Vector Light Fields Research Articles

Vector angular spectrum model for light traveling in scattering media

Strongly scattering media disrupt both the wavefront distribution and the polarization state of the incident light field. Controlling and effectively utilizing depolarization effects are crucial for optical applications in highly scattering environments, such as imaging through dense fog. However, current simulation models have difficulty simulating the evolution of vector light fields within scattering media, posing challenges for studying vector light fields in strongly scattering environments. Here, we propose the Vector Angular Spectrum (VAS) model for simulating the propagation of vector light fields within scattering media. By introducing the angular spectrum distribution of vector light scattering and polarization conversion mechanisms, this model can simulate the depolarization effects of vector light propagating through strongly scattering media. The VAS model has also been used to investigate the focusing of vector scattered light through scattering media. Furthermore, the simulation results of the model have been validated through experiments. The proposed VAS model is expected to play a role in the theoretical research of vector scattered light and optical applications in strongly scattering environments.

Multi-Mode Vector Light Field Generation Using Modified Off-Axis Interferometric Holography and Liquid Crystal Spatial Light Modulators

The increasing enhancement in the modulation accuracy of spatial light modulators has garnered significant attention towards real-time control technology for light fields based on these modulators. It has been demonstrated that this technology possesses a remarkable capability to generate vector beams with arbitrary complex amplitude distributions. Nevertheless, past studies indicate that the generation of only one vector beam at a time has been observed. The simultaneous generation of numerous vector light fields can give rise to several challenges, including compromised picture quality, limited single-mode operation, and intricate optical path configurations. In pursuit of this objective, we present a novel methodology that integrates the coding methodology of modified off-axis interferometric holography with the idea of optical superposition. This technique facilitates the concurrent generation of several vector beams. In this study, we present a demonstration of the simultaneous creation of twelve vector beams using a single spatial light modulator (SLM) as a proof of concept. Significantly, this technology has the ability to generate an unlimited quantity of vector light fields concurrently under the assumption that the resolution of the SLM does not impose any limitations. The findings indicate that the imaging quality achieved by this technology is of a high standard. Furthermore, it is possible to separately control the beam waist radius, topological charge, polarization order, and extra phase of each beam.

Generation of high radial node vector vortex beams based on digital micromirror device

The modulation of amplitude, phase, and polarization to generate complex vector light fields with spatially variant polarization distribution has become a hot research topic in recent years. We propose a new method for generating high radial node vector vortex beams (VVB) based on a digital micromirror device (DMD). Firstly, we propose a multiplexed binary hologram with varying ellipticity, which can significantly optimize the vortex beam generated by DMD while the mode purity of the scalar vortex beam after optimization can reach 97.23%. Secondly, a novel interference experimental setup is proposed based on the Wollaston prism, which can realize arbitrary control of VVBs. Based on this, the high radial node VVBs with p=10 and high polarization order VVBs with polarization order up to 25 are generated experimentally. Finally, we reconstruct the State of Polarization (SoP) of the vector beam l=4,m=-4,p=4 based on the Stokes parameter S1,S2,S3, and the variation of vector quality factor (VQF) on the high-order Poincaré sphere (HOPS) is analyzed. Our technology provides a high-quality vector beam generation scheme with important applications in laser detection, optical communication, and optical micro-manipulation.

Trapped atoms in spatially-structured vector light fields

Spatially-structured laser beams, eventually carrying orbital angular momentum, affect electronic transitions of atoms and their motional states in a complex way. We present a general framework, based on the spherical tensor decomposition of the interaction Hamiltonian, for computing atomic transition matrix elements for light fields of arbitrary spatial mode and polarization structures. We study both the bare electronic matrix elements, corresponding to transitions with no coupling to the atomic center-of-mass motion, as well as the matrix elements describing the coupling to the quantized atomic motion in the resolved side-band regime. We calculate the spatial dependence of electronic and motional matrix elements for tightly focused Hermite–Gaussian, Laguerre–Gaussian and for radially and azimuthally polarized beams. We show that near the diffraction limit, all these beams exhibit longitudinal fields and field gradients, which strongly affect the selection rules and could be used to tailor the light-matter interaction. The presented framework is useful for describing trapped atoms or ions in spatially-structured light fields and therefore for designing new protocols and setups in quantum optics, -sensing and -information processing. We provide open code to reproduce our results or to evaluate interaction matrix elements for different transition types, beam structures and interaction geometries.

