Two-dimensional Gratings Research Articles

Phase-transition metamaterial smart window for radiative cooling and privacy protection

This paper proposes a smart window for radiative cooling with adjustable transparency by leveraging the phase transition property of VO2. The proposed smart window exhibits daytime visible light transmission and near-infrared light reflection, all-day radiative cooling, and a nighttime privacy protection feature. It comprises a bottom layer of VO2/Ag/VO2 and top cubic two-dimensional SiO2 gratings, with structural parameters optimized by the genetic algorithm to ensure excellent optical performance. In the daytime, 75.4% visible light transmittance and 87.8% near-infrared reflectance can be achieved by utilizing the dielectric state of VO2. It also achieves low light transmission of 9.8% by using the metallic state of VO2, which is suitable for nighttime privacy protection. Furthermore, it has an all-day outside emissivity of 98.2% for radiative cooling, together with a low inside emissivity of 1.9% for effectively inhibiting the radiation heat transfer. In addition, the proposed structure is insensitive to the angles of incidence and the polarization of light, making it advantageous for radiative cooling. During the daytime, it reduces the temperature by 17.7 K compared to a glass of equal thickness when the non-radiative heat coefficient is 12 W/m2/K. At night, it achieves a cooling power of 124.7 W/m2, achieving a cooling effect of 8.9 K below ambient temperature. The proposed smart window is promising for various application scenarios for radiative cooling and privacy protection and could be used as windows for buildings and vehicles.

Self-traceable angle standards with simplified traceability chain for dimensional metrology

Abstract Traceability is a fundamental issue for ensuring accuracy of nanometrology. A shortened traceability chain is advantageous for reducing calibration steps, thus reducing errors and raising application efficiency. A novel kind of two-dimensional grating is manufactured by atom lithography, whose pitch and (orthogonal) angle values are directly determined by natural constants, offering a feasible approach for effectively shortening the traceability chain. The PTB’s calibration results show that the two-dimensional grating has excellent orthogonality with a deviation of only 0.001°. Application of the two-dimensional grating is demonstrated for the characterization of the angular distortion of a SEM, showing its great application potential.

A Review: Laser Interference Lithography for Diffraction Gratings and Their Applications in Encoders and Spectrometers

The unique diffractive properties of gratings have made them essential in a wide range of applications, including spectral analysis, precision measurement, optical data storage, laser technology, and biomedical imaging. With advancements in micro- and nanotechnologies, the demand for more precise and efficient grating fabrication has increased. This review discusses the latest advancements in grating manufacturing techniques, particularly highlighting laser interference lithography, which excels in sub-beam generation through wavefront and amplitude division. Techniques such as Lloyd’s mirror configurations produce stable interference fringe fields for grating patterning in a single exposure. Orthogonal and non-orthogonal, two-axis Lloyd’s mirror interferometers have advanced the fabrication of two-dimensional gratings and large-area gratings, respectively, while laser interference combined with concave lenses enables the creation of concave gratings. Grating interferometry, utilizing optical interference principles, allows for highly precise measurements of minute displacements at the nanometer to sub-nanometer scale. This review also examines the application of grating interferometry in high-precision, absolute, and multi-degree-of-freedom measurement systems. Progress in grating fabrication has significantly advanced spectrometer technology, with integrated structures such as concave gratings, Fresnel gratings, and grating–microlens arrays driving the miniaturization of spectrometers and expanding their use in compact analytical instruments.

Two-dimensional optical micro displacement sensing and crosstalk elimination based on the self-imaging effect of a grating pair

This paper proposes a straightforward method for measuring micro-displacement synchronously along two orthogonal axes. A single structure consists of a pair of two-dimensional gratings and a quadrant detector aligned with a collimated laser is used to detect the micro-displacement. The crosstalk and the common-mode noise are eliminated through a two-step differential process. Experimental results demonstrate that the displacement measurement resolution can reach 40 nm with a sensitivity of 0.483 V/µm within the linear range. The accuracy obtained is 0.29% on the X-axis and 0.31% on the Y-axis within a 500 µm range. The signal-to-noise ratio is improved by 4.56 dB after differential. The simplicity and high compactness of this measurement structure make it suitable for fabrication and alignment using microfabrication processes, which show great potential in many applications such as gyroscopes, accelerators, and multi-dimensional displacement measurements.

