Phase Discontinuities Research Articles

A coupled finite element formulation for the modeling of freezing processes within the Theory of Porous Media using a discontinuous approximation for the volume fraction ice

AbstractThis work presents a multi‐phase approach to model freezing processes within a coupled finite element formulation using the Theory of Porous Media (TPM), see also [1]. The focus of the study is to enhance the numerical stability for the volume fraction ice as is it highly sensitive to phase discontinuities. To address this issue, a discontinuous approximation is employed for the volume fraction ice while the remaining degrees of freedom are still continuously approximated. As a result, the corresponding degrees of freedom are independently solved for each element, as the element nodes are not interconnected with other elements. Academic examples are provided within a standard Galerkin procedure to highlight the optimization effect, comparing the results obtained with a continuous and discontinuous approximation for the volume fraction ice. Additionally, the implementation of the discontinuous approximation allows for the application of static condensation, resulting in reduced computation time.

Off‐Resonance Spin‐Locked Metasurfaces Empowered by Quasi‐Bound States in the Continuum for Optical Analog Computing

AbstractMetasurfaces with engineered phase discontinuity offer extra degrees of freedom to control the angular spectrum characteristics of light and can be used to construct planar metalenses with a variety of anomalous functionalities. Here, off‐resonance spin‐locked metasurfaces empowered by quasi‐bound states in the continuum are reported, in order to achieve a concept of hybridized analog computing over both frequency and angular spectrum domains. By introducing two types of asymmetric degrees, high‐quality resonance empowered by the symmetry‐protected bound states in the continuum emerges in an image‐coupled resonance system. Such high‐quality resonance can be excited in a broadband spin‐locked scattering spectrum, promising required functions for scalar multiplication and convolution operations. Off‐resonance meta‐splitter and meta‐deflector are experimentally implemented to verify the concept of hybridized analog computing in two domains, as well as providing an advantage of high robustness against scattering interference from environment. Optical spatial‐frequency processing by engineering the off‐resonance metasurfaces is also discussed. The findings provide an alternative approach toward optical analog computing over multi‐domains.

Broadband absorption and asymmetric reflection of flexural wave by deep-subwavelength lossy elastic metasurface

The elastic metasurface with phase discontinuities has received much attention for realizing diverse wave steering applications. To date, the elastic metasurfaces capable of realizing the multi-reflection-enhanced absorption of flexural waves at a deep subwavelength scale have rarely been reported. Here, we propose a novel concept of deep-subwavelength lossy elastic metasurface (DLEM) composed of gradient lossy force-moment resonators with a small amount of loss. Based on the diffraction theorem, we provide an accurate approach for predicting diffracted flexural wave behaviors considering the coupling of flexural and longitudinal diffraction modes in a plate and DLEM. The underlying mechanism of high-efficiency broadband absorption and asymmetric reflection of flexural wave is theoretically revealed, which stems from multi-reflection-enhanced absorption of the n=0 and n=-1 order diffractions. For the composite subunit of the DLEM implemented by a lead block atop damping silicone rubber block, a simplified two degree-of-freedom (2DOF) mass-spring-damping model and the corresponding accurate model are both theoretically derived to reveal the deep-subwavelength mechanism of controlling the reflected wave phase. The experiments of the broadband wave absorption and asymmetric reflection are further carried out to validate the performance of the designed DLEMs. The proposed methodology opens a new perspective for broadband vibration suppression and wave manipulation of lossy elastic metasurface with a deep-subwavelength thickness.

АЛГОРИТМ ОБНАРУЖЕНИЯ ФМ-СИГНАЛОВ НА ОСНОВЕ ВИНЕРОВСКОЙ ФИЛЬТРАЦИИ С ПРЕДВАРИТЕЛЬНОЙ НЕЛИНЕЙНОЙ ОБРАБОТКОЙ

In this paper, an algorithm for preprocessing of PSK - signals based on wiener filtration is proposed. The aim of preprocessing is to extract the phase discontinuities when filtering harmonic filling of a signal. This method allows us to avoid compensation of unknown frequency shift in the problems of determining the time delay of signals during multichannel propagation. The study checks the conditions of algorithm applicability and its stability to a noise level in the observed channels.

