Engineering of high purity ultra-long optical needle field through reversing the electric dipole array radiation

Experimental Realization of Stable Exceptional Chains Protected by Non-Hermitian Latent Symmetries Unique to Mechanical Systems

Lines of exceptional points are robust in the three-dimensional non-Hermitian parameter space without requiring any symmetry. However, when more elaborate exceptional structures are considered, the role of symmetry becomes critical. One such case is the exceptional chain (EC), which is formed by the intersection or osculation of multiple exceptional lines (ELs). In this Letter, we investigate a non-Hermitian classical mechanical system and reveal that a symmetry intrinsic to second-order dynamical equations, in combination with the source-free principle of ELs, guarantees the emergence of ECs. This symmetry can be understood as a non-Hermitian generalized latent symmetry, which is absent in prevailing formalisms rooted in first-order Schrödinger-like equations and has largely been overlooked so far. We experimentally confirm and characterize the ECs using an active mechanical oscillator system. Moreover, by measuring eigenvalue braiding around the ELs meeting at a chain point, we demonstrate the source-free principle of directed ELs that underlies the mechanism for EC formation. Our Letter not only enriches the diversity of non-Hermitian exceptional point configurations, but also highlights the new potential for non-Hermitian physics in second-order dynamical systems.

Coordinate-transformation iteration algorithm for phase modulation of arbitrary axial light distribution

Axial light distribution modulation is widely applied in optical tweezers, hard-brittle material cutting, multilayer laser direct writing, etc. To generate arbitrary axial light distribution, the coordinate-transformation iteration (CTI) algorithm is presented. The CTI algorithm unifies equations in low and high numerical aperture (NA) scenarios, using the same iterative algorithm to produce phase computer-generated holograms. In a low NA scenario, twin-foci, flattop, and sin² distributions have been achieved. In high NA scenarios, multirings, multifoci, and needle-like distributions have been realized in simulation with specific polarized incident beams. Since the CTI algorithm is inherently an efficient one-dimensional phase retrieval algorithm that is not limited by NA, this method has the potential to become a well-received solution for axial light distribution modulation.

Sinusoidal-amplitude binary phase mask and its application in achieving an ultra-long optical needle

Optical needle has become a hot research topic in recent years, due to the excellent properties and potential applications. To achieve a sub-diffraction optical needle, there are three common methods including planar diffractive lenses, reflective mirrors or axicons, and high-NA objective lenses with the designed phase or amplitude elements. Here, we propose a new kind of designed phase and amplitude element called the sinusoidal-amplitude binary phase mask (SA-BPM), which modulates the amplitude and phase distributions of the incident vector optical fields (VOFs) simultaneously. Based on Richards-Wolf vector diffraction integral, the corresponding parameters of SA-BPM and the optimal optical needle length are calculated by exhaustive method and genetic algorithm. We further upgrade the SA-BPM by adding a Gaussian function in the amplitude modulation, and design the Gaussian SA-BPM (GSA-BPM). We find that the ultra-long optical needles are achieved with the SA-BPM and GSA-BPM, and the depth of focus of the optical needles are improved by 30%-70% compared with the case of binary phase mask. Such SA-BPM and GSA-BPM we proposed have great potential for manipulation and utilization of the ultra-long optical needles.

Transversely oriented cylindrically polarized optical fields

Cylindrical vector (CV) beams have nonuniform polarization vector distribution with a singularity line directed along the optical axis. In this paper, we propose a method to synthesize transversely oriented cylindrically polarized optical fields in the focal region with a singularity line perpendicular to the optical axis. The scheme is based on the time-reversal method, the vectorial diffraction theory, and the 4Pi optical configuration. Both transversely oriented radially polarized and azimuthally polarized optical fields are demonstrated. The superposition of transverse cylindrically polarized optical fields leads to a peculiar distribution carrying controllable transverse spin angular momentum (SAM) and transverse orbital angular momentum (OAM) that may find applications in optical tweezing, light-matter interaction, and unidirectional beam propagation excitation.

