Planar Gratings Research Articles

Bottom-up Gold Filling of Curved X-Ray Gratings

Over the past five years an electrolyte-additive system has been demonstrated and applied to void-free extreme bottom-up filling of high aspect ratio etched silicon structures that are key to advanced grating-based X-ray interferometry. Effective use of the full area of the gratings with conventional X-ray sources requires they have a finite radius of curvature to align the high aspect ratio Au-filled trenches with divergent X-rays. With that in mind, this presentation details bottom-up Au filling in gratings attached to curved holders as in the accompanying figure. Contactless mapping of the Au-filled gratings, also shown in the figure, captures residual (i.e., intrinsic) curvature that is retained after their release from the curved holders. X-ray diffraction quantifies the elastic strains in the Si underlying the Au-filled trenches of the grating. Complementary measurements on the surfaces of unpatterned Si wafers mounted on curved holders are used to understand the curvatures actually imposed in the mounted gratings. Both intrinsically curved gratings and gratings that have been re-bent toward their radius while mounted provide high visibility across the entire field of view of an X-ray interferometer for bio-medical imaging applications. They also have internal strains substantially below those in planar gratings bent to the same radius. Figure 1

Association analysis of Talbot positive self-image and negative self-image for spherical wave illuminating on planar grating

Based on planar grating Fresnel diffraction theory, the correlation between Talbot positive self-image and negative self-image for spherical wave illuminating on planar grating is analyzed by theoretical and experimental methods. The results indicate that Talbot positive and negative self-images of orders 0 and ±1 show a checkerboard shape with periodic structure, with opposite phases when the period magnification factor M is the same. However, the detail of Talbot positive self-image is more detailed than the negative self-image, due to phase reversal and changes in Talbot distance, which imply a relationship of mutual constraints between the two images. Additionally, the peak light intensity of positive and negative self-image increases with the increase of M. Talbot positive and negative self-image are observed at corresponding Talbot distance by theoretical and experimental results, and Talbot distance of the two Talbot images is obviously divided into rapidly decreasing and slowly changing as z 0 increases.

Design of coma-free Hettrick-Underwood type spectrometers for high energy resolution RIXS experimental station.

The Hettrick-Underwood (HU) type design, consisting of a pre-focusing mirror and a varied-line-spacing planar grating (VLS-PG), for the high resolution resonant inelastic x-ray scattering spectrometer is considered. The light path of the HU design is analyzed, and the analytical functions determining the groove parameters of VLS-grating are given. Efforts are made to compare the different choices of the pre-focusing mirrors, circular cylindrical (HU-CM) and elliptical cylindrical (HU-EM). Although the HU-EM type offers great tuning properties with variable-included-angle, it imposes high requirement on the optical element manufacturing accuracy, while the HU-CM type design couples the coma contributions from the pre-mirror and the grating, allowing for mutual compensation of the manufacturing errors of the two optical elements.

Optical design of the time-resolved ARPES beamline of the new material spectroscopy experimental station for the update of CAEP THz-FEL facility

Abstract The Chinese Academy of Engineering Physics Terahertz Free Electron Laser Facility (CAEP THz FEL, CTFEL) is the only high-average power free electron laser terahertz source based on superconducting accelerators in China. The update of the CTFEL is now undergoing and will expand the frequency range from 0.1-4.2 THz to 0.1-125 THz. Two experimental stations for material spectroscopy and biomedicine will be built. A high harmonic generation (HHG) lightsource based beamline at the material spectroscopy experimental station for time-resolved angle-resolved photoemission spectroscopy (ARPES) research will be constructed and the optical design is presented. The HHG lightsource covers the extreme ultraviolet (XUV) photon energy range of 20-50 eV. A Czerny-Turner monochromator with two plane gratings worked in conical diffraction configuration is employed for maintaining the transmission efficiency and preserving the pulse time duration. The calculated beamline transmission efficiency is better than 5% in the whole photon energy range. To our knowledge, this is the first time in China to combine THz-infrared FEL with HHG light source, and this experimental station will be a powerful and effective instrument and give new research opportunities in the future for users doing research on dynamic evolution of excited electron band structure of material surface.

