Higher Diffraction Orders Research Articles

Transmitted wavefront testing of window glass with confocal photon-sieves radial-shearing interferometry based on deep learning

Two photon sieves with different focal lengths were used to construct a radial shearing interferometer. A patch-based UNet approach was utilized to extract the central skeleton of interferogram, and then an iterative algorithm was applied for wavefront reconstruction. The transmitted wavefront of a window glass was measured with different detectors, and their results were consistent with the measurement of ZYGO interferometer. Compared to zone plate, photon sieves can suppress higher-order diffraction by reasonably designing the arrangement of small holes, thereby improving the signal-to-noise ratio of the interferogram. Moreover, photon sieves that is self-supporting and multifunctional by use of design and optimization has great application in wavefront sensing and interferometric imaging.

Wavelength-multiplexed orbital angular momentum meta-holography

AbstractThe field of high-bandwidth holography has been extensively studied over the past decade. Orbital angular momentum (OAM) holography, which utilizes vortex beams with theoretically unbounded OAM modes as information carriers, showcases the large capacitance of hologram storage. However, OAM holography has been limited to a single wavelength, restricting its potential for full-color holography and displays. In this study, we propose wavelength and OAM multiplexed holography that utilizes the multiple dimensions of light—wavelength and OAM—to provide a multi-color platform that expands the information capacity of holographic storage devices. The proposed wavelength-OAM multiplexed holography is physically realized by a metasurface, the state-of-the-art optical element consisting of an array of artificially engineered nanostructures. Hydrogenated silicon meta-atoms, the constituents of the metasurface, are engineered to possess wavelength selectivity by tailoring the dispersion of polarization conversion. These meta-atoms are used to encode the calculated OAM-preserved phase maps based on our design. The sampling grid of the phase map is rotated by 45°, which effectively suppress higher-order diffraction, providing a great strategy for achieving large field-of-view (FOV) holography. We successfully demonstrate six holographic images that are selectively reconstructed under the illumination of light with specific wavelengths (λ = 450, 635 nm) and topological charges (l = -2, 0, 2), without high-order diffraction. Our work suggests that ultrathin meta-holograms can potentially realize ultrahigh-bandwidth full-color holography and holographic video displays with large FOV.

Hexagonal diffraction gratings generated by convolutional neural network-based deep learning for suppressing high-order diffractions

The st order diffraction of gratings is widely used in spectral analysis. However, when the incident light is non-monochromatic, the higher-order diffractions generated by traditional diffraction gratings are always superimposed on the useful first-order diffraction, complicating subsequent spectral decoding. In this paper, single-order diffraction gratings with a sinusoidal transmittance, called hexagonal diffraction gratings (HDGs), are designed using a convolutional neural network based on deep learning algorithm. The trained convolutional neural network can accurately retrieve the structural parameters of the HDGs. Simulation and experimental results confirm that the HDGs can effectively suppress higher-order diffractions above the third order. The intensity of third-order diffraction is reduced from 20% of the first-order diffraction to less than that of the background. This higher-order diffraction suppression property of the HDGs is promising for applications in fields such as synchrotron radiation, astrophysics, and soft x-ray lasers.

Electromagnetically induced grating via amplitude and phase modulations in a three-level V-type atomic medium

Abstract A probe laser beam can be completely absorbed in an atomic resonance frequency region, however, if a coupling laser beam is further applied to the atom, the atomic medium can exhibit electromagnetically induced transparency (EIT), i.e, the probe beam can be completely transmitted through the atomic medium. Thus, if the coupling beam is a standing wave field with nodes and antinodes, it will cause in space a periodic modulation of the transmitted spectrum of the probe field. This means that the probe field propagates through the atomic medium just as it passes through a diffraction grating which is called electromagnetically induced grating (EIG). Based on amplitude or phase modulation of transmission function, the absorption grating or the phase grating can be formed, respectively. In this work, based on controllable absorption and dispersion properties of a three-level V-type atomic system, we study the control of the absorption grating and the phase grating with respect to the intensity and the frequency of the laser fields. The absorption diffraction pattern at the two-photon resonance is obtained, while the phase diffraction pattern appears when there is a frequency shift of either the coupling frequency or the probe frequency compared to the corresponding atomic resonance frequency. By adjusting the coupling or/and probe laser frequency, the absorption grating can be converted into the phase grating and the high-order diffraction efficiency can also be improved.

