Grating Lines Research Articles

Versatile Metamaterial: Exploring the Resonances of Symmetry‐Protected Modes for Multitasking Functionality

AbstractIn this work, an experimental study supported by numerical modeling that demonstrates the possibility of exciting Symmetry Protected‐Bound states In the Continuum (SP‐BICs) in a 1D silicon grating fabricated on a lithium niobate substrate is presented. bBoth transverse electric and magnetic polarization states are investigated, leading to the excitation of four quasi‐ Bound states In the Continuum (quasi‐BIC) resonances, exhibiting distinct behaviors. Under standard illumination conditions (plane of incidence perpendicular to the 1D grating lines), two of these resonances are highly sensitive to illumination conditions, while the other two resonances involving unconventional illumination directions (plane of incidence parallel to the grating lines) are more robust to the angle of incidence, but just as sensitive to external stresses in terms of resonance wavelength and quality factor. Additionally, temperature detection is experimentally demonstrated with a Sensitivity of ST = 0.81∼nm °C−1, a state‐of‐the‐art value achieved due to significant electromagnetic field enhancement inside the lithium niobate substrate at the quasi‐BIC resonance. These findings pave the way for their use in various sensing applications (such as biology, electromagnetic, and temperature sensing), as well as nonlinear applications like second harmonic generation, and electro‐ and acousto‐optic modulation.

Constant period line gratings as a metric for patterning fidelity in electron beam lithography

As smaller critical dimensions of devices fabricated via electron-beam lithography (EBL) are achieved over large areas, the need for new metrology techniques follows. Large (cm × cm) substrates have traditionally been both time and labor intensive to measure using traditional techniques such as scanning electron microscopy (SEM) or atomic force microscopy. When optimizing an EBL process over large areas, stitch error must be eliminated to maximize feature placement fidelity. Simultaneously, traditional EBL requirements, such as low line-edge roughness, proximity effect correction, and appropriate write times, must be maintained. With this plethora of requirements, we propose a technique to characterize placement errors over large areas using interferometric measurements. This method, when combined with traditional techniques like SEM and optical microscopy, assesses the full domain of potential errors over large areas in a time- and cost-efficient manner. As a proof of concept, a set of five small format (5 × 10 mm2) gratings with an 855 nm period were written twice, each set produced under two different tool error conditions. We report on the efficacy of interferometric metrology to accurately assess feature placement errors and report measured groove displacement across all ten gratings.

Flat‐Field Lens Grating Microspectrometer for Spectroscopic Multiplex Bioassay

AbstractSpectroscopic multiplex bioassay allows the rapid and simultaneous detection of various biomarkers in biomedical applications. The high cost and bulky configuration of conventional spectrometers hinder the decentralization of biomedical instruments for point‐of‐care diagnostics. Here a flat‐field lens grating‐based microspectrometer (FLG‐µSPEC) is reported for continuous detection of multi‐target nucleic acid amplification. FLG‐µSPEC features the vertical integration of microslit, integrated flat‐field lens and transmission grating (FLG), concave mirror, and CMOS line sensor. FLG effectively corrects the field curvature by flattening the focal plane of dispersed wavelengths and also facilitates compact module packaging. FLG‐µSPEC module is precisely assembled into a dimension of 10 mm × 16 mm × 10 mm. The average spectral resolution exhibits 3.4 ± 0.9 nm over an operating range of 500 to 950 nm. A spectral detection system utilizing FLG‐µSPEC demonstrates the amplification of lambda DNA (𝜆‐DNA) for each target, exhibiting a high correlation with the obtained result from a conventional real‐time PCR (qPCR) machine. Furthermore, multiplex qPCR analysis using FLG‐µSPEC and spectral deconvolution successfully demonstrates simultaneous and accurate quantification of three different targets. The FLG‐µSPEC module offers diverse on‐demand analytical applications, including not only multiplex bioassay but also environmental monitoring.

