High Numerical Aperture Lens Research Articles

X-ray focusing below 3 nm with aberration-corrected multilayer Laue lenses

Multilayer Laue lenses are volume diffractive optical elements for hard X-rays with the potential to focus beams to sizes as small as 1 nm. This ability is limited by the precision of the manufacturing process, whereby systematic errors that arise during fabrication contribute to wavefront aberrations even after calibration of the deposition process based on wavefront metrology. Such aberrations can be compensated by using a phase plate. However, current high numerical aperture lenses for nanometer resolution exhibit errors that exceed those that can be corrected by a single phase plate. To address this, we accumulate a large wavefront correction by propagation through a linear array of 3D-printed phase correcting elements. With such a compound refractive corrector, we report on a point spread function with a full-width at half maximum area of 2.9 × 2.8 nm2 at a photon energy of 17.5 keV.

Magneto-optical-like effect in tight focusing of azimuthally polarized sine-Gaussian beams.

Magneto-optical effects, which have been known for over a century, are among the most fundamental phenomena in physics and describe changes in the polarization state of light when it interacts with magnetic materials. When a polarized plane wave propagates in or through a homogeneous and isotropic transparent medium, it is generally accepted that its transverse polarization structure remains unchanged. However, we show that a strong radial polarization component can be generated when an azimuthally polarized sine-Gaussian plane wave is tightly focused by a high numerical aperture lens, resulting in a magneto-optical-like effect that does not require external magnetic field or magnetic medium. Calculations show that the intensity structure and polarization distribution of the highly confined electric field strongly depend on the parameters m and φ0 in the sinusoidal term, where m can be used to control the number of the multifocal spots and φ0 can be used to control the position of each focal spot. Finally, we show that this peculiar electric field distribution can be used to realize multiple particles trapping with controllable numbers and locations.

Tightly focused optical skyrmions and merons formed by electric-field vectors with prescribed characteristics

Abstract Optical skyrmions, which are topological quasi-particles with nontrivial electromagnetic textures, have garnered escalating research interest recently for their potential in diverse applications. In this paper, we present a method for generating tightly focused optical skyrmion and meron topologies formed by electric-field vectors under 4π-focusing system, where both the topology types (including Néel-, Bloch-, intermediate- and anti-skyrmion/meron) and the normal direction of the two-dimensional topology projection plane can be tailored at will. By utilizing time-reversal techniques, we analytically derive the radiation pattern of a multiple concentric-ring array of dipoles (MCAD) to obtain the required illumination fields on the pupil planes of the two high numerical aperture lenses. The Deby vector diffraction integral theory is employed to calculate the corresponding tightly focused field, and their topology characteristics are quantitatively evaluated by the electric-field vector distribution. The results demonstrate that arbitrary electric-field based skyrmion and meron can be conveniently generated by adjusting the oscillation direction of each dipole in the MCAD and the normal direction of the dipole array. The generated optical topologies with fully controllable degrees of freedom provide potential applications in optical information processing, transmission, and storage.

Spatiotemporal coupling induced controllable orientation of photonic orbital angular momentum at subwavelength scale.

Recently, the emergence of transverse orbital angular momentum (OAM) as a novel characteristic of light has captured substantial attention, and the significance of adjustable OAM orientation has been underscored due to its pivotal role in the interaction between light and matter. In this work, we introduce a novel approach to manipulate the orientation of photonic OAM at subwavelength scales, leveraging spatiotemporal coupling. By tightly focusing a wavepacket containing dual spatiotemporal vortices and a spatial vortex through a high numerical aperture lens, the emergence of intricate coupling phenomena leads to entangled and intricately twisted vortex tunnels. As a consequence, the orientation of spatial OAM deviates from the conventional light axis. Through theoretical scrutiny, we unveil that the orientation of photonic OAM within the focal field is contingent upon the signs of the topological charges in both spatiotemporal and spatial domains. Additionally, the absolute values of these charges govern the precise orientation of OAM within their respective quadrants. Moreover, augmenting the pulse width of the incident light engenders a more pronounced deflection angle of photonic OAM. By astutely manipulating these physical parameters, unparalleled control over the spatial orientation of OAM becomes achievable. The augmented optical degrees of freedom introduced by this study hold considerable potential across diverse domains, including optical tweezers, spin-orbit angular momentum coupling, and quantum communication.

Highly localized continuous wave optical vortex with controllable orbital angular momentum orientation and topological charge.

