Geometrical Diffraction Research Articles

Modeling stochastic elastic wave diffraction by the tips of randomly rough defects

Elastic wave scattering from a randomly rough surface of a finite length includes surface reflections and diffractions from the tips. Previous research has focused upon reflection waves with applications in ultrasonic defect detection, seismic wave exploration and phonon boundary transport. However, waves diffracted from the tips/edges have been largely neglected so far for rough defects, despite their importance in engineering applications including ultrasonic defect sizing and imaging for assessment of structural integrity. Currently understanding the statistical nature of elastic wave tip diffraction and the role of roughness is limited due to the lack of theoretical studies. In this article, we develop a statistical geometrical tip diffraction (SGTD) theory to rapidly predict the stochastic properties of tip diffraction amplitude as a function of surface roughness and incident angle. By applying a small slope perturbation to the model, a simplified analytical solution of tip diffraction is obtained. It is found that for defects with small to medium roughness, the diffraction amplitude explicitly follows a Gamma distribution, and its mean and the standard deviation are both proportional to the square of the rms slope. High-fidelity Monte Carlo finite element simulations are then run to evaluate the accuracy of the theoretical model. The range of validity of the analytical solution with respect to the level of roughness and the incident angle is obtained. The SGTD method is accurate when the correlation length is approximately equivalent or larger than one wavelength, for a wide range of angles. It is also applicable for a correlation length as short as half wavelength, but only for small rms values and when the beam angle is larger than 45∘. In addition, at large angles, the tip diffraction is almost not affected by roughness, being very similar to that from a smooth crack. This is explained by the significant dependence on the beam angle factor explicitly shown in the theoretical solution.

Optimization and fabrication of chromium grating in self-traceable interferometer

Metrological methods rooted in natural constants present a robust strategy for ensuring traceability in nanometric measurements. A Chromium (Cr) grating, meticulously constructed through atom lithography and possessing a pitch of d = 212.7705 ± 0.0049 nm intrinsically traceable to the Cr transition frequency 7S3→7P40, exhibits promising potential as a self-traceable length standard in nano-length metrology via a grating interferometer. The objective of this research is to elucidate and optimize the diffraction characteristics that augment the Cr grating's functionality as a self-traceable length standard within the length traceability chain predicated on the Cr transition frequency. To this end, we explore the geometric morphology and diffraction characteristics of the Cr grating. This investigation also dissects the influence of the grating's polarization-sensitive traits on the Littrow configuration grating interferometer and establishes the criteria for Cr grating fabrication. Empirically, we fabricate an enlarged Cr grating through scanning atom lithography, delineate its diffraction performance, and perform an initial verification of length measurement in a self-traceable grating interferometer. This investigation aligns with the global progression towards a more streamlined metrology development, offering a valuable benchmark for propelling future advancements in metrological technologies within the new traceability chain.

Design of an off-axis axiparabola with inclined wavefront correction to obtain a straight focal line.

The axiparabola is a novel reflective element proposed in recent years, which can generate a long focal line with high peak intensity, and has important applications in laser plasma accelerators. The off-axis design of an axiparabola has the advantage of separating the focus from incident rays. However, an off-axis axiparabola designed by the current method always produces a curved focal line. In this paper, we propose a new method to design its surface by combining geometric optics design and diffraction optics correction, which can effectively convert a curved focal line into a straight foal line. We reveal that the geometric optics design inevitably introduces an inclined wavefront, which leads to the bending of the focal line. To compensate for the tilt wavefront, we use an annealing algorithm to further correct the surface through diffraction integral operation. We also carry out numerical simulation verification based on scalar diffraction theory, which proves that the surface of this off-axis mirror designed by this method can always obtain a straight focal line. This new method has wide applicability in an axiparabola with any off-axis angle.

