Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent

Needle of longitudinally polarized light using the circular Airy beam

An optical needle is created using a radially polarized circular Airy beam with a conical angle, stemmed from the auto-focusing property of light beams. The utilization of the angular spectrum representation serves to illustrate the field distributions of the optical needle, and an explicit formula is provided to describe the angular spectrum of the light beam. The findings suggest that the optical needle exhibits a long depth of focus and well uniformity, and the full width at half maximum of the transverse field distribution is approximately 0.38 λ beyond the diffraction limit. The uniformity of the optical needle can be tailored by adjusting the width of the primary ring, the decay parameter, and the conical angle. Additionally, the depth of focus of the optical needle significantly improves as the radius of the primary ring increases while still maintaining well uniformity. It may find applications in high-resolution optical imaging and optical manipulation.

Tight-focusing parabolic reflector schemes for petawatt lasers

A comparative study of three different tight-focusing schemes for high-power lasers is performed numerically. Using the Stratton-Chu formulation, the electromagnetic field in the vicinity of the focus is evaluated for a short-pulse laser beam incident upon an on-axis high numerical aperture parabola (HNAP), an off-axis parabola (OAP), and a transmission parabola (TP). Linearly- and radially-polarized incident beams are considered. It is demonstrated that while all the focusing configurations yield intensities above 10²³ W/cm² for a 1 PW incident beam, the nature of the focused field can be drastically modified. In particular, it is shown that the TP, with its focal point behind the parabola, actually converts an incoming linearly-polarized beam into an m = 2 vector beam. The strengths and weaknesses of each configuration are discussed in the context of future laser-matter interaction experiments. Finally, a generalization of NA calculations up to 4π-illumination is proposed through the solid angle formulation, providing a universal way to compare light cones from any kind of optics.

Creation of pure longitudinal super-oscillatory spot

We present a method that creates a super-oscillatory focal spot of a tightly focused radially polarized beam using the concept of a phase mask. Using vector diffraction theory, we report a super-oscillatory focal spot that is much smaller than the diffraction limit and the super-oscillation criterion. The proposed mask works as a special polarization filter that enhances the longitudinal component and filters out the transverse component of radial polarization at focus, permitting the creation of a pure longitudinal super-oscillatory focal spot.

Accelerating superluminal laser focus generated by a long-focal-depth mirror with high numerical aperture

The long-focal-depth mirror is a novel reflective element proposed in recent years. Due to the advantages of negligible dependence on wavelength and high damage threshold, it is suitable to focus ultra-short laser pulses with broadband spectra and high intensity with a focal depth of centimeter scale. To the best of our knowledge, the focusing properties of this mirror has been only studied under low numerical aperture (NA). In this paper, we extend it to the case of high NA and it is proved that an accelerating superluminal laser focus can be always generated by this extension, in which the degree of acceleration increases with the increase of NA. And the velocity of laser focus increases approximately linearly from c to 1.6c for NA = 0.707. Due to its properties of tight focusing, the Richards-Wolf integrals have been used to study the intensity distribution of each polarization component for different kinds of incident light. And these are linearly polarized light, radially polarized light, azimuthally polarized light, linearly polarized light with spiral phase, and linearly polarized light with ultrashort pulses. From comparisons of numerical results, the intensity distributions are obviously different for different kind of incident light, and accelerating superluminal laser focus with special structure (such as the hollow conical beam) can be produced under appropriate condition. We believe this study can expand the fields of application for the long-focal-depth mirror.

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.

Exact vectorial model for nonparaxial focusing of freeform wavefronts

We present a new formalism, based on Richards-Wolf theory, to rigorously model nonparaxial focusing of radially polarized electromagnetic beams with freeform wavefront. The beams can be expressed in terms of Zernike polynomials. Our approach is validated by comparing known results obtained by Richards-Wolf theory. Our integral representation is compliant with diffraction theory, is thoroughly discussed and solved for various freeform wavefront that, so far, have not been treated analytically. The extension of the method to other polarization states is straightforward.

Set of all possible stigmatic pairs of mirrors

Here, closed-form equations that express a pair of mirrors such that it forms a stigmatic optical system are presented. The mentioned equations are general enough to express the set of all possible pairs of stigmatic mirrors. Several examples for pairs of stigmatic mirrors are given and numerically tested with ray tracing, showing that their optical performance is, as expected, free of spherical aberration. Finally, the limitations and potential applications of stigmatic pairs are discussed.

