Wavevector Domain Research Articles

Angular Dispersion Analysis of Frequency-Selective Surfaces Based on Wavevector Domain Equivalent Impedance

Angular Dispersion Analysis of Frequency-Selective Surfaces Based on Wavevector Domain Equivalent Impedance

Dynamic multifield continualization of multilayered lattice-like metamaterials

This work focuses on dynamic continualization of multifield multilayered metamaterials in order to obtain energetically-consistent models able to provide an accurate description of the dispersive behavior of the corresponding discrete system. Continuum models, characterized by constitutive and inertial non-localities, have been identified through a recently proposed enhanced continualization scheme. They are identified by governing equations both of the integro-differential and higher-order gradient-type, whose regularization kernel or pseudo-differential functions accounting for shift operators are formally expanded in Taylor series. The adopted regularization kernel exhibits polar singularities at the edge of the first Brillouin zone, thus assuring the convergence of the frequency spectrum to the one of the Lagrangian system in the entire wave vector domain. The validity of the proposed approach is assessed through the investigation of multilayered discrete lattices with an antitetrachiral topology, where local resonators act as rigid links among the layers. The convergence of dispersion curves of the continuum model to the ones of the Lagrangian model is proved in the whole first Brillouin zone as the adopted continualization order increases, both considering the propagation and the spatial attenuation of Bloch waves inside the metamaterial. A low frequency continualization is also provided, leading to the identification of a first-order medium.

Numerical Simulation of a Three-Dimensional Strongly Magnetic Material Tensor in Wave Vector Domain

Numerical Simulation of a Three-Dimensional Strongly Magnetic Material Tensor in Wave Vector Domain

Dispersion-assisted high-dimensional photodetector.

Intensity, polarization and wavelength are intrinsic characteristics of light. Characterizing light with arbitrarily mixed information on polarization and spectrum is in high demand1-4. Despite the extensive efforts in the design of polarimeters5-18 and spectrometers19-27, concurrently yielding high-dimensional signatures of intensity, polarization and spectrum of the light fields is challenging and typically requires complicated integration of polarization- and/orwavelength-sensitive elements in the space or time domains. Here we demonstrate that simple thin-film interfaces with spatial and frequency dispersion can project and tailor polarization and spectrum responses in the wavevector domain. By this means, high-dimensional light information can be encoded into single-shot imaging and deciphered with the assistance of a deep residual network. To the best of our knowledge, our work not only enables full characterization of light with arbitrarily mixed full-Stokes polarization states across a broadband spectrum with a single device and a single measurement but also presents comparable, if not better, performance than state-of-the-art single-purpose miniaturized polarimeters or spectrometers. Our approach can be readily used as an alignment-free retrofit for the existing imaging platforms, opening up new paths to ultra-compact and high-dimensional photodetection and imaging.

Beating resonance patterns and extreme power flux skewing in anisotropic elastic plates.

Elastic waves in anisotropic media can exhibit a power flux that is not collinear with the wave vector. This has notable consequences for waves guided in a plate. Through laser-ultrasonic experiments, we evidence remarkable phenomena due to slow waves in a single-crystal silicon wafer. Waves exhibiting power flux orthogonal to their wave vector are identified. A pulsed line source that excites these waves reveals a wave packet radiated parallel to the line. Furthermore, there exist precisely eight plane waves with zero power flux. These so-called zero-group-velocity modes are oriented along the crystal's principal axes. Time acts as a filter in the wave-vector domain that selects these modes. Thus, a point source leads to beating resonance patterns with moving nodal curves on the surface of the infinite plate. We observe this pattern as it emerges naturally after a pulsed excitation.

