Vectorial optical fields: recent advances and future prospects

Generation of vectorial optical fields with complex spatial distribution in the cross section is of great interest in areas where exotic optical fields are desired, including particle manipulation, optical nanofabrication, beam shaping and optical imaging. In this work, a vectorial optical field generator capable of creating arbitrarily complex beam cross section is designed, built and tested. Based on two reflective phase-only liquid crystal spatial light modulators, this generator is capable of controlling all the parameters of the spatial distributions of an optical field, including the phase, amplitude and polarization (ellipticity and orientation) on a pixel-by-pixel basis. Various optical fields containing phase, amplitude and/or polarization modulations are successfully generated and tested using Stokes parameter measurement to demonstrate the capability and versatility of this optical field generator.

Compact vectorial optical field generator based on a 10-megapixel resolution liquid crystal spatial light modulator

Based on the Fraunhofer diffraction theory and the properties of dove prism, the coordinate relationships among the four spatial light modulator (SLM) sections in a vectorial optical field generator (VOF-Gen) are derived and experimentally verified. Taking the coordinate system of the first SLM section as reference, the coordinate displacements between the first SLM section and the subsequent ones are measured through employing the specially designed four-quadrant patterns with varying shifts of the corresponding cross point. Complex optical field could be accurately generated by combining the derived coordinate relationships and pre-compensation of the measured coordinate displacements. A typical complex optical field is generated and the experimental results demonstrate the validity of the proposed transverse alignment method for the VOF-Gen.

We experimentally demonstrate a vectorial optical field generator (VOF-Gen) with an adaptive close loop control. The close loop control capability is illustrated with the calibration of polarization modulation of the system. To calibrate the polarization ratio modulation, we generate 45° linearly polarized beam and make it propagate through a linear analyzer whose transmission axis is orthogonal to the incident beam. For the retardation calibration, circularly polarized beam is employed and a circular polarization analyzer with the opposite chirality is placed in front of the CCD as the detector. In both cases, the close loop control automatically changes the value of the corresponding calibration parameters in the pre-set ranges to generate the phase patterns applied to the spatial light modulators and records the intensity distribution of the output beam by the CCD camera. The optimized calibration parameters are determined corresponding to the minimum total intensity in each case. Several typical kinds of vectorial optical beams are created with and without the obtained calibration parameters, and the full Stokes parameter measurements are carried out to quantitatively analyze the polarization distribution of the generated beams. The comparisons among these results clearly show that the obtained calibration parameters could remarkably improve the accuracy of the polarization modulation of the VOF-Gen, especially for generating elliptically polarized beam with large ellipticity, indicating the significance of the presented close loop in enhancing the performance of the VOF-Gen.

We demonstrate a technique for the generation of vectorial optical fields based on a single pass of light onto a reflective twisted nematic spatial light modulator (TN-SLM). Using a beam splitter and a quarter-wave plate, a polarization rotator is implemented. A curve of the behavior of this polarization rotator with the twisted nematic modulator in use proves a modulation up to 177 deg, making this setup suitable for engineering of cylindrical vector fields. A mathematical justification and an experimental demonstration of the generation of these beams and their quality are presented. The experimental results show that despite the presence of a small component of elliptical polarization, a twisted nematic modulator can be used to achieve local polarization control. A series of vector fields with variations of the parameters of topological charge, phase offset, and quadratic phase are engineered, analyzed with a linear polarizer, and captured. The proposed setup represents a simple approach for polarization manipulation using a TN-SLM and few optical elements, achieving polarization purity greater than 94%.

We propose a vectorial optical field generation system based on two-dimensional blazed grating to high-efficiently generate structured optical fields with prescribed amplitude, phase, and polarization. In this system, an optimized blazed grating hologram is written on a spatial light modulator (SLM) and can diffract the majority of the incident light into the first-order diffractions of the x and y directions, which then serve as base vectors for synthesizing desired vector beams. Compared with the conventional cosine grating used in the previous work, the proposed two-dimensional, blazed grating has a much higher efficiency. Both computer simulation and optical experiment validate that a conversion efficiency up to 5 times that of the former work is achieved. Our method can facilitate applications of the optical field manipulation.

Nonlinear optical processes of spatially structured light such as optical vortices and vector optical fields have exhibited many interesting physical effects and found a variety of important applications from classical to quantum regimes. However, high-harmonic generation of a vector optical field with a space-varying polarization state is still a challenge. Here we present a solution to realize third-harmonic generation of spatially structured light including vector optical fields in a nonlinear Sagnac interferometer containing only one carefully designed quasi-periodically poled potassium titanyl phosphate, for the first time, to our knowledge. The experimental results well confirm our theoretical predictions. Our results will enable to manipulate spatially structured light or photons carrying higher orbital angular momentum at new wavelengths. Our scheme has potential applications such as in optical skyrmions and may open up new opportunities to produce spatially structured entangled photons for quantum communication and computation.

The ability to precisely generate and manipulate three-dimensional (3D) vectorial optical fields is crucial for advancing applications in volumetric displays, secure data encoding, and optical information processing. However, conventional holographic techniques generally lack the capability to simultaneously control both light intensity and polarization within a volumetric region, thereby limiting the full realization of complex 3D vectorial light fields. Here, we present a metasurface-based platform for 3D vectorial holography that enables independent and programmable control over axial intensity and polarization profiles within structured beam arrays. By decomposing complex volumetric holographic targets into a dense array of non-diffracting beams—each governed by a tailored longitudinal response function—we achieve broadband, high-fidelity reconstruction of vectorial light fields encoded in both spatial intensity and polarization domains. Moreover, we demonstrate a vectorial encryption scheme that exploits the combined axial intensity and polarization degrees of freedom to realize secure, key-based optical information encoding. This approach provides a compact, integrable, and scalable solution for 3D vectorial holographic projection and volumetric vector beam shaping, offering a versatile platform for high-capacity optical storage, secure communication, and emerging quantum photonic technologies.