Stigmatic singlet with a user-defined apodization pupil function

Here we present a method to design a stigmatic lens with a user-defined apodization pupil function. The motive is that the apodization pupil function is required by Richards-Wolf diffraction integrals to compute non-paraxial diffraction patterns. Then, the user-defined apodization pupil function can be chosen such that the focus spot obtained by the stigmatic lens is smaller. The mentioned method is based on numerically solving a non-linear differential equation.

Two-mirror system for tunable apodization

Here we present an optical system composed of two mirrors such that at the input/output, the light is a plane wave but with a user-defined apodization factor. The model presented is an analytic closed form with no numerical approximations or iterations. We test the model with illustrative scenarios, and the results are as expected; the system is stigmatic with the desired apodization factor. Thus, this system has several potential applications in high contrast imaging.

On the diffraction of a high-NA aplanatic and stigmatic singlet

We present a study of the diffraction pattern according to Richards-Wolf for an aplanatic and stigmatic singlet based on an exact analytical equation. We are able to put emphasis on the maximum diameter and illumination pattern, which are the two parameters that influence the diffraction pattern and how to compute it. Designs of low- and high-NA aplanatic and stigmatic lenses are implemented to display these effects.

Optical needles with arbitrary three-dimensional spin angular momentum

Based on our previous research on optical needles with arbitrary three-dimensional (3D) polarization, we investigate the relationship between the electric field and spin angular momentum (SAM). We have realized optical needles with arbitrary 3D spin-orientation and SAM per photon. To our best knowledge, it is the first time to obtain optical needles whose SAM can be customized on both direction and size. The relative error between the obtained spin and customized spin is always less than 5% even if SAM per photon is very small.

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.

Image scanning microscopy with a long depth of focus generated by an annular radially polarized beam

Image scanning microscopy (ISM) is a promising tool for bioimaging owing to its integration of signal to noise ratio (SNR) and super resolution superior to that obtained in confocal scanning microscopy. In this paper, we introduce the annular radially polarized beam to the ISM, which yields an axially extended excitation focus and enhanced resolution, providing a new possibility to obtain the whole information of thick specimen with a single scan. We present the basic principle and a rigorous theoretical model for ISM with annular radially polarized beam (ISM-aRP). Results show that the resolution of ISM-aRP can be enhanced by 4% compared with that in conventional ISM, and the axial extent of the focus is longer than 6λ. The projected view of the simulated fluorescent beads suspension specimen demonstrates the validity of ISM-aRP to obtain the whole information of volume sample. Moreover, this simple method can be easily integrated into the commercial laser scanning microscopy systems.

Far-field polarization signatures of surface optical nonlinearity in noncentrosymmetric semiconductors

We analyse possibilities to quantitatively evaluate the surface second-order optical nonlinearity in noncentrosymmetric materials based on polarization-resolved analysis of far-field radiation patterns of second-harmonic generation. We analytically demonstrate that for plane-wave illumination the contribution to the second-harmonic signal from the surface of a nonlinear medium exhibits different polarization properties and angular dependencies compared to the contribution from the bulk. In view of this, we optimize the illumination geometry in order to enable the most efficient separation and comparison of both nonlinearities. Furthermore, we consider the illumination of an AlGaAs slab by a tightly-focused linearly-polarized Gaussian beam as an alternative measurement geometry. It is found that the reliable separation of the surface nonlinearity contribution as well as a wide range of detectable values can be achieved with this geometry as well.

Optical needles with arbitrary homogeneous three-dimensional polarization

We propose a new method to generate optical needles by focusing vector beams comprised of radially polarized component and azimuthally polarized vortex components. The radial part can generate longitudinal polarization, while the azimuthal parts can generate left- and right-handed polarization. Hence, an arbitrary 3D polarization can be obtained. To our knowledge, it may be the first time that arbitrarily polarized optical needles whose transverse sizes are under 0.5λ have been achieved. The polarized homogeneity of the needles is beyond 0.97.