Complex Source Distributions in Wave-based Virtual Acoustics

In the typical scenario in time-domain wave-based acoustics, the solution to the acoustic wave equation is approximated over a three-dimensional volumetric grid using a time stepping method. In the setting of very large simulations, the grid is normally assumed to be regular (e.g. Cartesian) so that massive parallelism may be exploited. One difficulty has been in representing source distributions that do not conform neatly to a regular grid. Using a Fourier-based optimisation procedure in the wave vector domain, it is possible to represent arbitrary source distributions in a flexible way over a pre-defined collection of grid points. Such a methodology is independent of the particular choice of simulation method and depends only on the regularity of the grid. In this paper, approximations to various simple distributions, including the line source and piston, are examined, with regard to accuracy, rotation of the distribution relative to the grid, and the size of the point cloud used to represent the source. Numerical results are presented.

SUPER-RESOLUTION OF DIFFUSION MRI VIA JOINT CONSIDERATION OF SPATIAL AND ANGULAR SPACES USING GRAPH CNN

Diffusion magnetic resonance imaging (dMRI) is an essential technique for studying brain white matter. However, its application suffers from the tradeoff between resolution, signal-to-noise ratio (SNR), and scanning time. Under a given setting, post-acquisition super-resolution (SR) has displayed the exciting performance of increasing the spatial or angular resolution of dMRI without prolonging the acquisition time. dMRI is acquired from a heterogeneous space composed of the spatial domain (x-space) and the diffusion wave vector domain (q-space). We introduced a graph convolution neural network (GCNN) to fit the mapping from low-resolution (LR) dMRI to high-resolution (HR) counterpart by jointly considering x-space and q-space to make an effective learning in this non-Euclidean space to increase the spatial resolution. Real brain dMRI data were downloaded from the Human Connectome Project (HCP). Comparisons were made between different spaces, including x-space, q-space, and xq-space. The results indicated that the best performance was obtained when two spaces were considered jointly using GCNN. Compared with the traditional methods, our network fully used spatio-angular information to improve the quality of dMRI SR. Furthermore, some feature metrics, including fractional anisotropic mapping, fiber orientation distribution (FOD), and fiber tractography, were presented to support the improvement. The cross-phantom test on synthetic data generated by the Phantomas tool was performed to further evaluate our model. Extended experiments revealed that GCNN might serve as a new way of enhancing dMRI.

Contact angle hysteresis on random self-affine rough surfaces in Wenzel's wetting regime: Numerical study.

We present a numerical study of the advancing and receding apparent contact angles for a liquid meniscus in contact with random self-affine rough surfaces in Wenzel's wetting regime. Within the framework of the Wilhelmy plate geometry, we use the full capillary model to obtain these global angles for a wide range of local equilibrium contact angles and for different parameters that determine the self-affine solid surfaces: Hurst exponent, wave vector domain, and root-mean-square roughness. We find that the advancing and receding contact angles are single-valued functions that depend only on the roughness factor determined by the set of values of the parameters of the self-affine solid surface. Moreover, the cosines of these angles are found to depend linearly on the surface roughness factor. The relations between the advancing, the receding, and Wenzel's equilibrium contact angles are investigated. It is shown that for materials with self-affine surface structure, the hysteresis force is the same for different liquids and it depends only on the surface roughness factor. A comparison with existing numerical and experimental results is carried out.

Hydrogel‐Scalable Nanoslide for Switchable Optical Spatial‐Frequency Processing

AbstractSpatial frequency processing is an essential technology for extracting morphological information from an optical image. Although various Fourier‐based flat optical elements have been proposed as spatial‐frequency filters to realize image processing, their transfer functions are statically fixed once fabricated, thus limiting the versatile, dynamic functionalities and practical applications. Here, a novel practical tuning strategy is demonstrated to realize switchable spatial‐frequency processing for edge‐enhanced and bright‐field imaging by employing a tunable hydrogel‐scalable nanoslide. By utilizing multilayered metallic and hydrogel stacks construction, the nanoslide directly manipulates the optical spatial frequency in the wavevector domain and exhibits opposite image processing at different wavelength channels due to the cavity‐induced wavelength‐sensitivity. More intriguingly, via controlling the ambient humidity, the angular‐dependent optical response of the nanoslide can be effectively tuned for dynamic edge‐enhanced imaging due to the hydrogel's inflation from moisture. In addition, the nanoslide is readily fabricated at a large scale and integrated into compact imaging systems, such as a biomicroscope. With the advantages of a high numerical aperture ≈0.8, polarization‐insensitive, microscopy‐compatible, and facile architecture, the proposed hydrogel‐based nanoslide can find potential applications in machine vision, real‐time image processing, biological imaging, and analog computing.