Liquid microlens compound structure for enhanced sub-micron resolution imaging and accelerated reconfigurable deformation manipulation

The optical observation of sub-micron structures encounters significant challenges due to the inadequate spatial shape matching of optical devices and the limitations imposed by diffraction. These factors result in suboptimal imaging resolution and the introduction of defocus distortion. One approach to mitigating these limitations involves utilizing a liquid microlens (LML) assisted microscope, which offers real-time and localized control capabilities. However, the dynamic tuning of LML is subject to volatility and instability, adversely affecting sub-micron resolution imaging. To address this issue, a contour-following coating inspired by the natural cornea is applied to the droplet's surface, resulting in the formation of liquid microlens compound structures (LMLCS). Firstly, photoresist microholes are fabricated on the optical disc. Then, liquid self-assembly technology is used to fill glycerol in the microholes. At last, a conformal spreading method of UV-curable adhesive precursor film is developed to ensure the combination of the microlens bilayer structure. Through the application of optical information transmission theory, finite difference time domain (FDTD) method, and the principle of Abbe microscopic imaging, the imaging magnification process and sub-micron resolution characteristic of the LMLCS are revealed. Remarkably, the obtained focal width at half maximum (FWHM) of 1.54 μm is smaller than the theoretical value, enabling reconfigurable sub-micron resolution observation and 1.63 times imaging magnification of 226 nm grating lines under the optical microscope. Compared with unencapsulated LML, this compound structure exhibits better sub-micron resolution capability, greater imaging magnification, and faster adaptive dynamic response characteristics. Consequently, the LMLCS introduces exciting prospects for exploring optical sub-micron measurement and sensing devices with exceptional performance.

Versatile femtosecond laser interference patterning applied to high-precision nanostructuring of silicon

We present a high-precision nanostructuring technique based on beam interference from a commercial Ti:Sa femtosecond amplified laser (800 nm, 120 fs, 1 kHz, 1 mJ). Its potential and versatility is illustrated by applying the technique to the nanostructuring of silicon. Employing commercial and ad-hoc laser-fabricated diffractive optical elements together with standard optical components, periodic line gratings and spot arrays with tunable periods down to 650 nm can readily be fabricated. Moreover, fabrication of millimeter-size diffraction gratings via multipulse irradiation at processing speeds up to 0.5 mm/s is demonstrated. The variety of structures written in crystalline silicon feature amorphous fringes and dots with widths down to 300 nm. The corresponding complex topography profiles consist of surface elevations and depressions with sizes down to 120 nm that can be controlled by the laser fluence and fringe width, demonstrating the presence of several competing matter reorganization processes in the molten phase. The exceptional high-contrast ratio of the fringe intensity together with a near-Gaussian intensity envelope of the laser spot enable patterning with well-defined local fluences, paving the way for single-pulse fluence-dependent studies. The high-quality experimental data that can be obtained with this technique can prove critical for modelling attempts aimed at unravelling the underlying formation mechanisms of complex surface topographies in a wide range of materials. Furthermore, the technique presented here has outstanding potential for the rapid and versatile fabrication of high-precision metasurfaces.

Linewidth characterization of a self-traceable grating by SEM

To achieve high-precision nanometrology, a self-traceable grating reference material has been reported and prepared using atom lithography and soft x-ray interference techniques (Liu et al 2021 Nanotechnology 32 175 301). In this work, we employ a Monte Carlo simulation method to investigate the scanning electron microscopy (SEM) image contrast and linewidth characterization of the grating linewidth. The 3D structure of mushroom-shaped grating lines made of multilayers (Pt, SiO2 and Si) is modeled according to transmission electron microscopy (TEM) images, enabling the SEM linescan profiles of secondary electron signals to be obtained for different values of structural linewidth parameters from Monte Carlo simulations. Using the principle of the model-based library method, a model database of Monte Carlo-simulated SEM linescan profiles is thus constructed by varying the incident electron beam conditions and the grating linewidths; then, the grating linewidth is successfully characterized using experimental SEM images. The comparison with the TEM measurement reveals that the measurement accuracy is verified to within 0.3% for the linewidth of ∼25 nm.

