, in general, high efficiency and flexibility are not compatible. Here we present and experimentally demonstrate a solution to directly, flexibly, and efficiently generate vector vortex optical fields (VVOFs) with a reflective phase-only liquid crystal spatial light modulator (LC-SLM) based on optical birefringence of liquid crystal molecules. To generate the VVOFs, this approach needs in principle only a half-wave plate, an LC-SLM, and a quarter-wave plate. This approach has some advantages, including a simple experimental setup, good flexibility, and high efficiency, making the approach very promising in some applications when higher power is need. This approach has a generation efficiency of 44.0%, which is much higher than the 1.1% of the common path interferometric approach.

Fractal vector optical fields.

We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.

Hyperbolic-symmetry vector fields.

We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.

Arbitrarily tunable orbital angular momentum of photons.

Orbital angular momentum (OAM) of photons, as a new fundamental degree of freedom, has excited a great diversity of interest, because of a variety of emerging applications. Arbitrarily tunable OAM has gained much attention, but its creation remains still a tremendous challenge. We demonstrate the realization of well-controlled arbitrarily tunable OAM in both theory and experiment. We present the concept of general OAM, which extends the OAM carried by the scalar vortex field to the OAM carried by the azimuthally varying polarized vector field. The arbitrarily tunable OAM we presented has the same characteristics as the well-defined integer OAM: intrinsic OAM, uniform local OAM and intensity ring, and propagation stability. The arbitrarily tunable OAM has unique natures: it is allowed to be flexibly tailored and the radius of the focusing ring can have various choices for a desired OAM, which are of great significance to the benefit of surprising applications of the arbitrary OAM.