Vector optical field with the polarization varying along an arbitrary circular trajectory on the Poincaré sphere

As an inherent feature of vector optical field, the spatial distribution of polarization brings additional degrees of freedom to engineer the optical field and control the interaction between light and matters. Here we focus on the variation of polarization in single vector optical field, which can be defined by the trajectory on the Poincaré sphere. Based on the amplitude-phase-polarization joint modulation method we propose, vector optical field, whose variation of polarization follows arbitrary circular trajectory on the Poincaré sphere, can be generated. Moreover, the tightly focusing behaviors of the vector optical fields with the polarization varying along parallel circles on the Poincaré sphere are compared. Relations between the circular trajectory and the central intensity of the hollow focal field are concluded.

Focus shaping of high numerical aperture lens using physics-assisted artificial neural networks

We present a physics-assisted artificial neural network (PhyANN) scheme to efficiently achieve focus shaping of high numerical aperture lens using a diffractive optical element (DOE) divided into a series of annular regions with fixed widths. Unlike the conventional ANN, the PhyANN does not require the training using labeled data, and instead output the transmission coefficients of each annular region of the DOE by fitting weights of networks to minimize the delicately designed loss function in term of focus profiles. Several focus shapes including sub-diffraction spot, flattop spot, optical needle, and multi-focus region are successfully obtained. For instance, we achieve an optical needle with 10λ depth of focus, 0.41λ lateral resolution beyond diffraction limit and high flatness of almost the same intensity distribution. Compared to typical particle swarm optimization algorithm, the PhyANN has an advantage in DOE design that generates three-dimensional focus profile. Further, the hyperparameters of the proposed PhyANN scheme are also discussed. It is expected that the obtained results benefit various applications including super-resolution imaging, optical trapping, optical lithography and so on.

Optimization-free customization of optical tightly focused fields: uniform needles and hotspot chains

An optimization-free method based on an inverse problem of nonlinear equations is employed to design the binary phase diffraction optical element (BPDOE) that could modulate the incident light of a high-numerical-aperture (NA) objective lens so that the axisymmetric focal fields can be customized on demand. For example, a 43λ-long optical longitudinally polarized needle with its lateral size beyond diffraction limit is reported by using a 27-belt BPDOE, where the cost evaluated by the ratio of the belt number of BPDOE to the length of needle is record small compared with other optimization algorithms. Moreover, another longitudinal field with multiple hotspots along the propagation direction of light is also achieved with a 10-belt BPDOE. These achieved focal fields are verified doubly by using a finite-difference time-domain (FDTD) method, indicating the validity of Richards-Wolf vector diffraction theory. This optimization-free approach makes the design of BPDOEs with numerous belts viable to generate the expected focal fields, which might benefit various applications such as optical trapping, super-resolution imaging, and lithography.

Formation of polarization-dependent optical vortex beams via an engineered microsphere

In this work, we propose a method that can realize switchable spatial arrangement of the donut-shaped focusing beams through an engineered microsphere, tuned by changing the polarization state of an incident light. In this polarization-dependent light manipulation, the engineered microsphere is designed and fabricated by focused ion beam (FIB). We simulate and experimentally characterize the focus performance of the engineered microsphere. Under the light incidence with radial polarization, multiple focused donut beams are formed along optical axis. By adding an additional linear polarizer with a rotatable relative angle, the pair of donut beams can be re-arranged in the same transverse plane and stay close to each other. Experimental results and numerical simulation are in good agreement. Such tunable polarization-dependent micro-optics can be used for multiplane imaging applications.

Inverse design of optical needles with central zero-intensity points by artificial neural networks

Optical needles with central zero-intensity points have attracted much attention in the field of 3D super-resolution microscopy, optical lithography, optical storage and Raman spectroscopy. Nevertheless, most of the studies create few types of optical needles with central zero-intensity points based on the theory and intuition with time-consuming parameter sweeping and complex pre-select of parameters. Here, we report on the inverse design of optical needles with central zero-intensity points by dipole-based artificial neural networks (DANNs), permitting the creation of needles which are close to specific length and amplitude. The resolution of these optical needles with central zero-intensity points is close to axial diffraction limit (∼1λ). Additionally, the DANNs can realize the inverse design of several types on-axis distributions, such as optical needles and multifocal distributions.

