Diffraction Theory Research Articles

Accelerated second-order hydrodynamic load calculation on semi-submersible floaters

A rapid method for calculation of second-order hydrodynamic wave loads on semi-submersible platforms is developed and validated against radiation–diffraction theory. The method is based on slender-body theory and builds on modal truncation of the quadratic transfer function (QTF). The semi-submersible floater is split into individual members and the existing theory for vertical cylindrical columns is extended to include the heave force. Further expressions for the surge, heave and pitch load on the horizontal pontoons are derived and implemented. The accuracy of the method is assessed by comparison to radiation–diffraction results using the Pinkster approximation. We find that the slender-body approximation for the column surge force is most accurate for small values of the diameter-to-draft ratio. For the three sea states considered, this error is below 10% for diameter-to-draft ratios less than 0.2.Error analysis is provided for the column heave and pitch and the pontoon loads. For all members, application of 128 modes in the QTF approximation is found sufficient to accurately represent the full slender-body QTF solution.Next, the first- and second-order loads on the full floater under different sea state conditions are compared to radiation–diffraction theory. With 128 modes, the second-order loads are obtained 2500 times faster than with conventional approaches with error levels of 22% for surge, 10% for pitch and zero error for heave. The surge error is discussed and linked to the small draft of the columns. The numerical efficiency of the method allows the consideration of second-order loads in the first stages of the design and optimisation of semi-submersible floaters.

Exploring the Validity of Plane and Spherical Millimeter-Wave Incidences for Multiple-Diffraction Calculations in Wireless Communication Systems

The focus of this work is to determine at which threshold can the results for both plane and spherical wave incidence assumptions either converge or deviate when performing multiple diffraction attenuation calculations. The analysis has been carried out—for various millimeter-wave frequencies, inter-obstacle spacings, and angles of incidence—by employing a pair of two-dimensional (2D) hybrid formulations based on both the uniform theory of diffraction and physical optics (UTD-PO). This way, we seek to demonstrate under which circumstances each wave incidence assumption can be valid in environments that entail millimeter-wave bands. Based on this, we may ensure the minimum necessary distance from the transmitter to the first diffracting obstacle for the convergence of the spherical wave incidence solution onto that of the plane wave with a relative error below 0.1%. Our results demonstrate that for less than four diffracting elements, the minimum necessary distance engages in quasi-linear behavior under variations in both the angle of incidence and obstacle spacing. Notably, the considered frequencies (60–100 GHz) have almost no bearing on the results. Our findings will facilitate the simplified, more accurate and realistic planning of millimeter-wave radio communication systems, with multiple diffractions across various obstacles.

Study on the orthogonality property of Zernike modes in light beams undergoing free space propagation.

This paper presents a study to investigate how the orthogonality property of Zernike modes gets modified as a light beam carrying the mode in its phase propagates through free space. We use a numerical simulation using scalar diffraction theory to generate propagated light beams carrying the commonly encountered Zernike modes. We present our results in terms of the inner product and orthogonality contrast matrix at propagation distances ranging from near field to far field regions. Our study will help in the understanding of how far the Zernike modes describing the phase profile of a light beam in a given plane remain approximately orthogonal to one another on propagation.

Fraunhofer diffraction pattern of a Gaussian beam passing through a photorefractive crystal Bi12GeO20

In this theoretical–experimental study, we use the Fresnel–Kirchhoff diffraction theory to simulate the formation of the far-field diffraction pattern of a divergent Gaussian beam propagated through a photorefractive crystal Bi12GeO20 (BGO). We show that for the BGO, in addition to the wavefront curvature and change in the refractive index of the medium due to light intensity, there is a third contribution affecting the medium-induced nonlinear phase shift; the latter is related to the additional change in the refractive index produced by the photorefractive nature effect. We consider that this work contributes to the characterization of photorefractive materials using diffraction patterns.