The Correction of Keystone Distortion in Czerny–Turner Spectrometer Using Freeform Surface

In the past, conventional Czerny–Turner spectrometers were usually designed to achieve high resolution while often ignoring astigmatism in the sagittal direction. In contrast, by replacing the focusing mirror with a freeform surface in the structure, we can obtain a Czerny–Turner spectrometer with low keystone distortion by controlling the astigmatism. At the same time, the area sensor can receive all of the spectrum from the optical system. In this paper, we briefly describe the formation of keystone distortion and smile in a plane grating. Additionally, the validity of the method is verified through simulation. Finally, we evaluated the smile and keystone distortion of both the initial and final systems. The keystone and smile were reduced to 1.77 μm and 8.3 μm, respectively, over the wavelength range of 535 nm to 630 nm. Concurrently, the resolution achieved was 0.4 nm.

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.

Research on Dual-Grating Spacing Calibration Method Based on Multiple Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise Combined with Hilbert Transform

The paper proposes a method for the calibration of spacing in dual-grating based on Multiple Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) combined with Hilbert Transform (HT), referred to as Multiple ICEEMDAN-HT. This method addresses the potential impact of nonlinear factors on phase extraction accuracy, consequently on ranging precision in the homodyne interference of the dual-grating. Building upon the ICEEMDAN algorithm, the signal undergoes iterative decomposition and reconstruction using the sample entropy criterion. The intrinsic mode functions (IMFs) obtained from multiple iterations are then reconstructed to obtain the complete signal. Through a simulation and comparison with other signal decomposition methods, the repeatability and completeness of signal reconstruction by Multiple ICEEMDAN are verified. Finally, an actual dual-grating ranging system is utilized to calibrate the spacing of the planar grating. Experimental results demonstrate that the calibration relative error of the Multiple ICEEMDAN-HT phase unwrapping method can be reduced to as low as 0.07%, effectively enhancing the signal robustness and spacing calibration precision.

Comprehensive performance domain tolerance analysis methodology for freeform imaging spectrometers

In recent years, attention has been directed towards cost-effective and compact freeform Schwarzschild imaging spectrometers with plane gratings. The utilization of tolerance analysis serves as a potent approach to facilitate the development of prototypes. Conventional tolerance analysis methods often rely solely on the modulation transfer function (MTF) criterion. However, for a spectrometer system, factors such as the keystone/smile distortion and spectral resolution performance also require consideration. In this study, a tailored comprehensive performance domain tolerance analysis methodology for freeform imaging spectrometers was developed, considering vital aspects such as the MTF, keystone/smile distortion, and spectral resolution. Through this approach, meticulous tolerance analysis was conducted for a freeform Schwarzschild imaging spectrometer, providing valuable insights for the prototype machining and assembly processes. Emphasis was placed on the necessity of precise control over the tilt and decenter between the first and third mirrors, whereas the other fabrication and assembly tolerances adhered to the standard requirements. Finally, an alignment computer-generated hologram (CGH) was employed for the preassembly of the first and third mirrors, enabling successful prototype development. The congruence observed between the measured results and tolerance analysis outcomes demonstrates the effectiveness of the proposed method.

A Review: High-Precision Angle Measurement Technologies.

Angle measurement is an essential component of precision measurement and serves as a crucial prerequisite for high-end manufacturing. It guides the implementation of precision manufacturing and assembly. The current angle measurement methods mainly focus on multiple axes, high precision, and large measurement ranges. This article introduces the technology of angle measurement from the perspectives of single-axis and multi-axis measurement schemes. Firstly, the single-axis measurement scheme is primarily achieved through optical methods, such as encoder discs that measure energy changes and interferometric phase changes, as well as mechanical, electromagnetic, and inertial angle measurement methods, among which interferometric methods offer the highest accuracy, with high cost, and encoder discs provide the largest measurement range with an ordinary price. Secondly, in the multi-axis measurement scheme, autocollimation instruments, including plane mirrors, gratings, and self-designed targets, are the main options. Although grating encoders can achieve three degrees of freedom in angle measurement with an ordinary price, they are limited in terms of measurement range and sensitivity compared to self-designed targets. Lastly, artificial intelligence assistance precision measurement is increasingly being embraced due to significant advancements in computer performance, making it more convenient to identify the relationship between measured values and detection values. In conclusion, angle measurement plays a crucial role in precision manufacturing, and the evolving and improving technologies provide the manufacturing industry with greater choices. The purpose of this review is to help readers quickly find more suitable technical solutions according to current application requirements, such as single/multiple axes, accuracy level, measuring range, budget, etc.