Fabrication of slanted gratings by using glancing angle deposition

Slanted gratings, commonly used for manipulating light in various applications, are typically fabricated using conventional top-down methods. However, these methods have limitations on material choice. This paper explores the use of glancing angle deposition (GLAD) to fabricate slanted gratings with various materials and slant angles on silicon (Si) and quartz (SiO2) substrates. The process involves the first step of creating a template using electron beam lithography, lift-off, and dry etching, and the second step of electron beam evaporation at a glancing angle on the prefabricated template. The template consists of grating structures with very shallow trenches. Different materials, such as chromium (Cr), copper (Cu), aluminum oxide (Al2O3), and titanium oxide (TiO2), were used in the GLAD process to create slanted grating structures on Si or SiO2 substrates, showcasing their versatility. Here, the formation of the slanted grating is due to the shadowing effect that leads to deposition onto the protruded grating lines but not into the trench. Using TiO2 as the source material, the GLAD technique can produce slanted gratings with various angles by adjusting the deposition angle. The optical characteristics of the slanted grating prepared using GLAD were verified through simulations with COMSOL software, confirming its excellent light guide performance.

Single-Grating Monolithic Spatial Heterodyne Raman Spectrometer: An Investigation on the Effects of Detector Selection.

Spatial heterodyne Raman spectrometers (SHRSs) are modified forms of Michelson interferometers, except the mirrors in a Michelson interferometer are replaced with stationary diffraction gratings. This design removes the need for an entrance slit, as is the case in a dispersive spectrometer, and removes the need to scan the spectrum by using a moving mirror in a modern Michelson interferometer. In previous studies, various SHRS variants, such as free-standing two-grating SHRS, single-grating SHRS (1g-SHRS), monolithic SHRS (mSHRS), and single-grating mSHRS (1g-mSHRS), have been evaluated. However, the present study exclusively focuses on the 1g-mSHRS configuration. The 1g-mSHRS and 1g-SHRS increase the spectral range at fixed grating line density while trading off spectral resolution and resolving power. The mSHRS benefits from increased rigidity, lack of moving parts, and reduced footprint. In this study, we investigate how the choice of detector impacts the performance of the 1g-mSHRS system, with a specific focus on evaluating the performance of three types of cameras: charged-coupled device (CCD), intensified CCD (ICCD), and complementary metal-oxide-semiconductor (CMOS) cameras. These systems were evaluated using geological, organic, and inorganic samples using a 532 nm continuous wave laser for the CMOS and CCD cameras, and a 532 nm neodymium-doped yttrium aluminum garnet pulsed laser for the ICCD camera. The footprint of the 1g-mSHRS was 3.5 × 3.5 × 2.5 cm3 with a mass of 272 g or 80 g, depending on whether the monolith housing is included or not. We found that increasing the number of pixels utilized along the x-axis of the camera increases fringe visibility (FV) and optimizes the resolution (by capturing the entirety of the grating and magnifying the fringes). The number of pixels utilized in the y-axis, chip size, and dimensions, affect the signal-to-noise ratio of the systems. Additionally, we discuss the effect of pixel pitch on the recovery of Fizeau fringes, including the relationship between the Nyquist frequency, aliasing, and FV.

Robust multisensory deviance detection in the mouse parietal associative area

Context modulates how information is processed in the mammalian brain. For example, brain responses are amplified to contextually unusual stimuli. This phenomenon, known as "deviance detection,"1,2 is well documented in early, primary sensory cortex, where large responses are generated to simple stimuli that deviate from their context in low-order properties, such as line orientation, size, or pitch.2,3,4,5 However, the extent to which neural deviance detection manifests (1) in broader cortical networks and (2) to simple versus complex stimuli, which deviate only in their higher-order, multisensory properties, is not known. Consistent with a predictive processing framework,6,7 we hypothesized that deviance detection manifests in a hierarchical manner across cortical networks,8,9 emerging later and further downstream when stimulus deviance is complex. To test this, we examined brain responses of awake mice to simple unisensory deviants (e.g., visual line gratings, deviating from context in their orientation alone) versus complex multisensory deviants (i.e., audiovisual pairs, deviating from context only in their audiovisual pairing but not visual or auditory content alone). We find that mouse parietal associative area-a higher cortical region-displays robust multisensory deviance detection. In contrast, primary visual cortex exhibits strong unisensory visual deviance detection but weaker multisensory deviance detection. These results suggest that deviance detection signals in the cortex may be conceptualized as "prediction errors," which are primarily fed forward-or downstream-in cortical networks.6,7.