Research Status and Progress of Multiples Suppression Based on Radon Transform

The existence of multiple waves in seismic data has a substantial impact on earthquake imaging, inversion, and interpretation results. As a result, multiples are often suppressed as noise prior to seismic data preattack processing. Currently, there are two primary methods for suppressing multiple reflections in seismic data. One is a filtering technique based on geometric differences in the seismic waves, while the other is based on wave equation methods. The Radon transform, which suppresses multiple reflections, belongs to the class of geometric seismic diffraction filtering techniques. In the process of seismic data processing, it effectively separates multiple reflections from seismic data by utilizing the characteristic differences between primary and multiple reflections, thereby achieving noise attenuation and improving the signal-to-noise ratio of the data. This article primarily investigates the current state of methods for suppressing multiple reflections based on the Radon transform, both domestically and internationally. By introducing various forms and fundamental principles of the Radon transform, this study analyzes and compares the adaptability and pros and cons of each type of Radon transform. The high-precision Radon transform can effectively address the sawtooth phenomenon and energy dispersion issues that arise in the least-squares Radon transform. It also highlights the challenges associated with suppressing multiple reflections in the Radon transform and provides a glimpse into future developments.

Ray-Tracing Model for Generalized Geodesic-Lens Multiple-Beam Antennas

geodesic-lenses are a compelling alternative to traditional planar dielectric lens antennas, as they are low loss and can be manufactured with a simple mechanical design. However, a general approach for the design and analysis of more advanced geodesic-lens antennas has been elusive, limiting the available tools to rotationally symmetric surfaces. In this article, we present a fast and efficient implementation built on geometrical optics and scalar diffraction theory. A numerical calculation of the shortest ray path (geodesic) using an open-source library helps quantify the phase of the electric field in the lens aperture, while the amplitude is evaluated by applying ray-tube power conservation theory. The Kirchhoff-Fresnel diffraction formula is then employed to compute the far field of the lens antenna. This approach is validated by comparing the radiation patterns of a transversely compressed geodesic Luneburg lens (elliptical base instead of circular) with the ones computed using commercial full-wave simulators, demonstrating a substantial reduction in computational resources. The proposed method is then used in combination with an optimization procedure to study possible compact alternatives of the geodesic Luneburg lens with size reduction in both the transverse and vertical directions.

Microstates of position and momentum result in gravitational entropy

Measurements of a black hole’s position are limited in four different ways: Absorption of short-wavelength photons by the black hole, gravitational lensing’s interference with geometric diffraction, gravitational redshift decreasing the resolution of interactions close to the event horizon, and the relatively long wavelength of Hawking radiation. These limitations mean that a black hole cannot be localized more precisely than its Schwarzschild radius. Limitations on measuring mass and velocity mean that the position and momentum of a black hole cannot be simultaneously known more precisely than 2 h rs/lP , a value more restrictive than the Heisenberg uncertainty principle. Hidden information about a black hole’s position and momentum results in many possible microstates that are indistinguishable to an observer. One way to interpret the physical meaning of Bekenstein‐Hawking entropy is as a measure of the number of these microstates. This interpretation allows entropy to be generalized to objects in any gravitational field, because gravitational redshift increases uncertainty about position and momentum for objects in all gravitational fields, not just those of black holes.

A comprehensive review on optics and optical materials for planar waveguide-based compact concentrated solar photovoltaics

In recent years, the technology of waveguide-based planar solar concentrators has been getting more attention in the Concentrated Photovoltaics (CPV) sector due to its compact design and performance versatility and its extended potential applicability from large power plants to built environments, such as Building Integrated Photovoltaics (BIPV). Within the last two decades, geometric design-based Planar Light Concentrator (PLC) and diffraction grating-based PLC have been developed with versatile design architectures along with luminescent PLC, which relies primarily on the development of concerned luminescent optical materials. However, congregating and evaluating the technical advancement gained in the field seems challenging due to the segregated state-of-the-art approaches. Hence, this review attempted to organise the present state of waveguide-based PLC in the frame of reference of PLC optics and optical material design. A systematic comparison of optics and optical material design parameters and the merit of the different PLC systems have been explored within this review to serve as a ready reference for its adoption to develop compact planar waveguide-based CPV systems.