Diffraction efficiency management by complex binary gratings.

The diffraction efficiencies of a complex binary diffraction grating with a rectangular profile are controlled through the steps' phases, amplitudes, and duty cycle, based on analytical expressions. It is demonstrated that the zeroth-diffraction order can be canceled for any arbitrary value of the duty cycle, provided that a π-phase difference is imposed, along with a specific ratio of the steps' amplitudes. This feature is not feasible for separated amplitude-only and phase-only rectangular binary gratings in the context of one-dimensional gratings. In this framework, a key analytic relationship between the duty cycle and the steps' amplitude ratio is derived, allowing the design of such gratings with this desired feature across a wide range of conditions, not limited to a duty cycle of 0.5. Concerning the higher diffraction orders, it is proved that their intensities cancel or maximize for fixed duty cycle no matter the amplitude and phase values of the steps. The intensity of the m-th diffraction order possesses m maxima and m - 1 zeros on the full range of the duty cycle. All these features were corroborated experimentally. The broad insight of such a grating allows the design of gratings with diffraction efficiencies tailored for specific applications.

High-order diffraction for optical superfocusing

High-order diffraction (HOD) from optical microstructures is undesirable in many applications because of the accompanying ghosting patterns and loss of efficiency. In contrast to suppressing HOD with subwavelength structures that challenge the fabrication of large-scale devices, managing HOD is less developed due to the lack of an efficient method for independently manipulating HOD. Here, we report independent manipulation of HODs, which are unexploited for subdiffraction-limit focusing in diffractive lenses, through an analytical formula that correlates the diffraction order and the width of each zone. The large spatial frequencies offered by the HODs enable our lenses to reduce the lateral focal size down to 0.44 λ even without any subwavelength feature (indispensable in most high-NA diffractive lenses), facilitating large-scale manufacture. Experimentally, we demonstrate high-order lens-based confocal imaging with a center-to-center dry resolution of 190 nm, the highest among visible-light confocal microscopies, and laser-ablation lithography with achieved direct-writing resolution of 400 nm (0.385 λ).

Quality improvement of unfiltered holography by optimizing high diffraction orders with fill factor.

Computer-generated holography (CGH) suffers from high diffraction orders (HDOs) due to the pixelated nature of spatial light modulators (SLMs), typically requiring bulky optical filtering systems. To address this issue, a novel unfiltered holography approach known as the high-order gradient descent (HOGD) algorithm was previously introduced to optimize HDOs without optical filtering, enabling compact holographic displays. However, this algorithm overlooks a crucial physical parameter of SLMs-the fill factor-leading to limited optical quality. Here, we introduce a fill factor-based HOGD (FF-HOGD) algorithm, specifically designed to improve the quality of unfiltered holography by incorporating the fill factor into the optimization process. The quality advantage of FF-HOGD is demonstrated through numerical simulations and optical experiments.

Low-diffraction EMI-shielding multiband optical window based on randomized metallic mesh

Electromagnetic interference (EMI) shielding optical windows are crucial for the optimal performance of electro-optical systems in environments exposed to electromagnetic radiation. Traditionally, metallic mesh structures have been favored as the optimal solution, offering high spectral transmittance coupled with efficient electromagnetic shielding. However, these conventional periodic meshes often lead to diffraction effects that can degrade image quality. In contrast, random structures partially homogenize high-order diffraction but lack thorough optimization. To address these challenges, we employ a novel optimization process to develop an innovative multiband optical window based on layered functional structures. This design employs a randomized metallic mesh structure, dramatically reducing higher-order diffraction optical energy by 74% compared to its periodic counterparts. Additionally, the device's EMI shielding effectiveness exceeds 20 dB in the 12–18 GHz frequency band. Moreover, a multiband antireflection coating comprising a 9-layer ZnS/YbF3 stack has been applied to minimize residual reflections achieving an average optical transmittance of 86.1% in the 0.4-0.7µm band, 89.8% at 1.064µm, and 81.1% in the 3-5µm band. We anticipate that our proposed multiband optical window will greatly enhance the application and effectiveness of EMI shielding in optical windows.