Cross-spectral purity of nonstationary vector optical fields: A similarity with stationary fields

This study establishes a reduction formula for nonstationary cross-spectrally pure vector (or electromagnetic) light fields with any spectral bandwidth. In general, for nonstationary cross-spectrally pure electromagnetic fields, the reduction formula of the two-time Stokes parameters normalized by the corresponding usual Stokes parameters is not similar to the one for stationary fields since the correlation properties for nonstationary fields depend on two-time instants t1 and t2, in addition to their time difference. Here, we derive a reduction formula by including time-integrated correlations that share a similar mathematical structure to that of reduction formulas used for stationary vector fields if the normalized spectra of the interfering fields are identical. Additionally, we examine the requirement of strict cross-spectral purity for nonstationary electromagnetic fields using a time-integrated coherence function, which exhibits a mathematical form similar to that of strict cross-spectral purity in stationary vector fields. This investigation sheds light on the cross-spectral purity of pulse-type fields, which holds potential applications in statistical optics.

Vector Light Field Immediately behind an Ideal Spherical Lens: Spin–Orbital Conversion, Additional Optical Vortices, Spin Hall Effect, Magnetization

The Richards–Wolf formulas not only adequately describe a light field at a tight focus, but also make it possible to describe a light field immediately behind an ideal spherical lens, that is, on a converging spherical wave front. Knowing all projections of light field strength vectors behind the lens, the longitudinal components of spin and orbital angular momenta (SAM and OAM) can be found. In this case, the longitudinal projection of the SAM immediately behind the lens either remains zero or decreases. This means that the Spin–Orbital Conversion (SOC) effect where part of the “spin goes into orbit” takes place immediately behind the lens. And the sum of longitudinal projections of SAM and OAM is preserved. As for the spin Hall effect, it does not form right behind the lens, but appears as focusing occurs. That is, there is no Hall effect immediately behind the lens, but it is maximum at the focus. This happens because two optical vortices with topological charges (TCs) 2 and −2 and with spins of different signs (with left and right circular polarization) are formed right behind the lens. However, the total spin is zero since amplitudes of these vortices are the same. The amplitude of optical vortices becomes different while focusing and at the focus itself, and therefore regions with spins of different signs (Hall effect) appear. A general form of initial light fields which longitudinal field component is zero at the focus was found. In this case, the SAM vector can only have a longitudinal component that is nonzero. The SAM vector elongated only along the optical axis at the focus is used in magnetization task.

Optical asymmetric image encryption using vectorial light field encoding

We propose an asymmetric image encryption scheme that employs chaotic phase masks and vectorial light field. Vector light fields have non-uniform state of polarization across the transverse plane. In this encryption scheme, two security levels have been created; in the first level, a binary image is encrypted with two different chaotic phase masks in fractional Fourier domain and then phase and amplitude truncation approach is applied. In the second level, phase-truncated part is encoded into vectorial light field. Two layers of encryption under asymmetric process and vector field encoding ensure stronger security and being intensity-based approach offers ease in implementation. The proposed idea is supported by simulation and experimental results.