Tightly focused light field with controllable pure transverse polarization state at the focus

We report on a facile and flexible scheme for producing the controllable pure transverse polarization state at the focus within a tightly focused field. Toward this aim, a special type of hybrid vector beam exhibiting unusual "8-type" mapping tracks of azimuthal polarization states on the Poincaré sphere is employed. Due to the peculiar polarization structures, at the focus, there is only the transverse component, while the longitudinal component is zero for any 8-type vector beam. More strikingly, the transverse polarization state at the focus is exactly the same as that of the cross point of the 8-type mapping track. Benefiting from this appealing polarization relationship, an arbitrary transverse polarization state can be easily achieved at the focus via altering the mapping track of incident vector beams. These results may have potential applications in nano and spin photonics.

Enantioselective optical trapping of chiral nanoparticles using a transverse optical needle field with a transverse spin

Since the fundamental building blocks of life are built of chiral amino acids and chiral sugar, enantiomer separation is of great interest in plenty of chemical syntheses. Light-chiral material interaction leads to a unique chiral optical force, which possesses opposite directions for specimens with different handedness. However, usually the enantioselective sorting is challenging in optical tweezers due to the dominating achiral force. In this work, we propose an optical technique to sort chiral specimens by use of a transverse optical needle field with a transverse spin (TONFTS), which is constructed through reversing the radiation patterns from an array of paired orthogonal electric dipoles located in the focal plane of a 4Pi microscopy and experimentally generated with a home-built vectorial optical field generator. It is demonstrated that the transverse component of the photonic spin gives rise to the chiral optical force perpendicular to the direction of the light's propagation, while the transverse achiral gradient force would be dramatically diminished by the uniform intensity profile of the optical needle field. Consequently, chiral nanoparticles with different handedness would be laterally sorted by the TONFTS and trapped at different locations along the optical needle field, providing a feasible route toward all-optical enantiopure chemical syntheses and enantiomer separations in pharmaceuticals.

Dynamical generation of multiple focal spot pairs with controllable position and polarization

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.

Generation of exotic optical polarization Möbius strips

We report a method of generating exotic optical polarization Möbius strips through tightly focusing an arbitrary vector beam. A heart-shaped Möbius strip, an "8"-shaped twin Möbius strip, and a circular Möbius strip with varying polarization twisting rate are demonstrated. The ability of tailoring three-dimensional optical polarization topologies may spur novel studies of optics and physics and find their applications in sensing, light coupling to nanostructures, light-matter interaction, and metamaterial fabrication.

Nonlinear frequency conversion and manipulation of vector beams

Vector beams have been extensively investigated in recent years because of their fascinating vector character across the beam transverse section, which is demonstrated to be useful for optical micro-manipulation, optical micro-fabrication, optical communication, single molecule imaging, and so on. To date, it is still a challenge to realize nonlinear frequency conversion and manipulation of such vector beams because of the polarization sensitivity in most nonlinear processes. Here, for the first time, to the best of our knowledge, we generate second-harmonic vector beams by using three-wave mixing processes in our experiment, which occur in two orthogonally placed nonlinear crystals, and the vector property is recognized by using a Glan-Taylor polarizer. This nonlinear frequency conversion process enables vector beams to be obtained at new wavelengths, and opens up new possibilities for all-optical switching and manipulation of vector beams.

Tight focusing properties of a circular partially coherent Gaussian beam

Tight focusing properties of a circular partially coherent Gaussian (CPCG) beam with linear polarization have been studied based on vectorial Debye theory. Expressions for the intensity distribution and degree of coherence near the focus are derived. Numerical calculations are performed to show the intensity distribution and degree of coherence of the CPCG beam in the focal region. It is interesting to find that after focusing the CPCG beam through a high numerical-aperture objective we can obtain a super-length optical needle (>12λ) with homogeneous intensity along the propagation axis and wavelength beam size (∼λ). Moreover, the numerical calculations of coherence illustrate that, in the range of full width at half-maximum of the optical needle, for any two of the parallel electric field components of the optical needle the coherence is close to 1, but for any two of orthometric electric field components the value of coherence is between 0.4 and 0.9. Such a non-diffracting optical needle may have potential applications in atom optical experiments, such as in atom traps and atom switches.

