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Besides a linear momentum, optical fields carry an angular momentum (AM), which have two intrinsic components: one is spin angular momentum (SAM) related to the polarization state of the field, and the other is orbital angular momentum (OAM) caused by the helical phase due to the existence of topological azimuthal charge. The two AM components of the optical field may not be independent of each other, and the Spin-to-Orbital AM conversion (STOC) under focusing will create a spin-dependent optical vortex in the longitudinal filed. Here we demonstrate a new mechanism (or novel way, new way, specific process) for the STOC based on a radial intensity gradient. The radial phase provides an effective way to control the local AM density, which induce counterintuitive orbital motion of isotropic particles in optical tweezers without intrinsic OAM. Our work not only provides fundamental insights into the spin-orbit interaction of light, but also push towards possible applications in optical micro-manipulation., 17 pages, 6 figures

We theoretically analyze and verified the optical angular momentum (AM) arising from the gradient of the intensity and also depending on spin through optical trapping experiments and it may also be called spin to orbit conversion.

We perform a proof-of-principle experiment of High-dimensional QKD based on multiplexing of different orders of polarized structured photons with 4D-BB84 protocol. The secret key rate per sifted photon is estimated about 2.604 bits.

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 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 ∼ 800 deg has been achieved after a propagation distance of 120 mm, corresponding to a rotation rate of ∼ 6.7 deg/mm, which is about three times higher than in previous works.

We theoretically introduce a family of Hardy-like proofs which lead to stronger noncontextuality inequalities than that of extended KCBS. Meanwhile, we experimentally verify the simplest case of Hardy-like proof based on a fourdimensional photonic system.

We propose a method to realize the customized longitudinal polarized field in the tight focusing system. This method includes a modulated Fourier transform, so the Gerchberg-Saxton algorithm can also be used to perform complex designs.

Micromachining based on femtosecond lasers usually requires accurate control of the sample movement, which may be very complex and costly. Therefore, the exploration of micromachining without sample movement is valuable. Herein, we have illustrated the manipulation of optical fields by controlling the polarization or phase to vary periodically and then realized certain focal traces by real-time loading of the computer-generated holograms (CGHs) on the spatial light modulator. The focal trace is composed of many discrete focal spots, which are generated experimentally by using the real-time dynamically controlled CGHs. With the designed focal traces, various microstructures such as an ellipse, a Chinese character “Nan”, and an irregular quadrilateral grid structure are fabricated in the z-cut LiNbO3 wafers, showing good qualities in terms of continuity and homogeneity. Our method proposes a movement free solution for micromachining samples and completely abandons the high precision stage and complex movement control, making microstructure fabrication more flexible, stable, and cheaper.

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.

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.

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.

Orbital angular momentum (OAM) entanglement states have great potential in enhancing the information capacity in quantum communications. To make full use of the OAM degree of freedom, the measurement and distinction of OAM Bell states become a key step that needs to be accomplished. However, there is still no solution to achieve complete distinction of OAM Bell states at the single-photon level. Here we demonstrate the complete OAM Bell-state measurement without auxiliary photons by using linear optics. Furthermore, we propose a quantum communication network via OAM Bell-state multiplexing, perform a proof-of-principle experiment in the first- and second-order OAM subspaces for two users, and achieve average success probabilities of obtaining information of 91.6% for User-I and 89.1% for User-II. In principle, our scheme allows more users to be added by using high-order OAM Bell states. Our research extends the manipulation method for high-dimensional quantum states and paves the way for the application of OAM multiplexing in quantum communications.

Researchers manipulation and measure the eight hyperentangled Bell-like state in eight-dimensional Hilbert space., High-dimensional Bell-like states are necessary for increasing the channel capacity of the quantum protocol. However, their preparation and measurement are still huge challenges, especially for the latter. Here, we prepare an initial eight-dimensional Bell-like state based on hyperentanglement of spin and orbital angular momentum (OAM) of the first and the third orders. We design simple unitary operations to produce eight Bell-like states, which can be distinguished completely in theory among each other. We propose and illustrate a multiple projective measurement scheme composed of only linear optical elements and experimentally demonstrate that all the eight hyperentangled Bell-like states can be completely distinguished by our scheme. Our idea of manipulating the eight Bell-like states is beneficial to achieve the 3-bit channel capacity of quantum protocol, opening the door for extending applications of OAM states in future quantum information technology.

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.