Snapshot computed tomographic microscopic imaging spectrometer and its video-level tracking of poisonous Microcystis aeruginosa cells in mixed algae

Conventional microscopic spectral imaging suffers from extended scanning times across wavelength or spatial dimension. To improve capabilities of dynamic microscopic spectral imaging, we developed a snapshot computed tomographic microscopic imaging spectrometer (CTMIS) based on the zeroth and first orders dispersive diffraction of a two-dimensional grating. Utilizing the CTMIS-UNET reconstruction algorithm, we can reconstruct a spectral cube (541x541x26) for each frame of micro spectral imaging video. Experimental results demonstrate a sub-4 μm spatial resolution achievable through a 20x objective lens and a spectral resolution better than 10 nm among 450–700 nm, while maintaining spectral cosine similarities exceeding 0.9989 when comparing reconstructed spectra with ground truth data. Spectral imaging videos of four species of algae and mixed algae were captured under 10 ms exposure time using the CTMIS system. Leveraging the self-developed UNET-SI26 algae recognition network, precise identification and tracking of four types of algae and poisonous microcysts aeruginosa in mixed algae were conducted. The pixel-level recognition accuracy exceeds 95 %, while the accuracy for counting the numbers of different types of cells surpasses 85 %, offering an efficient and accurate spectral imaging method for real-time monitoring and early warning of harmful algae at the cellular level.

Focused microstructure analysis and fabrication for monolithic integration with high-speed MUTC photodiode

Back-incidence high-speed photodiodes with small mesa diameter use back-integrated microstructures, which utilize the convergence and high transmittance function of the microstructures on the light beam to compensate for the incident light alignment deviation and improve the optical coupling efficiency. Two kinds of microstructures integrated with the modified uni-traveling-carrier photodiode (MUTC-PD), microlens and two-dimensional concentric annular convergence grating, are designed theoretically and compared by simulation. It is found that the microlens have better optical performance when integrated. InP microlenses meeting the requirements were fabricated using the photoresist hot melt method and inductively coupled plasma (ICP) etching. Testing revealed that the microlens could reduce the incident light spot size to one-third of its original size. By optimizing the thickness and doping concentration of the PD layer structure, and prepared a high-speed MUTC-PD with monolithic integrated InP microlens, with a mesa diameter of 18 μm. The measured 3 dB bandwidth of the integrated chip is 43 GHz. Experimental results using incident light fiber movement showed that the responsivity of the integrated microlens MUTC-PD increased by 66.76 % when horizontally offset by 10 μm compared to the non-integrated microlens case. When shifted vertically by 20 μm, the MUTC-PD responsivity of the integrated microlens decreases to 83.7 % of the maximum value, which is 18.2 % higher than that of the one without integrated microlens.

Phase and contrast moiré signatures in two-dimensional cone beam interferometry

Neutron interferometry has played a distinctive role in fundamental science and characterization of materials. Moiré neutron interferometers are candidate next-generation instruments: they offer microscopy-like magnification of the signal, enabling direct camera recording of interference patterns across the full neutron wavelength spectrum. Here we demonstrate the extension of phase-grating moiré interferometry to two-dimensional geometries. Our fork-dislocation phase gratings reveal phase singularities in the moiré pattern, and we explore orthogonal moiré patterns with two-dimensional phase gratings. Our measurements of phase topologies and gravitationally induced phase shifts are in good agreement with theory. These techniques can be implemented in existing neutron instruments to advance interferometric analyses of emerging materials and precision measurements of fundamental constants. Published by the American Physical Society 2024

Polynomial modal method for crossed slanted gratings

Slanted gratings have emerged as a promising area of research due to their distinct properties, such as polarization control, beam steering, and enhanced interactions between light and matter. However, accurately and efficiently modeling these structures, particularly in the case of two-dimensional (2D) slanted gratings, has proven to be challenging. Traditional methods like the Fourier modal method (FMM or RCWA) and finite difference time domain (FDTD) are commonly used but involve approximations of the geometry to accommodate the slant effect. In this study, we address these challenges by employing the polynomial modal method (PMM) for 2D slanted gratings, which, to our knowledge, is a novel approach not previously explored for this type of grating. We introduce a 2D slanted coordinate system to rigorously handle the grating profile. For 2D slanted gratings, the PMM offers several advantages over the FMM, as it overcomes limitations associated with factorization rules and/or staircase approximation of the profile.