Bottom-up Gold Filling of Trenches in Curved Wafers

A Bi3+ -stimulated Au electrodeposition process in slightly alkaline Na3AuSO32+Na2SO3 electrolytes has been previously demonstrated for void-free extreme bottom-up filling of high aspect ratio trenches in gratings that are key to advanced X-ray imaging technologies. Effective use of the full area of the gratings with conventional X-ray sources requires they have a finite radius of curvature to align the high aspect ratio Au-filled trenches with divergent X-rays. With that in mind, this work demonstrates bottom-up Au filling in gratings that are attached to curved holders. Contactless mapping of the Au-filled gratings captures residual curvature that is retained after their release from the curved holders (i.e., intrinsic curvature). X-ray diffraction captures the elastic strains in the Si underlying the Au-filled trenches of the grating. Complementary measurements on the surfaces of unpatterned Si wafers mounted on curved holders capture the actual curvatures and strains imposed in the mounted gratings. The gratings, either intrinsically curved or re-bent, provide high visibility across the entire field of view of an X-ray phase contrast imaging system with elastic strains substantially below those in planar gratings bent to the same radius.

Analysis of Inside Response and Electric Field Distribution by Plane Grating in Dispersive Medium

Analysis of Inside Response and Electric Field Distribution by Plane Grating in Dispersive Medium

Planar crossed-fork gratings with sinusoidal transmittance for eliminating high-order diffraction

Planar crossed-fork gratings with sinusoidal transmittance for eliminating high-order diffraction

High energy x-ray Talbot-Lau interferometer employing a microarray anode-structured target source to extend the field of view.

High energy and large field of view (FOV) phase contrast imaging is crucial for biological and even medical applications. Although some works have devoted to achiving a large field of view at high energy through bending gratings and so on, which would be extremely challenging in medical high energy imaging. We analyze the angular shadowing effect of planar gratings in high-energy X-ray Talbot-Lau interferometer (XTLI). Then we design and develop an inverse XTLI coupled with a microarray anode-structured target source, to extend the FOV at high energy. Our experimental results demonstrate the benefit of the source in inverse XTLI and a large FOV of 106.6 mm in the horizontal direction is achieved at 40 keV. Based on this system, experiments of a mouse demonstrate the potential advantage of phase contrast mode in imaging lung tissue. We extend the FOV in a compact XTLI using a microarray anode-structured target source coupled with an inverse geometry, which eliminates grating G0 and relaxes the fabrication difficulty of G2. We believe the established design idea and imaging system would facilitate the wide applications of XTLI in high energy phase contrast imaging.

Grating designs for cone beam edge illumination X-ray phase contrast imaging: a simulation study.

Edge illumination is an emerging X-ray phase contrast imaging technique providing attenuation, phase and dark field contrast. Despite the successful transition from synchrotron to lab sources, the cone beam geometry of lab systems limits the effectiveness of using conventional planar gratings. The non-parallel incidence of X-rays introduces shadowing effects, worsening with increasing cone angle. To overcome this limitation, several alternative grating designs can be considered. In this paper, the effectiveness of three alternative designs is compared to conventional gratings using numerical simulations. Improvements in flux and contrast are discussed, taking into account practical considerations concerning the implementation of the designs.

Electron Beam Third Harmonic Amplification Generates High-Power Tunable Terahertz Radiation

A novel approach to extract and amplify the third harmonic of electron beam to generate high-power terahertz radiation is presented. Three planar grating structures operating in the backwave region are used for the extraction and amplification of the electron beam from the fundamental modulation, the fundamental amplification, and the third harmonic. This results in an amplified output of the fundamental wave and a high power output of the fundamental triplet frequency. The planar grating structure is easier to machine and assemble than conventional harmonic amplifiers and increases the flow rate of the electron beam. Calculations show that with an input signal of 119.5–120.6 GHz at 80 mW and a 35-A/cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\text{2}}$</tex-math> </inline-formula> electron beam in adjustment from 27.5 to 29.3 keV, the structure has an output signal of hundreds of milliwatts in the range of 358.5–361.8 GHz, with a power output of 583.2 mW at the central frequency point of 360 GHz. The harmonic signal is output while a watt-level fundamental signal can be output.

Dynamics of surface-plasmon lasing in planar metal gratings on semiconductor.

We investigate the dynamics of surface plasmon (SP) lasing in Au gratings fabricated on InGaAs with a period of around 400 nm, which locates the SP resonance near the semiconductor energy gap and facilitates efficient energy transfer. By optically pumping the InGaAs to reach the population inversion required for the amplification and the lasing, we observe SP lasing at specific wavelengths that satisfy the SPR condition depending on the grating period. The carrier dynamics in semiconductor and the photon density in the SP cavity was investigated from the time-resolved pump-probe measurement and the time resolved photoluminescence spectroscopy, respectively. Our results reveal that the photon dynamics is strongly correlated with the carrier dynamics and the lasing build-up is accelerated as the initial gain proportional to the pumping power increases, and this trend is satisfactorily explained using the rate equation model.

