Three-dimensional Optical Field Research Articles

Information structure of a polarization state: the concept of metaspin

A complete description of the polarization properties of a random, stationary, generally three-dimensional (3D) optical field in a point is provided by the 3×3 polarization matrix. We show that its nine degrees of freedom can be represented by nine independent and decoupled parameters with simple and significant physical meanings. These cover the three orientation angles determining the intrinsic reference frame with respect to an arbitrary one, the three principal intensities representing the strengths of the components of the electric field along the respective intrinsic reference axes, and a real-valued vector, which we term metaspin, whose three components are given by the intrinsic correlations of the field components. Consequently, any given polarization state has an associated intensity-isotropic state, called the metaspin state, whose spin vector is fully determined by the metaspin vector. We also show that the concept of metaspin provides an illustrative synthesis procedure for 3D polarization states. The results can straightforwardly be applied to any 3×3 density matrix.

Constructing Spin Density Vector Twists With Spin Density Singularity

In this article, we propose a non-orbital angular momentum (OAM) method for constructing the spiral twists of spin density (SD) vectors in three-dimensional (3D) optical fields. This is realized by generating strings of SD singularities in a longitudinal plane of a strongly focused HG10 mode beam with circular polarization. We demonstrate that in this plane, the SD singularities manifest themselves as the Gouy phase difference. Through observing the Gouy phase difference, the strings of the SD singularities and their topological reactions are examined. It is found that the spiral twists of SD vectors are constructed in the two-dimensional (2D) space between two strings and their twisting behaviors can be adjusted by the topological reactions of the strings. This finding shows that the spiral twists can be formed in a 2D space rather than the 1D space in previous studies, which provides a more flexible way to utilize this rotational degree of freedom. Our result also clarifies that although the spiral twists of SD vectors can be a result of spin-orbital angular momentum interaction, the OAM is not a necessary condition for the generation of these twists. Our theoretical proposal for structuring SD vectors may have applications in 3D optical manipulation.

Transient electromagnetic singularities in random three-dimensional optical fields.

We show that on all generic circular or elliptical paths in a random three-dimensional electromagnetic field, the electric and magnetic field vectors generate a cylinder throughout most of the optical cycle. At some point in the cycle, however, this cylinder transforms into a twisted ribbon with two sequential 180° twists. This ribbon exists for a short time and then unwinds, regenerating the cylinder. We discuss how and why these structures form and what determines their lifetimes.

Twisted ribbon carousels in random, three-dimensional optical fields.

The instantaneous electric vector in a random three-dimensional optical field is shown to generate twisted ribbon carousels that spin about their axes. The ribbons can be right or left handed and can unwind and rewind in time, changing their handedness during an optical cycle. Analytical formulas describing this behavior are presented.

Polarization Möbius strips on elliptical paths in three-dimensional optical fields.

Optical singularities in nonparaxial structured light are currently of special interest. Here we study polarization Möbius strips on elliptical paths surrounding lines of circular polarization in fully three-dimensional fields. We find that as the eccentricity, azimuthal orientation, or centering of the path changes, right-handed Möbius strips can change into left-handed ones, and vice versa, and that Möbius strips with one half twist can change into strips with three half twists, and vice versa. These transformations are shown to occur in a possibly unexpected way, not observed previously, that is universal for all two-component singularities.

Tunable degree of polarization of an unpolarized, partially coherent beam with circular coherence in a high numerical aperture system.

The polarization properties of a strongly focused, unpolarized, partially coherent beam with circular coherence are studied in this Letter. It is found that the degree of polarization (DoP) in the focal plane can be adjusted, not only by the initial coherence and the semi-aperture angle, but also through an annular pupil due to the unusual coherence of the source. Our results show that for an unpolarized, partially coherent incident beam, the field in the focal plane can go from almost an unpolarized state to almost a fully polarized state along a radial distance, although the initial coherence length is very short. Through adjusting the width of the annular pupil, the DoP on average can be significantly reduced or enhanced. Especially for the very narrow annulus, the approximation expression of the DoP is derived, from which the accurate positions of the peak values of the DoP can be easily calculated. Our findings provide an alternative way to tailor the DoP in three-dimensional optical fields.