Sentinel-1 Interferometry and UAV Aerial Survey for Mapping Coseismic Ruptures: Mts. Sibillini vs. Mt. Etna Volcano

The survey and structural analysis of surface coseismic ruptures are essential tools for characterizing seismogenic structures. In this work, a procedure to survey coseismic ruptures using satellite interferometric synthetic aperture radar (InSAR) data, directing the survey using Unmanned Aerial Vehicles (UAV), is proposed together with a field validation of the results. The Sentinel-1 A/B Interferometric Wide (IW) Swath TOPSAR mode offers the possibility of acquiring images with a short revisit time. This huge amount of open data is extremely useful for geohazards monitoring, such as for earthquakes. Interferograms show the deformation field associated with earthquakes. Phase discontinuities appearing on wrapped interferograms or loss-of-coherence areas could represent small ground displacements associated with the fault’s ruptures. Low-altitude flight platforms such as UAV permit the acquisition of high resolution images and generate 3D spatial geolocalized clouds of data with centimeter-level accuracy. The generated topography maps and orthomosaic images are the direct products of this technology, allowing the possibility of analyzing geological structures from many viewpoints. We present two case studies. The first one is relative to the 2016 central Italian earthquakes, astride which the InSAR outcomes highlighted quite accurately the field displacement of extensional faults in the Mt. Vettore–M. Bove area. Here, the geological effect of the earthquake is represented by more than 35 km of ground ruptures with a complex pattern composed by subparallel and overlapping synthetic and antithetic fault splays. The second case is relative to the Mt. Etna earthquake of 26 December 2018, following which several ground ruptures were detected. The analysis of the unwrapped phase and the application of edge detector filtering and other discontinuity enhancers allowed the identification of a complex pattern of ground ruptures. In the Pennisi and Fiandaca areas different generation of ruptures can be distinguished, while previously unknown ruptures pertaining to the Acireale and Ragalna faults can be identify and analyzed.

First-order transitions in spin chains coupled to quantum baths

We show that tailoring the dissipative environment allows us to change the features of continuous quantum phase transitions and even induce first-order transitions in ferromagnetic spin chains. In particular, using a numerically exact quantum Monte Carlo method for the paradigmatic Ising chain of one-half spins in a transverse magnetic field, we find that spin couplings to local quantum boson baths (in the Ohmic regime) can drive the transition from the second to the first order even for a low dissipation strength. Moreover, using a variational mean-field approach for the treatment of spin-spin and spin-boson interactions, we point out that phase discontinuities are ascribable to a dissipation-induced effective magnetic field which is intrinsically related to the bath quantum fluctuations and vanishes for classical baths. The effective field is able to switch the sign of the magnetization along the direction of spin-spin interactions. The results can be potentially tested in recent quantum simulators and are relevant for quantum sensing since the spin system could not only detect the properties of nonclassical baths, but also the effects of weak magnetic fields.

Ultrabroadband RCS Reduction and Gain Enhancement of Patch Antennas by Phase Gradient Metasurfaces

In this letter, a novel design based on phase gradient metasurfaces (PGMs) is proposed to reduce the radar cross section (RCS) and enhance the gain of patch antennas. The PGM unit consists of a cross-dipole and three square-dipole rings. The proposed antenna is composed of a conventional patch radiator and four surrounding sequential-rotated PGMs. On the one hand, an ultrabroadband RCS reduction is achieved due to the PGMs phase discontinuity deflects the signal away from the specular direction by the PGMs. On the other hand, a gain enhancement is achieved because the enlarged equivalent radiation aperture owing to the coupling effect between the PGMs and the patch. A prototype operating at Ku band is designed, fabricated, and measured. It is demonstrated that an over 6 dB RCS reduction is obtained from 9.31 to 28.22 GHz, and an average 1.5 dB gain enhancement is obtained within the working band of 14.2–15.5 GHz, which can be used in stealth platforms.

