Vector Angular Spectrum Research Articles

OAM crosstalk of multiple coaxial THz vortex beams propagating through an inhomogeneous unmagnetized plasma slab

An investigation into the orbital angular momentum (OAM) cross talk of multiple coaxial terahertz vortex beams propagating through an inhomogeneous unmagnetized plasma slab was conducted using the vector angular spectrum expansion method. For the double Gaussian distribution model of plasma sheath, considering the incidence of coherent vortex beams with single topological charge (TC), double, and four TCs, numerical simulations of the amplitude and OAM spectra of the reflected and transmitted beams were carried out and discussed in detail. The results showed that, as an oblique incidence of vortex beams, the effects of an inhomogeneous plasma slab on the distortions of the magnitude profiles and OAM spectra of the reflected and transmitted beams were critical, and due to the effects of several reflections between interfaces, the effects on the reflected beam were more serious. The distribution of the contours of the electric fields in transverse planes was closely related to the TCs of the incident beams. For coaxial incidence of multiple coherent vortex beams, the additional mutual cross talk, which was caused by interference, decreased with the increasing difference in the TCs and needed to be considered during OAM multiplexing. The selection of the radial integral distance had an obvious impact on the weights of the primary OAM states. This work provides an important theoretical reference for terahertz OAM multiplexing technology in solving the communication blackout caused by the plasma sheath.

Explicit analytical expressions for the electromagnetic field components of typical structured light beams

As typical structured light beams, Laguerre-Gaussian beams, Bessel beams, and Airy beams have attracted great attention for their fascinating features and wide potential applications. Explicit expressions for the electromagnetic field components of these beams obtained from a vector angular spectrum analysis are of particular importance to study a variety of problems involving the propagation, transmission, and reflection of laser beam, as well as light-matter interactions. In the present work, we first briefly recall the scalar expressions of typical structured light beams, including the Laguerre–Gaussian beams, Bessel beams, and Airy beams. Then we present the formulae of vector angular spectrum representation under different conditions. Finally, we derive in detail the analytical expressions for the electromagnetic field components of these structured light beams and provide some important integral formulae. Additionally, distributions of the electromagnetic fields, as well as the phase, Poynting vector and energy density are displayed and analyzed for these typical structured light beams.

Dynamics of angular momentum-torque conversion in silicon waveguides.

We present a refined theoretical analysis on the relationship between the optical total angular momenta (TAM) and the optical torque (OT) in a birefringent silicon waveguide. By using the vector angular spectrum method, we demonstrate the dynamic evolutions of the OT, TAM, spin angular momentum (SAM), and orbital angular momentum (OAM). The SAM and OAM coexist and evolve simultaneously in the propagation. The ratio between the OAM and TAM is related to the incident wavelength and the size of waveguide. Moreover, we design a three-layer waveguide structure to convert the light chirality and generate high torque. The performance of such torque-generator is analyzed numerically in detail.

Polarization transitions in the focus of radial-variant vector circular Airy beams.

We propose a new kind of light beam with both autofocusing ability and radial-variant distribution of polarization states, named radial-variant vector circular Airy beam (RVCAB). The polarization transitions in the focus of RVCABs are simulated based on vectorial angular spectrum formalism and theoretically explained by Stokes parameters. Our results reveal the dependence of the pure polarization state near the focus on the distribution of polarization states in the initial plane, which may lead to manipulation of the polarization state near the focus via controlling the distribution of polarization states in the initial plane.

Three-Dimensional Optical Spin Angular Momentum Flux of a Vector Beam with Radially-Variant Polarization in Near Field

The near-field characteristics of a radially-variant vector beam (RVVB) are analyzed by using the vectorial angular spectrum method. The non-paraxial RVVB can be decomposed into the propagating wave and the evanescent wave in near field. The coherent superposition of the longitudinal and transverse components of the RVVB results in a three-dimensional (3D) profile of the spin angular momentum flux density (SAM-FD). The evanescent wave part dominates the near field of a highly non-paraxial RVVB. The longitudinal component has a large impact on the 3D shape of the optical SAM-FD. Therefore, the 3D SAM-FD configuration of the RVVB can be manipulated by choosing the initial states of polarization arrangement. In particular, the transverse SAM-FD with a spin axis orthogonal to the propagation direction offers a promising range of applications spanning from nanophotonics and plasmonics to biophotonics.

