Tailoring nonuniform local orbital angular momentum density.

As is well known, a light beam with a helical phase carries an optical orbital angular momentum (OAM), which can cause the orbital motion of trapped microparticles around the beam axis. Usually, the speed of the orbital motion is uniform along the azimuthal direction and depends on the amount of OAM and the light intensity. Here, we present the reverse customized method to tailor the nonuniform local OAM density along the azimuthal direction of the focal field, which has a hybrid polarization distribution and maintains a doughnut-shaped intensity profile. Theoretical analysis and experimental results about the orbital motion of the trapped polystyrene sphere show that the nonuniform local OAM density can be tailored by manipulating the polarization states of the focal field. Our results provide an ingenious way to control the local tangential optical force and the speed of the orbital motion of particles driven by the local OAM density and will promote exciting possibilities for exploring ways to control the mechanical dynamics of microparticles in optical trapping and microfluidics.

Characterization of Orbital Angular Momentum Quantum States Empowered by Metasurfaces.

Twisted photons can in principle carry a discrete unbounded amount of orbital angular momentum (OAM), which are of great significance for quantum communication and fundamental tests of quantum theory. However, the methods for characterization of the OAM quantum states present a fundamental limit for miniaturization. Metasurfaces can exploit new degrees of freedom to manipulate optical fields beyond the capabilities of bulk optics, opening a broad range of novel and superior applications in quantum photonics. Here we present a scheme to reconstruct the density matrix of the OAM quantum states of single photons with all-dielectric metasurfaces composed of birefringent meta-atoms. We have also measured the Schmidt number of the OAM entanglement by the multiplexing of multiple degrees of freedom. Our work represents a step toward the practical application of quantum metadevices for the measurement of OAM quantum states in free-space quantum imaging and communications.

Two-Measurement Tomography of High-Dimensional Orbital Angular Momentum Entanglement.

High-dimensional (HD) entanglement enables an encoding of more bits than in the two-dimensional case and promises to increase communication capacity over quantum channels and to improve robustness to noise. In practice, however, one of the central challenges is to devise efficient methods to quantify the HD entanglement explicitly. Full quantum state tomography is a standard technology to obtain all the information about the quantum state, but it becomes impractical because the required measurements increase exponentially with the dimension in HD systems. Hence, it is highly anticipated that a new method will be found for characterizing the HD entanglement with as few measurements as possible and without introducing unwarranted assumptions. Here, we present and demonstrate a scan-free tomography method independent of dimension, which only requires two measurements for the characterization of two-photon HD orbital angular momentum (OAM) entanglement. Taking Laguerre-Gaussian modes of photons as an example, the density matrices of OAM entangled states are experimentally reconstructed with very high fidelity. Our method is also generalized to the mixed HD OAM entanglement. Our results provide realistic approaches for quantifying more complex OAM entanglement in many scientific and engineering fields such as multiphoton HD quantum systems and quantum process tomography.

Theoretical analysis based on mirror symmetry for tightly focused vector optical fields.

A theoretical analysis based on mirror symmetry is proposed to analyze and predict the symmetry in intensity, phase and polarization distributions of the tightly focused vector optical field (VOF). We extend the analysis to more cases including more complicated polarization states and weak focusing cases. We further show the symmetric tightly focused fields of the eccentric cylindrical VOF and the redesigned VOF with a radially variant polarization state, which are achieved by redesigning the polarization state of the incident VOF based on the symmetry analysis. We also take the laser fabrication as an example to further show how to apply this symmetry analysis in a specific application area. Such a theoretical analysis can improve the calculation efficiency, provide new insights into the tight focusing process and offer a convenient way to engineer the field distributions in the focal plane, which may have potential applications in areas needing flexibly controllable tightly focused fields, such as laser fabrication, optical trapping, and optical storage.

Bessel-like beams with controllable rotating local linear polarization during propagation.

Bessel-like beams with controllable rotation of local linear polarization upon propagation are generated, which in fact achieve the evolution of polarization states along the equator of the Poincaré sphere during propagation. Based on the amplitude-phase joint modulation method, the rotation direction and rate of polarizations of the Bessel-like beam can be controlled easily by adjusting the radial indices and intensity ratio of two superposed beams. A rotation angle of $\sim$∼800 deg has been achieved after a propagation distance of 120 mm, corresponding to a rotation rate of $\sim$∼6.7 deg/mm, which is about three times higher than in previous works.

