Numerical Aperture Research Articles

Design of a polarization-insensitive broadband achromatic metalens for mid-wave infrared detector.

Metalenses, boasting outstanding focusing efficiency and high-resolution imaging capabilities, have generated widespread usage in fields such as integrated optics, achromatic imaging, and optical holography. In this study, we have developed a broadband achromatic metalens within the detection range from 3 to 5 µm, and it has a numerical aperture (NA) of 0.71 with a remarkable maximum focusing efficiency of 63.8% at the focal plane within the specified bandwidth. We have further delved into the dispersion control mechanism that combines the geometric and transmission phases and optimized the constructed phase response simulation database using the particle swarm optimization (PSO) algorithm, ensuring a precise phase matching between the actual wavefront and the ideal focusing wavefront. This metalens with its ability to expand the array size has the potential to create a compact infrared imager, which holds significant importance in achieving efficient detection and integration within infrared detectors.

Terahertz photonic crystal fiber-based edible oil sensor: Performance evaluation and identification

This model introduced an innovative hollow-core optical waveguide with an octagonal core, specifically designed for rapid detection of various food oil contaminations is founded on the principles of Photonic Crystal Fiber (PCF). By analyzing the refractive index (RI) variations between pure and contaminated oil, we evaluate other essential optical parameters. The characteristics inherent to the suggested food oil sensor are examined using COMSOL Multiphysics v6.1, employing the Finite Element Method (FEM). Highly precise mesh components are included to provide optimal simulation accuracy. The outcomes from the suggested sensor model demonstrate exceptionally strong relative sensitivity of 98.52 % for castor oil, 98.46 % for sunflower oil, 98.41 % for mustard oil, 98.32 % for olive oil, and 98.03 % for coconut oil, all measured at 2 THz. Additionally, the simulation shows a very low confinement loss of 2.37 × 10−12 cm-1, a numerical aperture of 0.242, effective area of 1.1459 × 10–7 m², and effective material loss of 0.0038 cm-1 for castor oil under optimal structural circumstances. The straightforward design of the PCF in the sensor indicates that it can be implemented with ease, given these standard performance indicators. Therefore, it is anticipated that this sensor will open improved avenues for detection and identification of several distinct food oil contaminations. It can be produced using standard fabrication processes.

Wavefront shaping and imaging through a multimode hollow-core fiber

Multimode fibers recently emerged as compact minimally-invasive probes for high-resolution deep-tissue imaging. However, the commonly used silica fibers have a relatively low numerical aperture (NA) limiting the spatial resolution of a probe. On top of that, light propagation within the solid core generates auto-fluorescence and Raman background, which interferes with imaging. Here we propose to use a hollow-core fiber to solve these problems. We experimentally demonstrate spatial wavefront shaping at the multimode hollow-core fiber output with tunable high-NA. We demonstrate raster-scan and speckle-based compressive imaging through a multimode hollow-core fiber.

Aperiodic multilayer masks for M3D mitigation in high- and hyper-NA extreme ultraviolet lithography

As extreme ultraviolet lithography tools with higher image numerical apertures (NAi) are introduced, the range of angles at the multilayer mask stack is also increased. Lithography systems are designed to fulfill the “abbe sine rule,” where NAm is related to NAi by the reduction factor. As a result, increases in NAi will increase NAm. High-NA and hyper-NA systems will be implemented with anamorphic optics, 4× in “X,” and 8× in “Y” to reduce the necessary angles. Even so, hyper-NA masks may see illumination angles as high as 13.4°, up from 10.8° for 0.33 NA. This represents a challenge for maintaining through-angle mask reflection using the current periodic mask multilayer structures. In addition to the reflectance amplitude, the phase of reflected light, which plays an important role in imaging, is also strongly influenced by increasing angles. The propagation of light through each bilayer in the stack imparts a phase shift based on the incidence angle. This is then accumulated over many layers, inducing phase effects, which are unique to each illumination point. This will become especially true for high-NA and hyper-NA mask applications. While adjustments to the multilayer period are sufficient to achieve acceptable reflectance, periodic multilayers may suffer in normalized image log slope (NILS) and image placement error (IPE) metrics as a result of strong oblique multilayer M3D phase effects. In this work, we present a first principles methodology for the systematic reduction of oblique multilayer M3D effects through the use of aperiodic multilayer design. We find that when used for low-k1, hyper-NA patterning NILS is improved by 40+%, while IPE through pitch is similarly improved. Under high-NA conditions, a 5%–25% NILS gain is found alongside the enhanced depth of focus.