Capturing Vector Light Field on Azo Molecular Glass Submicron Pillar Array for Polarization Recording and Creating Optical Functional Surfaces

AbstractVector light fields possessing spatial‐variant states of polarization (SOPs) have attracted great research interest for various emerging applications. In this work, the responses of submicron pillar arrays of an azo molecular glass (IA‐Chol) to vector light fields are systematically investigated by using laser beams with different topological charges. The spatial‐variant SOPs in the illuminated areas are recorded by directional pillar deformations along the local electric field oscillation directions, and uncovered by scanning electron microscopy (SEM) and atomic force microscopy (AFM). The degrees of pillar deformations are proven to be correlated to the intensity distributions of the vector beams in the transverse planes. The pillar deformations caused by the vector beam irradiations generate several optical effects related to the surface structures, as revealed by optical microscopy, polarizing optical microscopy, and diffraction measurements. Based on the understanding, structural colors covering a wide spectral range are created for the pillar arrays after irradiated with the vector beams. The complex images with various structural colors are produced by the irradiations with vector beams through photomasks. These investigations reveal the unique correlations between the pillar deformations and transverse polarization morphologies of vector beams and demonstrate a promising approach to fabricate optical functional surfaces.

Influence of High-Order Twisting Phases on Polarization States and Optical Angular Momentum of a Vector Light Field

This study investigates the influence of high-order twisting phases on polarization states and optical angular momentum of a vector light field with locally linear polarization and a hybrid state of polarization (SoP). The twisted vector optical field (TVOF) is experimentally generated based on the orthogonal polarization bases with high-order twisting phases. The initial SoP of a TVOF modulated by the high-order twisting phase possesses various symmetric distributions. The propagation properties of a high-order TVOF with locally linear polarization and hybrid SoP are explored, including the intensity compression, expansion, and conversion between the linear and circular polarization components. In particular, orbital angular momentum (OAM) appears in a high-order TVOF during propagation where no OAM exists in the initial field. The variation of OAM distribution in cross-section becomes more frequent with the increase of the twisting phase order. In addition, a non-symmetric OAM distribution appears in a non-isotropic TVOF, leading to the rotation of the beam around the propagation axis during propagation. The optical energy flow distribution of a high-order TVOF provides a more profound understanding of the propagation dynamics of high-order TVOF. These results provide a new approach for optical field manipulation in a high-order TVOF.

Tight focusing field of cylindrical vector beams based on cascaded low-refractive index metamaterials

Abstract Using low-refractive-index metamaterials, we design a transmission-type radial-angular cylindrical vector beam generator. A high numerical aperture lens is constructed using an asymmetric meta-grating structure. The metamaterial vector beam generator and the meta-grating lens are physically cascaded to obtain the tight focusing characteristics of the vector light field. The vector beam generator module and the meta-lens module are prepared by 3D printing technology, and the near-field test has been carried out on the samples in the terahertz band. Using the physical cascading method, two modules are cascaded to construct a vector beam tight focusing device, and the focusing electric field distribution test has been carried out. The use of 3D printing technology for sample preparation further reduces the manufacturing difficulty and production cost, and ensures the realization of its design function on the basis of miniaturization and light weight, which provides the possibility for the research of tight focusing field regulation in the terahertz band.

Particle Trapping Properties of Metal Annular Slits under Vector Field Excitation

This article presents the particle capture performance of annular slits, which offer a simple alternative to complex micro/nano structures used to excite and focus surface plasmon polaritons (SPPs). Additionally, the annular slits are compatible with a variety of vector light fields, generating diverse SPP field distributions under their excitation. These SPP fields can be regulated by varying the vector light field parameters, thereby offering the annular slit structure the ability to flexibly capture and manipulate particles. The rotation and movement of captured objects can be achieved by changing the position and phase difference of the incident beams with linear polarization. Different material and sized metallic particles can be stably captured with a radially polarized beam excitation due to the strong convergence. These capabilities are demonstrated by evaluating the optical force and trapping potential based on the finite difference time domain (FDTD) simulation. This study provides valuable insights into the practical application of annular slits for particle capture and manipulation.