We report an approach to simultaneously control orbital angular momentum (OAM) orientation and topological charge in highly localized optical vortices by employing a 4π focusing system. The required continuous wave illumination field in the pupil planes is derived by superimposing the radiation pattern of only one dipole placed at the focal point of the high numerical aperture lens and the corresponding tailored spiral phase factor. The topological charge and OAM orientation of the obtained focused fields are quantitatively evaluated based on the focal field distributions calculated by the Richards-Wolf vector diffraction integration theory. Results show that the OAM of the generated optical vortices can be tailored by changing the oscillation orientation of the mimic dipole and the topological charge of the superimposed spiral phase term. The presented method may find potential applications in optical trapping, optical tweezers, light-matter interaction, etc.

Effect of primary astigmatism on the tight focusing of ellipse field singularities

The tight focusing of ellipse field singularities, namely bright and dark C-points, is studied using the Debye–Wolf diffraction integral in the presence of primary astigmatism. The effect of polarization distribution, the sign of polarization singularity index, amplitude, and handedness of the ellipse field singularities are investigated in the intensity distribution of the focal plane of a high numerical aperture lens system in the presence of primary astigmatism. Ellipse field singularities that are tightly focused can create an additional longitudinal component at the focal plane. At the focal plane, both the longitudinal and transverse components of the ellipse fields are found to be hosted with phase vortices of charge ±1. In the presence of primary astigmatism, the helicity inversion of input C-point does not rotate the focal plane intensity distributions by 180°.

Tight focusing field of cylindrical vector beams based on cascaded low-refractive index metamaterials

Abstract Using low-refractive-index metamaterials, we design a transmission-type radial-angular cylindrical vector beam generator. A high numerical aperture lens is constructed using an asymmetric meta-grating structure. The metamaterial vector beam generator and the meta-grating lens are physically cascaded to obtain the tight focusing characteristics of the vector light field. The vector beam generator module and the meta-lens module are prepared by 3D printing technology, and the near-field test has been carried out on the samples in the terahertz band. Using the physical cascading method, two modules are cascaded to construct a vector beam tight focusing device, and the focusing electric field distribution test has been carried out. The use of 3D printing technology for sample preparation further reduces the manufacturing difficulty and production cost, and ensures the realization of its design function on the basis of miniaturization and light weight, which provides the possibility for the research of tight focusing field regulation in the terahertz band.

Dual-wavelength UV-visible metalens for multispectral photoacoustic microscopy: A simulation study

Photoacoustic microscopy is advancing with research on utilizing ultraviolet and visible light. Dual-wavelength approaches are sought for observing DNA/RNA- and vascular-related disorders. However, the availability of high numerical aperture lenses covering both ultraviolet and visible wavelengths is severely limited due to challenges such as chromatic aberration in the optics. Herein, we present a groundbreaking proposal as a pioneering simulation study for incorporating multilayer metalenses into ultraviolet-visible photoacoustic microscopy. The proposed metalens has a thickness of 1.4 µm and high numerical aperture of 0.8. By arranging cylindrical hafnium oxide nanopillars, we design an achromatic transmissive lens for 266 and 532 nm wavelengths. The metalens achieves a diffraction-limited focal spot, surpassing commercially available objective lenses. Through three-dimensional photoacoustic simulation, we demonstrate high-resolution imaging with superior endogenous contrast of targets with ultraviolet and visible optical absorption bands. This metalens will open new possibilities for downsized multispectral photoacoustic microscopy in clinical and preclinical applications.

Tight-focusing evolution of linearly polarized auto-focusing circular Bessel-Gaussian vortex beam

In this paper, we analyzed the influence of on-axis and off-axis vortex on the intensity distribution of the linearly polarized auto-focusing Bessel-Gaussian vortex beam (LABGVB). By comparing its tight-focusing properties with that of the linearly polarized circular Airy beam, it is found that when transmitted in the tight-focusing system, the LABGVB not only generates multiple focusing, but also allows the focal points to be located away from the geometric focus of the high numerical aperture (HNA) lens. In addition, changing the focal length of the HNA lens not only causes the splitting and merging of the focal points, but also results in different control effects on the depth of focus and the distance between focal points due to different focusing times. In particular, the LABGVB can not only form multiple optical bottles for particle capture in the focusing region, but also exhibit two different distributions of the spin density vectors along the optical axis after choosing the appropriate scale factor and main ring radius, one being a circular line and the other being a helical line.