Efficient single-mode operation in a 10 dB/m absorption very-large-mode-area ytterbium-doped optical fiber via curvature-induced mode filtering

In this paper we report our findings on the design, manufacturing and testing of low numerical aperture active step-index optical fibers with very large mode area, operating in a truly single-mode regime. Our approach to efficiently filter higher-order modes in the core relies on applying curvature in a specific direction at a given diameter on a specially designed fiber containing boron-doped silica rods on both sides of the core. The fabricated ytterbium-doped fibers exhibit a mode field diameter of 32μm, a cladding pump absorption of 10 dB/m and were designed for use in a compact monolithic configuration due to its all-solid nature and its 14 cm targeted bend diameter.

Long wavelength fluoride optical glass fibers performance signature in high speed local area data networks

Abstract This paper has clarified long wavelength fluoride optical glass fibers performance signature in high speed local area data networks. The signal attenuation and the total fiber pulse broadening are studied versus network length for various fluoride optical glass fibers and AS2 Se3 glass fiber at various spectral wavelengths. The total signal delay time is demonstrated with fiber numerical aperture with 15 km network length for various fluoride optical glass fibers and AS2 Se3 glass fiber at 2.5 μm optimum spectral wavelength. Total fiber signal bandwidth, total Shannon channel bit rate, and NRZ/RZ channel data rate transmission are clarified with 15 km network length for various fluoride optical glass fibers and AS2 Se3 glass fiber at 2.5 μm optimum spectral wavelength.

High birefringent slotted core slotted cladding porous core PCF for THz waveguide

A novel design featuring a porous core photonic crystal fiber (PC-PCF) is proposed in this paper for terahertz (THz) waveguide application. This work uses finite element method (FEM) and a boundary condition related to perfectly matched layer (PML) for analyzing the guiding properties. This methodology is supported by a fiber type featuring a slotted core and slotted cladding, utilizing Zeonex as the material. It offers high birefringence valued at 0.0978, small confinement loss of 10−14 dB/cm, a meager amount of effective material loss (EML) valued at 0.011697 dB/cm and a very high core power fraction (CPF) of 67.156%. Additionally, it shows a flattened pattern of dispersion measuring 0.4 ± 0.2 ps/THz/cm at an extensive frequency range of 0.5 THz to 2 THz. Other significant waveguide properties: effective refractive index, numerical aperture (NA), V-parameter, effective area, spot size, and beam divergence of the suggested fiber are numerically analyzed and conferred thoroughly. Regarding its mode of operation, the proposed fiber primarily functions in multimode, but it can also operate in single mode for higher porosity levels and lower core diameters. This unique characteristic renders the proposed PC-PCF structure well-suited for a broad range of applications, offering versatility as to its mode of operation.

Calibration of the spherical tip radius of Rockwell hardness diamond indenters using a confocal laser scanning microscope

Abstract The precise form of an indenter is an essential part of hardness testing methods. It is therefore incumbent upon a user to ensure that the indenter geometry is calibrated before performing a hardness test. A geometric change of the tip radius by ±5 μm can cause a change of approximately 0.6 units of Rockwell hardness C scale (HRC) in a material with a hardness of 65 HRC. Keeping in mind that the measurement uncertainty is typically of the order of 0.3 HRC, it is critical to know the true value of the tip radius. Typically, tactile methods are used to determine the tip radius of a Rockwell hardness diamond indenter from the measured surface topography. Two main drawbacks of tactile measurements are the long duration of measurement and the limitation in capturing surface features of sizes smaller than the probe tip radius of 2 μm. Both could be overcome by using an optical 3D measurement. Confocal laser scanning microscopes (CLSM) allow a fast contactless 3D-mapping of the surface of Rockwell hardness diamond indenters and can be used to obtain geometric information such as the tip radius. The accuracy of these 3D measurements is still under question. Within this work, some of the influencing factors for fast 3D surface measurement are investigated. Using a CLSM with a 50x objective lens and a numerical aperture of 0.95, typical shape deviations of Rockwell diamond indenters are shown. Furthermore, an improved 3D based point cloud method for the evaluation of the indenter radius is presented. The aim of this paper is to explore the capabilities and limits of CLSM to obtain the 3D surface of a Rockwell hardness diamond indenter in order to calibrate the tip radius and compare their results with measurements from traceable stylus instruments.