Time-multiplexed vector light field display with intertwined views via metagrating matrix

Three-dimensional (3D) display is the future technology of display. The insufficient refreshable information provided by the screen is one of the major bottlenecks that hinders the development of light field 3D display. In this paper, a time-multiplexed vector light field display is proposed to increase the amount of information by exploiting the time redundancy. A view modulator with fully coverage of metagrating matrix is adopted to generate two groups of time-sequentially lit-up intertwined views. With a small deflection angle of incidence, the intertwined-view based time-multiplexing strategy is beneficial because of the less stray light and crosstalk, compared with the successively arranged views. Therefore, the system volume and complexity of directional backlight are reduced. In the experimental demonstration, a time-multiplexed vector light field 3D display is constructed with 18 views. The horizontal field of view reaches 51°. The potential applications include human-computer interaction, commercial exhibition, and medical hygiene.

Tight Focus Vector Light Field of Hybrid Double Circularly Polarized Beams

Based on the Richard-Wolf diffraction theory, we demonstrate the tightly focused optical field distribution with two beams circularly polarized light. We deduced the expression of the double-beam superimposed vortex light intensity of left-handed circularly polarized light and right-handed circularly polarized light under the focusing condition of a high numerical aperture objective lens. Based on the different vortex topological charge values, amplitudes and initial phases of the dual beams, we numerically simulated the light intensity distribution of the superimposed hybrid focused light field. It is found that a variety of peculiar vortex spots can be obtained through the tight focus stacking of the double beams. These complex hybrid focused light fields with different polarizations can be used in fields such as optical field micro-manipulation or nonlinear fluorescence microscopy imaging.

Generation of cross-spectrally pure electromagnetic fields using a pair of moving diffusers.

In this paper, we demonstrate that the vector light field is cross-spectrally pure if it passes through two diffusers (having similar correlation properties) moving with identical linear speeds in opposite directions. To determine the spatio-temporal coherence function of cross-spectrally pure light, a double slit is placed just after the second diffuser. We show that the normalized space-time coherence Stokes parameters of emerging light can be described in the form of a reduction formula, whereas the absolute values of the normalized space-frequency coherence Stokes parameters are the same for every frequency component of the light field. These are the conditions of cross-spectral purity of Stokes parameters. We further prove that at zero time delay, the condition of strict cross-spectral purity is validated. Furthermore, we establish the conditions for cross-spectral purity for a vector light field passing through the aforesaid diffusers, when they rotate with identical angular speeds in opposite directions, offering a possibility to optimize the scheme using only a single diffuser. For the first time, to our knowledge, an additional condition for equality of the degree of cross-polarization in space-time and space-frequency domains for strict cross-spectrally pure light beams is also introduced.

Multi-Function Reflective Vector Light Fields Generated by All-Dielectric Encoding Metasurface.

Traditional optics usually studies the uniform polarization state of light. Compared with uniform vector beams, non-uniform vector beams have more polarization information. Most of the research on generating cylindrical vector beams using metasurfaces focuses on generating transmitted beams using the geometric phase. However, the geometric phase requires the incident light to be circularly polarized, which limits the design freedom. Here, an all-dielectric reflective metasurface is designed to generate different output light according to the different polarization states of the incident light. By combining the two encoding arrangements of the dynamic phase and the geometric phase, the output light is a radial vector beam when the linearly polarized light is incident along the x-direction. Under the incidence of linearly polarized light along the y-direction, the generated output light is an azimuthal vector beam. Under the incidence of left-handed circularly polarized light, the generated output light is a vortex beam with a topological charge of -1. Under the incidence of right-handed circularly polarized light, the generated output light is a vortex beam with a topological charge of +1. The proposed reflective metasurface has potential applications in generating vector beams with high integration.

Inhomogeneously polarized light fields: polarization singularity indices derived by analogy with the topological charge

In this work, we study several different vector and hybrid light fields, including those with multiple polarization singularities. We derive polarization singularity indices by adopting a well-known M.V. Berry's formula, which is commonly used to obtain the topological charge of scalar vortex light fields. It is shown that fields whose polarization state depends only on the polar angle in the beam cross section can have either polarization singularity lines outgoing from the center, or a single polarization singularity in the center of the beam cross section. If the polarization state of the field depends only on the radial variable, then such fields have no polarization singularities and their index is equal to zero. If the polarization state of a vector field depends on both polar coordinates, then such a field can have several polarization singularities at different locations in the beam cross section. We also investigate a vector field with high-order radial polarization and with a real parameter. At different values of this parameter, such a field has either several polarization singularity lines outgoing from the center, or a single singular point in the center. The polarization singularity index of such a field for different parameters can be either half-integer, or integer, or zero.