Moving on from Silicon to the Heavier Tetrels: Germyl- and Stannyl-Substituted Phosphole Derivatives

Germyl- and stannyl-substituted phospholes have been prepared and isolated. The increased reactivity of the tetrel carbon bond requires increased effort in purification by initial transformation to the chalcogen derivatives and subsequent reduction to the phosphole after subsequent to chromatographic purification for the germanium derivative. The photophysical properties of the germyl phosphole are comparable to that of its silyl analogue, whereas the stannyl phospholes turned out to be nonluminescent. All isolated compounds have been characterized by NMR spectroscopy, mass spectrometry, and elemental analysis. Furthermore, single-crystal X-ray diffraction and density functional theory (DFT) calculations have been performed on selected compounds.

Dual-band and dual-polarized reflective Fresnel zone plate design based on Fractal shape

In this study, a dual-polarized and dual band reflective Fresnel zone plate with reconfigurable beam is proposed on the basis of fractal frequency selective surface (FSS) unit with nearly 360° phase tunability. Firstly, a new phase distribution calculation strategy based on Fresnel diffraction theory is proposed to improve the performance under certain scenarios like sparse arrays. Then, a novel fractal shape is put forward and applied to the design of the Fresnel zone plate. The introduction of the fractal structure makes the unit cell perform dual band, dual polarization and 309° phase tunability characteristics. Due to the self-symmetry of the unit cell, the proposed fractal Fresnel zone plate (FFZP) is capable of beam steering in ± 45° in both TE and TM incident waves. Besides, the proposed structure shows small performance degradation when it comes to oblique incidence up to 45°, which decreases the focal diameter ratio and profile of the proposed FFZP. The operating bandwidth of the FFZP can reach up to 700 MHz at X and Ku bands. It is applicable in a wide range of RF and microwave settings such as satellite and base station.

Numerical geometric acoustics: An eikonal-based approach for modeling sound propagation in 3D environments

We present algorithms for solving high-frequency acoustic scattering problems in complex domains. The eikonal and transport partial differential equations from the WKB/geometric optic approximation of the Helmholtz equation are solved recursively to generate boundary conditions for a tree of eikonal/transport equation pairs, describing the phase and amplitude of a geometric optic wave propagating in a complicated domain, including reflection and diffraction. Edge diffraction is modeled using the uniform theory of diffraction. For simplicity, we limit our attention to domains with piecewise linear boundaries and a constant speed of sound. The domain is discretized into a conforming tetrahedron mesh. For the eikonal equation, we extend the jet marching method to tetrahedron meshes. Hermite interpolation enables second order accuracy for the eikonal and its gradient and first order accuracy for its Hessian, computed using cell averaging. To march the eikonal on an unstructured mesh, we introduce a new method of rejecting unphysical updates by considering Lagrange multipliers and local visibility. To handle accuracy degradation near caustics, we introduce several fast Lagrangian initialization algorithms. We store the dynamic programming plan uncovered by the marcher in order to propagate auxiliary quantities along characteristics. We introduce an approximate origin function which is computed using the dynamic programming plan, and whose 1/2-level set approximates the geometric optic shadow and reflection boundaries. We also use it to propagate geometric spreading factors and unit tangent vector fields needed to compute the amplitude and evaluate the high-frequency edge diffraction coefficient. We conduct numerical tests on a semi-infinite planar wedge to evaluate the accuracy of our method. We also show an example with a more realistic building model with challenging architectural features. Finally, we demonstrate a simple approach to extending the method to handle nonconstant speeds of sound by modifying the semi-Lagrangian updates to account for a varying speed.

Revisiting the Design Strategies for Metasurfaces: Fundamental Physics, Optimization, and Beyond.

Over the last two decades, the capabilities of metasurfaces in light modulation with subwavelength thickness have been proven, and metasurfaces are expected to miniaturize conventional optical components and add various functionalities. Herein, various metasurface design strategies are reviewed thoroughly. First, the scalar diffraction theory is revisited to provide the basic principle of light propagation. Then, widely used design methods based on the unit-cell approach are discussed. The methods include a set of simplified steps, including the phase-map retrieval and meta-atom unit-cell design. Then, recently emerging metasurfaces that may not be accurately designed using unit-cell approach are introduced. Unconventional metasurfaces are examined where the conventional design methods fail and finally potential design methods for such metasurfaces are discussed.