Advancing full-field metrology: rapid 3D imaging with geometric phase ferroelectric liquid crystal technology in full-field optical coherence microscopy.

Optical coherence microscopy (OCM) is a variant of OCT in which a high-numerical aperture lens is used. Full-field OCM (FF-OCM) is an emerging non-invasive, label-free, interferometric technique for imaging of surface structures or semi-transparent biomedical subjects with micron-scale resolutions. Different approaches to three dimensional full-field optical metrology are reviewed. The usual method for the phase-shifting technique in FF-OCM involves mechanically moving a mirror to change the optical path difference for obtaining en-face OCM images. However, with the use of a broadband source in FF-OCM, the phase shifts of different spectral components are not the same, resulting in the ambiguities in 3D image reconstruction. In this study, we demonstrate, by imaging tissues and cells, a unique geometric phase-shifter based on ferroelectric liquid crystal technology, to realize achromatic phase-shifting for rapid three-dimensional imaging in a FF-OCM system.

Rapid Cellular-Resolution Skin Imaging with Optical Coherence Tomography Using All-Glass Multifocal Metasurfaces.

Cellular-resolution optical coherence tomography (OCT) is a powerful tool offering noninvasive histology-like imaging. However, like other optical microscopy tools, a high numerical aperture (N.A.) lens is required to generate a tight focus, generating a narrow depth of field, which necessitates dynamic focusing and limiting the imaging speed. To overcome this limitation, we developed a metasurface platform that generates multiple axial foci, which multiplies the volumetric OCT imaging speed by offering several focal planes. This platform offers accurate and flexible control over the number, positions, and intensities of axial foci generated. All-glass metasurface optical elements 8 mm in diameter are fabricated from fused-silica wafers and implemented into our scanning OCT system. With a constant lateral resolution of 1.1 μm over all depths, the multifocal OCT triples the volumetric acquisition speed for dermatological imaging, while still clearly revealing features of stratum corneum, epidermal cells, and dermal-epidermal junctions and offering morphological information as diagnostic criteria for basal cell carcinoma. The imaging speed can be further improved in a sparse sample, e.g., 7-fold with a seven-foci beam. In summary, this work demonstrates the concept of metasurface-based multifocal OCT for rapid virtual biopsy, further providing insights for developing rapid volumetric imaging systems with high resolution and compact volume.

Fast algorithm for the simulation of 3D-printed microoptics based on the vector wave propagation method.

In this work, we propose the Fast Polarized Wave Propagation Method (FPWPM), which is an efficient method for vector wave optical simulations of microoptics. The FPWPM is capable of handling comparably large simulation volumes while maintaining quick runtime. This allows for real-world application of this method for the rapid development process of 3D-printed microoptics. By comparison to established routines like the rigorous coupled wave analysis (RCWA) or the Richards-Wolf-Integral, accuracy and superior runtime efficiency of the FPWPM are demonstrated by simulation of interfaces, gratings, and lenses. By considering polarization in simulations, the FPWPM facilitates the analysis of optical elements which employ this property of electromagnetic waves as a feature in their optical design, e.g., diffractive elements, gratings, or optics with high angle of incidence like high numerical aperture lenses.

Numerical modeling for the characteristics study of a focusing ultrashort spatiotemporal optical vortex.

Spatiotemporal (ST) wave packet carrying pure transverse orbital angular moment (OAM) with subwavelength spatial size has attracted increasing attentions in recent years, which can be obtained by tightly focusing a linear superposition of ST vortices with different topological charges. In this work, numerical models are proposed to explore the impact of the pulse width of the ST vortex on the characteristics of its focal field. We demonstrate that the rigorous model for calculating the focused ST wave packet is essential for ultrashort optical pulse, while the simplified model has the advantage of high efficiency but can only provide credible results when the pulse width of the illumination is long enough. Specifically, when the pulse width decreases from 100 fs to 5 fs, the accuracy of the simplified model would decrease significantly from 99% to 65.5%. In addition, it is found that the pulse duration would still lead to the collapse of transverse OAM structure near the focus of a high numerical aperture lens, even though the ST astigmatism has already been corrected. To analyze the physical mechanism behind this distortion, Levenberg-Marquardt algorithm is adopted to retrieve the OAM distribution of the focal field. It is shown that the contributions from undesired OAM modes would become nontrivial for short pulse width, leading to the formation of the focal field with hybrid OAM structures. These findings provide insight for the focusing and propagation studies of ultrashort ST wave packets, which could have wide potential applications in microscopy, optical trapping, laser machining, nonlinear light-matter interactions, etc.