Staring laser situation awareness technology with wide-FOV and high-angle positioning accuracy based on two-dimensional grating and two-channels

Current and future battlefields face the emerging threat of laser weapon development. Existing laser situation awareness technology cannot provide simultaneous operation of wide field-of-view (FOV) and high angle positioning accuracy. This study introduces a system employing a two-dimensional grating and dual-channel approach that offers high precision in situation awareness about laser wavelengths and angle positioning across a wide FOV. The system consists of two main components: an approximate measurement channel and an accurate measurement channel. The former includes a wide-FOV lens and a focal plane array detector (FPA1), acquiring preliminary angle information of the laser. The latter, comprising a two-dimensional grating, a narrow-FOV lens, and a FPA2, captures the incoming laser’s wavelength and precise azimuth and pitch through the analysis of diffraction spot position and distance. Experimental findings confirm that the accuracies of angle and central wavelength measurements exceed 0.05° and 8 nm, respectively, for a FOV of 120°.

Research on Diffraction Patterns of Smartphone Screens

Smartphone screen is composed of pixels which are not of uniform size and arranged evenly. When illuminated by a laser, the reflected beam diffracts, producing a diffraction pattern with structure of mesh shape that exhibits characteristics similar to a two-dimensional reflection grating.In this paper, the general diffraction formula of a two-dimensional non-uniform grating is derived, while a simplified form in a special case is explored. The influence of laser incidence angle on the diffraction pattern is analyzed. The diffraction patterns by formula calculation and Fourier transform are obtained using MATLAB simulation. The rationality of the derived formula is verified through simulation and experiments. Also, the pixel density of the smartphone screen is calculated based on the diffraction pattern obtained from the experiment. The application scenarios of the research results are proposed.Comparing the discrepancy in diffraction patterns of different types of screens whose arrangements of sub pixels in smartphones are also different, the mechanism of grating diffraction is displayed directly. Theoretical calculations, simulations and experiments are applied for comparing and confirming each other.

High-efficiency polarization-selective two-dimensional diffraction gratings based on silver cuboid arrays

A two-dimensional (2D) diffraction grating based on silver cuboid arrays is demonstrated. With the structural optimization by three-dimensional (3D) finite-difference time-domain method, the proposed grating exhibits favorable polarization selectivity. At wavelength 1550 nm, high diffraction efficiency and polarization correlation can be realized in the case of two-port output ((0, ±1) or (±1, 0)) under TE polarization, as well as five-port output ((0, 0), (0, ±1) and (±1, 0)) under TM polarization. Under the two-port output state, the diffraction efficiency is nearly 48% with the extinction ratio of 16.44 dB and insertion loss of 0.20 dB. Under the five-port output status, the efficiency is larger than 19% for each diffraction order, meanwhile, the total efficiency and uniformity are 97% and 0.58%, respectively. The proposed grating with positive implications has good potentials in polarization multiplexing and polarization-correlated grating interferometry.

Analysis of two-dimensional planar gratings and metasurfaces in the quasi-static approximation