Impact study of numerical discretization accuracy on parameter reconstructions and model parameter distributions

In optical nano metrology numerical models are used widely for parameter reconstructions. Using the Bayesian target vector optimization method we fit a finite element numerical model to a Grazing Incidence x-ray fluorescence data set in order to obtain the geometrical parameters of a nano structured line grating. Gaussian process, stochastic machine learning surrogate models, were trained during the reconstruction and afterwards sampled with a Markov chain Monte Carlo sampler to determine the distribution of the reconstructed model parameters. The numerical discretization parameters of the used finite element model impact the numerical discretization error of the forward model. We investigated the impact of the polynomial order of the finite element ansatz functions on the reconstructed parameters as well as on the model parameter distributions. We showed that such a convergence study allows to determine numerical parameters which allows for efficient and accurate reconstruction results.

Influence of fluorescent dopants on the vat photopolymerization of acrylate-based plastic scintillators for application in neutron/gamma pulse shape discrimination.

Plastic scintillators, a class of solid-state materials used for radiation detection, were additively manufactured with vat photopolymerization. The photopolymer resins consisted of a primary dopant and a secondary dopant dissolved in a bisphenol A ethoxylate diacrylate-based matrix. The absorptive dopants significantly influence important print parameters, for example, secondary dopants decrease the light penetration depth by a factor > 12 ×. The primary dopant 2,5-diphenyloxazole had minimal impact on the printing process even when loaded at 25 % by mass of the resin. Working curve measurements, which relate energy dose to cure depth, were performed as a function of feature size to further assess the influence of dopants. Photopatterns smaller than 150 μm width had apparent increases in critical energy dose compared to larger photopatterns, while all resins maintained printed features in line gratings with 50 μm of separation. Printed scintillator monoliths were compared to scintillators cast by traditional molding, demonstrating that the layer-by-layer printing process does not decrease scintillation response. A maximum light output of 31 % of a benchmark plastic scintillator (EJ-200) and successful pulse shape discrimination were achieved with 20 % by mass 2,5-diphenyloxazole as the primary dopant and 0.1 % by mass 9,9-dimethyl-2,7-distyrylfluorene as the secondary dopant in printed scintillator samples.

Reconstruction of the in-depth profile of line gratings with critical dimension grazing incidence small angle x-ray scattering on laboratory equipment

We present a reconstruction of the in-depth profile of line gratings using critical-dimension grazing incidence small angle x-ray scattering with a compact Cu-Kα x-ray source mounted on a laboratory small angle x-ray scattering (SAXS). By taking advantage of the grazing-incidence configuration and with a rotation of the gratings under the x-ray beam, several orders of the Bragg rods were probed and led to the extraction of the in-depth profile of the lines. The extracted in-depth profile is compared with 3D atomic force microscopy results. The methodology developed mimics the one of critical dimension SAXS measurements, in transmission, to enable future comparison between the two approaches as well as building complementary modeling. These results open new perspectives for in-line x-ray metrology since the Cu-Kα x-ray source is widely spread and used by the x-ray community.

Enabling High Precision Gradient Index Control in Subsurface Multiphoton Lithography.