All-optical generation of magnetization with arbitrary three-dimensional orientations

In this Letter, all-optical generation of magnetization with arbitrary three-dimensional (3D) orientations is numerically demonstrated through the inverse Faraday effect (IFE) by using a reversing calculation method. The IFE-induced magnetization with an expected 3D orientation is initially conceived by coherently configuring two orthogonally arranged electric dipoles with a phase difference of π/2 in the focal region of a to-be-determined incident light field. Based on the dipole antenna theory, this required incident light field can be deduced analytically according to the orientations of the electric dipoles. By utilizing this field as illumination and reversing the field propagation, magnetization with the expected orientation can be obtained in the focal region through the IFE. Moreover, this method showcases a high magnetization orientation purity (greater than 93%) within the focal volume defined by the full width at half maximum when the numerical aperture of the focal lens is 0.95. This result demonstrates extended flexibility of magnetization manipulations in an all-optical fashion and possesses great potential in spintronics and all-optical magnetic recording.

Demonstration of longitudinally polarized optical needles

Longitudinally polarized optical needles are beams that exhibit ultra-long depth of field, subwavelength transverse confinement, and polarization oriented along the longitudinal direction. Although several techniques have been proposed to generate such needles, their scarce experimental observations have been indirect and incomplete. Here, we demonstrate the creation and full three-dimensional verification of a longitudinally polarized optical needle. This needle is produced by generating a radially polarized Bessel-Gauss beam at the focus of a high numerical aperture microscope objective. Using three-dimensional spatial mapping of second-harmonic generation from a single vertically aligned GaAs nanowire, we directly verify such a longitudinally polarized optical needle's properties, which are formed at the focus. The needle exhibits a dominant polarization, which is oriented along the longitudinal direction, an ultra-long depth of field (30 λ), and high spatial homogeneity. These are in agreement with corresponding focal field calculations that use vector diffraction theory. Our findings open new opportunities for manipulation and utilization of longitudinally polarized optical needles.

Non-iterative dartboard phase filter for achieving multifocal arrays by cylindrical vector beams

We proposed an analytically designed non-iterative dartboard phase filter (DPF) to achieve multifocal arrays by cylindrical vector beams. The DPF is composed of sectors, which is two-dimensionally divided in polar coordinates, along the radial and azimuthal directions. Meanwhile, a modulation factor was first proposed and introduced into the DPF to improve the intensity uniformity of the generated multifocal array. By the proposed DPF, the one-dimensional, two-dimensional and three-dimensional multifocal arrays are generated, which have intensity uniformities larger than 92.5%. The focal position and polarization of these generated multifocal arrays can be controlled, while the transverse sizes of each focal spot are subwavelength. The proposed DPF and the generated multifocal arrays have potential applications in the fields of polarization-multiplexed data storage, polarization-sensitive nanophotonic devices and parallel direct laser writing.

Planar Diffractive Lenses: Fundamentals, Functionalities, and Applications

Traditional objective lenses in modern microscopy, based on the refraction of light, are restricted by the Rayleigh diffraction limit. The existing methods to overcome this limit can be categorized into near-field (e.g., scanning near-field optical microscopy, superlens, microsphere lens) and far-field (e.g., stimulated emission depletion microscopy, photoactivated localization microscopy, stochastic optical reconstruction microscopy) approaches. However, they either operate in the challenging near-field mode or there is the need to label samples in biology. Recently, through manipulation of the diffraction of light with binary masks or gradient metasurfaces, some miniaturized and planar lenses have been reported with intriguing functionalities such as ultrahigh numerical aperture, large depth of focus, and subdiffraction-limit focusing in far-field, which provides a viable solution for the label-free superresolution imaging. Here, the recent advances in planar diffractive lenses (PDLs) are reviewed from a united theoretical account on diffraction-based focusing optics, and the underlying physics of nanofocusing via constructive or destructive interference is revealed. Various approaches of realizing PDLs are introduced in terms of their unique performances and interpreted by using optical aberration theory. Furthermore, a detailed tutorial about applying these planar lenses in nanoimaging is provided, followed by an outlook regarding future development toward practical applications.