Forming of three-dimensional optical fields consistent with the superposition of scalar spherical harmonics

Spherical functions are the angular part of the family of orthogonal solutions of the Laplace equation written in spherical coordinates. They are widely used to study physical phenomena in spatial domains bounded by spherical surfaces and in solving physical problems with spherical symmetry. In this paper, the superposition equation of spherical harmonics satisfying the Helmholtz equation was obtained. Modelling and visualization of three-dimensional fields, coordinated with separate spherical harmonics and their superpositions, was carried out.

Theoretical realization of three-dimensional nanolattice structure fabrication based on high-order waveguide-mode interference and sample rotation

A theoretical method of using high-order waveguide-mode interference combined with sample rotation is proposed to fabricate different kinds of three-dimensional nanolattice structures. The lithography sample is assisted by an asymmetric metal-cladding dielectric waveguide structure. High-order waveguide modes can be excited in the photoresist layer by both transverse magnetic and transverse electric polarized light. By utilizing multiple exposures of high-order waveguide-mode interference combined with sample-rotation, various three-dimensional nanolattice structures can be obtained. The resulting optical field distributions are simulated using the finite element method in this study, and sample rotation is expressed by coordinate matrix transformation. As examples, the three-dimensional optical field distributions resulting from fifth-order waveguide-mode interference were simulated with 90° and 60° sample rotations and multiple exposures. The results show that a quasi-cuboid structure with a simple tetragonal arrangement and a quasi-hexagonal structure with a hexagonal close-packed lattice can be obtained. Moreover, the numerical simulation results revealed that the shapes, sizes, arrangements, and periods of the structures can be controlled by the rotation method, photoresist thickness, waveguide modes used for exposure, and so on.

Geometric representation of polarization for a general three-dimensional optical field

On the basis of previous work in this area, we propose a new geometric representation of polarization for a general three-dimensional (3D) optical field. This representation is based on the characteristic and eigenvalue decompositions of the 3 × 3 coherency matrix, which is appropriate for all 3D polarized optical fields, including totally polarized, partially polarized and totally un-polarized optical fields. Based on this representation method, the degree of polarization for an arbitrary 3D optical field can be characterized by a unique point located on a spatial equilateral triangle. Correspondingly, the 3D state of polarization can be illustrated by the 3D distribution maps of polarization ellipse quantitatively.

Optical spatial differentiator for a synthetic three-dimensional optical field.

We propose a grating-based spatial differentiator to process a synthetic three-dimensional optical field, where several conventional two-dimensional optical images are stacked at multiple wavelengths. The device simultaneously enables both spatial differentiation and demultiplexing during light diffraction. We show the spatial differentiation resulting from coupling and interference of spatial modes and derive the theoretical condition for spatial differentiation based on spatial coupled-mode theory. We numerically investigate field transformation during diffraction and demonstrate spatial differentiation with image processing of edge detection for a synthetic three-dimensional optical field, where four images are stored at different wavelengths.

Nonlinear microscopy using cylindrical vector beams: Applications to three-dimensional imaging of nanostructures.

The three-dimensional (3D) optical fields that arise from the focusing of cylindrical vector beams (CVB) with radial and azimuthal polarizations provide new sources of contrast for optical microscopy of nano-objects. So far, these demonstrations have been restricted to two-dimensional transversal scanning, i.e., along the focal plane of interest, or use of point-like objects, i.e., single molecules and nanoparticles. Here, we demonstrate the first application of CVBs for 3D imaging of 3D nano-objects. This technique is done by acquiring 3D image scans of the second-harmonic generation signal from vertically-aligned semiconductor nanowires, whose second-order response is primarily driven by the longitudinal electric field, i.e., the field component along the nanowire axis. Our technique provides a new way to study individual nano-objects in three dimensions through the unique combination of nonlinear microscopy and CVBs.

Exploiting the speckle-correlation scattering matrix for a compact reference-free holographic image sensor.