Far-field sub-diffraction focusing and controlled focus shaping of circularly polarized light using a dielectric phase plate

In recent years, sub-diffraction focusing has received substantial attention due to its versatility. However, achieving a flexible sub-diffraction focusing in the far field remains stimulating. Existing techniques either require complex fabrication facilities or are limited to the short focal length and high numerical aperture (NA) of the imaging system. Here, we introduce an optimization method for sub-diffraction focusing of a circularly polarized beam in the far field with a lens of large focal length. A cost-effective dielectric phase plate serves the purpose. By employing a phase plate composed of a thin layer of dielectric Si3N4, the phase of the propagating beam is modulated in the beam’s cross-section, which is divided into two regions of the opposite phase by the plate. A sub-diffraction focusing is achieved for a proper tunning between the two regions. In addition to sub-diffraction focusing, the phase plate is also capable of shaping the focus into a doughnut-shaped and a flat-top profile in the far field. This design provides a simple solution for sub-diffraction focusing and focus shaping that will find potential applications in optical imaging, optical trapping, and material processing.

Diffractive microoptics in porous silicon oxide by grayscale lithography

We demonstrate focusing as well as imaging using diffractive microoptics, manufactured by two-photon polymerization grayscale lithography (2GL), that have been 3D printed into porous silicon oxide. While typical doublet lens systems require support structures that hold the lenses in place, our optics are held by the porous media itself, decreasing both the fabrication time and design constraints while increasing the optically active area. Compared to the typical two-photon polymerization fabrication process, 2GL offers better shape accuracy while simultaneously increasing throughput. To showcase 2GL manufactured optics in porous media, we fabricate singlet diffractive lenses with a diameter of 500 µm and numerical apertures of up to 0.6. We measure the intensity distribution in the focal plane, and along the optical axis. Furthermore, we design and fabricate a doublet lens system for imaging purposes with a diameter of 600 µm and thinner than 60 µm. We examine the imaging performance with a USAF 1951 resolution test chart and determine the resolution to be 287 lp/mm. 3D printing in porous SiO2 thus holds great promise for future complex and unconventional microoptical solutions.

Optical skyrmion and its "zipper-like" topological behavior in an energy flux field.

The optical skyrmion and its topological behavior are analyzed in an energy flux field constructed by an X-type vortex in a high numerical aperture system. The conditions for the formation of a skyrmion structure in this field are discussed, showing that the vortex pattern of the transverse energy flow and the inverse energy flow are crucial for the skyrmions and also are controlled by the phase gradient of the X-type vortex. Notably, the "zipper-like" topological reaction, which is the first, to our knowledge, found in ferromagnetic materials, is observed, and the physical mechanism is also explained by the relation of orbital angular momentum density and Poynting vectors. The results will reach the topological theory and may have applications in optical traps and data storage.

Enhancing Bioluminescence Imaging of Cultured Tissue Explants Using Optical Telecompression.

Long-term observation of single-cell oscillations within tissue networks is now possible by combining bioluminescence reporters with stable tissue explant culture techniques. This method is particularly effective in revealing the network dynamics in systems with slow oscillations, such as circadian clocks. However, the low intensity of luciferase-based bioluminescence requires signal amplification using specialized cameras (e.g., I-CCDs and EM-CCDs) and prolonged exposure times, increasing baseline noise and reducing temporal resolution. To address this limitation, we implemented a cost-effective optical enhancement technique called telecompression, first used in astrophotography and now commonly used in digital photography. By combining a high numerical aperture objective lens with a magnification-reducing relay lens, we significantly increased the collection efficiency of the bioluminescence signal without raising the baseline CCD noise. This method allows for shorter exposure times in time-lapse imaging, enhancing temporal resolution and enabling more precise period estimations. Our implementation demonstrates the feasibility of telecompression for enhancing bioluminescence imaging for the tissue-level network observation of circadian clocks.