Off-epicentral measurement of laser-ultrasonic shear-wave velocity and its application to elastic-moduli evaluation

This study investigates the off-epicentral measurement system and methodology of laser-ultrasonic shear waves in the ablative regime, subsequently focusing on its application to the elastic-moduli evaluation. The proposed scheme facilitates the measurement of the shear-wave velocity by using the crosscorrelation of successive shear-wave pulse echoes, ensuring high reliability and reproducibility of the calculation results. Since the geometric diffraction induced by the finite dimensions of laser-ultrasonic source and receiver can increase the measurement error, far-field diffraction correction for the off-epicenter detection has been derived theoretically. Results have shown that the far-field diffraction correction error is of the same order as random error mainly caused by the finite observation time, signal-to-noise ratio and frequency bandwidth, and therefore cannot be neglected. The feasibility of this approach is then demonstrated by inspecting annealed commercial purity titanium plates. Good agreement of experimentally measured and theoretical values of shear-wave velocity confirms the validity of the proposed approach. The ultrasonic measurement-determined shear modulus shows a maximum deviation of ＋3.6% from the standard value of an isotropic material.

Visible and short-wavelength infrared light collimation through carbon nanotube, parallel-hole collimators.

Traditional collimators typically require large optics and/or long pathlengths which makes miniaturization difficult. Carbon nanotube templated microfabrication offers a solution to pattern small 3D structures, such as parallel hole collimators. Here we present the characterization of a carbon nanotube parallel hole collimator design and its efficacy in visible and short wavelength infrared light. Comparison to geometric and far field diffraction models are shown to give a close fit, making this a promising technology for miniaturized diffuse light collimation.

Refraction of Oblique Shock Wave on a Tangential Discontinuity

The refraction of an oblique shock wave on a tangential discontinuity dividing two gas flows with different properties is considered. It is shown that its partial reflection occurs with the exception of the geometrical diffraction of an oblique shock. Another oblique shock, expansion wave or weak discontinuity that coincides with the Mach line can act as a reflected disturbance. This study focuses on the relationships that define the type of reflected discontinuity and its parameters. The domains of shock wave configurations with various types of reflected discontinuities, including characteristic refraction and refraction patterns with a reflected shock and a reflected rarefaction wave, are analyzed. The domains of existence of various shock wave structures with two types of reflected disturbance, and the boundaries between them, are defined. The domains of parameters with one or two solutions exist for the characteristic refraction. Each domain is mapped by the type of refraction with regard to the Mach number, the ratio of the specific heat capacities of the two flows and the intensity of a refracted oblique shock wave. The conditions of the regular refraction and the Mach refraction are formulated, and the boundaries between the two refraction types are defined for various types of gases. Refraction phenomena in various engineering problems (hydrocarbon gaseous fuel and its combustion products, diatomic gas, fuel mixture of oxygen and hydrogen, etc.) are discussed. The result can be applied to the modeling of the shock wave processes that occur in supersonic intakes and in rotating and stationary detonation engines. The solutions derived can be used by other researchers to check the quality of numerical methods and the correctness of experimental results.

Geometric Phase in Optics: From Wavefront Manipulation to Waveguiding

AbstractGeometric phase is a unifying and central concept in physics, including optics. As a matter of fact, optics played a pivotal role from the inception of this new paradigm, as some of the first experimental demonstrations have been carried out in optics. A specific type of geometric phase was first introduced by Pancharatnam while investigating interference effects between different polarizations. This specific type of geometric phase, nowadays called the Pancharatnam–Berry phase, is related to the variation of light polarization, encompassing exotic properties when compared with the dynamic phase associated with the optical path. The most widespread manifestation of the Pancharatnam–Berry phase occurs in the presence of a twisted anisotropic material, yielding a point‐wise phase modulation proportional to the local rotation angle of the material. Here the basic mechanism behind the Pancharatnam–Berry phase is discussed. The various applications of this relatively original concept in photonics are then reviewed, presenting both the most important results and manufactured devices reported in literature. The interplay between geometric phase and diffraction occurring in bulk structures is discussed in detail. In the latter case it is shown how geometric phase can be harnessed to generate a new kind of optical waveguide without the necessity of any index gradient.

Loss ratio parameter γ to analyze transmission characteristics for optical antenna systems.

Analyzing optical antenna systems through geometrical optics is quite popular for its convenience, which, however, may cause remarkable errors. This paper uses both geometrical optics and diffraction theory to analyze the performance of a traditional optical antenna system, and the results calculated through the two methods are carefully compared. Based on the comparison, it shows the situations in which geometric optics will cause significant errors. In addition, a parameter γ is defined to quickly determine whether geometrical optics is suitable for analyzing optical antenna systems under some situations. This paper can help engineers quickly choose the proper method for designing and analyzing optical antenna systems.