Digital-optical co-design enables athermalization of hybrid optical systems.

We proposed a digital-optical co-design that can effectively improve the image quality of refractive-diffractive hybrid imaging systems over a wide ambient temperature range. Diffraction theory was used to establish the degradation model and blind deconvolution image recovery algorithm was used to perform recovery for simulated images. The peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) were used to evaluate the algorithm performance. A cooled athermalization dual-band infrared optical system with a double-layer diffractive optical element (DLDOE) was designed, and the results show an overall improvement for both PSNR and SSIM overall the whole ambient temperature range. This demonstrates the effectiveness of the proposed method for the image quality improvement of hybrid optical systems.

Experimental and theoretical study of novel germanium tungstates compounds GexW1-xO3 (x ∼ 1/4, 1/2) and Ge1-xWO4 (x ∼ 0.2)

The crystal structures of three (03) novel germanium tungstates were investigated by single-crystal X-ray diffraction and density functional theory (DFT) calculations. The structures are characterized by distorted MO6(M = Ge/W) octahedral, forming infinite zigzag chains.In GexW1-xO3(x ∼ 1/4, 1/2), the systems display a transition from pure WO3 semiconducting to metal-like behavior by shifting down the Fermi level; this is due to germanium's lower valence, which acts as a p-type semiconductor by creating electron holes in the lattice.It was found that GexW1-xO3(x ∼ 1/4, 1/2) exhibits strong reflectivity and absorption in the near-infrared region, while weak reflectivity and absorption appear in the visible region.Compared to GeWO4, the estimated electronic density of states in Ge1-xWO4(x ∼ 0.2) shows a narrow band gap (0.89 eV) due to Ge-vacancies, which is considered the smaller band gap among analogous wolframites, resulting in an increase of the absorption and the relectivity in the visible region.

Effect of rotating target on speckle and orbital angular momentum characteristics of vector vortex beams

Based on angular spectrum diffraction theory, the scattering field of vector vortex beams (VVBs) passing through a rotating random rough surface is derived. The speckle produced by VVBs passing through the rotating ground glass is collected experimentally. The effects of ground glass roughness and rotational speed on the speckle and orbital angular momentum (OAM) of different order VVBs are discussed in detail. Furthermore, the speckle characteristics of the VVB are compared with the scalar vortex beam. The change in the OAM states of VVBs before and after passing through the rotating ground glass was detected by double-slit interference. The results show that the speckle of VVBs is generated after passing through the static ground glass, and the speckle contrast increases with the increment of roughness. Compared with the scalar vortex beam, the speckle contrast of the VVB changes faster with the roughness of ground glass. When the ground glass rotates, the speckle reduction effect appears and the contrast is reduced. When the rotational speed is >15 r / s, the speckle reduction effect is the strongest. The intensity distributions and OAM states of VVBs are not affected by the rotating ground glass. The research results provide a theoretical basis for the application of VVBs in optical communication, optical detection, and other fields.

Analyzing multiple acoustic diffraction over a wide barrier using equivalent knife-edge geometries and Babinet's principle (L)

We present a new method for the calculation of the multiple acoustic diffraction caused by the presence of a wide barrier. Our solution decomposes the initial scenario into an equivalent sum of geometries that only consider knife-edges. Then, by applying Babinet's principle, the total acoustic field that reaches the receiving point, which can be located at an arbitrary position, can be calculated via the uniform theory of diffraction. This method is mathematically less complex and computationally more efficient than most existing techniques. The results are validated (with and without ground reflection) by the solid agreement obtained with other solutions that solve the problem by considering the wide barrier as such, with our proposed method yielding a lower computational time (except against semi-empirical formulations) and better accuracy when compared with measurements. The presented solution can be applied in urban environments where the impact of traffic noise on residential buildings located along roads or highways needs to be evaluated, as well as in scenarios in which the insertion loss caused by a rectangular obstacle, such as a noise barrier, is to be calculated.

