Diffraction Orders Research Articles

2M NaCl by XPS using monochromatic Al K α x rays

Cryo-XPS enables the study of many substances that are unsuitable for standard XPS analysis, such as moderately volatile liquids, biological samples, porous materials, and polymeric materials that may outgas significantly under ultrahigh vacuum conditions. In this article, XPS spectra of a 50 μl frozen droplet of 2M sodium chloride solution (NaCl) in Millipore water purified to 18.2 MΩ cm at 25 °C were obtained using an Al Kα (1486.6 eV) source with a quartz (1010) crystal monochromator through first order diffraction and irradiating the sample at 54.7° to the surface normal. The sample was sputter cleaned using a Gas Cluster Ion Source pre-acquisition to remove the minor layer of adventitious carbon contamination on the surface. Spectra of the principal lines include Na 1s, O 1s, and Cl 2p. Spectra of O KLL, Na KLL, Cl 2s, Na 2s, Na 2p, O 2s, and valence band were also acquired.

Effects of Thermal Variables of Solidification on the Microstructure and Hardness of the Manganese Bronze Alloy Cu-24Zn-6Al-4Mn-3Fe

The Cu-24Zn-6Al-4Mn-3Fe alloy is mainly used for the manufacture of sliding bushings in the agricultural sector due to its high mechanical properties in the cast state. Understanding how the casting thermal parameters affect the microstructure and impact the properties of alloys is fundamental to optimizing manufacturing processes and improving performance during their application. In this study, the Cu-24Zn-6Al-4Mn-3Fe alloy was unidirectionally solidified under non-steady heat flow conditions using a water-cooled graphite base for heat exchange. Seven points were monitored along the longitudinal region of this ingot, and the data to obtain the solidification variables were extracted using an acquisition system. The cooling rates varied from 4.50 °C/s to 0.22 °C/s from the closest to the furthest position from the heat extraction point. The microstructure was analyzed via optical microscopy, scanning electron microscopy and X-ray diffraction in order to characterize the phases and intermetallic elements present in the material. The mechanical properties were evaluated through hardness and microhardness tests throughout longitudinal extension of the solidified part. The results showed an increase in hardness and microhardness with a decrease in the cooling rate, which may be related to the increase in size and the κ phase fraction with a decrease in the cooling rate, as analyzed via optical microscopy and scanning electron microscopy. Furthermore, in all positions, there was no significant change in the amount of the α phase retained, with the matrix being mainly composed of the β phase and a small content of approximately 2% of the α phase.

In-plane and out-of-plane domain orientation dispersions in 1 to 3 monolayers epitaxial WS2 and MoS2 films on GaN(0001) film/sapphire(0001)

Transition-metal dichalcogenides and their heterostructures have attractive potential applications in electronics and optoelectronics. Wafer scale 1 to 3 monolayers WS2 and MoS2 ultrathin films on GaN/sapphire substrates were grown by metal organic chemical vapor deposition. Azimuthal reflection high-energy electron diffraction (ARHEED) was used to characterize the long-range order of these TMDC ultrathin films. The RHEED patterns of WS2 and MoS2 show stripes and arcs but the MoS2 on GaN shows sharp spots in addition to stripes and arcs. The 2D map constructed from ARHEED patterns shows that WS2 is epitaxial and has an in-plane domain orientation dispersion. For the MoS2 on GaN/sapphire substrate, the 2D map shows concentric continuous rings for each diffraction order of MoS2 and GaN indicating that the in-plane MoS2 domain orientation and GaN nanocrystals are random. The out-of-plane orientation dispersion of MoS2 on the GaN substrate is larger than that of WS2 on the GaN substrate. The observations of stripes, arcs, and spots from RHEED patterns and the 2D maps reveal the deviation of ultrathin epitaxial films from its perfect epitaxy, especially the TMDC domain orientation dispersion over a large area. These rich findings from 2D maps broaden the application of ARHEED in more than one monolayer thick 2D materials.

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.

DMD and microlens array as a switchable module for illumination angle scanning in optical diffraction tomography.