Pancharatnam-Berry geometric phase memory based on spontaneous parametric down-conversion.

Phase memory is an effect in which the interaction between a coherent pump beam and a nonlinear crystal generates photon pairs via the spontaneous parametric down-conversion process, then the down-converted photons (signal and idler) can carry the phase information of the pump beam. There has been much research on the memory of the dynamic phase so far; however, there is no report on the memory of non-dynamic phase, to the best of our knowledge. Here we acquire a Pancharatnam-Berry (PB) geometric phase in a physical system when light travels along a trajectory in polarization-state space. Induced coherence occurs in a cascaded scheme composed of two nonlinear crystals, when the idler photons in both crystals are aligned to be indistinguishable. A NOON ($N\; = \;{2}$N=2) state is established when blocking the two idler photons. We explore the PB geometric phase memory of the NOON state and induced coherence. We find that the first-order interference of the two-photon state or signal photons can be controlled by introducing the PB geometric phase to the pump light. This may facilitate precise control of the phase of the down-converted photons.

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.

Compact, robust, and high-efficiency generator of vector optical fields.

We design and realize a generator that can convert an orbital angular momentum (OAM) state into a vector polarization state. The generator is integrated by several commonly used optical elements and easy to make or glued. Compared with traditional interferometric ways for generating the vector optical fields, this integrated generator has compact and robust advantages and especially a high-efficiency of 87%.

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.

Control on helical filaments by twisted beams in a nonlinear CS2 medium.

Curved filament with large bent angle and controllable propagation behavior has always been great expectation and challenge due to its novelty and complexity. The unique properties of curved filaments make it possible to achieve many applications in micro-fabrication, spectroscopy and meteorology. Here we realize experimentally and theoretically control on helical filaments induced by twisted beams in CS2. The results show that helical filaments exhibit a robust pattern and high rotation rate. Specific intensity pattern of the twisted beam confines the filaments in fixed relative position and the azimuthal energy flux drives the rotating of the filamentation pattern. In addition, we demonstrated that the global orbital angular momentum (OAM) of twisted beams is still conservative to be zero, but local OAMs exhibit distinct variation during nonlinear propagation. Our idea has its significance which realizes the construction of helical filaments with flexibility and controllability and then facilitates to push the development of related researches.

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.

Femtosecond polarization-structured optical field meets an anisotropic nonlinear medium.

Filamentation, as a universal femtosecond phenomenon that could occur in various nonlinear systems, has aroused extensive interest, owing to its underlying physics, complexity and applicability. It is always anticipated to realize the controllable and designable filamentation. For this aim, the crucial problem is how to actively break the symmetry of light-matter nonlinear interaction. A kind of extensively used approaches is based on the controllable spatial structure of optical fields involving phase, amplitude and polarization. Here we present an idea to control the optical field collapse by introducing optical anisotropy of matter as an additional degree of freedom, associated with polarization structure. Our theoretical prediction and experimental results reveal that the synergy of optical anisotropy and polarization structure is indeed a very effective means for controlling the optical field collapse, which has the robust feature against random noise.

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.

Measurement of the topological charge and index of vortex vector optical fields with a space-variant half-wave plate.

Vortex vector optical fields (VVOFs) refer to a kind of vector optical field with an azimuth-variant polarization and a helical phase, simultaneously. Such a VVOF is defined by the topological index of the polarization singularity and the topological charge of the phase vortex. We present a simple method to measure the topological charge and index of VVOFs by using a space-variant half-wave plate (SV-HWP). The geometric phase grating of the SV-HWP diffracts a VVOF into ±1 orders with orthogonally left- and right-handed circular polarizations. By inserting a polarizer behind the SV-HWP, the two circular polarization states project into the linear polarization and then interfere with each other to form the interference pattern, which enables the direct measurement of the topological charge and index of VVOFs.

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.

Microstructures fabricated by dynamically controlled femtosecond patterned vector optical fields.

We have presented and demonstrated a method for the fabrication of various complicated microstructures based on dynamically controlled patterned vector optical fields (PVOFs). We design and generate dynamic PVOFs by loading patterned holograms displayed on the spatial light modulator and moving traces of focuses with different patterns. We experimentally fabricate the various microstructures in z-cut lithium niobate plates. The method we present has some benefits such as no motion of the fabricated samples and high efficiency due to its parallel feature. Moreover, our approach is able to fabricate three-dimensional microstructures.

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.