Analytical inversion of the focusing of high-numerical-aperture aplanatic systems

We propose a method for an analytical inversion of the electric and magnetic fields at the focus of a high-NA aplanatic system to obtain incident light beam distribution. Our approach is based on an inverse Fourier transform of the Richards-Wolf formalism for targeted longitudinal fields along the radial or axial directions at the non-paraxial focus. Analytical solutions are discussed for both axial and radial focal fields for a radially polarized incident light beam, and a criterion is defined to access a physically valid solution. We also validate the method according to results found in the literature. Finally, we show how the method can be generalized to other incident field distributions.

Theoretical generation of arbitrarily homogeneously 3D spin-orientated optical needles and chains

The generation of homogeneously 3D spin-orientated optical needles and optical chains is investigated by focusing the annular collimated beam composed of radially polarized component and azimuthally polarized vortex components with aplanatic focusing systems. Using the Richards-Wolf vector diffraction theory, analytic expressions of focal electric fields and target spin-orientation are given. The results show that the spin-orientation is tunable by changing two parameters of the incident beam while keeping the mean size of the focal spot under 0.5λ. Spin-orientation homogeneity purity is introduced to evaluate spin-orientation homogeneity quantitatively and the results present that spin-orientation homogeneity purity is always beyond 0.996 when spin-orientation varies.

Superoscillation: from physics to optical applications

The resolution of conventional optical elements and systems has long been perceived to satisfy the classic Rayleigh criterion. Paramount efforts have been made to develop different types of superresolution techniques to achieve optical resolution down to several nanometres, such as by using evanescent waves, fluorescence labelling, and postprocessing. Superresolution imaging techniques, which are noncontact, far field and label free, are highly desirable but challenging to implement. The concept of superoscillation offers an alternative route to optical superresolution and enables the engineering of focal spots and point-spread functions of arbitrarily small size without theoretical limitations. This paper reviews recent developments in optical superoscillation technologies, design approaches, methods of characterizing superoscillatory optical fields, and applications in noncontact, far-field and label-free superresolution microscopy. This work may promote the wider adoption and application of optical superresolution across different wave types and application domains.

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.

Resolution enhancement in laser scanning microscopy with deconvolution switching laser modes (D-SLAM)

Laser scanning microscopy is limited in lateral resolution by the diffraction of light. Superresolution methods have been developed since the 90s to overcome this limitation. However superresolution is generally achieved at the expense of a greater complexity (high power lasers, very long acquisition times, specific fluorophores) and limitations on the observable samples. In this paper we propose a method to improve the resolution of confocal microscopy by combining different laser modes and deconvolution. Two images of the same field are acquired with the confocal microscope using different laser modes and used as inputs to a deconvolution algorithm. The two laser modes have different Point Spread Functions and thus provide complementary information leading to an image with enhanced resolution compared to using a single confocal image as input to the same deconvolution algorithm. By changing the laser modes to Bessel-Gauss beams we were able to further improve the efficiency of the deconvolution algorithm and obtain images with a residual Point Spread Function having a width of 0.14 λ (72 nm at a wavelength of 532 nm). This method only requires a laser scanning microscope and is not dependent on certain specific properties of fluorescent proteins. The proposed method requires only a few add-ons to classical confocal or two-photon microscopes and can easily be retrofitted into an existing commercial laser scanning microscope.

Redistributing the energy flow of a tightly focused radially polarized optical field by designing phase masks

Redistributing the transverse energy flow in the focal plane of a tightly focused radially polarized optical field is described. We develop from theory a generalized analytical model for calculating the distributions of the electromagnetic field and the Poynting vector for a tightly focused radially polarized laser beam superposed with an optical vortex. We further explore the redistribution of the energy flow by designing phase masks, including traditional and annular vortex phase masks. Flexible control of the transverse energy flow rings is obtained with these phase masks. They provide a simple solution to transport absorptive particles along certain paths and therefore might be help in optical tweezer manipulations.

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.