Optical diffraction tomography (ODT) enables label-free and morphological 3D imaging of biological samples using refractive-index (RI) contrast. To accomplish this, ODT systems typically capture multiple angular-specific scattering measurements, which are used to computationally reconstruct a sample's 3D RI. Standard ODT systems employ scanning mirrors to generate angular illuminations. However, scanning mirrors are limited to illuminating the sample from only one angle at a time. Furthermore, when operated at high speeds, these mirrors may exhibit mechanical instabilities that compromise image quality and measurement speed. Recently, newer ODT systems have been introduced that utilize digital-micromirror devices (DMD), spatial light modulators (SLMs), or LED arrays to achieve switchable angle-scanning with no physically-scanning components. However, these systems associate with power inefficiencies and/or spurious diffraction orders that can also limit imaging performance. In this work, we developed a novel non-interferometric ODT system that utilizes a fully switchable module for angle scanning composed of a DMD and microlens array (MLA). Compared to other switchable ODT systems, this module enables each illumination angle to be generated fully independently from every other illumination angle (i.e., no spurious diffraction orders) while also optimizing the power efficiency based on the required density of illumination angles. We validate the quantitative imaging capability of this system using calibration microspheres. We also demonstrate its capability for imaging multiple-scattering samples by imaging an early-stage zebrafish embryo.

Stretchable Distributed Bragg Reflectors as Strain-Responsive Mechanochromic Sensors.

Mechanochromic materials exhibit color changes upon external mechanical stimuli, finding wide-ranging applications in colorimetric sensing, display technology, and anticounterfeiting measures. Many of these materials rely on fluorescence properties and therefore necessitate external optical or electrical excitation. However, for broader applicability, the detection of color changes by the naked eye only or without complicated detection instrumentation is highly desirable. Photonic crystals offer a promising avenue for attaining such performances. In this work, we present elastomeric distributed Bragg reflectors (DBRs) characterized by a series of photonic bandgaps exhibiting mechanochromic response from the near-infrared to the visible wavelengths. To achieve this, we engineered alternating thin films of a thermoplastic fluoropolymer and a styrene-butadiene copolymer using different elastomeric substrates to attain different behaviors. The reported system demonstrates a reversible and instantaneous shift of the photonic bandgaps in response to 100% strain in multiple deformation cycles. Comparing the DBR stress-strain response with the optical strain response confirms a mechanochromic sensitivity of ∼1.7-6.9 nm/% and ∼80 nm/MPa, with an optical Poisson's ratio in the range 0.3-0.7. All these properties are spectrally dependent, as demonstrated by exploiting the properties of different diffraction order photonic band gaps.

Efficient Redirection of Trapped Broad-Band Fluorescence from Substrates into Free Space Using c-Si Metasurfaces.

Fluorescent dye films on transparent substrates are essential for OLEDs, flexible displays, X-ray detection, and wireless optical communications. However, their efficiency is often hampered by fluorescence trapping due to total internal reflection (TIR) and waveguiding. This study tackles this longstanding challenge by reconceptualizing the integration of dye films with nanoantenna metasurfaces. Traditional methods involve directly spin-coating films onto c-Si metasurfaces on quartz substrates, resulting in edge luminescence and weak inner signals. We present a straightforward, adjustable approach by integrating dye films on the opposite side of quartz substrates, reaching a 2.5-fold photoluminescence enhancement and improving the uniformity of the emission compared to the conventional methods. These gains stem from redirecting a significant portion of leaked fluorescence light trapped inside the substrate into free space, surpassing TIR conditions through in-plane diffraction orders of the metasurfaces across the full RGB spectrum. Our findings facilitate the design of more efficient luminescent devices.

High-efficiency hard X-ray blazed diffraction via refraction by nanometer-scale prism arrays

X-ray transmission gratings are widely utilized as wavelength dispersion elements in inertial confinement fusion and X-ray astronomy fields due to their high tolerance for alignment errors, light weight and compact size. However, the high transmittance of the grating bars in the hard X-ray range can lead to reduced efficiency of all other diffraction orders except for straight through zeroth order. We propose a novel blazed refraction grating design for the hard X-ray range that combines the advantages of transmission gratings and compound refraction lenses for the first time, demonstrating its superior performance in high broadband efficiency through compound refraction and diffraction from nanometer-scale periodic arrays of silicon prisms using beam propagation method and Fraunhofer diffraction simulation. This research develops blaze methods in gratings design and provides a new solution for compact and sensitive spectrum measurement in hard X-ray range.

Polarization-Mode Transformation of the Light Field during Diffraction on Amplitude Binary Gratings

In this paper, a comparative analysis and numerical simulation of operation of two types of amplitude binary gratings (conventional and fork), both in the focal plane and near-field diffraction under illumination by mode beams with different polarization states, were performed. The simulation of the field formation in the focal plane was performed using the Richards–Wolf formalism. The diffraction calculation in the near-field diffraction was performed based on the FDTD method, considering the 3D structure of optical elements. The possibility of multiplying the incident beam in different diffraction orders of binary gratings and the polarization transformation associated with spin–orbit interaction at tight focusing were shown. In this case, various polarization transformations were formed in ±1 diffraction orders of the fork grating due to different signs of the introduced vortex-like phase singularity. The obtained results can be useful for the laser processing of materials and surface structuring.