Fast diffraction pathfinding for dynamic sound propagation

In the context of geometric acoustic simulation, one of the more perceptually important yet difficult to simulate acoustic effects is diffraction, a phenomenon that allows sound to propagate around obstructions and corners. A significant bottleneck in real-time simulation of diffraction is the enumeration of high-order diffraction propagation paths in scenes with complex geometry (e.g. highly tessellated surfaces). To this end, we present a dynamic geometric diffraction approach that consists of an extensive mesh preprocessing pipeline and complementary runtime algorithm. The preprocessing module identifies a small subset of edges that are important for diffraction using a novel silhouette edge detection heuristic. It also extends these edges with planar diffraction geometry and precomputes a graph data structure encoding the visibility between the edges. The runtime module uses bidirectional path tracing against the diffraction geometry to probabilistically explore potential paths between sources and listeners, then evaluates the intensities for these paths using the Uniform Theory of Diffraction. It uses the edge visibility graph and the A* pathfinding algorithm to robustly and efficiently find additional high-order diffraction paths. We demonstrate how this technique can simulate 10th-order diffraction up to 568 times faster than the previous state of the art, and can efficiently handle large scenes with both high geometric complexity and high numbers of sources.

Investigation on a 220 GHz Quasi-Optical Antenna for Wireless Power Transmission

This paper investigates a 220 GHz quasi-optical antenna for millimeter-wave wireless power transmission. The quasi-optical antenna consists of an offset dual reflector, and fed by a Gaussian beam that is based on the output characteristics of a high-power millimeter-wave radiation source-gyrotron. The design parameter is carried on by a numerical code based on geometric optics and vector diffraction theory. To realize long-distance wireless energy transmission, the divergence angle of the output beam must be reduced. Electromagnetic simulation results show that the divergence angle of the output beam of the 5.6 mm Gaussian feed source has been significantly reduced by the designed quasi-optical antenna. The far-field divergence angle of the quasi-optical antenna in the E plane and H plane is 1.0596° and 1.0639°, respectively. The Gaussian scalar purity in the farthest observation field (x = 1000 m) is 99.86%. Thus, the quasi-optical antenna can transmit a Gaussian beam over long-distance and could be used for millimeter-wave wireless power transmission.

End-to-end nanophotonic inverse design for imaging and polarimetry

AbstractBy codesigning a metaoptical front end in conjunction with an image-processing back end, we demonstrate noise sensitivity and compactness substantially superior to either an optics-only or a computation-only approach, illustrated by two examples: subwavelength imaging and reconstruction of the full polarization coherence matrices of multiple light sources. Our end-to-end inverse designs couple the solution of the full Maxwell equations—exploiting all aspects of wave physics arising in subwavelength scatterers—with inverse-scattering algorithms in a single large-scale optimization involving≳104$\gtrsim {10}^{4}$degrees of freedom. The resulting structures scatter light in a way that is radically different from either a conventional lens or a random microstructure, and suppress the noise sensitivity of the inverse-scattering computation by several orders of magnitude. Incorporating the full wave physics is especially crucial for detecting spectral and polarization information that is discarded by geometric optics and scalar diffraction theory.

Study of the Possibility Of Replacing an Integrated Airframe with a Flat Polygonal Screen to Estimate The Efficiency of Noise Screening of Engines Using Geometric Diffraction Theory

Using the example of an integrated airframe, we performed a computational and experimental study of the possibility of using geometric diffraction theory (GDT) to calculate the sound diffraction when the airframe is replaced with simulating flat polygonal screen as pertains to the effectiveness of noise screening of aircraft power plants. We compared (1) impulse responses experimentally measured with maximum length sequences and the reciprocity theorem for both a three-dimensional model of the airframe and its plane model with (2) the responses calculated using GDT; the results showed good qualitative agreement for observation points in the geometric shadow zone and in the illuminated area, as well as quantitative coincidence in the frequency range characteristic of jet noise and the first harmonics of the blade passing frequency of a propeller or fan.