Optimization-free approach for generating sub-diffraction quasi-non-diffracting beams

Sub-diffraction quasi-non-diffracting beams with sub-wavelength transverse size are attractive for applications such as optical nano-manipulation, optical nano-fabrication, optical high-density storage, and optical super-resolution microscopy. In this paper, we proposed an optimization-free design approach and demonstrated the possibility of generating sub-diffraction quasi-non-diffracting beams with sub-wavelength size for different polarizations by a binary-phase Fresnel planar lens. More importantly, the optimization-free method significantly simplifies the design procedure and the generation of sub-diffracting quasi-non-diffracting beams. Utilizing the concept of normalized angular spectrum compression, for wavelength λ₀ = 632.8 nm, a binary-phase Fresnel planar lens was designed and fabricated. The experimental results show that the sub-diffraction transverse size and the non-diffracting propagation distances are 0.40λ₀-0.54λ₀ and 90λ₀, 0.43λ₀-0.54λ₀ and 73λ₀, and 0.34λ₀-0.41λ₀ and 80λ₀ for the generated quasi-non-diffracting beams with circular, longitudinal, and azimuthal polarizations, respectively.

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.

Focusing properties of arbitrary optical fields combining spiral phase and cylindrically symmetric state of polarization

The tight focusing properties of optical fields combining a spiral phase and cylindrically symmetric state of polarization are presented. First, we theoretically analyze the mathematical characterization, Stokes parameters, and Poincaré sphere representations of arbitrary cylindrical vector (CV) vortex beams. Then, based on the vector diffraction theory, we derive and build an integrated analytical model to calculate the electromagnetic field and Poynting vector distributions of the input CV vortex beams. The calculations reveal that a generalized CV vortex beam can generate a sharper focal spot than that of a radially polarized (RP) plane beam in the focal plane. Besides, the focal size decrease accompanies its elongation along the optical axis. Hence, it seems that there is a trade-off between the transverse and axial resolutions. In addition, under the precondition that the absolute values between polarization order and topological charge are equal, a higher-order CV vortex can also achieve a smaller focal size than an RP plane beam. Further, the intensity for the sidelobe admits a significant suppression. To give a deep understanding of the peculiar focusing properties, the magnetic field and Poynting vector distributions are also demonstrated in detail. These properties may be helpful in applications such as optical trapping and manipulation of particles and superresolution microscopy imaging.

Focus shaping by tailoring arbitrary hybrid polarization states that have a combination of orthogonal linear polarization bases

We report a focus shaping method by tailoring hybrid states of polarization of arbitrary polarized beams that have a combination of orthogonal linear polarization bases. Such hybridly polarized beams comprising linear, elliptical, and circular polarizations in the beam cross section, have completely different optical properties compared to the scalar and locally linear-polarized vector beams. We demonstrate that, apart from the orientation of the local polarization state, another two degrees of freedom including the local ellipticity and the handedness in the beam cross section can be used in focus shaping. Square-shaped patterns, multiple foci, three-dimensional optical cages, optical needles, and channels can be obtained due to the increased control without any additional phase or amplitude modulations.

Ultra-long magnetization needle induced by focusing azimuthally polarized beams with a spherical mirror

Based on extended Richards-Wolf theory for axisymmetric surfaces and the inverse Faraday effect, we propose the generation of a purely longitudinal magnetization needle by focusing Gaussian annular azimuthally polarized beams with a spherical mirror. The needle obtained has a longitudinal length varying hundreds to thousands of wavelengths while keeping the lateral size under 0.4λ, and the corresponding aspect ratio can easily reach more than 2000. It may be the first time that a magnetization needle whose aspect ratio is over 500 has been achieved. The approximate analytical expressions of the magnetization needle are given, and the longitudinal length is tunable by changing the value of the angular thickness and the position of the annular beams.

Synthesis of light needles with tunable length and nearly constant irradiance

We introduce a new method for producing optical needles with tunable length and almost constant irradiance based on the evaluation of the on-axis power content of the light distribution at the focal area. According to theoretical considerations, we propose an adaptive modulating continuous function that presents a large derivative and a zero value jump at the entrance pupil of the focusing system. This distribution is displayed on liquid crystal devices using holographic techniques. In this way, a polarized input beam is shaped and subsequently focused using a high numerical aperture (NA) objective lens. As a result, needles with variable length and nearly constant irradiance are produced using conventional optics components. This procedure is experimentally demonstrated obtaining a 53λ-long and 0.8λ-wide needle.