The Impact of 1030 nm fs-Pulsed Laser on Enhanced Rayleigh Scattering in Optical Fibers.

This article presents a comprehensive study on the impact of irradiation optical fiber cores with a femtosecond-pulsed laser, operating at a wavelength of 1030 nm, on the signal amplitude in Rayleigh scattering-based optical frequency domain reflectometry (OFDR). The experimental study involves two fibers with significantly different levels of germanium doping: the standard single-mode fiber (SMF-28) and the ultra-high numerical aperture fiber (UHNA7). The research findings reveal distinct characteristics of reflected and scattered light amplitudes as a function of pulse energy. Although different amplitude changes are observed for the examined fibers, both can yield an enhancement of amplitude. The paper further investigates the effect of fiber Bragg grating inscription on the overall amplitude of reflected light. The insights gained from this study could be beneficial for controlling the enhancement of light scattering amplitude in fibers with low or high levels of germanium doping.

Contact Hole Shrinkage: Simulation Study of Resist Flow Process and Its Application to Block Copolymers.

For vertical interconnect access (VIA) in three-dimensional (3D) structure chips, including those with high bandwidth memory (HBM), shrinking contact holes (C/Hs) using the resist flow process (RFP) represents the most promising technology for low-k1 (where CD=k1λ/NA,CD is the critical dimension, λ is wavelength, and NA is the numerical aperture). This method offers a way to reduce dimensions without additional complex process steps and is independent of optical technologies. However, most empirical models are heuristic methods and use linear regression to predict the critical dimension of the reflowed structure but do not account for intermediate shapes. In this research, the resist flow process (RFP) was modeled using the evolution method, the finite-element method, machine learning, and deep learning under various reflow conditions to imitate experimental results. Deep learning and machine learning have proven to be useful for physical optimization problems without analytical solutions, particularly for regression and classification tasks. In this application, the self-assembly of cylinder-forming block copolymers (BCPs), confined in prepatterns of the resist reflow process (RFP) to produce small contact hole (C/H) dimensions, was described using the self-consistent field theory (SCFT). This research paves the way for the shrink modeling of the enhanced resist reflow process (RFP) for random contact holes (C/Hs) and the production of smaller contact holes.

Rapid aberration correction for diffractive X-ray optics by additive manufacturing: erratum

An erratum is presented to correct the stated numerical aperture of the employed multilayer Laue lenses in our previously published paper [Opt. Express 30, 31519 (2022)10.1364/OE.454863].

Applications of Lightsheet Fluorescence Microscopy by High Numerical Aperture Detection Lens.

This Review explores the evolution, improvements, and recent applications of Light Sheet Fluorescence Microscopy (LSFM) in biological research using a high numerical aperture detection objective (lens) for imaging subcellular structures. The Review begins with an overview of the development of LSFM, tracing its evolution from its inception to its current state and emphasizing key milestones and technological advancements over the years. Subsequently, we will discuss various improvements of LSFM techniques, covering advancements in hardware such as illumination strategies, optical designs, and sample preparation methods that have enhanced imaging capabilities and resolution. The advancements in data acquisition and processing are also included, which provides a brief overview of the recent development of artificial intelligence. Fluorescence probes that were commonly used in LSFM will be highlighted, together with some insights regarding the selection of potential probe candidates for future LSFM development. Furthermore, we also discuss recent advances in the application of LSFM with a focus on high numerical aperture detection objectives for various biological studies. For sample preparation techniques, there are discussions regarding fluorescence probe selection, tissue clearing protocols, and some insights into expansion microscopy. Integrated setups such as adaptive optics, single objective modification, and microfluidics will also be some of the key discussion points in this Review. We hope that this comprehensive Review will provide a holistic perspective on the historical development, technical enhancements, and cutting-edge applications of LSFM, showcasing its pivotal role and future potential in advancing biological research.

