Two-dimensional Gratings Research Articles

Design of two-dimensional multilevel optical anisotropic diffraction gratings with a generative adversarial network.

This study uses a generative adversarial network to design multilevel optical anisotropic diffraction gratings with specific customizable characteristics. As input, this method uses the far electric field of polarization and intensity in each diffracted light through the gratings to design. Using the finite-difference time-domain method, the designed structures are numerically evaluated, confirming that they can be created with the intended parameters. Multilevel optical anisotropic diffraction gratings created this way can be used in various fields to develop improved optical elements.

Measurement of Two-Dimensional Orthogonal Gratings Using Grazing-Incidence Small-Angle X-Ray Scattering

Measurement of Two-Dimensional Orthogonal Gratings Using Grazing-Incidence Small-Angle X-Ray Scattering

Two-dimensional grating interferometer with nanometer accuracy

A two-dimensional grating interferometer with the nanometer accuracy is proposed, which employs a transmissive two-dimensional diffraction grating and a corner cube prism in its optical configuration. The distinctive features of this optical path configuration are as follows: (i) Fourfold optical subdivision is achieved based on the principle of secondary diffraction, enhancing optical subdivision capability. (ii) The utilization of a corner cube prism configuration enables parallel retroreflection of diffracted light, facilitating ease of optical alignment. Utilizing a two-dimensional transmissive grating with a period of 4 µm (resulting in an optical signal period of 1 µm after fourfold optical subdivision), the two-dimensional grating interferometer achieves measurement resolutions better than 8 nm along the x and y directions. Within a 100 µm range, the grating displacement errors are superior to ±38 and ±36 nm. The repeatability (standard deviation of error) during a reciprocating motion with a 4 µm stroke is superior to 14 nm. The proposed two-dimensional grating interferometer enables nanoscale resolution measurements, showcasing notable linear measurement capabilities and repeatability. It finds potential applications in ultra-accuracy positioning and machining equipment. The utilization of gratings with smaller periods holds the promise of realizing picometer-level measurement potential.

Integrated silicon photonics chip fabricated by CMOS compatible technology for low-bit-error-rate quantum key distribution

Quantum communication has extremely high security and is a development direction of future communication networks. In this paper, an on-chip path, off-chip polarization encoded quantum key distribution (QKD) chip is designed and fabricated using advanced silicon photonics fabrication technology. Using a special two-dimensional grating, we can convert light of different path states into corresponding polarization states and propagate in fiber. The performance of the basic optics, waveguides, gratings, and Mach–Zehnder interferometers on the chip is characterized. In the demonstrated QKD experiment, the quantum bit error rate is as low as 1.08%. It provides an important device for the future development of advanced integrated quantum information.

Optical generation and detection of GHz longitudinal and transverse acoustic waves in solids assisted by two-dimensional metallic grating structure

Absorption of laser pulses with picosecond temporal width in a two-dimensional nano-scale metallic grating deposited on a transparent substrate launches both longitudinal and transverse acoustic waves in to the sample. The periodic metallic structure makes the generated acoustic waves propagate several different directions. The propagating acoustic waves are monitored optically by the delayed light pulses (probe light) as the transient reflectivity change which is known as the Brillouin oscillation. The probe light is also diffracted by the metallic grating, allowing the detection of the acoustic waves propagating in the multiple directions efficiently. The analysis of the Brillouin oscillation frequencies brings the longitudinal and transverse sound velocities and the optical refractive index simultaneously from a single measurement. We verify the above mentioned scheme using a sample with two-dimensional square lattice (period 380 nm) of aluminum square islands of lateral dimension 200 × 200 nm2 and thickness of 50 nm on a fused silica substrate of thickness 1 mm. From the obtained Brillouin oscillation frequencies in several tens GHz, the acoustic and optical properties of the substrate material are successfully retrieved. The technique would be applicable to investigate the acoustic and optical properties of more complicated systems, such as anisotropic and/or inhomogeneous medium.