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).

Orbital angular momentum beam-based interferometry for an in-plane displacement measurement.

In this Letter, a novel, to the best of our knowledge, robust interferometry based on orbital angular momentum (OAM) is proposed for an in-plane displacement measurement. A vortex beam (VB) is incident onto a diffraction grating, and the ±1st order diffraction beams with conjugate OAM interfere with each other. By demodulating the petal-like interferogram, the in-plane displacement of the grating can be determined. Theoretically, a 1° rotation of the interferogram corresponds to a displacement of 2.31 nm. Experimental results revealed that the maximum measurement error was less than 3.35%. The proposed measurement system combines the advantages of both OAM interferometry and grating interferometry. It adopts the grating pitch instead of the wavelength as the measurement reference, providing robust immunity to environmental disturbances while maintaining high resolution simultaneously.

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.

Trapezoidal units for (0,±1) and (±1,0) splitter in the terahertz band

This paper presents a two-dimensional grating splitter based on a trapezoidal array. Under vertical incidence of light in the terahertz band at 2.52 THz, it is possible to suppress the (0,0) order, which has an efficiency of 0.5%, while simultaneously achieving high-efficiency outputs for the (0,±1) and (±1,0) orders, with efficiencies of 25.1% and 24.7%, respectively. And it has good uniformity and extinction rate, where the uniformity (E U ) is 99.1% and the extinction rate (E T ) is 0.07 dB. The research process uses the finite element method (FEM) to optimize the grating parameters, and the corresponding grating parameters are the optimal solution when the target diffraction order efficiency is optimal. In order to verify the feasibility of practical applications of gratings, the bandwidth ranges of the grating parameters are discussed, and the results show that the grating parameters all possess a sizable bandwidth range. Therefore, this work has a promising application in the fields of 3D imaging and reconstruction, microscopy technology, and it also provides a new and efficient scheme for modeling 2 × 2 splitters.

Multiwavelength Achromatic Deflector in the Visible Using a Single-Layer Freeform Metasurface.

Deflectors are essential for modulating beam direction in optical systems but often face form factor issues or chromatic aberration with conventional optical elements, such as prisms, mirrors, and diffractive/holographic optical elements. Despite recent efforts to address such issues using metasurfaces, their practicality remains limited due to operation wavelengths in the near-infrared or the fabrication difficulties inherent in the multilayer scheme. Here, we propose a novel single-layer metasurface achieving multiwavelength chromatic aberration-free deflection across the visible spectrum by employing the robust freeform design strategy to simplify the fabrication process. By properly selecting diffraction orders for red, green, and blue wavelengths to achieve identical wavelength-diffraction-order products, the metasurface deflects light at a consistent angle of 41.3° with a high efficiency. The coupled Bloch mode analysis explains the physical properties, and experimental fabrication and characterization confirm its effectiveness. This approach holds potential for various applications such as AR/VR, digital cameras, and high-quality optical systems.

Prediction of simultaneous enhancement of Goos-Hänchen shift and reflectance in VO2 grating structure

Vanadium dioxide (VO2) material stands out in the family of the phase change materials due to its temperature-dependent phase transition properties, which make it a promising candidate for the temperature-dependent optoelectronic devices. Enhancement of the Goos-Hänchen (GH) shift is essential in VO2-based nanostructures for their applications, but it has been limited to the multilayered structures with VO2 materials so far. Here, we theoretically investigate the GH shift and corresponding reflectance in the VO2-based grating structure. We evidence that this structure has two GH peaks (3107λ and 2266λ) and high reflectance values (both up to 1) when VO2 is in the insulating phase as well as the maximum GH valley (−1061λ) and low reflectance (0.19) when VO2 is in the metallic phase. The electromagnetic field distributions in this hybrid structure suggest that the guided mode resonances (GMRs) can be excited no matter whether VO2 is in its insulating or metallic phases due to the couplings between the incident waves and the adjacent evanescent diffracted order waves, which produces their enhanced GH shifts. Different from the former case with the high reflectances and the large GH shifts, the latter has the low maximum magnetic field intensity due to the lossy property of the metallic VO2, which leads to the low reflectance and small GH valley value. Additionally, we have also found that by the alterations of the temperature-dependent conductivity of VO2 and the geometric parameters of the structure allows for the control the magnitude and position of the GH peak or valley. The simultaneously enhanced GH shifts and reflectances in the VO2-based grating structure, associated with its controllable features, enable it an effective configuration for establishing the temperature sensors and optoelectronic switches.