Focusing Characteristics and Widefield Imaging Performance of the Silicon Metalens in the Visible Range

Conventional optical high numerical aperture lenses are essential for high-resolution imaging, but bulky and expensive. In comparison, metalens-based optical components are the subjects of intensive investigation for their flexible manipulation of light. Methods of detecting and characterizing focal spots and scanning imaging produced by metalenses are well established. However, widefield imaging by metalenses is experimentally challenging. This study demonstrates the design and realization of silicon-based metalenses with numerical apertures of 0.447 and 0.204 in the broadband spectrum of 580–780 nm for microscopic widefield imaging. The optimized aspect ratio of the single nanorod is 5.1:1, which reduces the fabrication difficulty compared to other, more complicated designs and fabrication. Furthermore, we successfully demonstrate widefield imaging by the designed metalens and compare the simulated and the experimentally extracted modulation transfer function curves of the metalens.

Precise wavefront characterization of x-ray optical elements using a laboratory source.

Improvements in x-ray optics critically depend on the measurement of their optical performance. The knowledge of wavefront aberrations, for example, can be used to improve the fabrication of optical elements or to design phase correctors to compensate for these errors. At present, the characterization of such optics is made using intense x-ray sources, such as synchrotrons. However, the limited access to these facilities can substantially slow down the development process. Improvements in the brightness of lab-based x-ray micro-sources in combination with the development of new metrology methods, particularly ptychographic x-ray speckle tracking, enable characterization of x-ray optics in the lab with a precision and sensitivity not possible before. Here, we present a laboratory setup that utilizes a commercially available x-ray source and can be used to characterize different types of x-ray optics. The setup is used in our laboratory on a routine basis to characterize multilayer Laue lenses of high numerical aperture and other optical elements. This typically includes measurements of the wavefront distortions, optimum operating photon energy, and focal length of the lens. To check the sensitivity and accuracy of this laboratory setup, we compared the results to those obtained at the synchrotron and saw no significant difference. To illustrate the feedback of measurements on performance, we demonstrated the correction of the phase errors of a particular multilayer Laue lens using a 3D printed compound refractive phase plate.

Vascularization of Cell-Laden Microfibres by Femtosecond Laser Processing.

To face the increasing demand for organ transplantation, currently the development of tissue engineering appears as the best opportunity to effectively regenerate functional tissues and organs. However, these approaches still face the lack of an efficient method to produce an efficient vascularization system. To answer these issues, the formation of an intra-volume channel within a three-dimensional, scaffold free, mature, and cell-covered collagen microfibre is here investigated through laser-induced cavitation. An intra-volume channel was formed upon irradiation with a near-infrared, femtosecond laser beam, focused with a high numerical aperture lens. The laser beam directly crossed the surface of a dense and living-cell bilayer and was focused behind the bilayer to induce channel formation in the hydrogel core while preserving the cell bilayer. Channel formation was assessed through confocal microscopy. Channel generation inside the hydrogel core was enhanced by the formation of voluminous cavitation bubbles with a lifetime longer than 30 s, which also improved intra-volume channel durability. Twenty-four hours after laser processing, cellular viability dropped due to a lack of sufficient hydration for processing longer than 10 min. However, the processing automation could drastically reduce the cellular mortality, this way enabling the formation of hollowed microfibres with a high density of living-cell outer bilayer.

Time-resolved fluorescence and anisotropy studies of red pigments present in acrylic formulations

Red organic pigments are frequently found in modern paintings and murals based on acrylic formulations. The detection of these molecules is valuable to guide investigations about cultural heritage and for restoration efforts. These studies usually employ microscopic amounts of materials that are obtained through swabbing or micro-sampling. In this contribution we describe the time-resolved emission properties of a set of red pigments with the objective of characterizing their excited state properties and developing strategies to identify their presence through fluorescence lifetime measurements, even in concentrations of the order of 10−9 M. As we show, using different solvent systems, the emission decay measurements can be setup to be a robust identification technique that avoids problems with evaporation or partial solubility. We also show that the sensitivity of these determinations is improved using a confocal type of setup with a high numerical aperture lens to ensure a high photon capture. This setup also allows for the samples to be prepared in microliter level volumes which implies a relatively high concentration of the pigments. In addition, we show that the lifetime measurements can be complemented with determinations of the emission anisotropy decays with the same experimental setup, which provides an additional property specific to each pigment, permitting an accurate differentiation between fluorophores.