Two-dimensional sub-200 nm pitch Si gratings with natural orthogonality

As a standard for length and angle, two-dimensional (2D) grating reference materials can be used for performance verification and calibration of various microscopes and 2D stages. This paper proposes a 2D nanoscale reference grating manufactured by combining laser-focused atomic deposition (LFAD) and extreme ultraviolet interference lithography. The theoretical pitch of the 2D grating is 150.46 nm, which is only times the pitch of the Cr grating manufactured by LFAD which can be traceable to the resonance transition frequency of Cr. Moreover, the angle between two periodic directions of the 2D nanograting has natural orthogonality.

Study on the influence of surface roughness on the diffraction efficiency of two-dimensional gratings.

This study investigates the effect of surface roughness on the diffraction efficiency of two-dimensional gratings. Firstly, a roughness model was constructed using FDTD, followed by a significant analysis of the ridge roughness, groove roughness, and sidewall roughness on diffraction efficiency. Then, the impact of each roughness type on diffraction efficiency was studied separately. Results indicate that ridge roughness has a negative impact on diffraction efficiency, whereas groove roughness and sidewall roughness have a positive impact on the diffraction efficiency of two-dimensional gratings. When ridge, groove, and sidewall roughness coexist, diffraction efficiency decreases with an increase in roughness, consistent with previous research. However, under conditions of minimal roughness, diffraction efficiency actually increases. Finally, an experiment was conducted to verify the conclusions. The results of this study have significant reference value for the application and development of precision measurement techniques for gratings.

High-resolution 3D nanoprinting based on two-step absorption via an integrated fiber-coupled laser diode.

Three-dimensional (3D) laser nanoprinting with high resolution and low cost is highly desirable for fabricating arbitrary 3D structures with fine feature size. In this work, we use a 405-nm integrated fiber-coupled continuous wave (cw) laser diode to establish an easy-to-build 3D nanoprinting system based on two-step absorption. Two-dimensional (2D) gratings with a sub-150-nm period and 3D woodpile nanostructures with a lateral period of 350 nm have been printed at a low speed. At a faster scan velocity of 1000 µm/s, 2D gratings with sub-200-nm resolution and sub-50-nm linewidth can still be fabricated with laser power less than 1 mW. The two-step absorption of the used benzil initiator enables us to use a second cw laser with 532-nm wavelength to enhance the polymerization with sub-100-nm feature size when starting with insufficient 405-nm laser power, which possess the potential to find applications in high-speed high-resolution parallel-writing and in situ manipulation.

Tailored diffractions of asymmetric columns and symmetric rows in two-dimensional multi-element phase gratings.

Two-dimensional multi-element phase gratings can be engineered to show an even symmetry along one direction while an odd symmetry along the other direction in terms of offset refractive indices in each unit cell. The interplay of such even and odd symmetries has been explored to tailor diffraction columns and rows on demand by making offset refractive indices to satisfy specific requirements and hence attain different types of destructive interference. The resultant tailoring effects include the directional column elimination, the grouped column elimination, and the directional column selection as well as the natural row absence, the grouped row elimination, and the central row selection.

Two-Dimensional Polarization Holographic Gratings in Azopolymer Thin Films: Polarization Properties in the Presence or Absence of Surface Relief

During polarization holographic recording in azopolymer thin films, usually together with the volume anisotropic grating, a surface relief grating (SRG) is also formed. By using two consecutive exposures, it is possible to obtain a two-dimensional (2D) grating. To the best of our knowledge, the polarization properties of such gratings have not been studied yet. To determine the influence of the surface relief on the polarization selectivity of the 2D gratings, we propose two methods to suppress the SRG formation: by varying the recording conditions or varying the sample structure. In these experiments we have used the commercially available azopolymer PAZO, poly[1-4-(3-carboxy-4-hydrophenylazo) benzene sulfonamido]-1,2-ethanediyl, sodium salt] to perform the polarization holographic recording using a 442 nm He-Cd laser. As indicated by our results, when the surface relief is present, it strongly dominates the response of the 2D grating and it behaves almost as a scalar polarization insensitive grating. Conversely, when the SRG formation is suppressed, the polarization properties of the 2D grating in all four diffracted orders are very well pronounced. In this way, we demonstrate that we can easily control SRG formation and, if desired, obtain 2D grating with high surface relief modulation, or alternatively record polarization-selective 2D gratings with virtually no surface relief.