Multiphoton lithography inside a mesoporous host can create optical components with continuously tunable refractive indices in three-dimensional (3D) space. However, the process is very sensitive at exposure doses near the photoresist threshold, leading previous work to reliably achieve only a fraction of the available refractive index range for a given material system. Here, we present a method for greatly enhancing the uniformity of the subsurface micro-optics, increasing the reliable index range from 0.12 (in prior work) to 0.37 and decreasing the standard deviation (SD) at threshold from 0.13 to 0.0021. Three modifications to the previous method enable higher uniformity in all three spatial dimensions: (1) calibrating the planar write field of mirror galvanometers using a spatially varying optical transmission function which corrects for large-scale optical aberrations; (2) periodically relocating the piezoelectrically driven stage, termed piezo-galvo dithering, to reduce small-scale errors in writing; and (3) enforcing a constant time between each lateral cross section to reduce variation across all writing depths. With this new method, accurate fabrication of optics of any index between n = 1.20 and 1.57 (SD < 0.012 across the full range) was achieved inside a volume of porous silica. We demonstrate the importance of this increased accuracy and precision by fabricating and characterizing calibrated two-dimensional (2D) line gratings and flat gradient index lenses with significantly better performance than the corresponding control devices. As a visual representation, the University of Illinois logo made with 2D line gratings shows significant improvement in its color uniformity across its width.

Challenging deep learning models with image distortion based on the abutting grating illusion

Even state-of-the-art deep learning models lack fundamental abilities compared with humans. While many image distortions have been proposed to compare deep learning with humans, they depend on mathematical transformations instead of human cognitive functions. Here, we propose an image distortion based on the abutting grating illusion, which is a phenomenon discovered in humans and animals. The distortion generates illusory contour perception using line gratings abutting each other. We applied the method to MNIST, high-resolution MNIST, and "16-class-ImageNet" silhouettes. Many models, including models trained from scratch and 109 models pretrained with ImageNet or various data augmentation techniques, were tested. Our results show that abutting grating distortion is challenging even for state-of-the-art deep learning models. We discovered that DeepAugment models outperformed other pretrained models. Visualization of early layers indicates that better-performing models exhibit the endstopping property, which is consistent with neuroscience discoveries. Twenty-four human subjects classified distorted samples to validate the distortion.

General mathematical model for the period chirp in interference lithography.

We present a general analytical model for the calculation of the spatial distribution of the grating period, enabling the unification of all configurations of classical laser interference lithography (LIL) and scanning-beam interference lithography (SBIL) into one formalism. This is possible due to the consideration of Gaussian beams instead of point sources which allow for the accurate description of not only the laser's far-field but also its near-field. The proposed model enables the calculation of the grating period, the inclination and the slant of the grating lines on arbitrarily shaped substrates, originating from the interference of arbitrarily orientated and positioned Gaussian beams.

Monitoring sidewall tilting of pixelated nanogratings in 3D display.

Sidewall tilting is an important parameter to describe the grating morphology and would affect the diffraction efficiency of three-dimensional (3D) display devices based on pixelated nanogratings. However, there is currently a lack of a non-destructive measurement method that can accurately measure the sidewall tilting of the pixelated nanogratings. This is mainly because the kind of nanograting is manufactured in a micron-scale pixel region and the grating lines generally have various directions to ensure that the display device can display images smoothly. In this work, we propose to use a home-made imaging Mueller matrix ellipsometer (IMME) to monitor sidewall tilting of pixelated nanogratings. Simulation and experiments were carried out to characterize the sidewall tilting angle. Through the combination of Mueller matrix elements, we can quickly and qualitatively identify the tilting angle for the purpose of on-line quality monitoring of the device. Through the inverse calculation of the Mueller matrix, we can accurately and quantitatively obtain the value of the tilting, so as to meet the demands of the device design. It is expected the proposed method can provide guidance for the identification and detection of tilting in 3D display elements based on pixelated gratings.

Slope error correction on X-ray reflection gratings by a variation of the local line density.