Currently, composite materials based on metal gratings with a period D much smaller than the wavelength l are widely used. With the use of such materials, it is possible to control the amplitude, phase and polarization of an electromagnetic wave, which opens wide possibilities for the creation of new types of antennas, radio-absorbing coatings, etc. This paper considers gratings of metallic strip or patches on the surface of a thin metal-backed dielectric slab to control the phase of the reflected wave. In the quasi-static approximation, the input impedance of such materials can be calculated using simple analytical formulas. This paper investigates the accuracy of the quasi-static approximation at different angles of incidence of the electromagnetic wave on two-dimensional gratings. Using the equivalent circuits method, analytical expressions for the input impedance of metasurfaces are obtained. The dispersion properties of composite materials “inductive or capacitive grating on the surface of a thin metal-backed dielectric slab” are investigated, and a technique for determining the resonant frequency, which corresponds to the maximum of the input impedance of the metasurface, is presented. The obtained results show that at any angle of incidence, it is possible to evaluate the condition of the quasi-static approximation applicability for two-dimensional gratings and for metasurfaces based on such gratings. If this condition is satisfied, that simple analytical expressions can be used to calculate the input impedance. The use of these expressions allows us to determine the frequency at which the input impedance reaches its maximum. It is established that for inductive and capacitive gratings the impedance boundary condition of M.A. Leontovich is equivalent to the averaged boundary condition of M.I. Kontorovich. It is obtained that for grating in free space, quasi-static approximation corresponds to the M.A. Leontovich impedance condition. The dispersion properties of composite materials “inductive or capacitive grating on a thin metal-backed dielectric slab” are investigated. It is shown that the phase transition of the reflection coefficient through zero occurs at maximum values of the input impedance. Using the considered method of equivalent circuits, the presented results can be easily generalized to any type of multilayer metasurfaces.

Angular dispersion and diffraction imaging analysis in a light wave oblique incident two-dimensional crossed grating

Based on the vector diffraction theory, the angular dispersion and diffraction imaging are analyzed in parallel light oblique incident two-dimensional crossed gratings. The results show that the angular dispersion presents a kind of increase-decrease-increase oscillatory change, and the maximum value of diffractive polar angle dispersion and total dispersion present an abrupt point. The angular dispersion is limited by the light wave incidence angle and two-dimensional gratings crossed angle. In addition, some obvious pincushion distortion has been formed in some cases. The angular dispersion increases with the increase of grating crossed angle in the permissible range, leading to enhancement of the diffraction imaging distortion. The results imply that there is an inherent relationship between the angular dispersion and the diffraction imaging in parallel light oblique incident crossed gratings.

Design and fabrication of two-dimensional holographic grating waveguide with large field of view and high uniformity

Augmented Reality (AR) technology is a technique that integrates virtual im- ages with the real environment. With the continuous improvement of comput- ing power in mobile electronic products, mobile devices with AR capabilities are gradually becoming the next generation computing platform. When eval- uating the performance of holographic waveguides, key indicators include the field of view (FOV), eye relief, and eye box uniformity. This study proposes a method for designing holographic waveguides with a large field of view and high uniformity based on a two-dimensional holographic grating (2DHG). By lever- aging the multiplexing characteristics of photopolymer, we superimposed two incoherent one-dimensional gratings on a holographic material layer, achieving dual-channel propagation of the field of view, with each channel responsible for half of the FOV. In the end, these two channels are stitched together to form a complete FOV. This method not only enlarges the eye box but also helps im- prove the system's FOV. By controlling the transmittance of the exposure area, the uniformity of the brightness of the wide-field eye box is improved. Finally, we conducted a performance analysis of the prepared holographic waveguide, verifying the feasibility and correctness of the proposed 2DHG waveguide in two-dimensional eye box expansion and field of view extension. Through eye box expansion, the eye box reached 14 mm × 17 mm, the diagonal field of view reached 58◦, the eye relief is 15 mm, and the eye box brightness uniformity reached 79.7 %.

Isospectral open cavities and gratings

Open cavities are often an essential component in the design of ultra-thin subwavelength metasurfaces and a typical requirement is that cavities have precise, often low frequency, resonances while simultaneously being physically compact. To aid this design challenge, we develop a methodology to allow isospectral twinning of reference cavities with either smaller or larger ones, enforcing their spectra to coincide so that open resonators are identical in terms of their complex eigenfrequencies. For open systems, the spectrum is not purely discrete and real, and we pay special attention to the accurate twinning of leaky modes associated with complex-valued eigenfrequencies with an imaginary part orders of magnitude lower than the real part. We further consider twinning of two-dimensional gratings, and model these with Floquet–Bloch conditions along one direction and perfectly matched layers in the other one; complex eigenfrequencies of special interest are located in the vicinity of the positive real line and further depend upon the Bloch wavenumber. The isospectral behaviour is illustrated, and quantified, throughout by numerical simulation using finite-element analysis.

