Analysis of the shape of a subwavelength focal spot for the linearly polarized light

Silicon Fresnel Zone Plate Metalens with Subwavelength Gratings

Metalenses are planar optical components that have demonstrated immense potential for integrated optics. In particular, they are capable of high-efficiency subwavelength focusing without the bulkiness of traditional lenses. Dielectric metalenses operating in the C-band typically employ relatively tall, amorphous silicon structures arranged in a periodic array. Phase control spanning from 0 to 2π is accessed by varying the geometry of these scattering structures. The full 2π phase range is necessary to impose a hyperbolic focusing phase profile, but this is difficult to achieve without custom fabrication practices. In this work, we propose a binary phase Fresnel zone plate metalens designed for the standard 500 nm silicon-on-insulator platform. Our design uses subwavelength gratings with trapezoidal segmentation to form concentric rings. The effective index of the grating is set with the duty cycle using a single full-etch step to form the binary phase profile of the zone plate. The metalens design can be easily tuned to achieve longer focal lengths at different wavelengths. It offers a simple platform for high-throughput wavelength-scale focusing elements in free-space optics, including for microscopy and medical imaging.

Superposition of vortex beams generated by polarization conversion in uniaxial crystals

An optical system comprising a c-cut uniaxial crystal positioned between two axicons and illuminated by a Gaussian or a Laguerre–Gauss mode was used to demonstrate the generation of various vector vortex beams. We focused the generated beams using a 1 m focal length lens and we investigated their intensity profile and the polarization state in the focal plane of the focusing element. We showed that the achieved intensity profile can be controlled by changing the polarization state of the beam incident on the crystal. We observed that, for a particular configuration of the system, the initial circular symmetry of the beam is no longer preserved. The experiments were performed with Ti:Sapphire lasers that were operated in continuous wave mode, as well as in pulsed regime. The optical system presented here ensures a convenient way to generate a great variety of vector vortex beams and it is expected to be of interest for applications that use low and high-power laser sources, such as STED microscopy, light trapping, or material processing.

Experimental estimation of the longitudinal component of a highly focused electromagnetic field

The detection of the longitudinal component of a highly focused electromagnetic beam is not a simple task. Although in recent years several methods have been reported in the literature, this measure is still not routinely performed. This paper describes a method that allows us to estimate and visualize the longitudinal component of the field in a relatively simple way. First, we measure the transverse components of the focused field in several planes normal to the optical axis. Then, we determine the complex amplitude of the two transverse field components: the phase is obtained using a phase recovery algorithm, while the phase difference between the two components is determined from the Stokes parameters. Finally, the longitudinal component is estimated using the Gauss's theorem. Experimental results show an excellent agreement with theoretical predictions.

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.

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.

Optimising superoscillatory spots for far-field super-resolution imaging

Optical superoscillatory imaging, allowing unlabelled far-field super-resolution, has in recent years become reality. Instruments have been built and their super-resolution imaging capabilities demonstrated. The question is no longer whether this can be done, but how well: what resolution is practically achievable? Numerous works have optimised various particular features of superoscillatory spots, but in order to probe the limits of superoscillatory imaging we need to simultaneously optimise all the important spot features: those that define the resolution of the system. We simultaneously optimise spot size and its intensity relative to the sidebands for various fields of view, giving a set of best compromises for use in different imaging scenarios. Our technique uses the circular prolate spheroidal wave functions as a basis set on the field of view, and the optimal combination of these, representing the optimal spot, is found using a multi-objective genetic algorithm. We then introduce a less computationally demanding approach suitable for real-time use in the laboratory which, crucially, allows independent control of spot size and field of view. Imaging simulations demonstrate the resolution achievable with these spots. We show a three-order-of-magnitude improvement in the efficiency of focusing to achieve the same resolution as previously reported results, or a 26 % increase in resolution for the same efficiency of focusing.

Tight focusing of laser light using a chromium Fresnel zone plate

Using near-field scanning microscopy, we demonstrate that a 15-µm zone plate fabricated in a 70-nm chromium film sputtered on a glass substrate and having a focal length and outermost zone's width equal to the incident wavelength λ = 532 nm, focuses a circularly polarized Gaussian beam into a circular subwavelength focal spot whose diameter at the full-width of half-maximum intensity is FWHM = 0.47λ. This value is in near-accurate agreement with the FDTD-aided numerical estimate of FWHM = 0.46λ. When focusing a Gaussian beam linearly polarized along the y-axis, an elliptic subwavelength focal spot is experimentally found to measure FWHMx = 0.42λ (estimated value FWHMx = 0.40λ) and FWHMy = 0.64λ. The subwavelength focal spots presented here are the tightest among all attained so far for homogeneously polarized beams by use of non-immersion amplitude zone plates.