Vectorial optical fields: recent advances and future prospects

Driven by their potential applications, vectorial optical fields with spatially inhomogeneous states of polarization within the cross section have drawn significant attention recently. This work intends to review some of the latest development of this rapidly growing field of optics and offer a general overview of the current status of this field in a few areas. Mathematical descriptions of generalized vectorial optical fields are provided along with several special examples. A time-reversal methodology for the creation of a wide variety of exotic optical focal fields with prescribed characteristics within the focal volume is presented. Recently developed methods for the generation of vectorial optical fields that utilize fiber lasers, digital lasers, vectorial optical field generator, metasurfaces or photoalignment liquid crystals are summarized. The interactions of these vectorial optical fields with various micro- and nano-structures are presented and the prospects of their potential applications are discussed. The connection of vectorial optical fields with higher dimensionality in quantum information is summarized.

Creation of a multi-segmented optical needle with prescribed length and spacing using the radiation pattern from a sectional-uniform line source

This paper presents a method to generate a multi-segmented optical needle with a strong longitudinally polarized field, uniform intensity along the optical axis, and a transverse size (~0.36λ). The length of each segment in the optical needle and the spacing between adjacent segments are controllable by reversing and focusing the radiation pattern from a sectional-uniform line source antenna to the focal volume of a 4Pi focusing system. By solving the inverse problem, we can obtain the required incident field distribution at the pupil plane to create the multi-segmented optical needle. Numerical examples demonstrate that a multi-segmented optical needle with variable focal depth, adjustable interval, narrow lateral width, homogeneous intensity, and high longitudinal polarization purity can be formed using the proposed approach. The length of each needle segment is approximately equal to the length of the corresponding sectional uniform line source. The multi-segmented optical needle may be employed in applications such as multi-particle acceleration, multi-particle trapping and manipulation, laser machining, and laser material processing.

Tightly focused optical field with controllable photonic spin orientation

The spin angular momentum of photons offers a robust, scalable and high-bandwidth toolbox for many promising applications based upon spin-controlled manipulations of light. In this work, we develop a method to achieve controllable photonic spin orientation within a diffraction limited optical focal spot produced by a high numerical aperture objective lens. The required pupil field is found analytically through reversing the radiation patterns from two electric dipoles located at the focal point of the lens with orthogonal oscillation directions and quadrature phase. The calculated pupil fields are experimentally generated with a vectorial optical field generator. The produced photonic spin orientations are quantitatively evaluated by their spin densities according to the tightly focused electric fields calculated by Richard-Wolf vectorial diffraction theory to demonstrate the validity and capability of the proposed technique.

Experimental generation of complex optical fields for diffraction limited optical focus with purely transverse spin angular momentum

We demonstrate a method to generate complex optical fields at the pupil plane of a high numerical aperture (NA) objective lens for the creation of diffraction limited optical focus with purely transverse spin angular momentum. The complex optical fields are analytically deduced through reversing the radiated patterns from two electric dipoles, which are located at the focal point of the high NA lens and oscillate respectively in x- and z- directions with phase difference of π/2. The derived fields can be experimentally created with a vectorial optical field generator. Using the Richard-Wolf vectorial diffraction theory, the electric fields within the focal region are calculated to evaluate the intensities and polarization distributions of the tightly focused beams corresponding to both the theoretical and experimentally generated pupil fields and the results clearly demonstrate the validity of the proposed technique.

Reflection type metasurface designed for high efficiency vectorial field generation

We propose a reflection type metal-insulator-metal (MIM) metasurface composed of hybrid nano-antennas for comprehensive spatial engineering of the properties of optical fields. The capability of such structure is illustrated in the design of a device that can be used to produce a radially polarized vectorial beam for optical needle field generation. This device consists of uniformly segmented sectors of high efficiency MIM metasurface. With each of the segment sector functioning as a local quarter-wave-plate (QWP), the device is designed to convert circularly polarized incidence into local linear polarization to create an overall radial polarization with corresponding binary phases and extremely high dynamic range amplitude modulation. The capability of such devices enables the generation of nearly arbitrarily complex optical fields that may find broad applications that transcend disciplinary boundaries.

