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

An entropy-controlled objective chip for reflective confocal microscopy with subdiffraction-limit resolution

Planar diffractive lenses (PDLs) with optimized but disordered structures can focus light beyond the diffraction limit. However, these disordered structures have inevitably destroyed wide-field imaging capability, limiting their applications in microscopy. Here, we introduce information entropy S to evaluate the disorder of an objective chip by using the probability of its structural deviation from standard Fresnel zone plates. Inspired by the theory of entropy change, we predict an equilibrium point [Formula: see text] to balance wide-field imaging (theoretically evaluated by the Strehl ratio) and subdiffraction-limit focusing. To verify this, a [Formula: see text] objective chip with a record-long focal length of 1 mm is designed with [Formula: see text], which is the nearest to the equilibrium point among all reported PDLs. Consequently, our fabricated chip can focus light with subdiffraction-limit size of 0.44 λ and image fine details with spatial frequencies up to 4000 lp/mm experimentally. These unprecedented performances enable ultracompact reflective confocal microscopy for superresolution imaging.

Design of a Metasurface with Long Depth of Focus Using Superoscillation

Longitudinal optical field modulation is very important for applications such as optical imaging, spectroscopy, and optical manipulation. It can achieve high-resolution imaging or manipulation of the target object, but it is also limited by its depth of focus. The depth of focus determines whether the target object can be clearly imaged or manipulated at different distances, so extending the depth of focus can improve the adaptability and flexibility of the system. However, how to extend the depth of focus is still a significant challenge. In this paper, we use a super-oscillation phase modulation optimization method to design a polarization-independent metalens with extended focal depth, taking the axial focal depth length as the optimization objective. The optimized metalens has a focal depth of 13.07 μm (about 22.3 λ), and in the whole focal depth range, the transverse full width at half maximum values are close to the Rayleigh diffraction limit, and the focusing efficiency is above 10%. The results of this paper provide a new idea for the design of a metalens with a long focal depth and may have application value in imaging, lithography, and detection.

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.

Superoscillation focusing with suppressed sidebands by destructive interference

Optical superoscillation, a phenomenon that the local optical field can oscillate much faster than that allowed by its highest harmonic, can significantly overcome the Abbe diffraction limit. However, as the spot size is compressed below the superoscillation criteria of 0.38λ/NA, huge sidebands will inevitably appear around the central lobe with intensity hundreds of times higher than that of the central lobe. Here, we propose an approach to realize superoscillation by using destructive interference. The central lobe size can be compressed beyond the superoscillation criteria without formation of strong sidebands by destructive interference between focused fields. Such a super-resolution metalens can find its application in label-free far-field super-resolution microscopy.

Varifocal diffractive lenses for multi-depth microscope imaging

Flat optical elements enable the realization of ultra-thin devices able to either reproduce or overcome the functionalities of standard bulky components. The fabrication of these elements involves the structuration of material surfaces on the light wavelength scale, whose geometry has to be carefully designed to achieve the desired optical functionality. In addition to the limits imposed by lithographic design-performance compromises, their optical behavior cannot be accurately tuned afterward, making them difficult to integrate in dynamic optical systems. Here we show the realization of fully reconfigurable flat varifocal diffractive lens, which can be in-place realized, erased and reshaped directly on the surface of an azopolymer film by an all-optical holographic process. Integrating the lens in the same optical system used as standard refractive microscope, results in a hybrid microscope capable of multi-depth object imaging. Our approach demonstrates that reshapable flat optics can be a valid choice to integrate, or even substitute, modern optical systems for advanced functionalities.

High-quality longitudinally polarized photonic nanojet created by a microdisk

The Letter reports the generation of a high-quality longitudinally polarized photonic nanojet by illuminating a dielectric microdisk with a focused radially polarized light. High-quality longitudinally polarized beams can be generated using a microdisk with a wide range of refractive indices. By optimizing the shape and refractive index of the microdisk, the radial component can be effectively suppressed, and a maximum beam quality of 90% and a field enhancement factor of up to two orders can be achieved with a sub-diffraction-limited spot size. Moreover, the focusing performance of the microdisk is observed to be stable within a wide range of focusing numerical aperture values of the incident light.