Heptagonal quasicrystals: Construction of 2D lattices and demonstrations using laser pointers – Concluding part

Photographic slides of an aperiodic heptagonal tiling were used as two-dimensional diffraction gratings (as a standard approach) to describe and demonstrate the basic properties of dodecagonal quasicrystals. The paper completes our earlier two publications dealing with (1) Penrose (decagonal) and Ammann (octagonal) quasicrystals and (2) dodecagonal quasicrystals, the diffraction gratings of which were constructed and presented in an analogous manner.

A simple experiment to study the array theorem using Fraunhofer diffraction of a two-dimensional grating

A transmission electron microscopy (TEM) grid comprises an array of identical square apertures. In this study, the Fraunhofer diffraction pattern of a TEM grid was obtained by a 532 nm wavelength diode laser. It was compared with the Fraunhofer diffraction pattern computed by using the array theorem and employed to estimate the mesh size of the TEM grid.

Design of a Completely Vertical, Polarization-Independent Two-Dimensional Grating Coupler with High Coupling Efficiency

An efficient optical coupler to transfer the signal between an optical fiber and a silicon waveguide is essential for realizing the applications of silicon photonic integrated circuits such as optical communication and optical sensing. In this paper, we numerically demonstrate a two-dimensional grating coupler based on a silicon-on-insulator platform to obtain completely vertical and polarization-independent couplings, which potentially ease the difficulty of packaging and measurement of photonic integrated circuits. To mitigate the coupling loss induced by the second-order diffraction, two corner mirrors are respectively placed at the two orthogonal ends of the two-dimensional grating coupler to create appropriate interference conditions. Partial single-etch is assumed to form an asymmetric grating to obtain high directionalities without a bottom mirror. The two-dimensional grating coupler is optimized and verified with finite-difference time-domain simulations, achieving a high coupling efficiency of −1.53 dB and a low polarization-dependent loss of 0.015 dB when coupling to a standard single-mode fiber at approximately 1310 nm wavelength.

Effect of composite vortex beam on a two-dimensional gain assisted atomic grating

We propose an atomic grating based on an electromagnetically induced transparency phenomenon that switches between zeroth-order diffraction to a distinct higher-order diffraction pattern by driving a planar gaseous medium of a four-level tripod () atoms with three laser beams: modulation of standing wave control beam propagating nearly perpendicular to the planar medium, while vortex and weak plane probe beams directed perpendicular to the medium. We numerically investigate the behavior of the amplitude, phase modulations, and probe field diffraction intensities of different orders by the variation of the field detunings and orbital angular momentum number of the composite vortex light beam. Specifically, in the off-resonant case, the interplay between a square lattice of the control and an additional spatial variation of the vortex beam allows the emergence of higher diffraction orders and variable gain due to double transparency windows in this complex optical system. We believe that our proposed scheme might be useful in optical memory devices via the storage of information to diffraction orders of the atomic grating.

Calibrate the non-orthogonal error of AFM with two-dimensional self-traceable grating

The calibration of the non-orthogonal error in nanoscale measurements is of paramount importance for analytical measuring instruments. Particularly, the calibration of non-orthogonal errors in atomic force microscopy (AFM) is essential for the traceable measurements of novel materials and two-dimensional (2D) crystals. The 2D self-traceable grating with a theoretical non-orthogonal angle of less than 0.0027° and an expanded uncertainty of 0.003° (k = 2) are measured by the Metrological Large Range Scanning Probe Microscope (Met. LR-SPM). In this study, we characterized the local and overall non-orthogonal error in AFM scans and proposed a protocol to tune the optimal scanning parameters of AFM minimizing the non-orthogonal error. We presented the method for accurately calibrating a commercial AFM system for non-orthogonal by establishing a detailed uncertainty budget and errors analysis. Our results verified the important advantages of the 2D self-traceable grating in calibrating precision instruments.