Single Order Diffraction at a Negative Angle Based on a Chiral Liquid Crystal with an Inclined Helix

Single Order Diffraction at a Negative Angle Based on a Chiral Liquid Crystal with an Inclined Helix

Efficient generation of octave-separating orbital angular momentum beams via forked grating array in lithium niobite crystal

Abstract The concept of orbital angular momentum (OAM) of light has not only advanced fundamental physics research but also yielded a plethora of practical applications, benefitting from the abundant methods for OAM generation based on linear, nonlinear and combined schemes. The combined scheme could generate octave-separating OAM beams, potentially increasing the channels for optical communication and data storage. However, this scheme faces a challenge in achieving high conversion efficiency. In this work, we have demonstrated the generation of multiple OAM beams at both fundamental frequency and second harmonic (SH) wavelengths using a three-dimensional forked grating array with both spatial χ (1) and χ (2) distributions in a lithium niobate nonlinear photonic crystal platform. The enhancements of the fundamental and SH OAM beams have been achieved by employing linear Bragg diffraction and nonlinear Bragg diffraction, respectively, i.e., quasi-phase matching. The experimental results show that OAM beams with variable topological charges can be enhanced at different diffraction orders via wavelength or angle tuning, achieving conversion efficiencies of 60.45 % for the linear OAM beams and 1.08 × 10−4 W −1 for the nonlinear ones. This work provides a promising approach for parallel detection of OAM states in optical communications, and extends beyond OAM towards the control of structured light via cascaded linear and nonlinear processes.

Diffraction order penalization to improve spectrometer calibrations

Wavelength calibration in diffraction spectroscopy typically depends on identifying strong, well-known lines in the recorded spectra and fitting a calibration function to them. In this paper, we outline a novel method (order penalization) for improving spectroscopic calibrations by extending non-linear least squares fitting of the calibration curve. The method introduces an extra term into the minimized quantity that penalizes disagreement in the positions of spectral lines observed in multiple diffraction orders. The primary advantage of this method is that the lines used do not have to be identified, except for establishing the fact that they are different orders of the same line. This increases the number of constraints on the calibration curve, potentially in spectral regions where no regular calibration lines are available. The mathematical basis of this method is described, and the performance of this method is evaluated on simulated data and experimental data from the National Institute of Standards and Technology (NIST) Electron Beam Ion Trap. We demonstrate the effectiveness of the method on the spectra of highly charged Ag-like Re28+ and nearby charge state ions.

Selective amplification effect on the diffraction efficiency of a phase grating generated by femtosecond laser pulses.

A phase grating that selectively amplifies diffraction orders that are multiples of a determined integer is designed. For the proposed grating, multiples of the fourth order are enhanced. These results are supported by experiments. The structure is inscribed in the volume of a lithium niobate crystal by employing the femtosecond laser pulse micro-machining technique. A model based on the Raman-Nath behavior of the grating predicts a diffraction efficiency enhancement for those selected orders. Moreover, it is observed that by changing the incidence angle allows transferring energy from multiples of fourth orders to multiples of three. These findings have potential applications in optical spectroscopy and optical communications as well as for photonic devices in which a controlled energy exchange between orders is necessary. The basic wave nature of the mentioned effect allows finding a counterpart in different wavelength ranges of the electromagnetic spectrum.

The Nature of X-Rays from Young Stellar Objects in the Orion Nebula Cluster—A Chandra HETGS Legacy Project

The Orion Nebula Cluster (ONC) is the closest site of very young (∼1 Myr) massive star formation The ONC hosts more than 1600 young and X-ray bright stars with masses ranging from ∼0.1–35 M ⊙. The Chandra HETGS Orion Legacy Project observed the ONC with the Chandra High Energy Transmission Grating Spectrometer (HETGS) for 2.1 Ms. We describe the spectral extraction and cleaning processes necessary to separate overlapping spectra. We obtained 36 high-resolution spectra, which include a high-brilliance X-ray spectrum of θ 1 Ori C with over 100 highly significant X-ray lines. The lines show Doppler broadening between 300 and 400 km s−1. Higher spectral diffraction orders allow us to resolve line components of high Z He-like triplets in θ 1 Ori C with unprecedented spectral resolution. Long-term light curves spanning ∼20 yr show all stars to be highly variable, including the massive stars. Spectral fitting with thermal coronal emission line models reveals that most sources show column densities of up to a few times 1022 cm−2 and high coronal temperatures of 10–90 MK. We observe a bifurcation of the high-temperature component where some stars show a high component of 40 MK, while others show above 60 MK, indicating heavy flaring activity. Some lines are resolved with Doppler broadening above our threshold of ∼200 km s−1, up to 500 km s−1. This data set represents the largest collection of HETGS high-resolution X-ray spectra from young pre-main-sequence stars in a single star-forming region to date.