In recent years, the vector optical field (VOF) with space-variant polarization distribution has attracted great attention due to its unexpected effects and applications in a wide range of areas. The focal engineering plays the most important role, as the focused VOF provides various interesting properties. Here, we propose a kind of binary array VOF (BA-VOF), which can be applied in focal array engineering. The BA-VOF comprises an array of the first base field of radially polarized VOF and an array of the second base field of superposed subfields with phase modulations. We theoretically design and experimentally generate the BA-VOF. Based on the BA-VOF, we present a flexible method to manipulate the amount of the focal spots in the focal array. Moreover, the polarization state and spin angular momentum of each focal spot in the focal spot array can also be flexibly manipulated. The BA-VOF and the flexibly manipulated focal array are inspirable in the area of structured light, which can be applied in regions needing focal engineering, such as optical tweezers, optical fabrication, optical imaging, and so on.

Vector optical fields (VOFs) with space-variant polarizations have attracted great attention in various areas, and the VOFs have been applied to study the spin angular momentum (SAM) of the photon, leading to many new effects and applications. Here, we propose the multi-polar coordinate and design and generate the multi-polar VOF (MP-VOF) with an arbitrary even number of singularities. We further find that the SAM appears or annihilates in the focal plane, which means the processes of “0-1” and “1-0” of the SAM can be accomplished in propagation. The corresponding theoretical explanation is also provided, indicating that the SAM appears or annihilates due to the interaction of the fields at central symmetric positions on the wavefront. Moreover, the appearance of transverse SAM (also known as the “photonic wheel”) can also be achieved in tight focusing cases. In this way, we can achieve three cases of SAM under different conditions, including purely longitudinal SAM, purely transverse SAM, and three-dimensional SAM with both components. This new kind of MP-VOF significantly enriches the family of VOFs and provides new insights in studying the focal behavior of the SAM, which can be applied in realms such as spin absorbing particles in a more flexible way.

We present a vectorial optical field (VOF) framework that surpasses the diffraction limit in both long-range imaging and energy delivery. By jointly engineering spatial and temporal dimensions, reflective Fourier ptychography is extended to 3.2 km with 0.37× the classical diffraction limit, while a single-photon LiDAR tomography system achieves centimeter-scale, sub-diffraction imaging at 3.3 km using superconducting nanowire single-photon detectors. These advances demonstrate super-resolution, turbulence-resilient imaging over kilometer-range distances. Beyond super-resolution optical, high power VOFs are able to counteract thermal blooming during atmospheric laser propagation, enhancing on-target power density by a factor larger than 2. Together, these results may outline a cross-scale paradigm that links high-power vector-field structuring, single-photon detection, and adaptive control—offering a pathway toward next-generation optical systems that integrate imaging, sensing, communication and directed energy within a common physical framework.

We report a camera system, associated motorized opto-mechanics, and data handling routines for imaging the three-dimensional structure of singularities within scalar and vector optical fields. Using Fourier techniques to analyse a series of cross-sectional images, we measure either the relative phase or state of polarization of monochromatic fields and analyse this for the identification and mapping of their associated singularities.

Polarization singularity beams (PSB) possess specific topological structures and exhibit stability and resistance to interference during propagation. These characteristics bestow vector optical fields (VOFs) with unique physical properties and enhanced degrees of manipulation, offering potential application in optical microfabrication, optical micromanipulation, and optical information processing. Within this study, an experimental generation and detection system for VOFs is introduced. Leveraging the technique of dynamically loading holograms onto a spatial light modulator and using a movable measurement platform, it can achieve the basic generation, manipulation, and detection of PSBs. Specifically tailored for college-level physics education, this system enables undergraduates to understand the fundamental principles of VOF generation. Using PSBs as representatives of VOFs and incorporating hands-on experiments on generating and controlling these beams, students can not only master theoretical concepts but also enhance their practical skills in experimental design, instrument operation, and data analysis.

Vector optical field (VOF) manipulation greatly extended the boundaries of traditional scalar optics over the past decades. Meanwhile, the newly emerging techniques enabled by structural functional optical materials have driven the research domain into the subwavelength regime, where abundant new physical phenomena and technologies have been discovered and exploited for practical applications. In this Tutorial, we outline the basic principles, methodologies, and applications of VOF via structural functional materials. Among various technical routes, we focus on the metasurface-based approaches, which show obvious advantages regarding the design flexibility, the compactness of systems, and the overall performances. Both forward and inverse design methods based on the rigorous solution of Maxwell's equations are presented, which provide a valuable basis for future researchers. Finally, we discuss the generalized optical laws and conventions based on VOF manipulation. The applications in optical imaging, communications, precision measurement, laser fabrication, etc. are highlighted.

We report a flexible method to dynamically generate multiple sub-wavelength focal spot pairs with adjustable polarization, position and number at the focal plane of a high numerical aperture (NA) objective lens. The desired incident field on the pupil plane can be analytically derived by employing the time-reversed method combined with the dipole antenna radiation theory. The numerical simulations of the corresponding tightly focused field are conducted using the Richards-Wolf vectorial diffraction theory. The validity of the presented method is demonstrated through experimental generation of several designed pupil fields with a versatile vectorial optical field generator and characterization of the produced focused fields with Stokes parameter measurements.