The word ‘holography' means a drawing that contains all of the information for light—both amplitude and wavefront. However, because of the insufficient bandwidth of current electronics, the direct measurement of the wavefront of light has not yet been achieved. Though reference-field-assisted interferometric methods have been utilized in numerous applications, introducing a reference field raises several fundamental and practical issues. Here we demonstrate a reference-free holographic image sensor. To achieve this, we propose a speckle-correlation scattering matrix approach; light-field information passing through a thin disordered layer is recorded and retrieved from a single-shot recording of speckle intensity patterns. Self-interference via diffusive scattering enables access to impinging light-field information, when light transport in the diffusive layer is precisely calibrated. As a proof-of-concept, we demonstrate direct holographic measurements of three-dimensional optical fields using a compact device consisting of a regular image sensor and a diffusor.

Three-dimensional mapping of optical near field with scattering SNOM.

Scattering-type scanning near-field optical microscopy (s-SNOM) is applied to investigate three-dimensional optical near field distribution, including both amplitude and phase information. A method analogous to the force volume mode of the atomic force microscopy (AFM) technique is adapted for the measurement. The results show high lateral resolution of tens of nanometers, and even higher vertical resolution of only a few nanometers. The experiment results provide a straightforward illustration of the optical near fields in the space above the sample surface. Numerical computations support the experimental data. The ability to map the 3D optical near filed helps to reveal the factors that influence the performance of the designed near-field structures.

Special Section Guest Editorial: High-Speed 3-D Optical Metrology and Applications

Recent innovations in computational and electronic technologies have drastically enhanced the three-dimensional (3-D) optical metrology field in terms of measuring speed and accuracy, as well as expanded applications. High-speed 3-D optical metrology is a platform technology that could benefit numerous scientific studies and engineering concerns including but not limited to manufacturing, medical sciences, robotics, etc. Lately, a number of novel high-speed 3-D optical metrology methods have been developed, and these technologies have been applied to fields ranging from medicine, computer science, robotics, biometrics, homeland security, agriculture, and biology, to automotive, manufacturing, and entertainment industries. For example, Microsoft Kinect has penetrated 3-D optical metrology into our daily lives; real-time 3-D metrology techniques have permitted in situ inspection in the electronics industry; and high-speed 3-D sensing devices have enabled better robotic navigation. This special section assembles a good number of highspeed 3-D optical metrology technologies, as well as a few representative applications. Active high-speed 3-D shape measurement based on fringe projection requires generating

Optical Möbius strips and twisted ribbon cloaks

Optical Möbius strips that surround points of circular polarization, C points, in a generic three-dimensional optical field are cloaked by lines of twisted ribbons attached to the C points. When cloaking occurs, the observable signed twist index that counts the number of half-twists (one or three), and also measures the handedness (right or left), of a generic Möbius strip is determined by the twisted ribbon cloaks. Although some cloaks can be detached, they can never all be removed.

The Retinal Disease Screening Study: Retrospective Comparison of Nonmydriatic Fundus Photography and Three-Dimensional Optical Coherence Tomography for Detection of Retinal Irregularities

To determine the sensitivity of three-dimensional optical coherence tomography (3D-OCT) versus single field nonmydriatic fundus photography (FP) for detection of a variety of retinal abnormalities. Images from consecutive patients in a retina clinic undergoing simultaneous 3D-OCT (512 × 128) and single, foveal nonmydriatic 45° color fundus imaging with 3D-OCT-1000 in a 4 month-period were retrospectively collected. Findings from each modality were graded independently by two graders as present, questionable, or absent. Irregularities were separated into three categories for intermodality comparisons: epiretinal, retinal/subretinal, and RPE/choroidal irregularities. The approximate location of findings in relation to the 3D-OCT field was noted as in field and out of field. Findings from both modalities were combined to form the gold standard for comparison for each modality. Five hundred and one sets of 3D-OCT scans and fundus images of 395 eyes of 223 patients were found in the study period, of which, 474 unique visits were included. Ninety-six percent of the scans had abnormal findings. Twenty-six fundus images (5.5%) were ungradable. 3D-OCT identified some abnormality in 25/26 (96.2%) of the ungradable fundus images. For overall detection of a variety of retinal irregularities or irregularity of each category (epiretinal, intraretinal, or RPE/choroidal irregularity), 3D-OCT was found to be more sensitive than that of nonmydriatic color fundus images. When single specific feature was speculated, 3D-OCT demonstrated various detection abilities: higher than FP for abnormal retinal thickness (or intraretinal hyporeflective features); similar as FP for RPE atrophy; however, lower for pigment migration (or intraretinal hemorrhage). In this study, sensitivities of 3D-OCT were higher than nonmydriatic fundus images for overall detection of retinal abnormalities or irregularities in each category. 3D-OCT demonstrated good ability to detect most features; however, with limitation to intraretinal hemorrhage and pigment migration. It is likely that OCT will be added to photography screening for chorioretinal diseases in the near future.