Validation of vectorial theories for the focusing of high numerical aperture Fresnel zone plates

Abstract To study the applicability of vectorial angular spectrum (VAS) theory and vectorial Debye–Wolf diffraction integral for the focusing of high numerical aperture (NA) Fresnel Zone Plates (FZPs), these two vectorial methods have been rigorously examined by the three-dimensional finite-difference time-domain (FDTD) method under general and specific conditions. It is found that for a low total annulus number and when the wavelength dispersion or obstruction are existing, Debye–Wolf diffraction integral has failed to describe the light field distribution in the focal region. On the contrary, VAS theory can generally predict the focusing properties. However, when a FZP only contains one or two transparent annuli, both VAS and Debye–Wolf diffraction theories are invalid. Wavelength dispersion and purpose obstruction can produce the multi-focus or focal shift, which can be used for the axial wavelength scanning, the precise measurement of laser wavelength, or optical trapping.

Electromagnetic exploration of focusing properties of high-numerical-aperture micro-Fresnel zone plates

Focusing properties of high-numerical-aperture micro-Fresnel zone plates (FZP) have been rigorously investigated at the wavelength from deep ultraviolet to visible based on the combination of the vectorial angular spectrum theory and three-dimensional finite-difference time-domain method. New insights are found. The axial spot size evaluated by full-width-at-half-maximum is in direct proportion to the inverse of the total annulus number. Linearly negative focal shift phenomenon can be observed due to the wavelength dispersion over a finite range of tens of nanometers. A proper wavelength deviation can lead to the maximum focal intensity. A simple method has been demonstrated to probe either multi-focus or a light needle using a composite microstructure based on high-NA FZPs. The findings of this study expand the common understandings of the classic widely-used FZPs.

A new method to produce optical nano-needle

A method is described to design a microstructure comprised of multi-Fresnel zone plate (FZP) fragments for shaping an optical needle with arbitrary length. Thus, a microstructure comprised of three planar FZP fragments with different focal lengths f1, f2, and f3 is designed to form a long optical needle by delicate interference of coherent light beams diffracted from these three FZP fragments. For a 74.34-μm-diameter microstructure illuminated with a linearly x-polarized beam, a 7.87-λ-long optical needle is produced at a distance of 12.31 λ away from the mask surface. The sizes of transverse beam are 0.97 and 0.4 λ in x and y directions, respectively. For this work, the vectorial angular spectrum (VAS) theory is employed to describe the electric field of light behind the microstructure, as well as the three-dimensional finite-difference time-domain (3D FDTD) method is adopted to further verify the results obtained.

Intensity, phase, and polarization of a vector Bessel vortex beam through multilayered isotropic media.

This paper investigates the characteristics of reflected and transmitted fields of a vector Bessel vortex beam through multilayered isotropic media on the basis of the vector angular spectrum expansion and presents the effects of media on intensity, phase, and polarization. The method is verified by studying the reflection and transmission on a single interface at vertical incidence. For both paraxial and nonparaxial incident beam cases, numerical simulations of the field components and the time-averaged Poynting vector power density of the reflected and transmitted beams for the three-layered media are presented and discussed in detail. It is shown that as the incident angle increases, the magnitude distribution of the reflected beams illustrates significant distortions and no longer represents similar patterns to that of the incident beam, whereas the magnitude distribution of the transmitted beams can maintain similar profiles to the incident beam, apart from the notable distortion of the central ring. For the same incident angle, the effects of media on the magnitude distribution for the nonparaxial case are more evident than those for the paraxial case. The results of phase distribution and polarization of the reflected and transmitted fields show that as the incident angle increases, the distortion of the phase distribution and polarization for the reflected fields are more significant and the topological charge cannot be preserved.

Accurate experimental detection method for characterizing superoscillatory lenses made from multiannular metasurfaces

To verify the superoscillatory optical diffraction focusing characteristics of multiannular metasurfaces (MAMs), we propose an experimental detection method. It consists of two parts, the reflection positioning optical system and transmission detection imaging system. The best focal plane of the superoscillatory optical diffraction focus for the MAM can be precisely positioned through the reflection positioning optical system, which is the core part of the experimental detection method and is based on the structured illumination optical sectioning principle. A typical MAM is designed using vectorial angular spectrum (VAS) theory and a genetic algorithm. It was fabricated by focused ion-beam milling. The three-dimensional finite-difference time-domain method is used to verify the intensity distribution of the focus predicted by the VAS theory. For the designed 14-μm-diameter MAM at a wavelength of 640 nm, the simulation result broadly agrees with the experimental result obtained from the transmission microscopic imaging system. The proposed detection method can be used in fields such as optical diffraction focusing and subwavelength resolution imaging.