Axial intensity distribution of a micro-Fresnel zone plate at an arbitrary numerical aperture

The axial focus number (the number of focal spots along the axial direction) and focus intensity of a micro-Fresnel zone plate (FZP) are analyzed from deep ultraviolet to infrared using the Fourier decomposition, the vectorial angular spectrum (VAS) theory, and the three-dimensional finite-difference time-domain (FDTD) method. For a low-numerical aperture (NA) micro-FZP (NA<0.1), there are multiple axial high-order foci, and the intensity of each focus decreases slowly. However, the intensity of each high-order focus decreases rapidly with NA increasing. For a relatively high-NA micro-FZP (NA>0.3), the axial high-order foci are suppressed and there is one single focus. A fast, precise, and cost-efficient additive manufacturing method, i.e. two-photon polymerization, is used to fabricate high-NA phase-type micro-FZPs. The experiment has validated the phenomenon of linear negative focal shift of a high-NA micro-FZP. This property can be particularly applied in precise measurement of micro-displacement, film thickness, micro/nano step height, and wavelength.

Generation of subdiffraction longitudinal bifoci by shaping a radially polarized wave

Lenses with two or more foci along the longitudinal direction exhibit immense potential in several optical applications. In this study, we propose an approach for generating subdiffraction longitudinal bifoci by binary-phase bifocal super-oscillatory lenses (SOLs), which are realized by simple AND operation between two single-foci SOLs with different focal lengths. Three bifocal SOLs with radiusRlens=70λ are designed at an operating wavelength of λ=118.8µm. Simulation results demonstrate that the minimum full width at half maximum (FWHM) is 0.397λ, and the maximum FWHM is 0.449λ, which is still smaller than the Abbe diffraction limit of 0.510λ, while all the sidelobe ratios are small (<15.1%). By properly choosing the focal length of the single-foci SOLs in the design process, the distance between the two foci can be easily controlled. Significantly, the generated bifoci with relatively uniform intensity contain a strong longitudinal electric field, which indicates their excellent prospects in optical imaging, particle acceleration, and other optical applications. In addition, the proposed bifoci-SOLs are based on the binary phase modulation, which facilitates easy fabrication compared with other approaches. These outstanding properties indicate the wide application prospects of bifocal SOLs.

Sub-wavelength annular-slit-assisted superoscillatory lens for longitudinally-polarized super-resolution focusing

A binary metallic superoscillatory lens assisted with annular subwavelength slits is proposed, which generates a longitudinally-polarized super-resolution focal point. The annular slits are designed to selectively transmit radially-polarized light. Simulations using the finite element method show a 0.24 λ focal spot with 21.8 dB of polarization purity and only 0.342 dB reduction in efficiency compared to a standard superoscillatory lens.

Modifying Bessel beam profiles with a spherulite-based radial polarizer

We present a radial polarizer prepared by growing a thickness-constrained spherulite from an oleoresin polymer. As an insert between crossed linear polarizers, the fabricated device is used to alter the intensity profile of an incident zero-order Bessel beam. Radially polarized output beams have an intensity profile with a pronounced singularity at the center. Beams may be rotated by a simple reorientation of the crossed polarizers. Experimental results with our radial polarizer correspond to a transformation of the Bessel beam order from l=0 to l=2.

A Tunable Graphene 0-90° Polarization Rotator Achieved by Sine Equation Voltage Adjustment

Polarization Manipulation has been widely used and plays a key role in wave propagation and information processing. Here, we introduce a polarization rotator in the terahertz range with a polarization conversion ratio up to 99.98% at 4.51 terahertz. It has a single graphene layer on top of the structure patterned by 45° tilted space elliptical rings. By changing the Fermi level from 0.3 ev to 0.7 ev of the graphene, we can turn the reflective light polarization direction between 0° to 90°withnearly unique magnitude. Surface currents theories and graphene characteristics clarify the relationship between polarization angle and Fermi level to be a sine equation adjusted voltage. We firstly put forward an equation to thetunable graphene changing the reflective light polarization angle. It can be widely used in measurement, optic communication, and biology. Besides, with nearly the unique reflective light in different directions, the rotator is designed into a novel radially polarization converter. The latter can be switched from radially polarized light to linearly polarized light, and vice versa, in the terahertz region.