Early diagnosis of Chikungunya virus utilizing square core photonic crystal fiber (SC-PCF) with extremely high relative sensitivity

Chikungunya virus (CHIKV) poses a significant public health threat due to its capacity to cause widespread and debilitating outbreaks. The virus is responsible for CHIKV fever, a disease characterized by severe joint pain, sudden onset of fever, headache, muscle pain, and rash. The virus has been reported in various regions globally, with outbreaks occurring in parts of Africa, Asia, the Americas, and the Indian subcontinent. Consequently, the scientific community expends substantial efforts in developing dependable, rapid, highly sensitive, and cost-effective techniques in order to identify the CHIKV virus. In this study, an innovative biomedical sensor using photonic crystal fiber technology enables precise detection of the CHIKV virus through uric acid, normal and infected plasma, red blood cells, and platelets in the blood. The introduced sensor identifies those kinds with extremely increased relative sensitivity and minimal losses in contrast to alternative photonic crystal fiber-based biosensors. The introduced sensor showcases a minimal confinement loss of 2.25 × 10− 13 cm− 1, a relative sensitivity of 99.37%, an effective area of 1.36 × 105 µm2, with a minimal effective material loss of 0.001966 cm–1, a numerical aperture of 0.1874, and low dispersion of 0.06. Also, the demonstrated sensor is able to function within the terahertz spectrum, covering a substantial span from 0.8 to 2.6 THz. Furthermore, an extensive comparison analysis is performed between the showcased sensor and related literature on photonic crystal fibers to verify the reliability and effectiveness of the introduced structure.

Frequency selective illumination for high aperture coherence scanning interferometry

Abstract Coherence scanning interferometry is a widely used optical topography measurement technique, which can achieve axial resolutions in the sub-nanometer regime. Nevertheless, in the lateral dimension it is inherently diffraction limited and multiple problems arise when approaching this limit. Especially for challenging surface topographies like steep slopes or small grating periods measurement artifacts start to cause massive deviations in the 3D reconstruction of the surface due to the increased influence of noise on increasingly weak signals. In this study we present an illumination approach for Linnik-type CSI, which highlights oblique incident angles of the illuminating light cone in high numerical aperture (0.95) systems. It is demonstrated, that this approach can significantly improve the signal-to-noise ratio for measurements at steep surface slopes and therefore increase the subsequent surface reconstruction.

Generation of variable light fields by radially polarized chirped circular Airy vortex beams

Based on Richards-Wolf vector diffraction theory, the tight focusing properties of radially polarized chirped circular Airy vortex beams (RP-CCAVBs) are theoretically investigated using a high numerical aperture objective lens in the paper. The results shown that super-resolution scalable optical needles, dark channels, elliptical optical cages, and optical oscillations can be obtained by adjusting the scale factor, exponential attenuation coefficient, main ring radius, and topological charge of optical vortex in the incident RP-CCAVBs. The DOF of optical needle and dark channels is exponent dependent on scaling factor ω of RP-CCAVBs. And the position optical needle and dark channels can be moved by changing chirped parameter of RP-CCAVBs. The size of obtained optical cages can be adjusted by changing the radius of main rings in RP-CCAVBs. The intensity distribution of the obtained optical oscillations is intensely affected by parameter a and chirp parameter of RP-CCAVBs.

Deep-ultraviolet Fourier ptychography (DUV-FP) for label-free biochemical imaging via feature-domain optimization

We present deep-ultraviolet Fourier ptychography (DUV-FP) for high-resolution chemical imaging of biological specimens in their native state without exogenous stains. This approach uses a customized 265-nm DUV LED array for angle-varied illumination, leveraging the unique DUV absorption properties of biomolecules at this wavelength region. We implemented a robust feature-domain optimization framework to overcome common challenges in Fourier ptychographic reconstruction, including vignetting, pupil aberrations, stray light problems, intensity variations, and other systematic errors. By using a 0.12 numerical aperture low-resolution objective lens, our DUV-FP prototype can resolve the 345-nm linewidth on a resolution target, demonstrating at least a four-fold resolution gain compared to the captured raw images. Testing on various biospecimens demonstrates that DUV-FP significantly enhances absorption-based chemical contrast and reveals detailed structural and molecular information. To further address the limitations of conventional FP in quantitative phase imaging, we developed a spatially coded DUV-FP system. This platform enables true quantitative phase imaging of biospecimens with DUV light, overcoming the non-uniform phase response inherent in traditional microscopy techniques. The demonstrated advancements in high-resolution, label-free chemical imaging may accelerate developments in digital pathology, potentially enabling rapid, on-site analysis of biopsy samples in clinical settings.