Polarization singularities, describing the points where the state of polarization is indeterminate, reveal the polarization topology in vectorial optical fields, which include two-/three-dimensional topologies such as C-points, V-points, L-lines, Mobius strips, links, and knots. Compared with the phase singularities, it has more parameters to manipulate, which bring forth a series of novel optical phenomena and potential applications. In this Perspective, the research progress and development of polarization singularities are reviewed from the mathematical description, generation, detection, propagation dynamics, and related applications. In particular, we focused on the three-dimensional spatial propagation and the topological characteristics of polarization singularities in detail and revealed some basic fundamental physical phenomena and the novel effects of polarization singularities. We aim to touch on the key research studies in this field and provide insight into the current status and the challenges to the research studies. Finally, we outline the exciting prospects for the future that are yet to be realized.

Based on a parabolic coordinate system, we theoretically design and experimentally generate hybridly polarized vector optical fields with parabolic symmetry of the first and second kinds, which can further enrich the family of vector optical fields. The wavefront of this new-kind vector optical field contains circular, elliptic and linear polarizations, and the polarizations can keep the same or change along the parabolic curves. Then we present the realization of tunable focal shift with the hybridly polarized vector optical field, and show a specific law of the focal shift of the focused hybridly polarized vector optical field with the parabolic symmetry. We hope these results can provide a new way to flexibly modulate focal fields, which can be applied in realms such as optical machining, optical trapping and information transmission.

High-dimensional (HD) entanglement provides a very promising way of transcending the limitations of the two-dimensional entanglement between qubits for increasing channel capacity in many quantum protocols. In the pursuit of capitalizing on the HD entangled states, one of the central issues is to unambiguously and comprehensively quantify and reconstruct them. The full quantum state tomography is a unique solution, but it is undesirable and even impractical because the measurements increase rapidly in d 4 for a bipartite d-dimensional quantum state. Here we present a very efficient and practical tomography method—asymptotical locking tomography (ALT), which can harvest full information of bipartite d-dimensional entangled states by very few measurements less than 2d 2 only. To showcase the validity and reasonableness of our ALT, we carry out the test with the two-photon spin-orbital angular momentum hyperentangled states in a four-dimensional subspace. Besides high-efficiency and practicality, our ALT is also universal and can be generalized into multipartite HD entanglement and other quantum systems.

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 ) 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.

Optical orbital angular momentum (OAM) is a special property of photons and has evoked research onto the light–matter interaction in both classical and quantum regimes. In classical optics, OAM is related to an optical vortex with a helical phase structure. In quantum optics, photons with a twisted or helical phase structure will carry a quantized OAM. To our knowledge, however, so far, no experiment has demonstrated the fundamental property of the OAM at the single-photon level. In this Letter, we have demonstrated the average photon trajectories of twisted photons in a double-slit interference. We have experimentally captured the double-slit interference process of twisted photons by a time-gated intensified charge-coupled device camera, which is trigged by a heralded detection. Our work provides new perspectives for understanding the micro-behaviors of twisted particles and enables new applications in imaging and sensing.

Orbital angular momentum (OAM), as a fundamental parameter of a photon, has attracted great attention in recent years. Although various properties and applications have been developed by modulating the OAM of photons, there is rare research about the non-uniform OAM. We propose and generate a new kind of continuously tunable azimuthally non-uniform OAM for the first time, to the best of our knowledge, which is carried by a hybridly polarized vector optical field with a cylindrically symmetric intensity profile and a complex polarization singularity. We also present the perfect vector optical field carrying non-uniform OAM with a fixed radius independent of topological charges, which can propagate steadily without radial separation, solving the problem of the unsteady propagation due to the broadened OAM spectrum of the non-uniform OAM. This new kind of tunable non-uniform OAM with a cylindrical symmetric intensity profile, complex polarization singularity, and propagation stability enriches the family of OAMs and can be widely used in many regions such as optical manipulation, quantum optics, and optical communications.

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 CS

In recent years, orbital angular momentum (OAM), as a new usable degree of freedom of photons, has been widely applied in both classical optics and quantum optics. For example, digital spiral imaging uses the OAM spectrum of the output beam from the object to restore the symmetry information of the object. However, the related experiments have been carried out in free space so far. Due to the poor anti-noise performance, limited transmission distance and other reasons, the practicability is seriously restricted. Here, we have carried out a digital spiral imaging experiment through a few-mode fiber, to achieve the identification of the symmetry of object by measuring the OAM spectrum of the output beam. In experiment, we have demonstrated the identification of the symmetry of amplitude-only and phase-only objects with the two-, three- and four-fold rotational symmetries. We also give the understanding of the physics. We believe that our work has greatly improved the practical application of digital spiral imaging in remote sensing.