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.

Flexible focusing pattern realization of centimeter-scale planar super-oscillatory lenses in parallel fabrication

Planar super-oscillatory lenses (SOLs) can exert far-field foci beyond the diffraction limit free from the contribution of evanescent waves. However, the reported design methods of SOLs are always complicated and divergent, leading to a poor control over the desired focusing patterns. Furthermore, the existing device sizes of SOLs are mainly within hundreds of micrometers accompanied by a subwavelength-scale feature size. Here, we propose a general optimization design model for realizing flexible focusing patterns, e.g. multifocal and achromatic contours. Additionally, a novel design called the chromatic-customized SOL fighting against the dispersion rule of traditional diffractive optical elements (DOEs) is also demonstrated based on the proposed flexible algorithm. The diameters for all the SOLs reach 12 mm with 30 μm minimum feature size, which can be easily fabricated by employing the conventional optical lithography technique. Such centimeter-scale, light weight and low-cost lenses reveal new capacities of arbitrarily customized optical patterns in various interdisciplinary fields including parallel particle trapping, full-color high-resolution imaging, and compact spectral imaging.

Non-near-field sub-diffraction focusing in the visible wavelength range by a Fibonacci subwavelength circular grating

This study proposes a Fibonacci subwavelength circular grating (FiSCG) arranged with Au concentric annuli. The numerical results show that, when illuminated by radially polarized light with a wavelength of 632.8 nm, four foci can be observed in the non-near-field with full width at half-maximum (FWHM) of 0.378λ, 0.421λ, 0.520λ, and 0.496λ, respectively. These possess low sidelobe intensity. Moreover, FiSCG achieves non-near-field sub-diffraction focusing in the visible wavelength range by varying the widths of the air slit and the Au ring. The ratio of the widths and the incident wavelength is about 0.4. This finding provides a wider applied range for FiSCG and a reference for the research on Fibonacci-arranged structures.

Realizing a terahertz far-field sub-diffraction optical needle with sub-wavelength concentric ring structure array

The terahertz (THz) lens is an essential and strategic element of THz optical systems, while a conventional THz lens cannot even reach high resolution due to the diffraction limit. Optical super-oscillation paves a way to generate sub-diffraction hotspots in the far field, and demonstrates the capacity for resolution improvement of microscopic imaging in the visible range. However, there are few demonstrations of THz lenses for focusing hotspots or needles based on super-oscillation. We propose and experimentally demonstrate a far-field sub-diffraction focusing planar lens, consisting of a sub-wavelength concentric ring structure array, for a wavelength of 118.8 μm with focal length 420λ and radius 160λ. Utilizing the silicon-etching process, a sub-diffraction focusing lens is fabricated. The experimental results show that the planar lens can generate a sub-diffraction needle with length 19.7λ in the focal region along the optic axis. Moreover, the smallest focal spot, with a transverse size of 1.212λ, is smaller than the diffraction limit of 1.476λ. The proposed sub-diffraction optical needle planar lens can substitute for its traditional counterpart, and it has great potential in super-resolution tomography THz imaging systems.

Tailoring polarization singularities in a Gaussian beam with locally linear polarization

Here we theoretically study Gaussian beams with arbitrarily located polarization singularities (PSs). Under PSs, we mean here an isolated intensity null with radial, azimuthal, or radial-azimuthal polarization around it. An expression is obtained for the complex amplitude of such beams. We study in detail cases in which there is one off-axis PS, two opposite PSs, or more than two PSs located in the vertices of a regular polygon. If such a beam has one or two opposite PSs, these PSs are the centers of radial polarization. If there are three PSs, then one of them has radial polarization, and the other two have mixed radial-azimuthal polarization. If the beam has four PSs, then there are two PSs with radial polarization and two PSs with azimuthal polarization. When propagating in space, PSs are shown to appear in a discrete set of planes, in contrast to the phase singularities existing in any plane. If the beam has two PSs, their polarization is shown to transform from the radial in the initial plane to the azimuthal in the far field. The results can find application in optical communications by using non-uniform polarization.