Needles of light produced with a quasi-parabolic mirror

We propose a quasi-parabolic mirror that can produce a long needle of light by focusing a radially polarized annular beam. The quasi-parabolic mirror can be acquired by moving the axis of rotation of a parabolic mirror. Using the extended Richards-Wolf theory for axisymmetric surfaces, we calculated that the needle obtained can have a longitudinal FWHM over hundreds to thousands of wavelengths by keeping the transverse FWHM under 0.36λ. The consistent expression of the approximate relationship between the angular thickness of the incident beam and the longitudinal FWHM based on both geometrical optics and wave optics is presented.

Synthesis of sub-diffraction quasi-non-diffracting beams by angular spectrum compression

Quasi-non-diffracting beams are attractive for various applications, including optical manipulation, super-resolution microscopes, and materials processing. However, it is a great challenge to design and generate super-long quasi-non-diffracting beams with sub-diffraction and sub-wavelength size. In this paper, a method based on the idea of compressing a normalized angular spectrum is developed, which makes it possible and provides a practical tool for the design of a quasi-non-diffracting beam with super-oscillatory sub-wavelength transverse size. It also presents a clear physical picture of the formation of super-oscillatory quasi-non-diffracting beams. Based on concepts of a local grating and super-oscillation, a lens was designed and fabricated for a working wavelength of λ = 632.8 nm. The validity of the idea of normalized angular spectrum compression was confirmed by both numerical investigations and experimental studies. An optical hollow needle with a length of more than 100λ was experimentally demonstrated, in which an optical hollow needle was observed with a sub-diffraction and sub-wavelength transverse size within a non-diffracting propagation distance of 94λ. Longer non-diffracting propagation distance is expected for a lens with larger radius and shorter effective wavelength.

Theoretical guideline for generation of an ultralong magnetization needle and a super-long conveyed spherical magnetization chain

Considering an azimuthally polarized vortex beam with a Gaussian annulus as an incoming light, light induced magnetization fields for both a single high NA lens and a pair of high NA lenses are investigated theoretically. We deduce analytical formulas for the parameters of a magnetization needle and a magnetization chain when the angular width of the incident beam is far less than its central angular position. Through these analytical formulas, the properties of the magnetization needle and the magnetization chain are very clear and distinct. Compared with parameter optimizing to produce an ultralong magnetization needle with lateral sub-wavelength scale and a super-long spherical magnetization chain with three-dimensional super resolution, the analytical method is direct and has a theoretical guideline. The validity of these formulas is proved, compared to numerical solutions. The present work regarding these super-resolution magnetization patterns is of great value in high density all-optical magnetic recording, atomic trapping as well as confocal and magnetic resonance microscopy.

Focus engineering based on analytical formulae for tightly focused polarized beams with arbitrary geometric configurations of linear polarization

Highly confined electromagnetic fields with controllable intensity profiles and polarization orientations are greatly desired in many fields. In this paper, we report on the generation of highly confined fields through tightly focused locally linearly polarized beams. Using the Richards-Wolf vectorial diffraction method, we derive and build integrated analytical formulae for calculating the tightly focused field of polarized beams with arbitrary geometric configurations of linear polarization. Based on the analytical model, the focusing properties of four types of polarized light beams, i.e., linearly, azimuthally, radially, and spatially variant polarized beams, with locally linear states of polarization are investigated numerically and discussed in detail. By manipulating the radial and azimuthal indices and initial phases, we obtain a tunable three-dimensional optical cage, multifoci, optical needles, and channels in the focal volume of a high-numerical-aperture objective lens. These peculiar properties may find applications in fields such as optical trapping and manipulation of nanoparticles and super-resolution microscopy imaging.

Magnetization shaping generated by tight focusing of azimuthally polarized vortex multi-Gaussian beam

Combining the vector diffraction theory with the inverse Faraday effect, we have theoretically studied magnetization shaping generated by tight focusing of an azimuthally polarized multi-Gaussian beam superimposed with a helical phase. By selecting optimized parameters of a multi-Gaussian beam and topological charge of a spiral phase plate, not only a super-long and sub-wavelength longitudinal magnetization needle with single/dual channels for a single-lens high numerical aperture focusing system, but also an extra-long and three-dimensional super-resolution longitudinal magnetization chain with single/dual channels for a 4π high numerical aperture focusing system is achieved in the focal region. Furthermore, by continuously changing the phase difference between two counter-propagating beams, these super-long longitudinal magnetization chains with three-dimensional super-resolution can dynamically move along the z-axis. It is expected that these results pave the path for fabricating magnetic lattices for spin wave operation, multiple atoms or magnetic particle trapping and transportation, confocal and magnetic resonance microscopy, as well as multilayer ultrahigh density magnetic storage.