Vectorial structure of arbitrary vector vortex beams diffracted by a circular aperture in the far field

In terms of the vector angular spectrum representation and the method of stationary phase, the analytical vectorial structure of the arbitrary vector vortex Laguerre–Gaussian beam on the higher-order Poincaré sphere diffracted by a circular aperture is obtained in the far field. The far-field energy flux distributions of the arbitrary apertured vector vortex beams including cylindrical vector beam, circularly polarized vortex beam, and elliptically polarized vortex beam are numerically demonstrated from the vectorial structure. The analyses show that the topological charge, the truncation parameter, and the ellipticity angle play an important role in the vectorial structure and the evolution properties of the apertured vector vortex beam in the far field. This research is useful for manipulating the vector vortex beams by adjusting states of polarization on the higher-order Poincaré sphere.

Modified vectorial angular spectrum formula for propagation of non-paraxial beams

We presented modified forms of full-vector angular spectrum formula without singular points for longitudinal spectral components. In paraxial limitation, the modified angular spectrum formula has the same form as usual angular spectrum formula. Since there are not any singular points at the angular spectrum formula, we can apply it to analyze the propagation of non-paraxial beams with subwavelength-size waist and give results that strictly satisfy Maxwell’s equations because the calculating process includes contributions from all field components and angular spectral components.

Rigorous full-wave calculation of optical forces on dielectric and metallic microparticles immersed in a vector Airy beam.

Based on the generalized Lorenz-Mie theory and the Maxwell stress tensor approach we present the first rigorous full-wave solution of the optical forces acting on spherical microparticles immersed in a two-dimensional vector Airy beam beyond the paraxial approximation. The critical aspect lies in evaluating efficiently and accurately the partial wave expansion coefficients of the incident Airy beam, which are achieved by using the vector angular spectrum representation for a variety of polarizations. The optical field distributions are then simulated to show the self-accelerating and self-healing effects of the Airy beam. The dielectric and gold microparticles are shown to be trapped within the main lobe or the nearby side-lobes mostly by the transverse gradient optical force while driven forward along the parabolic trajectory of the Airy beam by the longitudinal scattering force. It is thus demonstrated theoretically that the vector Airy beam has the capability of precisely transporting both dielectric and metallic microparticles along the prespecified curved paths.

Energy flux density and angular momentum density of radial Pearcey-Gauss vortex array beams in the far field

The longitudinal and transverse energy flux density (EFD) and angular momentum density (AMD) of the radial Pearcey-Gauss vortex array beams are studied by using the vector angular spectrum representation and stationary phase method, where the influence of topological charge, initial phase index, noncanonical strength and the number of beamlet on far-field vectorial structures of the corresponding beam is emphasized. The results show that the topological charge of center optical vortex is always equal to initial phase index for different noncanonical strength. The longitudinal EFDs exhibit different structures by varying initial phase index and the number of beamlet. For an odd-N, the topological charge of center optical vortex can be determined by distinguishing the longitudinal EFD, however for an even-N the topological charge cannot be identified due to the equivalence of longitudinal EFD in the case of positive and negative initial phase index m. The AMD tends to split more branches from the positive and negative direction with increasing the absolute value of topological charge l, The inner structures of AMD are also affected by different beamlets while the zero value of AMD is always retained.

Intensity and orbital angular momentum density of nonparaxial anomalous vortex beams

The intensity and the orbital angular momentum density of an anomalous vortex beam beyond the paraxial approximation are studied. By using the vectorial angular spectrum method, analytical expressions of the electric field of the nonparaxial anomalous vortex beam are derived. Based on the expressions, an analytical expression of the orbital angular momentum density of the nonparaxial anomalous vortex beam is deduced. Through the numerical simulation method, the intensity distribution and orbital angular momentum density distribution characteristics are studied, and then the effects of topological charge, beam order, and propagation distance on the distributions of the intensity and orbital angular momentum density are analyzed. The results show that the intensity distribution of an nonparaxial anomalous vortex beam is similar to that of an paraxial anomalous vortex beam, while the orbital angular momentum density distribution is not.

Negative optical radiation force and spin torques on subwavelength prolate and oblate spheroids in fractional Bessel-Gauss pincers light-sheets.

Fractional Bessel-Gauss light-sheets [J. Opt.19, 055602 (2017)JOOPDB0150-536X10.1088/2040-8986/aa649a], which correspond to finite optical "slices" in 2D and possess asymmetric slit openings and bending characteristics, are examined from the standpoint of optical radiation force and spin torque theories for a subwavelength spheroid with arbitrary orientation in space. The vector angular spectrum decomposition method in addition to the Lorenz gauge condition and Maxwell's equations are used to determine the Cartesian components of the incident radiated electric field of the Bessel-Gauss light-sheets. In the framework of the dipole approximation, the numerical results for the Cartesian components of the optical radiation force and spin torque vectors show that negative forces (oriented in the opposite direction of wave motion) and spin torques arise depending on the beam parameters, the orientation of the subwavelength spheroid in 3D space, and its aspect ratio (i.e., prolate versus oblate). The spin torque sign reversal reveals that counter-clockwise or clockwise rotations around the center of mass of the spheroid can occur. The results find important applications in the application of auto-focusing light-sheets in particle manipulation, rotation, and optical sorting devices.