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.

Realization of an ultrathin acoustic lens for subwavelength focusing in the megasonic range

In this study, we report the first experimental realization of an ultrathin (0.14λ, λ = 1.482 mm means wavelength at 1 MHz in the water medium) subwavelength focusing acoustic lens that can surpass the Rayleigh diffraction limit (0.61λ/NA, NA means numerical aperture). It is termed a Super-Oscillatory Acoustic Lens (SOAL), and it operates in the megasonic range. The SOAL represents an interesting feature allowing the achievement of subwavelength focusing without the need to operate in close proximity to the object to be imaged. The optimal layout of the SOAL is obtained by utilizing a systematic design approach, referred to here as topology optimization. To this end, the optimization formulation is newly defined. The optimized SOAL is fabricated using a photo-etching process and its subwavelength focusing performance is verified experimentally via an acoustic intensity measurement system. From these measurements, we found that the proposed optimized SOAL can achieve superior focusing features with a Full Width at Half Maximum (FWHM) of ~0.40λ/NA ≃ 0.84 mm (for our SOAL, NA = 0.707) with the transmission efficiency of 26.5%.

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.

An Investigation of Influencing Factors on Practical Sub-Diffraction-Limit Focusing of Planar Super-Oscillation Lenses

Planar super-oscillation lenses (SOLs) can fulfill super-resolution focusing and nanoscopic imaging in the far field without the contribution of evanescent waves. Nevertheless, the existing deviations between the design and experimental results have been seldomly investigated, leaving the practical applications of SOLs unpredictable and uncontrollable. In this paper, some application-oriented issues are taken into consideration, such as the inevitable fabrication errors and the size effect of the designed SOLs, with the aim of providing an engineering reference to elaborately customize the demanded focusing light field. It turned out that a thicker structural film makes the focal spots enlarged, while the sloped sidewalls just weaken the intensity of the focal hotspot. Furthermore, the focal lengths are diminished with the decrease of device size, while the focal spots are enlarged. This research will promote the wide-spread applications of SOLs for sub-diffraction-limit far-field focusing in the areas of nanoscopy and high-density optical storage.

Large-scale high-numerical-aperture super-oscillatory lens fabricated by direct laser writing lithography

In this study, direct laser writing (DLW) lithography is employed to fabricate a large-scale and high-numerical-aperture super-oscillatory lens (SOL), which is capable of achieving a sub-Abbe–Rayleigh diffraction limit focus in the optical far-field region by delicate interference. Large-diameter (600 μm), amplitude-modulated and phase-type SOLs with the smallest annular ring width of 1 μm are fabricated, and they have high quality. The dependence of DLW printing on the fabrication parameters including substrate materials, laser power, and scanning speed is well investigated. A standard procedure to manufacture high-quality binary amplitude SOLs is presented, which avoids direct printing patterns on metal films and reduces the surface roughness dramatically. Random displacements between squares constituting SOLs are discussed, and their influence on the focusing performance is studied by both numerical simulations and experiments. The optical performances of the SOLs fabricated by the DLW method are experimentally characterized, and a needle-like focus with a spot size of 0.42λ and a depth of focus of ∼6 μm are confirmed at a working distance of 100 μm for λ = 633 nm, thus giving an effective numerical aperture as high as 1.19 in air. As a complementary sub-micrometer fabrication method between traditional lithography and nanofabrication method, DLW is proved to be a promising approach to manufacture SOLs, presenting advantages of relatively high speed, low equipment volume, less complexity and sub-micrometer lateral resolution. Such SOLs can be very useful in high resolution bio-imaging on rough surfaces and in the related research fields.

Super-oscillatory lens achieving sub-Abbe–Rayleigh diffraction limit focusing in the optical far-field were produced by direct laser writing (DLW) lithography method.