Classical analog of qubit logic based on a magnon Bose–Einstein condensate

Advances in quantum computing and telecommunications stimulate the search for classical systems allowing partial implementation of a similar functionality under less stringent environmental conditions. Here, we present a classical version of several quantum bit (qubit) functionalities using a two-component magnon Bose–Einstein condensate (BEC) formed at opposite wavevectors in a room-temperature yttrium-iron-garnet ferrimagnetic film. Employing micromagnetic numerical simulations, we show the use of wavelength-selective parametric pumping to controllably initialize and manipulate the two-component BEC. Next, by modeling the interaction of this BEC with a pulse- and radio-frequency-driven dynamic magnonic crystal we translate the concept of Rabi-oscillations into the wavevector domain and demonstrate how to manipulate the magnon-BEC system regarding the polar and azimuthal angles in the Bloch sphere representation. We hope that our study provides a significant stimulus on the boundary between qubit functionality and classical systems of interacting BECs, which use a subset of qubit-based algorithms.

Wavelet-Based 2-D Sea Surface Reconstruction Method From Nearshore X-Band Radar Image Sequences

A 2D Wavelet-based radar analysis method for sea surface reconstruction is presented. The Wavelet-based Sea Surface Reconstruction (WSSR) method resolves the traditional limitations of the Fourier analysis, such as the requirement of the homogeneity and periodicity of the analyzed image sequences which is hardly found in nearshore wave shoaling conditions. The method is based on a filtration of the corresponding 2D wavelet spectra of the radar images in the pseudo wavevector domain and includes band-pass filtration and phase correction as well as the application of an empirical modulation transfer function. In extending the method to 2D images, the main numerical and computational challenge is to realize the inverse wavelet transform. This challenge is overcome by using the Dirac delta-function as a mother wavelet in the synthesis step to reduce the computational requirements of the integration procedures via an analytical solution. A statistical comparison between the original and the reconstructed surface elevations shows mean absolute error on the level of 6-14% of the significant wave height, which is quite an improvement when compared to conventional 2D Fourier-based techniques (≈27% for the tested case). Another main advantage of the WSSR method is its near real-time capabilities, as it can work on a single or a small number of images unlike conventional methods, which require a few minutes integration time. In addition to various synthetic data consistency checks, the WSSR was employed on real radar data collected in Haifa bay, Israel, with good qualitative agreements in comparison with a near wave buoy.

Reconfigurable Metasurface for Image Processing.

Optical Fourier transform-based processing is an attractive technique due to the fast processing times and large-data rates. Furthermore, it has recently been demonstrated that certain Fourier-based processors can be realized in compact form factors using flat optics. The flat optics, however, have been demonstrated as static filters where the operator is fixed, limiting the applicability of the approach. Here, we demonstrate a reconfigurable metasurface that can be dynamically tuned to provide a range of processing modalities including bright-field imaging, low-pass and high-pass filtering, and second-order differentiation. The dynamically tunable metasurface can be directly combined with standard coherent imaging systems and operates with a numerical aperture up to 0.25 and over a 60 nm bandwidth. The ability to dynamically control light in the wave vector domain, while doing so in a compact form factor, may open new doors to applications in microscopy, machine vision, and sensing.

Efficient Bloch mode calculation of periodic systems with arbitrary geometry and open boundary conditions in the complex wavevector domain.