Dual-wavelength terahertz two-dimensional phase gratings based on all dielectric metasurfaces

Efficient and accurate phase gratings hold immense significance in the realization of large format heterodyne array receivers at terahertz frequencies. Metallic phase gratings have made substantial advancements in terms of operating wavelength and the number of diffraction beams. Like most other diffractive optical devices, metallic phase gratings are primarily optimized to operate at one specific wavelength. Metasurfaces compositing arrays of subwavelength nanostructures have been demonstrated with various optical functions, by freely modifying the polarization, phase, and amplitude of light. In this study, we present an approach to create a multi-wavelength phase grating compositing segments that incorporate multiple nanostructures. The resulting transmission phase grating not only exhibits uniform diffraction beams (2 × 2) but also achieves the same diffraction angles at both 1.31 and 2.7 THz. The measured total power efficiency of the diffraction beam pattern is 53.2% for 1.31 THz and 42.4% for 2.7 THz. These devices can be applied in terahertz astronomical observations and fluorescence microscopy applications, where multi-wavelength operation is necessary.

Evolution of template-assisted two-dimensional porphyrin chiral grating structure by directed self-assembly using chiral second harmonic generation microscopy

Directed self-assembly has been used to create micro-nano scale patterns, including chiral periodic structures of organic molecules, for potential applications in optics, photonics, metamaterials, and medical and sensing technologies. This study presents a straightforward approach for fabricating large-scale chiral grating porphyrin assemblies through template-assisted techniques. The solution of tetrakis(4-sulfonatophenyl)porphyrin (TPPS) was induced by chiral amino acids (l/d-arginine and l/d-serine) to self-assemble into highly ordered chiral grating structures with the assistance of sodium dodecyl sulfate (SDS). The structures show precise line widths (5.5 µm) and gaps (18 µm). Using in situ optical microscopy and second harmonic generation (SHG) microscopy, the chiral characteristics and dynamic evolution of the template-assisted self-assembly are investigated. It is found that the chirality of amino acids induced TPPS self-assembled into chiral structures and the liquid contraction interface significantly enhanced the chirality of the assemblies. This study is significant for understanding the mechanism of chiral evolution and designing novel micro-nano materials with predetermined chiral properties.

Two-dimensional binary phase gratings for zero-order and high-order diffraction suppression.

A two-dimensional binary phase grating is proposed in this paper. Unlike a conventional transmission grating, in theory, the proposed phase grating can simultaneously eliminate the zero- and high-order diffraction along certain axes on the image plane, forming a pure sinusoidal transmission modulation that leaves only the first-order diffraction. The first-ever, to the best of our knowledge, theoretical model for achieving sinusoidal transmission modulation is suggested in this paper; then the theoretical calculation and experiment results are displayed to investigate the physical mechanism of the proposed grating. Moreover, the manipulation on the arrangement of grating design can disperse or concentrate the diffraction energy at a specific axis. Finally, almost first-order-only diffraction is achieved on a single axis by introducing random changes to certain geometrical parameters of the two-dimensional binary phase grating. Our work provides potential applications in optical science and engineering fields.

Polarization-independent two-dimensional dielectric grating for 3 × 3 beam splitter

Conventional multi-port beam splitters with spot arrays, while being key components in diversiform optical systems, show polarization sensitivity and insufficient uniformity. Here, we proposed a polarization-independent high-efficiency 3 × 3 beam splitter based on the two-dimensional(2D) cylindrical dielectric grating (CDG), which could redistribute the incident light into nine beams with equal power. The proposed grating consists of a double-layer dielectric cylinder on the substrate of fused silica. The parameters of grating structure and fabrication tolerance are calculated by using rigorous coupled wave analysis (RCWA) and simulated annealing algorithm. The numerical results show that nine diffraction orders ((0, 0), (±1, 0), (0, ±1), (±1, ±1)) have average diffraction efficiencies of 10.12 % with uniformity of 2.8 % and mean polarization-independent loss (PDL) of 0.076 dB for TE and TM polarization. This work can open a new and positive way for researching the 2D multi-spot beam splitter and has promising applications in the field of three-dimensional(3D) imaging and reconstruction, microscopy techniques, material processing, etc.

Two-Dimensional Polarization Gratings Realized via Photopatterning Liquid Crystals

Two-Dimensional Polarization Gratings Realized via Photopatterning Liquid Crystals