Scalar and electromagnetic nonparaxial bases composed as superpositions of simple vortex fields with complex foci

We derive bases constructed from simple vortices and complex focus fields and show that they are useful in the description of strongly focused fields. Both scalar and electromagnetic fields are considered, and in each case two types of basis are discussed: bases that use standard polynomials but whose orthogonality condition requires a non-uniform directional weight factor, and bases that are orthogonal with uniform weight but that require new polynomials. Their performance is studied by fitting prescribed fields, where it is seen that the accuracy provided by both types of bases is comparable.

Thin high numerical aperture metalens

We designed, fabricated, and characterized a thin metalens in an amorphous silicon film of diameter 30 µm, focal length equal to the incident wavelength 633 nm. The lens is capable of simultaneously manipulating the state of polarization and phase of incident light. The lens converts a linearly polarized beam into radially polarized light, producing a subwavelength focus. When illuminated with a linearly polarized Gaussian beam, the lens produces a focal spot whose size at full-width half-maximum intensity is 0.49λ and 0.55λ (λ is incident wavelength). The experimental results are in good agreement with the numerical simulation, with the simulated focal spot measuring 0.46λ and 0.52λ. This focal spot is less than all other focal spots obtained using metalenses.

Microlens-aided focusing of linearly and azimuthally polarized laser light

We have investigated a four-sector transmission polarization converter (4-SPC) for a wavelength of 633 nm, that enables the conversion of a linearly polarized incident beam into a mixture of linearly and azimuthally polarized beams. It was numerically shown that by placing a Fresnel zone plate of focal length 532 nm immediately after the 4-SPC, the incident light can be focused into an oblong subwavelength focal spot whose size is smaller than the diffraction limit (with width and breadth, respectively, measuring FWHM = 0.28λ and FWHM = 0.45λ, where λ is the incident wavelength and FWHM stands for full-width at half maximum of the intensity). After passing through the 4-SPC, light propagates in free space over a distance of 300 μm before being focused by a Fresnel zone plate (ZP), resulting in focal spot measuring 0.42λ and 0.81λ. The focal spot was measured by a near-field microscope SNOM, and the transverse E-field component of the focal spot was calculated to be 0.42λ and 0.59λ. This numerical result was verified experimentally, giving a focal spot of smaller and larger size, respectively, measuring 0.46λ and 0.57λ. To our knowledge, this is the first implementation of polarization conversion and subwavelength focusing of light using a pair of transmission micro-optic elements.

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.

Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave

The generation of a sub-diffraction optical hollow ring is of great interest in various applications, such as optical microscopy, optical tweezers, and nanolithography. Azimuthally polarized light is a good candidate for creating an optical hollow ring structure. Various of methods have been proposed theoretically for generation of sub-wavelength hollow ring by focusing azimuthally polarized light, but without experimental demonstrations, especially for sub-diffraction focusing. Super-oscillation is a promising approach for shaping sub-diffraction optical focusing. In this paper, a planar sub-diffraction diffractive lens is proposed, which has an ultra-long focal length of 600 λ and small numerical aperture of 0.64. A sub-diffraction hollow ring is experimentally created by shaping an azimuthally polarized wave. The full-width-at-half-maximum of the hollow ring is 0.61 λ, which is smaller than the lens diffraction limit 0.78 λ, and the observed largest sidelobe intensity is only 10% of the peak intensity.

Far-field sub-diffraction focusing lens based on binary amplitude-phase mask for linearly polarized light

Planar lenses are attractive photonic devices due to its minimized size and easy to integrate. However, planar lenses designed in traditional ways are restricted by the diffraction limit. They have difficulties in further reducing the focal spot size beyond the diffraction limit. Super-oscillation provides a possible way to solve the problem. However, lenses based on super-oscillation have always been affected by huge sidelobes, which resulted in limited field of view and difficulties in real applications. To address the problem, in the paper, a far-field sub-diffraction lens based on binary amplitude-phase mask was demonstrated under illumination of linearly polarized plane wave at wavelength 632.8 nm. The lens realized a long focal length of 148λ (94 µm), and the full width at half maximum of the focal line was 0.406λ, which was super-oscillatory. More important is that such a flat lens has small sidelobes and wide field of view. Within the measured range of [-132λ, + 120λ], the maximum sidelobe observed on the focal plane was less than 22% of the central peak. Such binary amplitude-phase planar lens can also be extended to long focal length far-field sub-diffraction focusing lens for other spectrum ranges.

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.

Rigorous electromagnetic test of super-oscillatory lens

Thus far, the vector field of light probed by a nanostructured super-oscillatory lens (SOL) has mostly been studied by approximate theoretical means. Here the first rigorous electromagnetic (EM) test has been presented through an established electromagnetic model solved by the three-dimensional (3D) finite-difference time-domain (FDTD) method. It is found through comparisons that scalar/vectorial theories currently used for designing the metal-film-coated SOL can effectively predict the on-axis intensity behind a SOL simulated by FDTD for both linearly and circularly polarized beams; however, they cannot reflect the true 3D EM vector field distribution particularly for the linearly polarized beam and imprecise results for the total electric energy density have appeared in certain transverse planes, e.g. a relative error as high as 26% is produced for the size of the main focus behind a SOL of 14 μm large in diameter. Besides, it is found that current theories cannot be used for designing the glass-etched phase-type SOL.