CORDIC-Based General Multiple Fading Generator for Wireless Channel Digital Twin

A wireless channel digital twin is a useful tool to evaluate the performance of a communication system at the physical or link level by generating the physical channel controllably. In this paper, a stochastic general fading channel model is proposed, which considered most of the channel fading types for various communication scenarios. By using the sum-of-frequency-modulation (SoFM) method, the phase discontinuity of the generated channel fading was well addressed. On this basis, a general and flexible generation architecture for channel fading was developed on a field programmable gate array (FPGA) platform. In this architecture, improved CORDIC-based hardware circuits for the trigonometric function, exponential function, and natural logarithm were designed and implemented, which improved the real-time performance of the system and the utilization rate of the hardware resources compared with the traditional LUT and CORDIC method. For a 16-bit fixed-point data bit width single-channel emulation, the hardware resource consumption was significantly reduced from 36.56% to 15.62% for the overall system by utilizing the compact time-division (TD) structure. Moreover, the classical CORDIC method brought an extra latency of 16 system clock cycles, while the latency caused by the improved CORDIC method was decreased by 62.5%. Finally, a generation scheme of a correlated Gaussian sequence was developed to introduce a controllable arbitrary space-time correlation for the channel generator with multiple channels. The output results of the developed generator were consistent with the theoretical results, which verified the correctness of both the generation method and hardware implementation. The proposed channel fading generator can be applied for the emulation of large-scale multiple-input, multiple-output (MIMO) channels under various dynamic communication scenarios.

Effects of Shock Waves on Shack–Hartmann Wavefront Sensor Data

Shock waves will form by turning supersonic or locally supersonic flow and result in an increase in the freestream density downstream of the shock. This increase leads to optical distortions that limit the effectiveness of aircraft-mounted laser systems. In this paper, analytic expressions are developed to describe these optical distortions in terms of the optical-path difference (OPD). Pupil-plane disturbances imposed by the shock are studied for two cases: when the shock is parallel to the propagation direction and when the shock is on an angle relative to the propagation direction. Upon propagation from the pupil plane, the analysis shows that shock-induced phase discontinuities can sometimes cause the irradiance pattern in the image plane to bifurcate. Despite a large amount of tilt in the pupil plane, the bifurcated irradiance pattern does not map to a proportional shift in the image plane. The implications that these findings have on Shack–Hartmann wavefront sensor (SHWFS) data are also explored. The results show that least-squares reconstruction from the SHWFS data yield accurate estimates of the change in OPD across the shock when the magnitude of the phase difference caused by the shock is between 0 and approximately . However, when , the results show that least-squares reconstruction begins to severely underestimate the change in OPD across the shock. Such results will inform future efforts looking to develop aircraft-mounted laser systems.

A Parallel InSAR Phase Unwrapping Method Based on Separated Continuous Regions

Phase unwrapping is an imperative step in interferometry processing that has a significant influence on the quality of subsequent products. Many existing phase unwrapping algorithms have been designed to solve for the unwrapped phase under the assumption that noisy areas with discontinuities are small or that reliable continuity can be recovered there. They attempt to restore the unwrapped phase by using continuity and data quality measures, such as residues. However, when the observing field is divided into separate zones of continuous phase due to a large range of noise, such as those caused by rivers or mountains, it is difficult to use traditional phase unwrapping techniques to recover global continuity in these noisy areas. To address this challenge, we present a two-dimensional parallel phase unwrapping method that is designed to handle cases where the continuity of the phase is separated by closed noisy loops. Based on continuity distances, this method aims to identify continuous regions that are free of hidden phase discontinuities and restore phase continuity between the separated regions. A heterogeneous residual diffusion scheme is used to restore the unwrapped phase outside continuous regions. The parallel algorithm for extracting continuous regions, restoring continuity between the regions, and diffusing residuals was implemented on a GPU device to increase the processing efficiency. We applied our method to typical TanDEM-X data covering rivers, islands, and mountains and demonstrated that it is a promising solution for large-scale, heavily noisy phase unwrapping problems.