Time-Varying Optical Spin-Orbit Interactions in Tight Focusing of Self-Torqued Beams

Self-torque has recently been observed as a novel property of light that features time-varying orbital angular momentum (OAM) along a light pulse. This property offers an additional degree of freedom for manipulating light fields and light-matter interactions on ultrafast time scales. In this work, we theoretically study the self-torque's role in modulating tightly focused fields and reveal spin-orbit interactions (SOIs) in the focused fields using time-dependent vectorial diffraction theory. It is found that time-varying SOIs occur between the spin angular momentum (SAM), intrinsic OAM and extrinsic OAM. Specifically, the spin-to-orbit conversion, orbit-to-local-spin conversion, and optical spin-Hall effect are observed in the focused self-torqued beams. In particular, when the incident beams are circularly polarized, the time-dependent transverse SAM distributions will appear in the focal plane. Moreover, the self-torque of the focused light fields can be controlled via spin-to-orbit conversion. These observations could benefit potential applications in ultrafast light field modulation, microscopy, and optical manipulation.

Study on UV optical field distribution of partial discharge in GIS disconnector based on ray tracing method

Abstract In order to clarify the distribution law of the radiation optical field of the gas insulated switchgear disconnector defect and determine the detection range of partial discharge optical sensor, the optical model of the gas insulated switchgear disconnector based on the uniform geometrical theory of diffraction theory is established based on ray tracing method, and the distribution of the radiation light field is calculated when partial discharge occurs at the key positions such as the basin insulator, shield, and support insulator barrel. Based on the maximum irradiance, average irradiance and attenuation characteristics on the shell interface, the distribution law is further analysed, and based on this, the optimal location of the ultraviolet detector is proposed.

Dynamic freeform diffractive lens

In the framework of the scalar theory of diffraction a surface-pixeled convergent lens for arbitrary amplitude and phase modulation along the depth of focus is introduced. This complex diffractive lens is computer-generated from an exact solution of the inverse focal shaping problem obtained by using the Fresnel diffraction integral. The spatial multiplexing technique of the double-phase method is employed to encode the complex diffractive lens into a phase optical element that can be dynamically implemented with a commercial liquid-crystal spatial light modulator. The optical surface of this lens, capable of generating not only a single axial focus but also multiple parallel foci, has neither linear nor rotational symmetry but phase jumps from one pixel to another. In addition to intensity shaping, the introduced lens provides simultaneous control over the phase of light along the depth of focus, which can be very attractive for improving and/or developing photonic applications related to the interaction of coherent laser beams with matter.

Direct Separation of UO2 2+ by Coordination Sieve Effect via Spherical Coordination Traps.

Molecule sieve effect (MSE) can enable direct separation of target, thus overcoming two major scientific and industrial separation problems in traditional separation, coadsorption, and desorption. Inspired by this, herein, the concept of coordination sieve effect (CSE) for direct separation of UO2 2+ , different from the previously established two-step separation method, adsorption plus desorption is reported. The used adsorbent, polyhedron-based hydrogen-bond framework (P-HOF-1), made from a metal-organic framework (MOF) precursor through a two-step postmodification approach, afforded high uptake capacity (close to theoretical value) towards monovalent Cs+ , divalent Sr2+ , trivalent Eu3+ , and tetravalent Th4+ ions, but completely excluded UO2 2+ ion, suggesting excellent CSE. Direct separation of UO2 2+ can be achieved from a mixed solution containing Cs+ , Sr2+ , Eu3+ , Th4+ , and UO2 2+ ions, giving >99.9% removal efficiency for Cs+ , Sr2+ , Eu3+ , and Th4+ ions, but <1.2% removal efficiency for UO2 2+ , affording benchmark reverse selectivity (SM/U ) of >83 and direct generation of high purity UO2 2+ (>99.9%). The mechanism for such direct separation via CSE, as unveiled by both single crystal X-ray diffraction and density-functional theory (DFT) calculation, is due to the spherical coordination trap in P-HOF-1 that can exactly accommodate the spherical coordination ions of Cs+ , Sr2+ , Eu3+ , and Th4+ , but excludes the planar coordination UO2 2+ ion.