Development of improved higher-order correction for the NIF opacity spectrometer.

X-ray opacity measurements on the National Ignition Facility (NIF) are in the process of reproducing earlier measurements from the Sandia Z Facility, in particular for oxygen and iron plasmas. These measurements have the potential to revise our understanding of the "solar problem" and of the hot degenerate Q class white dwarf structure by probing plasma conditions near the base of their convection zones. Accurate opacity measurements using soft x-ray Bragg crystal spectrometers require correction for higher-order diffraction effects. Extending prior work in this area [Dutra etal., Review of Scientific Instruments 93, 113527 (2022)], we have developed a new method to remove higher-order spectral components from NIF opacity spectrometer data. By modeling absorption and backlighting continuum spectra and subtracting the second- and third-order components from the measured data, we are able to perform this correction while avoiding imprinting first-order model line features onto the data.

Analyzing radiowave multiple diffraction from a low transmitter in vegetated urban areas using a spherical-wave UTD–PO approach

This article introduces a uniform theory of diffraction–physical optics (UTD–PO) formulation for analyzing radiowave multiple diffraction emanating from trees and buildings in green urban areas, considering illumination from a low transmitter and assuming spherical-wave incidence. Based on Babinet’s principle, this solution models buildings as rectangular sections and accounts for the influence of tree crowns (assuming these rise above the average rooftop height) by incorporating appropriate attenuation factors/phasors into the diffraction phenomena of buildings. The validation of the formulation is achieved through measurements made at the 39 GHz 6G mmWave frequency on a scale model of a green urban environment comprising bonsai trees and bricks. The main advantage of the proposed solution is that the calculations only include single diffractions due to recursion, circumventing the need to use higher-order diffraction terms in the diffraction coefficients, thus reducing the computation time and power. Our results may be beneficial for the design of mobile communication systems, including 6G networks, situated in green urban areas and with transmission source positioned lower than the surrounding infrastructure.

Eyebox expansion of a lensless near-eye display using diverging spherical wave illumination and a multiplexed holographic optical element

We expand the eyebox size of a lensless holographic near-eye-display (NED) using passive eyebox replication technique that incorporates a spatial light modulator (SLM) and a holographic optical element (HOE). In holographic NEDs, the space-bandwidth product (SBP) of the SLM determines the exit pupil dimensions and corresponding eyebox size. The base eyebox size is replicated in the horizontal direction by using the horizontal high-order diffractions of an SLM under spherical wave illumination and a multiplexed HOE combiner. When a digital blazed grating and a digital lens phase are added to the computed phase hologram sent to the SLM, two spatially separated, horizontal high-order diffraction terms with identical intensity and information can be uniformly formed without the zero-order term. When the eyebox size is expanded, the field-of-view (FOV) is not sacrificed; spherical divergence wave illumination alleviates the need for a tradeoff between FOV and eyebox size. The astigmatism introduced during HOE fabrication is counterbalanced by pre-correcting the target image using a computer-generated, holographic computation algorithm. The prototype system shows simple and effective, distortion-free eyebox expansion of a wide-angle, lensless, holographic NED.

CFZA camera: a high-resolution lensless imaging technique based on compound Fresnel zone aperture.