Structured Vector Field Manipulation of Terahertz Wave along the Propagation Direction Based on Dielectric Metasurfaces

AbstractThe generation and manipulation of vector light fields are of great significance for both fundamental research and industrial applications of polarized optics. In recent years, the spatial domain control of structured vector fields has gradually expanded from two‐ to three‐dimensional, including traditional optics and meta‐optics. Here, a new method to generate and manipulate structured vector light fields along the propagation direction is proposed, and the functionality in terahertz band using all‐silicon metasurfaces is demonstrated. The coherent superposition of orthogonal circularly polarized terahertz waves through long focal depth and multifocal metalens is completed, and varying phase differences between them in the propagation direction via path accumulation or initial phase design are introduced, thereby continuous variation or independently designed vector polarization distributions in multiple planes are obtained. It is worth mentioning that the proposed scheme is not only for the design of transverse electric field components, but also shows a strong ability for manipulation of the longitudinal component. This scheme realizes the polarization distribution designs of three‐dimensional vector fields in three‐dimensional space, and provides a new inspiration for the generation and manipulation of vector beams based on meta‐optics.

Generation of Elliptic-Symmetry Radially Polarized Optical Beam by Circle-Cassinian Optical Coordinate Transformation

Recently, optical coordinate transformation has garnered considerable research interest for manipulating structured light in emerging optical communication applications. Herein, we propose a circle-Cassinian optical coordinate transformation based on polarization invariance to generate an elliptical-symmetry radially polarized (ESRP) optical beam. Accordingly, we designed three isotropic phase plates for placement in the 4f optical system. The numerical simulations demonstrated accurate generation of the ESRP beam with specified intensity, including an overall intensity adjustment applied in the input plane. Therefore, the proposed method can aid in designing vector light fields, and the ESRP beam can be applied to optical tweezers and surface plasmonic-field generation.

Super-resolution optical microscopy using cylindrical vector beams

AbstractSuper-resolution optical microscopy, which gives access to finer details of objects, is highly desired for fields of nanomaterial, nanobiology, nanophotonics, etc. Many efforts, including tip optimization and illumination optimization etc., have been made in both near-field and far-field super-resolution microscopy to achieve a spatial resolution beyond the diffraction limit. The development of vector light fields opens up a new avenue for super-resolution optical microscopy via special illumination modes. Cylindrical vector beam (CVB) has been verified to enable resolution improvement in tip-scanning imaging, nonlinear imaging, stimulated emission depletion (STED) microscopy, subtraction imaging, superoscillation imaging, etc. This paper reviews recent advances in CVB-based super-resolution imaging. We start with an introduction of the fundamentals and properties of CVB. Next, strategies for CVB based super-resolution imaging are discussed, which are mainly implemented by tight focusing, depletion effect, plasmonic nanofocusing, and polarization matching. Then, the roadmap of super-resolution imaging with CVB illumination in the past two decades is summarized. The typical CVB-based imaging techniques in fields of both near-field and far-field microscopy are introduced, including tip-scanning imaging, nonlinear imaging, STED, subtraction imaging, and superoscillation imaging. Finally, challenges and future directions of CVB-illuminated super-resolution imaging techniques are discussed.

Color image encryption using vectorial light field through a compact optical set-up

Vector light fields have spatially non-uniform polarization across the transverse plane. In this study, a color image encryption scheme has been proposed in which the data is encoded into the spatially varying polarization states of light to achieve higher degrees of freedom. This scheme provides a strong security and a straightforward way for optical implementation. Simulation and experimental results have been presented to verify the feasibility of the proposed scheme.