Interaction of Bessel pincers light-sheets with an absorptive subwavelength sphere coated by a plasmonic layer

The interaction of Bessel pincers light-sheets (i.e., finite optical beam “slices” in 2D) with a light-absorptive subwavelength sphere coated by a plasmonic layer in vacuum is examined in the framework of the electric dipole approximation. The vector angular spectrum decomposition method in addition to the Lorenz gauge condition and Maxwell’s equations are used to determine the Cartesian components of the incident radiated electric field of the Bessel pincers light-sheets. Two main effects are thoroughly investigated from the standpoint of the optical radiation force and spin torque theories. The numerical results for the optical radiation force and spin torque components show that a plasmonic layer of optimal thickness coating a small sphere can enhance the longitudinal and transverse force components as well as the axial spin torque induced by Bessel pincers light-sheets at the plasmonic resonance. Moreover, sign reversal of the longitudinal force component is manifested off the plasmonic resonance, resulting in particle trapping in a confined region in space. An axial spin torque sign reversal also occurs, which induces counterclockwise or clockwise rotation around the center of mass of the coated absorptive sphere depending on its position in the cross-sectional transverse plane. Furthermore, based on Newton’s second law of motion, a particle dynamics numerical analysis is performed, which reveals the emergence of retrograde motions of the coated sphere off-resonance as well as complex non-rectilinear/wiggly trajectories depending on its position in the transverse cross-sectional plane. At the plasmonic resonance, the coated sphere is propelled away from the source in the transverse cross-sectional plane along quasi-rectilinear trajectories. The results find related applications using autofocusing Bessel pincers light-sheets in particle manipulation and optical sorting devices.

Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci

The conventional multifocal optical elements cannot precisely control the focal number, spot size, as well as the energy distribution in between. Here, the binary amplitude-type super-oscillatory lens (SOL) is utilized, and a robust and universal optimization method based on the vectorial angular spectrum (VAS) theory and the genetic algorithm (GA) is proposed, aiming to achieve the required focusing performance with arbitrary number of foci in preset energy distribution. Several typical designs of multifocal SOLs are demonstrated. Verified by the finite-difference time-domain (FDTD) numerical simulation, the designed multifocal SOLs agree well with the specific requirements. Moreover, the full-width at half-maximum (FWHM) of the achieved focal spots is close to λ/3 for all the cases (λ being the operating wavelength), which successfully breaks the diffraction limit. In addition, the designed SOLs are partially insensitive to the incident polarization state, functioning very well for both the linear polarization and circular polarization. The optimization method presented provides a useful design strategy for realizing a multiple sub-diffraction-limit foci field of SOLs. This research can find its potentials in such fields as parallel particle trapping and high-resolution microscopy imaging.

Pulling and spinning reversal of a subwavelength absorptive sphere in adjustable vector Airy light-sheets

In the framework of the electric dipole approximation, this work demonstrates the generation of a pulling/attractive longitudinal force and an axial spin torque sign reversal causing counterclockwise or clockwise rotation of a subwavelength absorptive sphere placed in adjustable Airy light-sheets. Based on the vector angular spectrum decomposition method, the Lorenz gauge condition and Maxwell's equations, the Cartesian components of the incident radiated electric field of the generalized adjustable solution are derived, for which the main maximum Airy-lobe (i.e. caustic) is translated in space. The results find potential applications in the design/manufacture of particle manipulation and optical sorting devices using adjustable Airy-light sheets.

Investigation of axial and transverse focal spot sizes of Fresnel zone plates.

An axial spot size formula is given for a standard binary Fresnel zone plate (FZP) illuminated with a linearly polarized beam. The axial spot size, characterized by the full width at half-maximum (FWHM), can be accurately expressed by the Jiang-Wilson formula, viz., dz=0.9λ0/[η-(η2-NA2)1/2], when the number of transparent annuli is no less than 3. λ0 is the illumination light wavelength, η is the refractive index, and NA is the equivalent numerical aperture of a FZP. The transverse spot sizes are near linear with the radial width of the outmost annulus when the corresponding numerical aperture is not very large. This study is carried out based on vectorial angular spectrum theory and has been rigorously confirmed by the three-dimensional finite-difference time-domain method. This finding provides the theoretical basis for applying FZPs in a variety of applications, such as nanolithography, nanoscopy, and high-density data storage.