Focus modulation of cylindrical vector beams by using 1D photonic crystal lens with negative refraction effect

Sub-wavelength focusing of cylindrical vector beams (CVBs) has attracted great attention due to the specific physical effects and the applications in many areas. More powerful, flexible and effective ways to modulate the focus transversally and also longitudinally are always being pursued. In this paper, cylindrically symmetric lens composed of negative-index one-dimensional photonic crystal is proposed to make a breakthrough. By revealing the relationship between focal length and the exit surface shape of the lens, a quite simple and effective principle of designing the lens structure is presented to realize specific focus modulation. Plano-concave lenses are parameterized to modulate the focal length and the number of focuses. An axicon constructed by one-dimensional photonic crystal is proposed for the first time to obtain a large depth of focus and an optical needle focal field with almost a theoretical minimum FWHM of 0.362λ is achieved under radially polarized incident light. Because of the almost identical negative refractive index for TE and TM polarization states, all the modulation methods can be applied for any arbitrary polarized CVBs. This work offers a promising methodology for designing negative-index lenses in related application areas.

Generation of vectorial optical fields with slot-antenna-based metasurface

A transmission-type metasurface composed of carefully designed rectangular slot antennas for the generation of vectorial optical fields is proposed and demonstrated. Acting as local linear polarizers, these slot antennas enable the spatial modulation of optical fields in amplitude, phase, and polarization for the cross-polarized component of the scattered field. As an illustration, a metasurface capable of forming a radially polarized scattered field with specific vectorial beam patterns with appropriate excitation at normal incidence is designed, fabricated, and tested. The radially polarized scattered field is designed to be further tightly focused by a high numerical aperture objective lens in order to obtain a uniform longitudinally polarized optical needle field along the propagation direction. Characterization experiments demonstrate that its overall extinction ratio satisfies the amplitude modulation requirement, and a corresponding π phase modulation is realized as proposed.

Creation of identical multiple focal spots with prescribed axial distribution

We present a scheme for the construction of coaxially equidistant multiple focal spots with identical intensity profiles for each individual focus and a predetermined number and spacing. To achieve this, the radiation field from an antenna is reversed and then gathered by high numerical aperture objective lenses. Radiation patterns from three types of line sources, i.e., the electric current, magnetic current and electromagnetic current distributions, with cosine-squared taper are respectively employed to generate predominately longitudinally polarized bright spots, azimuthally polarized doughnuts, and focal spots with a perfect spherically symmetric intensity distribution. The required illuminations at the pupil plane of a 4Pi focusing configuration for the creation of these identical multiple focal spots can be easily derived by solving the inverse problem of the antenna radiation field. These unique focal field distributions may find potential applications in laser direct writing and optical microscopy, as well as multiple-particle trapping, alignment, and acceleration along the optical axis.

Optical sharper focusing in an anisotropic crystal

Optical super-resolution technique through tight focusing is a widely used technique to image material samples with anisotropic optical properties. The knowledge of the field distribution of a tightly focused beam in anisotropic media is both scientifically interesting and technologically important. In this paper, the optical properties of a uniaxial crystal with the optic axis perpendicular to the interface under a tight focusing configuration are studied with rigorous theoretical and numerical analysis. The significant effect of the Poynting vector on the focal position introduces an obvious displacement of the focal spot formed by the extraordinary waves (e-ray). Moreover, a sharper focus with a lateral size of 0.22λ is obtained as a result of the effective separation of the ordinary waves (o-ray) and the e-ray. It provides a new tool to fabricate optical structures with higher resolutions than that in an isotropic medium through the far-field method.

Optimization-free optical focal field engineering through reversing the radiation pattern from a uniform line source

A simple and flexible method is presented for the generation of optical focal field with prescribed characteristics. By reversing the field pattern radiated from a uniform line source, for which the electric current is constant along its extent, situated at the focus of a 4Pi focusing system formed by two confocal high-NA objective lenses, the required illumination distribution at the pupil plane for creating optical focal field with desired properties can be obtained. Numerical example shows that an arbitrary length optical needle with extremely high longitudinal polarization purity and consistent transverse size of ~0.36λ over the entire depth of focus (DOF) can be created with this method. Coaxially double-focus with spot size of ~0.36λ in the transversal direction and ~λ in the axial direction separated by a prescribed spacing is illustrated as another example. The length of optical needle field and the interval between double-focus are determined by the length of uniform line source. These engineered focal fields may found potential applications in particle acceleration, optical microscopy, optical trapping and manipulations.