We show how existing iterative methods can be used to efficiently and accurately calculate Bloch periodic solutions of Maxwell's equations in arbitrary geometries. This is carried out in the complex-wavevector domain using a commercial frequency-domain finite-element solver that is available to the general user. The method is capable of dealing with leaky Bloch mode solutions, and is extremely efficient even for 3D geometries with non-trivial material distributions. We perform independent finite-difference time-domain simulations of Maxwell's equations to confirm our results. This comparison demonstrates that the iterative mode finder is more accurate, since it provides the true solutions in the complex-wavevector domain and removes the need for additional signal processing and fitting. Due to its efficiency, generality and reliability, this technique is well suited for complex and novel design tasks in integrated photonics, and also for a wider range of photonics problems.

A Numerical and Experimental Study on an Interconnected Metamaterial for Flexural Vibration Control Based on Modal Strain Energy

In this study, an interconnected metamaterial was proposed to suppress flexural vibration. The interconnected metamaterial can improve the manufacturing and installation processes in terms of convenience because it can be fabricated in the form of a modular multi-celled structure with a single-phase material. To evaluate the vibration reduction performance of the metamaterial, stopband analysis was performed, as it solves an iterative eigenvalue problem for the wave vector domain. In order to identify the Bloch mode that contributes to flexural vibration, a concept to extract the Bloch mode based on the modal strain energy was proposed. The vibration-reduction performance of the interconnected metamaterial was numerically verified by using a frequency-response analysis of the multi-celled structure. The interconnected metamaterial proposed in this study was fabricated by using a 3D printer. Finally, the vibration-reduction performance of the multi-celled structure was experimentally verified by using impact testing.

Acoustic metamaterials

Waves are generally characterized by angular frequency ω and wavevector k. Accordingly, this tutorial is structured into two parts, one on resonance-based acoustic metamaterials, in the frequency domain, and one on topological acoustics, based on the wavevector domain as topological structures inherently involve spatial configurations that are a step beyond the simple periodic lattices. Each part will begin with a brief introduction of the basic principles, followed by two examples described in detail. In the first part, we present decorated membrane resonators and the broadband optimal acoustic absorption structures, the latter being crucial for the potential applications of acoustic metamaterials. In the second part, we discuss how to construct the Dirac cone, a special type of dispersion from either accidental degeneracy or symmetry protection, which can be shown to lead to negative, zero, or positive refractive indices. The shifting and gapping of these Dirac cones in the reciprocal space can result in effects on acoustic waves similar to that of a magnetic field on an electron. More generally, they lead to edge states resulting from a real-space gauge field as well as topological bandgaps.

Domain multiplexed computer-generated holography by embedded wavevector filtering algorithm

Computer-generated holography can obtain the wavefront required for constructing arbitrary intensity distributions in space. Currently, speckle noises in holography remain an issue for most computational methods. In addition, there lacks a multiplexing technology by which images from a single hologram and light source can be switched by a lens. In this work, we first come up with a new algorithm to generate holograms to project smoother images by wavevector filtering. Thereupon, we propose a unique multiplexing scheme enabled by a Fourier lens, as the incident light can be decomposed either by a superposition of spherical waves or plane waves. Different images are obtained experimentally in the spatial and wavevector domains, switchable by a lens. The embedded wavevector filtering algorithm provides a new prospective for speckle suppression without the need for postprocessing. The multiplexing technology can double the capacity of current holographic systems and exhibits potential for various interesting display applications.

XQ-SR: Joint x-q space super-resolution with application to infant diffusion MRI.