In lensless imaging using a Fresnel zone aperture (FZA), it is generally believed that the resolution is limited by the outermost ring breadth of the FZA. The limitation has the potential to be broken according to the multi-order property of binary FZAs. In this Letter, we propose to use a high-order component of the FZA as the point spread function (PSF) to develop a high-order transfer function backpropagation (HBP) algorithm to enhance the resolution. The proportion of high-order diffraction energy is low, leading to severe defocus noise in the reconstructed image. To address this issue, we propose a Compound FZA (CFZA), which merges two partial FZAs operating at different orders as the mask to strike a balance between the noise and resolution. Experimental results verify that the CFZA-based camera has a resolution that is double that of a traditional FZA-based camera with an identical outer ring breadth and can be reconstructed with high quality by a single HBP without calibration. Our method offers a cost-effective solution for achieving high-resolution imaging, expanding the potential applications of FZA-based lensless imaging in a variety of areas.

Acoustic Metagrating Holograms.

Metasurface holograms represent a common category of metasurface devices that utilize in-plane phase gradients to shape wavefronts, forming holographic images through the application of the generalized Snell's law (GSL). While conventional metasurfaces focus solely on phase gradients, metagratings, which incorporate higher-order wave diffraction, further expand the GSL's generality. Recent advances in certain acoustic metagratings demonstrate an updated GSL extension capable of reversing anomalous transmission and reflection, whose reversal is characterized by the parity of the number of wave propagation trips through the metagrating. However, the current extension of GSL remains limited to 1D metagratings, unable to access 2D holographic images in 3D spaces. Here, the GSL extension to 2D metagratings for manipulating waves within 3D spaces is investigated. Through this analysis, a series of acoustic metagrating holograms is experimentally demonstrated. These holographic images exhibit the unique ability to switch between transmission and reflection types independently. This study introduces an additional dimension to modern holography design and metasurface wavefront manipulation.

Structured-Light 3D Imaging Based on Vector Iterative Fourier Transform Algorithm.

Quasi-continuous-phase metasurfaces overcome the side effects imposed by high-order diffraction on imaging and can impart optical parameters such as amplitude, phase, polarization, and frequency to incident light at sub-wavelength scales with high efficiency. Structured-light three-dimensional (3D) imaging is a hot topic in the field of 3D imaging because of its advantages of low computation cost, high imaging accuracy, fast imaging speed, and cost-effectiveness. Structured-light 3D imaging requires uniform diffractive optical elements (DOEs), which could be realized by quasi-continuous-phase metasurfaces. In this paper, we design a quasi-continuous-phase metasurface beam splitter through a vector iterative Fourier transform algorithm and utilize this device to realize structured-light 3D imaging of a target object with subsequent target reconstruction. A structured-light 3D imaging system is then experimentally implemented by combining the fabricated quasi-continuous-phase metasurface illuminated by the vertical-cavity surface-emitting laser and a binocular recognition system, which eventually provides a new technological path for the 3D imaging field.

Spin-wave self-imaging: Experimental and numerical demonstration of caustic and Talbot-like diffraction patterns

Extending the scope of the self-imaging phenomenon, traditionally associated with linear optics, to the domain of magnonics, this study presents the experimental demonstration and numerical analysis of spin-wave (SW) self-imaging in an in-plane magnetized yttrium iron garnet film. We explore this phenomenon using a setup in which a plane SW passes through a diffraction grating, and the resulting interference pattern is detected using Brillouin light scattering. We have varied the frequencies of the source dynamic magnetic field to discern the influence of the anisotropic dispersion relation and the caustic effect on the analyzed phenomenon. We found that at low frequencies and diffraction fields, the caustics determine the interference pattern. However, at large distances from the grating, when the waves of high diffraction order and number of slits contribute to the interference pattern, the self-imaging phenomenon and Talbot-like patterns are formed. This methodological approach not only sheds light on the behavior of SW interference under different conditions but also enhances our understanding of the SW self-imaging process in both isotropic and anisotropic media.