Lateral image reconstruction of optical coherence tomography using one-dimensional deep deconvolution network.

Optical coherence tomography (OCT) is a cross-sectional imaging method utilizing a low coherence interferometry. The lateral resolution of the OCT is limited by the numerical aperture (NA) of the imaging lens. Using a high NA lens improves the lateral resolution but reduces the depth of focus (DOF). In this study, we propose a method to improve the lateral resolution of OCT images by end-to-end training of a deep 1-D deconvolution network without use of high-resolution images. To improve the lateral resolution of the OCT, we trained the 1-D deconvolution network using lateral profiles of OCT images and the beam spot size. We used our image-guided laparoscopic surgical tool (IGLaST) to acquire OCT images of nonbiological and biological samples ex vivo. The OCT images were then blurred by applying Gaussian functions with various full width half maximums ranging from 40to 160 µm. The network was trained using the blurred OCT images as input and the non-blurred original OCT images as output. We quantitatively evaluated the developed network in terms of similarity and signal-to-ratio (SNR), using in-vivo images of mesenteric tissue from a porcine model that was not used for training. In addition, we performed knife-edge tests and qualitative evaluation of the network to show the lateral resolution improvement of ex-vivo and in-vivo OCT images. The proposed method showed an improvement of image quality on both blurred images and non-blurred images. When the proposed deconvolution network was applied, the similarity to the non-blurred image was improved by 1.29 times, and the SNR was improved by 1.76 dB compared to the artificially blurred images, which was superior to the conventional deconvolution method. The knife-edge tests at distances at 200 to 1000 µm from the imaging probe showed an approximately 1.2 times improvement in lateral resolution. In addition, through qualitative evaluation, it was found that the image quality of both ex-vivo and in-vivo tissue images was improved with clear structure and less noise. This study showed the ability of the 1-D deconvolution network to improve the image quality of OCT images with variable lateral resolution. We were able to train the network with a small amount of data by constraining the network in 1-D. The quantitative evaluation showed better results than conventional deconvolution methods for various amount of blurring. Qualitative evaluation showed analogous results with quantitative results. This simple yet powerful image restoration method provides improved lateral resolution and suppresses background noise, making it applicable to a variety of OCT imaging applications.

3D-Printed Micro Lens-in-Lens for In Vivo Multimodal Microendoscopy.

Multimodal microendoscopes enable co-located structural and molecular measurements in vivo, thus providing useful insights into the pathological changes associated with disease. However, different optical imaging modalities often have conflicting optical requirements for optimal lens design. For example, a high numerical aperture (NA) lens is needed to realize high-sensitivity fluorescence measurements. In contrast, optical coherence tomography (OCT) demands a low NA to achieve a large depth of focus. These competing requirements present a significant challenge in the design and fabrication of miniaturized imaging probes that are capable of supporting high-quality multiple modalities simultaneously. An optical design is demonstrated which uses two-photon 3D printing to create a miniaturized lens that is simultaneously optimized for these conflicting imaging modalities. The lens-in-lens design contains distinct but connected optical surfaces that separately address the needs of both fluorescence and OCT imaging within a lens of 330 µm diameter. This design shows an improvement in fluorescence sensitivity of >10x in contrast to more conventional fiber-optic design approaches. This lens-in-lens is then integrated into an intravascular catheter probe with a diameter of 520µm. The first simultaneous intravascular OCT and fluorescence imaging of a mouse artery in vivo is reported.

Primary aberrations in tightly focused polarized anomalous vortex beams

Based on the Richards Wolf vector diffraction theory, the intensity profiles of the radially and azimuthally polarized anomalous vortex beams focused by a high numerical aperture (NA) lens in the presence of primary aberration are obtained. The effects of the primary aberration coefficient on the intensity distribution, longitudinal field and the quality of the aberrated focused field through calculating the Strehl ratio under various polarized input beams are analyzed. The results show that spherical aberration destroys the rotational symmetry of the focused intensity about the optical axis. Coma will shift the focal spot which gradually presents an obvious comet shape. Astigmatism will elongate the focal spot. Meanwhile, defocus technology on compensating aberrations is studied. The results have potential applications in the design and assembly of high NA systems or overcoming aberrations in the future.