Diffusion MRI (DMRI) is a powerful tool for studying early brain development and disorders. However, the typically low spatio-angular resolution of DMRI diminishes structural details and limits quantitative analysis to simple diffusion models. This problem is aggravated for infant DMRI since (i) the infant brain is significantly smaller than that of an adult, demanding higher spatial resolution to capture subtle structures; and (ii) the typically limited scan time of unsedated infants poses significant challenges to DMRI acquisition with high spatio-angular resolution. Post-acquisition super-resolution (SR) is an important alternative for increasing the resolution of DMRI data without prolonging acquisition times. However, most existing methods focus on the SR of only either the spatial domain (x-space) or the diffusion wavevector domain (q-space). For more effective resolution enhancement, we propose a framework for joint SR in both spatial and wavevector domains. More specifically, we first establish the signal relationships in x-q space using a robust neighborhood matching technique. We then harness the signal relationships to regularize the ill-posed inverse problem associated with the recovery of high-resolution data from their low-resolution counterpart. Extensive experiments on synthetic, adult, and infant DMRI data demonstrate that our method is able to recover high-resolution DMRI data with remarkably improved quality.

Refinement of the Quantum Scattering Theory Approximation for the Yukawa Potential Using the Meijer’s-Function Technique

Our goal is to find and apply simple methods for calculating the scattering cross sections of particles in a screened Coulomb potential in a wider range of wave vector magnitudes than is possible in the Born approximation. Using the technique of Meijer’s G-function, we obtain expressions for the scattering amplitude and the quantum scattering cross section in the limit kd ≫ 1, where d is the screening radius and k is the wavenumber. We compare the analytic results with quantum computations of the elastic scattering process by expanding the solution in a power series of partial waves. We investigate the domain of wave vectors where the Born approximation is no longer applicable but the new approximation works. In this domain, the number of angular momenta that must be taken into account in summing the partial cross sections increases abruptly, and a more precise analytic approximation might therefore noticeably reduce the computational effort. We also show that calculations of the classical integrated scattering cross section must take into account that the finite screening length of an interaction potential causes a cross section to shift off the mass shell. Taking this shift into account allows obtaining a good coincidence of numerical and analytic data for the scattering cross section, including beyond the applicability limits of the Born approximation.

Denoising of Diffusion MRI Data via Graph Framelet Matching in x-q Space.

Diffusion magnetic resonance imaging (DMRI) suffers from lower signal-to-noise-ratio (SNR) due to MR signal attenuation associated with the motion of water molecules. To improve SNR, the non-local means (NLM) algorithm has demonstrated state-of-the-art performance in noise reduction. However, existing NLM algorithms do not take into account explicitly the fact that DMRI signal can vary significantly with local fiber orientations. Applying NLM naïvely can hence blur subtle structures and aggravate partial volume effects. To overcome this limitation, we improve NLM by performing neighborhood matching in non-flat domains and removing noise with information from both x -space (spatial domain) and q -space (wavevector domain). Specifically, we first encode the q -space sampling domain using a graph. We then perform graph framelet transforms to extract robust rotation-invariant features for each sampling point in x-q space. The resulting features are employed for robust neighborhood matching to locate recurrent information. Finally, we remove noise via an NLM framework. To adapt to the various types of noise in multi-coil MR imaging, we transform the signal before denoising so that it is Gaussian-distributed, allowing noise removal to be carried out in an unbiased manner. Our method is able to more effectively locate recurrent information in white matter structures with different orientations, avoiding the blurring effects caused by naïvely applying NLM. Experiments on synthetic, repetitively-acquired, and infant DMRI data demonstrate that our method is able to preserve subtle structures while effectively removing noise.

Longitudinal Prediction of Infant Diffusion MRI Data via Graph Convolutional Adversarial Networks.

Missing data is a common problem in longitudinal studies due to subject dropouts and failed scans. We present a graph-based convolutional neural network to predict missing diffusion MRI data. In particular, we consider the relationships between sampling points in the spatial domain and the diffusion wave-vector domain to construct a graph. We then use a graph convolutional network to learn the non-linear mapping from available data to missing data. Our method harnesses a multi-scale residual architecture with adversarial learning for prediction with greater accuracy and perceptual quality. Experimental results show that our method is accurate and robust in the longitudinal prediction of infant brain diffusion MRI data.