Spatially synchronous fringe detection: a method to facilitate the alignment of an echelle grating mosaic by separating the compensative angular errors

Alignment of mosaic gratings is traditionally supported by two interferometric verifications: on the zero order to verify the grating surfaces and on the blaze to verify the groove direction. In the case of low frequency echelle grating an interferometric measurement on the zero order is hardly feasible due to extremely low contrast of the fringes. The complete alignment has then to be carried out on high order (close to the blaze) where the two misalignment errors (the tip and rotation) show the same effect on the interferogram. The acquisition of a low and a high diffraction order image simultaneously, referred to as the spatially synchronous fringe detection method (SSFD), is used to analyze the misalignment. Iterative adjustment with the autocollimation configuration at the low and high order is used to separate the compensative errors of Δθ x and Δθ z . A prototype mosaic with two 110mm×220mm segments has been aligned with the support of this method. A numerical simulation of the alignment procedure as well as the error orientation analysis of this mosaic grating are presented. The mosaic grating with an accuracy of Δθ x <0.64µrad, Δθ y <1.13µrad, Δθ z <0.65µrad and a wavefront RMS error of 0.149λ has been completed. This method can greatly facilitate the alignment of an echelle mosaic for an astronomical spectrograph.

Microwave assisted Fraunhofer diffraction pattern in a four-level light–matter coupling scheme

The experimental realization of two-dimensional (2D) electromagnetically induced grating is explored by monitoring the Fraunhofer diffraction pattern in a microwave-driven four-level Y-type atomic medium under the action of two orthogonal standing-wave (SW) fields. Due to the position-dependent atom–field interaction, the information about the high diffraction order of the probe light can be obtained via the Fraunhofer diffraction pattern of the probe light. It is found that the diffraction behavior is significantly improved due to the joint quantum interference induced by the SW and microwave-driven cycling fields. Most importantly, the amplitude and phase diagram of the transmission function of the probe light can be modulated at a particular position and the probe energy may transfer to the high orders of the diffraction by properly adjusting the system parameters. The proposed scheme may provide a promising way to achieve highly sensitive diffraction patterns with applications in quantum information processing.

Solution to the issue of high-order diffraction images for cylindrical computer-generated holograms

The cylindrical computer-generated hologram (CCGH), featuring a 360° viewing zone, has garnered widespread attention. However, the issue of high-order diffraction images due to pixelated structure in CCGH has not been previously reported and solved. For a cylindrical model offering a 360° viewing zone in the horizontal direction, the high-order diffraction images always overlap with the reconstruction image, leading to quality degradation. Furthermore, the 4f system is commonly used to eliminate high-order diffraction images in planar CGH, but its implementation is predictably complex for a cylindrical model. In this paper, we propose a solution to the issue of high-order diffraction images for CCGH. We derive the cylindrical diffraction formula from the outer hologram surface to the inner object surface in the spectral domain, and based on this, we subsequently analyze the effects brought by the pixel structure and propose the high-order diffraction model. Based on the proposed high-order diffraction model, we use the gradient descent method to optimize CCGH accounting for all diffraction orders simultaneously. Furthermore, we discuss the issue of circular convolution due to the periodicity of the Fast Fourier Transform (FFT) in cylindrical diffraction. The correctness of the proposed high-order diffraction model and the effectiveness of the proposed optimization method are demonstrated by numerical simulation. To our knowledge, this is the first time that the issue of high-order diffraction images in CCGH has been proposed, and we believe our solution can offer valuable guidance to practitioners in the field.

Multiple electromagnetically induced grating in the 85Rb five-level atomic medium

In this work, a multiple electromagnetically induced grating is realized based on multiple electromagnetically induced transparency in the 85Rb five-level atomic medium. We demonstrate that the diffraction pattern of the probe light field is observed at three different frequency regions corresponding to the three transparent spectral regions of the system. The influence of the intensity and frequency of the coupling laser field on the diffraction pattern of the electromagnetically induced grating and its diffraction efficiency is also investigated, which can find the optimal parameters to improve the higher-order diffraction efficiencies. The appearance of the multiple electromagnetically induced grating in multi-level atomic systems can be applied to photonic devices operating with multiple frequency channels.

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.