Fast calculation method for parabolic-mirror-reflection holographic 3D display using wavefront segmentation.

Convex-parabolic-mirror reflection enables a very wide viewing zone in a holographic three-dimensional (3D) display. In this work, segmentation is introduced to reduce the calculation time of holograms in a convex-parabolic-mirror-reflection holographic 3D display. Wavefront segmentation can practically limit the lateral spread of the wavefront to be considered, which enables the application of geometrical approximation and conventional diffraction theories such as Fresnel diffraction. Thus, diffraction calculation via the convex parabolic mirror can be derived analytically and calculated rapidly using fast Fourier transform (FFT). Our proposed FFT-based method can calculate the diffraction integral 7000 times faster than our previous method, which involved calculating directly the diffraction integral without FFT. In addition, numerical simulation and an optical experiment are presented to verify our proposal.

Using the Correlation Model of Random Quadrupoles of Sources to Calculate the Efficiency of Turbulent Jet Noise Screening with Geometric Diffraction Theory

The paper presents the results of a computational–experimental study of jet noise reduction using the screening effect. According to correlation theory, the noise sources of a single circular jet are represented by a set of uncorrelated quadrupoles. Using the basic relations of geometric diffraction theory (GDT), expressions are obtained for the sound field emitted by a point quadrupole source located near an acoustically rigid infinite half-plane. Using the expressions obtained in the framework of the GDT, the correlation model of the jet noise sources was adapted to the calculation of the sound field in the presence of a flat rectangular screen. A comparison of the calculated and experimentally measured spectra of sound pressure levels, performed at a given jet velocity and various screen positions, showed good qualitative, and for certain observation angles, quantitative agreement.

Fast rigorous mask model for extreme ultraviolet lithography.

The calculation of extreme ultraviolet (EUV) mask diffraction spectrum is the key of EUV lithography simulation. In this paper, a fast rigorous EUV mask model is proposed to calculate the diffraction spectrum fast and accurately. Based on the mask structure decomposition method, the relationship among the region diffraction, the boundary diffraction of the absorber, and the direction of incident light is analyzed at first. Then the frequency-domain functions related to angle of incidence and diffraction angle are established to model the geometrical and boundary diffraction of the absorber. The fast rigorous EUV mask model is established by combining the equivalent layer multilayer model based on the Fresnel formula and the accurate absorber model. Simulations and comparisons show the effectiveness of the proposed model. For the 14 nm vertical line-space pattern, the calculation errors of critical dimension (CD) via the proposed model are reduced by 80.6% and 93.9% compared with the structure decomposition method for dense and isolate features.

Effect of Defective Microstructure and Film Thickness on the Reflective Structural Color of Self-Assembled Colloidal Crystals.

Structural color arises from geometric diffraction; it has potential applications in optical materials because it is more resistant to environmental degradation than coloration mechanisms that are of chemical origin. Structural color can be produced from self-assembled films of colloidal size particles. While the relationship between the crystal structure and structural color reflection peak wavelength is well studied, the connection between assembly quality and the degree of reflective structural color is less understood. Here, we study this connection by investigating the structural color reflection peak intensity and width as a function of defect density and film thickness using a combined experimental and computational approach. Polystyrene microspheres are self-assembled into defective colloidal crystals via solvent evaporation. Colloidal crystal growth via sedimentation is simulated with molecular dynamics, and the reflection spectra of simulated structures are calculated by using the finite-difference time-domain algorithm. We examine the impact of commonly observed defect types (vacancies, stacking fault tetrahedra, planar faults, and microcracks) on structural color peak intensity. We find that the reduction in peak intensity scales with increased defect density. The reduction is less sensitive to the type of defect than to its volume. In addition, the reflectance of structural color increases as a function of the crystal thickness, until a plateau is reached at thicknesses greater than about 9.0 μm. The maximum reflection is 78.8 ± 0.9%; this value is significantly less than the 100% reflectivity predicted for a fully crystalline, defect-free material. Furthermore, we find that colloidal crystal films with small quantities of defects may be approximated as multilayer reflective materials. These findings can guide the design of optical materials with variable structural color intensity.