Creation of Sub-diffraction Longitudinally Polarized Spot by Focusing Radially Polarized Light with Binary Phase Lens

The generation of a sub-diffraction longitudinally polarized spot is of great interest in various applications, such as optical tweezers, super-resolution microscopy, high-resolution Raman spectroscopy, and high-density optical data storage. Many theoretical investigations have been conducted into the tight focusing of a longitudinally polarized spot with high-numerical-aperture aplanatic lenses in combination with optical filters. Optical super-oscillation provides a new approach to focusing light beyond the diffraction limit. Here, we propose a planar binary phase lens and experimentally demonstrate the generation of a longitudinally polarized sub-diffraction focal spot by focusing radially polarized light. The lens has a numerical aperture of 0.93 and a long focal length of 200λ for wavelength λ = 632.8 nm, and the generated focal spot has a full-width-at-half-maximum of about 0.456λ, which is smaller than the diffraction limit, 0.54λ. A 5λ-long longitudinally polarized optical needle with sub-diffraction size is also observed near the designed focal point.

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.

Exact vectorial model for nonparaxial focusing by arbitrary axisymmetric surfaces

We present a new approach, based on Richards-Wolf formalism, to rigorously model nonparaxial focusing of radially and azimuthally polarized electromagnetic beams by axisymmetric systems without a single-point focus. Our approach is based on a combined method that uses ray tracing and diffraction integrals. Our method is validated by comparing known results obtained with a parabolic mirror. Our integral representation of the focused beams, compliant with diffraction theory, is thoroughly discussed and solved for various conics that, so far, have not been treated analytically. The extension of the method to other polarization states is straightforward.

Controllable design of super-oscillatory planar lenses for sub-diffraction-limit optical needles

Sub-diffraction-limit optical needle can be created by a binary amplitude mask through tailoring the interference of diffraction beams. In this paper, a controllable design of super-oscillatory planar lenses to create sub-diffraction-limit optical needles with the tunable focal length and depth of focus (DOF) is presented. As a high-quality optical needle is influenced by various factors, we first propose a multi-objective and multi-constraint optimization model compromising all the main factors to achieve a needle with the prescribed characteristics. The optimizing procedure is self-designed using the Matlab programming language based on the genetic algorithm (GA) and fast Hankel transform algorithm. Numerical simulations show that the optical needles' properties can be controlled accurately. The optimized results are further validated by the theoretical calculation with the Rayleigh-Sommerfeld integral. The sub-diffraction-limit optical needles can be used in wide fields such as optical nanofabrication, super-resolution imaging, particle acceleration and high-density optical data storage.

Sub-wavelength sized transversely polarized optical needle with exceptionally suppressed side-lobes

It is well known that radially polarized beam could produce an ultra-long longitudinally polarized focus, referred to as "optical needle". In this work, we reveal that the counterpart transversely polarized optical needle (~5.83λ) with exceptionally suppressed sidelobes (9.9% of the maximum of the principal lobe) can be generated by tightly focusing a hybridly polarized beam through a multibelt binary phase filter. A universal analytical model is built up for investigating the depth, uniformity and polarization properties of the needle. We find that there is a trade-off between needle length and intensity uniformity, and the main lobe keeps almost transverse polarization at each observation plane. Such a nondiffraction transversely polarized optical needle has potential applications in ultrahigh density magnetic storage as well as atomic trap and switches.

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

This is the reply to the comment by Chavez-Cerda and Pu [J. Opt. Soc. Am. A32, 1209 (2015)JOAOD61084-752910.1364/JOSAA.32.001209] on our recent work about the 50,000λ long needle-like field [J. Opt. Soc. Am. A31, 500 (2014)JOAOD60740-323210.1364/JOSAA.31.000500]. First, they employed an incorrect boundary condition as the fundament of their argument. In fact, it is not the electric field but its tangential component that must be zero at the surface of the perfect metal. Our result is completely consistent with the correct boundary condition. Second, a constant phase factor in the incident radially polarized beam, exp(jπ/4), for instance, has no influence on the result. Accordingly, our initial condition is proper.