Stealth performance evaluation of helicopter against airborne early warning radar considering trimming control

Airborne pulse Doppler radar is a key threat to the military helicopter, and assessing the stealth performance of helicopter against airborne early warning radar is helpful to the helicopter’s stealth design and operational planning. In this paper, the Shooting and Bouncing Ray (SBR) and Uniform Theory of Diffraction (UTD) based high-frequency algorithms are used to calculate the Radar Cross Section (RCS) of helicopter, and the radar range equations are used to evaluate the stealth performance. In order to account for the effects of rotor flapping motions during actual flight, the aerodynamics model of whole helicopter is established and the attitudes and controls of helicopter at different flight states are trimmed and input into the RCS calculation module. The effects of helicopter flight speed, flying direction and operational environment on radar stealth performance are studied in focus. It is demonstrated by the results that the trimming control does have a great influence of more than 5 dB on the RCS of helicopter, and the introduction of the trim calculation brings the helicopter’s returns calculation closer to the reality. Variations in flight speed lead to the changes in the stealth performance of helicopter against Early Warning Aircraft (EWA), and the helicopter flight speed can be planned according to the operational requirements to minimize exposure distance or exposure time. Variations in flying direction mainly affect the detection properties of helicopter returns, and flying in the same direction with EWA usually gives the helicopter better low-observability than flying head-on. Variations in operational environment mainly affect the radar detection performance and the sensitivity of the detection performance to external factors; the same amount of change in some external factor causes a different amount of change in the helicopter’s detectability in different environments.

The Limits of X-ray Diffraction Theory

X-ray diffraction theory allows the interpretation of experiments to build a structural model that fits the collected data. As with any experimental science, the observations are subject to uncertainty through the instrument and user limitations. Similarly, the theory can never be perfectly complete; it will have limits, and therefore the resultant model will have uncertainties associated with it. This article discusses the limits of X-ray kinematical and dynamical diffraction theories. These are not the only theories, but are the most widely used. These theories are often extended to accommodate new findings, which can reach the stage at which their fundamental premise is clouded. At that point, the theory requires a rethink. There should be nothing sacrosanct about a theory; it should represent the best usable explanation that will allow a good interpretation of the data. Both kinematical and dynamical theories assume that the X-rays see an average structure, which is not what a photon experiences. The observed diffraction pattern is the average of the diffraction patterns created by all the photons, which is not the same as the diffraction pattern from the average structure. Accounting for this has a profound influence on the interpretation of the data.

Design of computer-generated holograms based on semi-rigorous simulations of sub-wavelength structures.

Conventional design methods for computer-generated holograms often rely on the scalar diffraction theory because the calculation effort of rigorous simulations is too high. But for sub-wavelength lateral feature sizes or large deflection angles, the performance of realized elements will show distinct deviations from the expected scalar behavior. We propose a new design method that overcomes this issue by incorporating high-speed semi-rigorous simulation techniques that allow the modeling of light propagation at an accuracy close to the rigorous methods. This includes an approach to solve the inverse problem of calculating a geometric structure that is able to form a certain physical field distribution.

Characterization and design of a freeform holographic optical element

ObjectiveThe aberrations of a conventional lens holographic optical element (HOE) are considerable because of the off-axis recording and diffraction nature. A freeform HOE was introduced to alleviate these aberrations. To design and optimize the recording wavefront of a freeform HOE, it is important to figure out the imaging properties of an HOE. MethodsWe systematically derived a general characterization of the conjugate imaging equation of an elementary HOE recorded by two spherical wavefronts using the scalar diffraction theory. In our design, each patch of a freeform HOE is considered as an elementary HOE. The recording wavefronts of a freeform HOE is designed by determining each elementary HOE through the conjugate imaging equation. ResultsThe image position predicted by the imaging equation is consistent with that of the finite ray-tracing method. The error when the imaging equation is applied to off-axis object points and different reconstruction wavelengths is eliminated effectively through coordinate transformation. Furthermore, based on this equation, a freeform HOE with 3 × 3 tiling elementary HOEs is designed to eliminate distortion and astigmatism of the HOE imaging system. A holographic printer to fabricate this freeform HOE is recommended.