The patterning of x-ray grating surfaces by electron-beam lithography offers large flexibility to realize complex optical functionalities. Here, we report on a proof-of-principle experiment to demonstrate the correction of slope errors of the substrates by modulating the local density of the grating lines. A surface error map of a test substrate was determined by optical metrology and served as the basis for an aligned exposure of a corrected grating pattern made by electron-beam lithography. The correction is done by a variation of the local line density in order to compensate for the local surface error. Measurements with synchrotron radiation and simulations in the soft X-ray range confirm that the effects of slope errors were strongly reduced over an extended wavelength range.

Soft Contact Lens With Embedded Moiré Patterns-Based Intraocular Pressure Sensors

Soft contact lenses with built-in sensors have shown great potential for real-time monitoring of intraocular pressure (IOP). This paper reports a contact lens IOP sensor based on the moiré patterns. One concentric ring grating (G1) is fabricated on a commercial contact lens, the other line grating (G2) is stored in a computer. Images of G1 are captured using a smartphone camera. Then moiré patterns are generated by superimposing the images of the two gratings in a computer. The central angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> formed between two innermost adjacent moiré patterns is extracted as the IOP transducing signals. The performance of the sensor has been evaluated using a home-made hollow hemispherical silicone model eye. The sensitivity of the contact lens IOP sensor is ~0.15°/mmHg with high repeatability. Additionally, the sensor sensitivity is essentially independent of the initial IOP exerted on the contact lens. Furthermore, the virtual G2 provides great flexibility for the design and fabrication of the sensor, the fabrication of G1 directly on commercial contact lenses paves the way for clinic use. All these results indicate the suitability of this type of sensor for monitoring IOP. [2022-0111]

Fabrication of ultra-high aspect ratio silicon grating using an alignment method based on a scanning beam interference lithography system.

The high-aspect-ratio silicon grating (HARSG) is an important X-ray optical device that is widely used in X-ray imaging and spectrum detection systems. In this paper, we propose a high-precision alignment method based on the scanning beam interference lithography (SBIL) system to realize precise alignment between the <111> orientation on the (110) wafer plane and the grating lines direction, which is an essential step in HARSG manufacture to obtain the high-aspect-ratio grating structure. After the location of the <111> orientation through fan-shaped mask etching and reference grating fabrication, a two-step method that combines static preliminary alignment and dynamic precision alignment is used to align the reference grating lines direction with the interference field fringes of the SBIL system through the interference of the diffracted light from the reference grating near the normal direction, which can realize a minimal alignment error of 0.001°. Through the overall alignment process, HARSGs with groove densities of 500 gr/mm, 1800 gr/mm, and 3600 gr/mm were fabricated through anisotropic wet etching in KOH solution, producing ultra-high aspect ratios and etch rate ratios greater than 200.

Design of Compact Mid-Infrared Cooled Echelle Spectrometer Based on Toroidal Uniform-Line-Spaced (TULS) Grating.

A traditional flat-panel spectrometer does not allow high-resolution observation and miniaturization simultaneously. In this study, a compact, high-resolution cross-dispersion spectrometer was designed based on the theoretical basis of echelle grating for recording an infrared spectrum. To meet the high-resolution observation and miniaturization design requirements, a reflective immersion grating was used as the primary spectroscopic device. To compress the beam aperture of the imaging system, the order-separation device of the spectrometer adopted toroidal uniform line grating, which had both imaging and dispersion functions in the spectrometer. The aberration balance condition of the toroidal uniform line grating was analyzed based on the optical path difference function of the concave grating, and dispersion characteristics of the immersed grating and thermal design of the infrared lens were discussed based on the echelle grating. An immersion echelle spectrometer optical system consisting of a culmination system, an immersed echelle grating, and a converged system was used. The spectrometer was based on the asymmetrical Czerny-Turner and Littrow mount designs, and it was equipped with a 320 × 256 pixel detector array. The designed wavelength range was 3.7–4.8 μm, the F-number was 4, and the central wavelength resolution was approximately 30,000. An infrared cooling detector was used. The design results showed that, in the operating band range, the root implied that the square diameter of the spectrometer spot diagram was less than 30 μm, the energy was concentrated in a pixel size range, and the spectrometer system design met the requirements.