Ultrashort X-ray Free Electron Laser Pulse Manipulation by Optical Matrix

Free electron laser (FEL) is capable of producing ultra-short X-ray pulses. The estimation of X-ray pulse propagation is the key process of X-ray FEL beamline design. By using the Kostenbauder matrix approach, the evolution of an ultra-short pulse in a beamline system can be calculated. Therefore, it is of significant importance to investigate the Kostenbauder matrices of different kinds of X-ray optics. In this work, we derive a unified 6 × 6 optical matrix to describe various kinds of X-ray optical elements, including varied-line-spacing (VLS) toroidal grating, VLS spherical grating, VLS cylindrical grating, VLS plane grating, toroidal grating, spherical grating, cylindrical grating, plane grating, toroidal mirror, spherical mirror, cylindrical mirror, and plane mirror. These optics are usually adopted in soft X-ray regime. We apply this method to describe the transverse focusing, pulse front tilt, and pulse stretching after an X-ray pulse going through a VLS plane grating monochromator (VLS-PGM). We also use this approach to simulate a grating compressor which can be used to compress chirped soft X-ray pulse. This work is helpful in the design and optimization of X-ray beamline systems.

A Long-Period Waveguide Grating Sensor for Accurate Simultaneous Detection of Dual Analytes

To the best of our knowledge, we are the first to report the existence of two dispersion turning points (DTP) in an optimized planar waveguide long-period grating (LPG) sensor for the lowest order cladding mode. Using numerical simulation, we investigate the potential of the sensor structure for bulk refractive index (RI) and surface sensing, with the goal of predicting its possible application as an integrated photonic biosensor. The proposed sensor exhibits an exceptionally high RI sensitivity ~7500 nm/refractive index unit (RIU) (~10000 nm/RIU) near lower (higher) DTP. The surface sensitivity, which is incredibly high in this form of structure, is found to be 6.5 nm/nm (7 nm/nm) near lower (higher) DTP for the RI relevant for biosensing. Utilizing the sensing characteristics of both the DTP, we propose a dual-slot biosensor by cascading two LPGs having different grating periods. The proposed biosensor shows two independent dual-resonance phenomena and is, therefore, capable of simultaneous detection of dual analytes. Utilizing the proposed dual-slot biosensor, we present simulation results for specific detection of Hepatitis B antigen and DNA hybridization simultaneously. The proposed biosensor will reduce the sensor cost as well as detection time since a single source and detector are required to sense two different analytes at once.

Miniaturized two-channel broadband spectrometer based on variable-spacing concave blazed gratings

Recently, it becomes a tendency for cost-effective, portable spectrometers to have more applications from scientific research to daily life, e.g., in food safety and air pollution analysis. While most spectrometers utilize plane gratings, we demonstrate a more miniaturized, two-channel, broadband spectrometer based on variable-spacing concave gratings, combining the functionality of imaging optics and diffraction grating in one component. The added degree of design freedom in the micro-sized grating spacing further corrects most optical aberrations, thus the design achieves a tiny volume of <26 × 12 × 10 mm3 with a high spectral resolution. Simulation results show an optical resolution of <1.6 nm in the VIS-channel (400 to 790 nm) and <3.1 nm in the NIR-channel (760 to 1520 nm). The blazed structure of grating grooves provides a high overall diffraction efficiency in the whole spectral range, more than 50% on average. To further validate the feasibility for mass production, we successfully manufactured the variable-spacing concave gratings by using diamond tooling for fabricating the master mold and hot embossing for replication. Our fabricated variable-spacing grating replicas have a diffraction efficiency up to 70% in the VIS-channel and up to 60% in the NIR-channel. We built the prototype with fabricated concave gratings, and experimental results show a good match (error < 7 % ) in spectral resolution with the nominal design.

Investigation into the writing dynamics of planar Bragg gratings using pulsed 213 nm radiation

We present the first substantive investigation into the photosensitivity response of planar-doped silica to pulsed 213 nm light. We look at the response over a broad range of fluences and average powers to identify suitable regimes for simultaneous waveguide and Bragg grating writing. Unlike previously reported work, we do not observe any clear evidence of a similar non-linear photosensitivity response in B/Ge doped silica. We discuss laser-induced damage, saturation of photosensitivity, and grating response. This paper presents writing regimes for small spot direct UV writing where the photosensitivity and grating response are optimum, thereby confirming the suitability of the fabrication approach for complex devices.