Imaging-based intelligent spectrometer on a plasmonic rainbow chip

Compact, lightweight, and on-chip spectrometers are required to develop portable and handheld sensing and analysis applications. However, the performance of these miniaturized systems is usually much lower than their benchtop laboratory counterparts due to oversimplified optical architectures. Here, we develop a compact plasmonic “rainbow” chip for rapid, accurate dual-functional spectroscopic sensing that can surpass conventional portable spectrometers under selected conditions. The nanostructure consists of one-dimensional or two-dimensional graded metallic gratings. By using a single image obtained by an ordinary camera, this compact system can accurately and precisely determine the spectroscopic and polarimetric information of the illumination spectrum. Assisted by suitably trained deep learning algorithms, we demonstrate the characterization of optical rotatory dispersion of glucose solutions at two-peak and three-peak narrowband illumination across the visible spectrum using just a single image. This system holds the potential for integration with smartphones and lab-on-a-chip systems to develop applications for in situ analysis.

P‐12.1: Two‐dimensional Edge Detection Implementation of Liquid Crystal Computing Metasurfaces

Computing metasurfaces have received widespread attention since they were proposed, and the ability to realize mathematical operations has enabled real time image processing with new breakthroughs, such as optical edge detection. In this paper, a new method for two-dimensional edge detection is presented, and the two-dimensional liquid crystal polarization grating is designed from the theoretical derivation. The gratings with different periods are fabricated by photoalignment technology. The one-dimensional and two-dimensional imaged edge detection are experimental realized in this work. By measuring the displacement of edge detection, the experimental results with different periods are in line with theoretical formula. The low cost and easily fabricated photoaligned liquid crystal polarization gratings achieved the real time optical computation with broadband and adjustable, which can be further applied in biological image edge and other optical display related fields.

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.

Diffraction of a Laguerre-Gaussian beam in Raman interaction with a spatially periodic pump field

We studied Fresnel diffraction of a Laguerre-Gaussian beam ${\text{LG}}_{p,l}$ with arbitrary azimuthal $l$ and radial $p$ indices on a grating induced during its Raman interaction with a spatially periodic pump field in an atomic medium. The diffraction pattern turned out to be more complex than the classical Talbot effect observed when a plane wave illuminates a two-dimensional grating. The simulation results show that, under certain conditions, at distances corresponding to the classical Talbot planes (integer and fractional), periodic amplitude-phase distributions appear. The diffraction patterns are not a probe-field image in the induced grating plane, but a regular array of vortex annular-shaped microbeams with an inhomogeneous intensity distribution depending on the $l$ and $p$ indices and with a topological charge equal to that of the initial probe beam. The intensity and spatial distribution of diffraction patterns can be controlled by Raman amplification in the induced grating by varying the pump-field intensity or the Raman detuning.

A 1 × 2 Two-Dimensional Slanted Grating Based on Double-Layer Cylindrical Structure

Diffraction gratings play an increasingly important role in various planar optical systems, such as near-eye display systems for virtual reality (VR) and augmented reality (AR). The slanted gratings have more advantages than other elements. A 1 × 2 transmission two-dimensional (2D) slanted grating based on a double-layer cylindrical structure was proposed in this paper. In the initial phase of this study, this kind of grating was proposed and designed. We used rigorous coupled-wave analysis (RCWA) and simulated annealing algorithm (SA) to optimize the grating parameters. The effects of the grating geometric parameters on the diffraction efficiency were investigated using rigorous coupled-wave analysis (RCWA). The simulated annealing algorithm (SA) optimization results show that the diffraction efficiency of the (0, −1) and (−1, 0) order exceed 35% under normal incidence in the range of 429–468 nm wavelength for TE and TM polarization. Meanwhile, the total diffraction efficiency can reach up to 78%. In the last section, we discuss the tolerances for the grating parameters to ensure high quality manufacturing processes. The total effective efficiency is greater than 75% when the MgF2 thickness is from 300 nm to 350 nm and the SiO2 thickness is from 525 nm to 550 nm. Moreover, the grating period has a 53 nm fabrication tolerance, and the slanted angle has a 8.8-degree fabrication tolerance. The relatively large tolerances ensure that it is easy to fabricate the two-dimensional slanted grating and to achieve the targeted objectives. The proposed 2D slanted grating can be applied to 2D exit pupil expansion, which is of great importance in AR/VR applications.