Visualizing polarization singularities in Bessel-Poincaré beams

We demonstrate that an annulus of light whose polarization is linear at each point, but the plane of polarization gradually rotates by π radians can be used to generate Bessel-Poincaré beams. In any transverse plane this beam exhibits concentric rings of polarization singularities in the form of L-lines, where the polarization is purely linear. Although the L-lines are invisible in terms of light intensity variations, we present a simple way to visualize them as dark rings around a sharp peak of intensity in the beam center. To do this we use a segmented polarizer whose transmission axes are oriented differently in each segment. The radius of the first L-line is always smaller than the radius of the central disk of the zero-order Bessel beam that would be produced if the annulus were homogeneously polarized and had no phase circulation along it.

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.

Numerical analysis of resolution enhancement in laser scanning microscopy using a radially polarized beam

The spatial resolution characteristics in confocal laser scanning microscopy (LSM) and two-photon LSM utilizing a higher-order radially polarized Laguerre-Gaussian (RP-LG) beam are numerically analyzed. The size of the point spread function (PSF) and its dependence on the confocal pinhole size are compared with practical LSM using a circularly polarized Gaussian beam on the basis of vector diffraction theory. The spatial frequency response in terms of the optical transfer function (OTF) is also evaluated for LSM using the RP-LG beam. The smaller focal spot characteristics of higher-order RP-LG beams contribute to a dramatic enhancement of the lateral spatial resolution in confocal LSM and two-photon LSM.

Needles of light produced with a spherical mirror

We describe how laterally confined and axially stretched needles of light can be produced by focusing a radially polarized annular optical beam with a spherical mirror. Our analysis is based on an extension of the Richards-Wolf formalism appropriate for nonaplanetic focusing systems operated under nonparaxial conditions. While maintaining their lateral confinement near the theoretical limit of 0.36λ, the needles of light that are produced can extend axially over 1000's of λ, in full compliance with geometrical and electromagnetic considerations. Relationships are established between the thickness of the incident annular beam and the length of the needle of light.

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.

Extended two-photon microscopy in live samples with Bessel beams: steadier focus, faster volume scans, and simpler stereoscopic imaging

Two-photon microscopy has revolutionized functional cellular imaging in tissue, but although the highly confined depth of field (DOF) of standard set-ups yields great optical sectioning, it also limits imaging speed in volume samples and ease of use. For this reason, we recently presented a simple and retrofittable modification to the two-photon laser-scanning microscope which extends the DOF through the use of an axicon (conical lens). Here we demonstrate three significant benefits of this technique using biological samples commonly employed in the field of neuroscience. First, we use a sample of neurons grown in culture and move it along the z-axis, showing that a more stable focus is achieved without compromise on transverse resolution. Second, we monitor 3D population dynamics in an acute slice of live mouse cortex, demonstrating that faster volumetric scans can be conducted. Third, we acquire a stereoscopic image of neurons and their dendrites in a fixed sample of mouse cortex, using only two scans instead of the complete stack and calculations required by standard systems. Taken together, these advantages, combined with the ease of integration into pre-existing systems, make the extended depth-of-field imaging based on Bessel beams a strong asset for the field of microscopy and life sciences in general.

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.

Sharper focal spot generated by 4π tight focusing of higher-order Laguerre-Gaussian radially polarized beam

The focal electric fields for a 4π high numerical aperture (NA) focusing system with both the doughnut and higher-order Laguerre-Gaussian (LG) radially polarized (RP) beams are investigated in the case of NA=1, and the full width at half-maximum values of the focal spots are calculated. Compared with the single-lens high NA focusing configuration, a sharper spot, whose size is reduced efficiently in the transverse as well as the axial direction, can be formed. Such size reduction is attributed to not only the destruction interference of the longitudinal component caused by the π phase shift between any two adjacent rings of the incident higher-order LG RP beam coming from one particular direction but also the perfect destruction interference of the radial component formed by the two counter-propagating incident beams.

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.