Holographic plasmonic lenses for surface plasmons with complex wavefront profile

We present a direct-method solution toward the general problem of plasmonic wavefront manipulation and shaping to realize pre-designated functionalities based on the surface-wave holography (SWH) method. We demonstrate theoretically and experimentally the design and fabrication of holographic plasmonic lenses over surface plasmons with complex wavefront profiles. We show that visible light at 632.8 nm transmitting through a high-aspect-ratio slit or a micro-rectangle hole in a silver film can be focused to a preset three-dimensional point spot in free space via appropriately manipulating the interaction of excited surface plasmons with the nanoscale groove pattern of the holographic lens. The experiment results of scanning near-field optical microscopy for measuring the three-dimensional optical field distribution agree well both with designs and with numerical simulations, and this strongly supports the effectiveness and efficiency of the SWH method in the design of plasmonic devices that can fulfill manipulation and transformation of complicated-profile surface plasmons.

Thermal probing in single microparticle and microfiber induced near-field laser focusing

Microparticle and microfiber induced near-field laser heating has been widely used in surface nanostructuring. Information about the temperature and stress fields in the nanoscale near-field heating region is imperative for process control and optimization. Probing of this nanoscale temperature, stress, and optical fields remains a great challenge since the heating area is very small (~100 nm or less) and not immediately accessible for sensing. In this work, thermal probing of a single microparticle and microfiber induced near-field focusing on a substrate with laser light is conducted experimentally and interpreted by high-fidelity simulations. The laser (λ = 532 nm) serves as both heating and Raman probing sources. It is very interesting to note that variation of the Raman intensity, wavenumber, and linewidth all can be used to precisely capture the size of the micro-size subject on the substrate. Nanoscale mapping of conjugated optical, thermal, and stress effects, and the de-conjugation of these effects are performed. The effect of the laser fluence on the temperature and stress in the nanoscale heating region is investigated. With laser fluence of 3.9 ×10(9) W/m(2) and for a 1.21 μm silica particle induced laser heating, the maximum temperature rise and local stress are 58.5 K and 160 MPa, respectively. For a 6.24 μm glass fiber, they are 33.0 K and 120 MPa, respectively. Experimental results are explained and consistent with three-dimensional high-fidelity optical, thermal and stress field simulation.

Circular lines of circular polarization in three dimensions, and their transverse-field counterparts

A superficially paradoxical phenomenon is associated with curved c lines, on which the polarization of a three-dimensional optical field in space is purely circular. If the c line has fixed index (signed half-integer winding number), its two intersections with an observation plane, each with the same index, coalesce and annihilate when the c line is tangent to the plane, seeming to contradict the conservation of index. But there is no paradox: for the associated C line (distinct from the c line) on which the field transverse to the observation plane is circularly polarized, the two intersections have opposite indices, so their total index is zero, which is conserved during the annihilation. The different geometries of the c and C lines are studied in detail for model fields where the c line is a circle.

Rotational transformations of polarization singularities in three-dimensional optical fields: I. Ordinary points

In three-dimensional (3D) optical fields every ordinary point is a polarization singularity, here an ordinary polarization singularity, or O point, in three orthogonal planes oriented normal to the three principal axes (major, minor, and ellipse normal) of the polarization ellipse at the point. The canonical point polarization singularities: points of circular polarization, C points on C lines, and points of linear polarization, L points on L lines, are embedded in, and interact with, this sea of O points. O, C, and L points undergo a variety of democratic reactions in which O points collide with and replace C or L points, inverting the sign of the “topological charge” associated with the point. These reactions highlight the fact that not only must a consistent description of 3D light include O points and their reactions, but also that the charge of a C or L line segment is not an invariant, but is context dependent.