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.

The eccentricity of the spatial polarization distribution provides a new degree of freedom to achieve the controllable collapse. The coupling between the intensity and polarization affects the nonlinear dynamic properties of the structured optical fields.

We study the nonparaxial propagation behavior of Laguerre–Gaussian (LG) beams under the tight focusing condition by using the Rayleigh–Sommerfeld integrals. We obtain an analytical formula and show the focal shift with respect to the geometric focus of a high numerical-aperture objective. An analytical expression for the focal shift of a tightly focused LG beam increases with the focal length while decreases with the beam waist. This approach can be extended to deal with the tight focusing field and the focal shift of LG vector fields with space-variant polarization distributions or other focusing behaviors such as the 4π focusing and the Fresnel zone plates.

We predict theoretically and demonstrate experimentally the novel collapsing behaviors of the vector optical fields in an anisotropic lithium niobate crystal, which are controllable, designable and have the robust feature insensitive to the random noise.

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%.

In free-space or in optical fibers, orbital angular momentum (OAM) multiplexing for information transmission has been greatly developed. The light sources used were well coherent communication bands, and the fibers used were customized. Here, we use an 810 nm femtosecond laser to generate optical vortices carrying OAM and then feed them into two kinds of commercial step-index few-mode fibers to explore the transmission characteristics of OAM modes. We also propose a method without multiple-input multiple-output digital signal processing to identify the input OAMs. It is of great guiding significance for high-dimensional quantum information experiments via the OAMs as a degree of freedom, using the light generated by the spontaneous parametric down-conversion as the source and the commercial fibers for information transmission.

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.

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.

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.

We theoretically and experimentally explore the redistribution of polarization states and orbital angular momentum (OAM) in the output plane, induced by the symmetry breaking in the spatial frequency domain. When the vector fields are obstructed by sector-shaped filters in the spatial frequency domain, the local polarization states in the output plane undergo an abrupt transition from linear to circular polarization. The results reveal the polarization-dependent splitting and the appearance of a series of opposite OAMs in the output plane. We also find the self-healing effect of the vector fields broken in the spatial frequency domain and further explore its potential application. If the vector optical fields are used for information transferring or for imaging, even if the optical field carrying the information or image is partially blocked, the complete information or image can still be obtained, implying that which may increase the robustness of the information transferring and the imaging.

We have numerically simulated the operation of the Fourier-domain mode-locked (FDML) fiber laser based on the wavelength reconstruction method instead of numerical solving the nonlinear Schrodinger equation. We studied the influences of the filter bandwidth and the relative time delay caused by the fiber chromatic dispersion on the instantaneous linewidth of the FDML fiber laser. The results show that the instantaneous linewidth broadens as the filter bandwidth and the relative time delay increase. When the filter has the bandwidth of 0.02 nm, the narrowest and broadest instantaneous linewidths are 0.024 and 0.042 nm, respectively. We give an understanding for the oscillation of the instantaneous linewidth of FDML. The presented result can be used to evaluate the performance achievable in the FDML fiber lasers.

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.

The frequency doubling of femtosecond pulses from an Yb-doped fiber laser source was demonstrated in a PPKTP waveguide fabricated by femtosecond laser direct writing. The PPKTP waveguide contains a fixed period of 8.9 μm and the feomtosecond fundamental pulses have a central wavelength of 1044 nm. A maximum SHG power of 406 mW was produced, yielding a conversion efficiency of 5.6%. Numerical simulations were carried out to investigate the property of frequency doubling for femtosecond pulses. The results show that the SHG process proceeds even the quasi-phase-matching (QPM) condition is not well satisfied, which is significantly different from that of “long” pulses or CW light and is accorded with the experimental results.

Extending the length of femtosecond laser filamentation has always been desired for practical applications. Here, we demonstrate that significant extending of a single filament in BK7 glass can be achieved by constructing phase-nested beams. The filamentation and the following energy replenishment are assembled in a single phase-nested beam. The central part of the phase-nested beam is an apertured Gaussian beam, which is focused into one focal spot to produce a short filament. In contrast, the rest of the annular part converges gradually towards the central axis to continuously replenish the energy for supporting the regeneration of filaments. The common-path generating system ensures the stability of generated filaments and easily optimizes the beam parameters to obtain the longest high-quality filament due to its flexibility. In addition, we discuss the significance of continuous replenishment for extending filaments and the potential for generating more extended filaments based on this method.