Manipulation of acoustic focusing with an active and configurable planar metasurface transducer

It has a pivotal role in medical science and in industry to concentrate the acoustic energy created with piezoelectric transducers (PTs) into a specific area. However, previous researches seldom consider the focal resolution, whose focal size is much larger than one wavelength. Furthermore, there is to date no such design method of PTs that allows a large degree of freedom to achieve designed focal patterns. Here, an active and configurable planar metasurface PT prototype is proposed to manipulate the acoustic focal pattern and the focal resolution freely. By suitably optimized ring configurations of the active metasurface PT, we demonstrate the manipulation of focal patterns in acoustic far fields, such as the designed focal needle and multi foci. Our method is also able to manipulate and improve the cross-sectional focal resolution from subwavelength to the extreme case: the deep sub-diffraction-limit resolution. Via the acoustic Rayleigh-Sommerfeld diffraction integral (RSI) cum the binary particle swarm optimization (BPSO), the free manipulation of focusing properties is achieved in acoustics for the first time. Our approach may offer more initiatives where the strict control of acoustic high-energy areas is demanding.

Ultralong pure longitudinal magnetization needle induced by annular vortex binary optics

In this Letter, based on the Richards and Wolf diffraction theory, an ultralong optical needle with pure transverse polarization is numerically generated by tightly focusing an azimuthally polarized beam through an annular vortex binary filter. Such an ultralong transversely polarized optical needle is generated through the π phase shift between adjacent rings of the binary filter. We show that such a pure transverse optical needle can induce pure longitudinal magnetization with a subwavelength lateral size (0.38λ) and an ultralong longitudinal depth (7.48λ) through the inverse Faraday effect. The corresponding needle aspect ratio of 20 is twice as large as that of the longitudinal magnetization needle generated by electron beam lithography.

Creation of a 50,000λ long needle-like field with 0.36λ width

It is a great challenge to create a needle-like field with properties of long beam length, narrow lateral width, uniformity, and high optical efficiency. Here we show a method that can realize these properties all at once. The key element is a 90° apex-angle concave conical mirror. By using this condenser along with a radially polarized incident beam of a specific field distribution, we numerically created a super slim, uniform, pure needle-like axially polarized field. This axially polarized field has a length of 50,000λ along the optical axis, and its lateral width still maintains a minimum 0.36λ size.

Achievement of needle-like focus by engineering radial-variant vector fields

We present and demonstrate a novel method for engineering the radial-variant polarization on the incident field to achieve a needle of transversally polarized field without any pupil filters. We generate a new kind of localized linearly-polarized vector fields with distributions of states of polarization (SoPs) describing by the radius to the power p and explore its tight focusing, nonparaxial focusing, and paraxial focusing properties. By tuning the power p, we obtain the needle-like focal field with hybrid SoPs and give the formula for describing the length of the needle. Experimentally, we systematically investigate both the intensity distributions and the polarization evolution of the optical needle by paraxial focusing the generated vector field. Such an optical needle, which enhances the light-matter interaction, has intriguing applications in optical microma-chining and nonlinear optics.

Modulation of a super-Gaussian optical needle with high-NA Fresnel zone plate

A high NA Fresnel zone plate (FZP) is studied using vectorial angular spectrum theory for realizing the sharpest possible super-Gaussian optical needle with purely longitudinal polarization illuminated by a radially polarized vector beam. Strong dispersion of the FZP results in a light field resembling a super-Gaussian optical needle by selecting an optimal FZP structural wavelength relative to the illumination wavelength and inserting a narrow comb window function into the center-shaded FZP. A 25 μm long longitudinally polarized flattop optical needle with a transverse beam width of about 0.366λ is focused at a distance of 222.5 μm away from a binary amplitude 3.46 mm diameter FZP for a 532.4 nm wavelength in free space.

On focused fields with maximum electric field components and images of electric dipoles

We study focused fields which, for a given total power and a given numerical aperture, have maximum electric field amplitude in some direction in the focal point and are linearly polarized along this direction. It is shown that the optimum field is identical to the image of an electric dipole with unit magnification. In particular, the field which is the image of an electric dipole whose dipole vector is parallel to the optical axis, is identical to the field whose longitudinal component is maximum at the image point.