Design of binary phase filters for depth-of-focus extension via binarization of axisymmetric aberrations

We present a novel design approach for a binary phase mask with depth-of-focus (DoF) extension ability. Our method considers that the binarized version of an axisymmetric continuous phase pupil generates twin-intensity profiles that are symmetric with respect to the focal plane, each of which resembles the focal behavior of its continuous original. The DoF extension is realized by repositioning and coherently summing the twin foci to achieve an elongated focus along the axial direction. The shift of the two foci towards the focal plane can be handled by superimposing the defocus term in the continuous pupil function. We demonstrate our proposed design approach for two representative axisymmetric aberration functions, i.e., defocused phase axicon and spherical aberration. The manipulation of topological parameters in the phase axicon and spherical aberration, along with the defocus strength, enables the multiple binary phase-filter designs of DoF extension of 3.2-7.1 fold with a phase axicon and 2.8-14.8 fold with a spherical aberration, compared to the case with a clear aperture.

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.

Planar binary-phase lens for super-oscillatory optical hollow needles

Optical hollow beams are suitable for materials processing, optical micromanipulation, microscopy, and optical lithography. However, conventional optical hollow beams are diffraction-limited. The generation of sub-wavelength optical hollow beams using a high numerical aperture objective lens and pupil filters has been theoretically proposed. Although sub-diffraction hollow spot has been reported, nondiffracting hollow beams of sub-diffraction transverse dimensions have not yet been experimentally demonstrated. Here, a planar lens based on binary-phase modulation is proposed to overcome these constraints. The lens has an ultra-long focal length of 300λ. An azimuthally polarized optical hollow needle is experimentally demonstrated with a super-oscillatory transverse size (less than 0.38λ/NA) of 0.34λ to 0.42λ, where λ is the working wavelength and NA is the lens numerical aperture, and a large depth of focus of 6.5λ. For a sub-diffraction transverse size of 0.34λ to 0.52λ, the nondiffracting propagation distance of the proposed optical hollow needle is greater than 10λ. Numerical simulation also reveals a good penetrability of the proposed optical hollow needle at an air-water interface, where the needle propagates through water with a doubled propagation distance and without loss of its super-oscillatory property. The proposed lens is suitable for nanofabrication, optical nanomanipulation, super-resolution imaging, and nanolithography applications.

Fabrication of Fresnel plates on optical fibres by FIB milling for optical trapping, manipulation and detection of single cells

The development of economical optical devices with a reduced footprint foreseeing manipulation, sorting and detection of single cells and other micro particles have been encouraged by cellular biology requirements. Nonetheless, researchers are still ambitious for advances in this field. This paper presents Fresnel zone and phase plates fabricated on mode expanded optical fibres for optical trapping. The diffractive structures were fabricated using focused ion beam milling. The zone plates presented in this work have focal distance of ~5 µm, while the focal distance of the phase plates is ~10 µm. The phase plates are implemented in an optical trapping configuration, and 2D manipulation and detection of 8 µm PMMA beads and yeast cells is reported. This enables new applications for optical trapping setups based on diffractive optical elements on optical fibre tips, where feedback systems can be integrated to automatically detect, manipulate and sort cells.

Creating a nondiffracting beam with sub-diffraction size by a phase spatial light modulator

Due to its unique properties of nondiffracting propagation, highly-localized intensity distribution, small beam cross-section, and self-healing, a nondiffracting beam is attractive for materials processing, microscopy, and optical research. Various methods have been investigated to generate such beams with conventional optics. However, the transverse size of those nondiffracting beams is restricted by the diffraction-limit. To overcome the diffraction limit, we use the concepts of super-oscillation and the vectorial angular spectrum method to design a phase mask mirror with a focal length of 1 m, radius of 5 mm, and numerical aperture of about 0.005 for a wavelength of 632.8 nm. The phase mask mirror was created with a phase spatial light modulator. Under the illumination of a linearly polarized Gaussian wave, a nondiffracting beam was created with sub-diffraction transverse size. The maximum transverse size of the beam is smaller than the diffraction limit of 0.5λ/NA for a propagation distance greater than 43.3 mm. A nondiffracting beam with smaller transverse size can be realized by further increasing the NA value.