Tight focus of light using micropolarizer and microlens

Using a binary microlens of diameter 14 μm and focal length 532 nm (NA=0.997) in resist, we focus a 633 nm laser beam into a near-circular focal spot with dimensions (0.35 ± 0.02)λ and (0.38 ± 0.02)λ (λ is incident wavelength) at full width half-maximum intensity. The area of the focal spot is 0.105λ(2). The incident light is a mixture of linearly and radially polarized beams generated by reflecting a linearly polarized Gaussian beam at a 100  μm × 100  μm four-sector subwavelength diffractive optical microelement with a gold coating. The focusing of a linearly polarized laser beam (the other conditions being the same) is found to produce an elliptical focal spot measuring (0.40 ± 0.02)λ and (0.50 ± 0.02)λ. To our knowledge, this is the first implementation of subwavelength focusing of light using a pair of micro-optic elements (a binary microlens and a micropolarizer).

Scanning metallic nanosphere microscopy for vectorial profiling of optical focal spots

Recent years have witnessed fast progress in the development of spatially variant states of polarization under high numerical aperture focusing, and intensive exploration of their applications. We report a vectorial, broadband, high contrast and subwavelength resolution method for focal spot profiling. In this experiment, a 100 nm diameter gold nanosphere on a silica aerogel substrate is raster scanned across the focal spots, and the orthogonal polarization components can be obtained simultaneously by measuring the scattering far field in a confocal manner. The metallic-nanosphere-on-aerogel structure ensures negligible distortion to the focal spots, low crosstalk between orthogonal polarization components (1/39 in experiment), and a low level background noise (1/80 of peak intensity in experiment), while high contrast imaging is not limited by the resonance bandwidth.

Super-oscillation focusing lens based on continuous amplitude and binary phase modulation

In this paper, we numerically demonstrate the advantage of utilizing continuous amplitude and phase modulation in super-oscillation focusing lens design. Numerical results show that compared with simple binary amplitude modulation, continuous amplitude and phase modulation can greatly improve the super-oscillation focusing performance by increasing the central lobe intensity and the ratio of its energy to the total energy, reducing the sidelobe intensity, and substantially extending the field of view. Our study also reveals the role of phase distribution in reducing the spatial frequency bandwidth of the super-oscillation optical field on the focal plane. Based on continuous amplitude and binary phase modulation, a lens was designed with double layer metal slit array for wavelength of 4.6 µm. COMSOL is used to carry out the 2D simulation. The lens focal length is 40.18λ and the focal spot FWHM is 0.308λ. Two largest sidelobes are located right next to the central lobe with intensity about 40% of the central lobe intensity. Except for the two sidelobes, other sidelobes have intensity less than 25% of the central lobe intensity, which leads to a clear field of view on the whole focal plane.

Photonic nanojets generated using square-profile microsteps

We have shown experimentally that square-profile microsteps on a silica substrate, with square sides of 0.4, 0.5, 0.6, and 0.8 μm and height of 500 nm, illuminated through the substrate by a linearly polarized laser beam of wavelength λ=633  nm, produce, near the surface, enhanced-intensity regions (termed photonic nanojects), with their intensity being six times higher than that of the incident light and their respective full width at half-maximum diameters being 0.44λ, 0.43λ, 0.39λ, and 0.47λ, which is below the diffraction limit of 0.51λ. It is worth noting that when the step side is smaller than the wavelength, the focus is found within the step; otherwise the focus is outside the step, which is similar to an optical candle.

Study of polarization properties of fiber-optics probes with use of a binary phase plate

We conduct a theoretical and experimental study of the distribution of the electric field components in the sharp focal domain when rotating a zone plate with a π-phase jump placed in the focused beam. Comparing the theoretical and experimental results for several kinds of near-field probes, an analysis of the polarization sensitivity of different types of metal-coated aperture probes is conducted. It is demonstrated that with increasing diameter of the non-metal-coated tip part there occurs an essential redistribution of sensitivity in favor of the transverse electric field components and an increase of the probe's energy throughput.

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.

Vectorial design of super-oscillatory lens

A design and optimization method based on vectorial angular spectrum theory is proposed in this paper for the vectorial design of a super-oscillatory lens (SOL), so that the radially polarized vector beam can be tightly focused. The structure of a SOL is optimized using genetic algorithm and the computational process is accelerated using fast Hankel transform algorithm. The optimized results agree well with what is obtained using the vectorial Rayleigh-Sommerfeld diffraction integral. For an oil immersed SOL, a subwavelength focal spot of about 0.25 illumination wavelength without any significant side lobe can be created at a distance of 184.86 μm away from a large SOL with a diameter of 1mm. The proposed vectorial design method can be used to efficiently design a SOL of arbitrary size illuminated by various vector beams, with the subwavelength hotspot located in a post-evanescent observation plane.