Spiral fractional vortex beams.

A new type of spatially structured light field carrying orbital angular momentum (OAM) mode with any non-integer topological order, referred to as the spiral fractional vortex beam, is demonstrated using the spiral transformation. Such beams have a spiral intensity distribution and a phase discontinuity in the radial direction, which is completely different from an opening ring of the intensity pattern and an azimuthal phase jump, common features that all previously reported non-integer OAM modes (referred to as the conventional fractional vortex beams) shared. The intriguing properties of a spiral fractional vortex beam are studied both in simulations and experiments in this work. The results show that the spiral intensity distribution will evolve into a focusing annular pattern during its propagation in free space. Furthermore, we propose a novel scheme by superimposing a spiral phase piecewise function on spiral transformation to convert the radial phase jump to the azimuthal phase jump, revealing the connection between the spiral fractional vortex beam and its conventional counterpart, of which OAM modes both share the same non-integer order. Thus this work is expected to inspire opening more paths for leading fractional vortex beams to potential applications in optical information processing and particle manipulation.

Low-False-Alarm-Rate Timing and Duration Estimation of Noisy Frequency Agile Signal by Image Homogeneous Detection and Morphological Signature Matching Schemes.

Frequency hopping spread spectrum (FHSS) applies widely to communication and radar systems to ensure communication information and channel signal quality by tuning frequency within a wide frequency range in a random sequence. An efficient signal processing scheme to resolve the timing and duration signature from an FHSS signal provides crucial information for signal detection and radio band management purposes. In this research, hopping time was first identified by a two-dimensional temporal correlation function (TCF). The timing information was shown at TCF phase discontinuities. To enhance and resolve the timing signature of TCF in a noisy environment, three stages of signature enhancement and morphological matching processes were applied: first, computing the TCF of the FHSS signal and enhancing discontinuities via wavelet transform; second, a dual-diagonal edge finding scheme to extract the timing pattern signature and eliminate mismatching distortion morphologically; finally, Hough transform resolved the agile frequency timing from purified line segments. A grand-scale Monte Carlo simulation of the FHSS signals with additive white Gaussian noise was carried out in the research. The results demonstrated reliable hopping time estimation obtained in SNR at 0 dB and above, with a minimal false detection rate of 1.79%, while the prior related research had an unattended false detection rate of up to 35.29% in such a noisy environment.

Phase-Discontinuity Correction Method With an Overlapped Signal Structure in Stepped-Carrier OFDM Radar With Dual Transmitters

A phase-discontinuity correction method for a stepped-carrier orthogonal frequency-division multiplexing (SC-OFDM) radar is proposed. Correction is accomplished using an overlapped signal structure in both the time and frequency domains, made possible by implementing a radar system with dual transmitters (DTs). The overlap in the frequency domain is used to correct phase discontinuities in the frequency steps, and the overlap in the time domain allows lowering the effective measurement time loss due to guard intervals. The subband phase discontinuity of DTs is extracted by cross-correlating a received subsymbol with the frequency-overlapped subsymbol from the next frequency step. After the gain and phase values at the maximum correlation output are obtained, subband and subsymbol correction processes are applied alternately for each frequency step in a chained manner. Simulated range-Doppler maps are presented without and with phase-discontinuity corrections using the proposed signal structure. Also, an SC-OFDM radar system with DTs is implemented to prove the concept. The results show that phase discontinuities among the frequency steps in a block can be readily corrected using the proposed signal structure and correction method without precalibration using a reference target.

Terahertz isotropic transmissive metasurfaces for generation of different wavefronts

Metasurfaces are highly advantageous in realizing the phase discontinuity of an electromagnetic wave. Aiming at manipulating electromagnetic wavefront in terahertz band, a subwavelength multilayer meta-atom is designed, and it is composed of gold mesh, gold disk, and polyimide. By varying the diameter of the central gold disk, eight meta-atoms are prepared to provide full phase modulation with phase increase of 45°. A series of transmissive metasurfaces consisting of these meta-atoms are designed with different arrays. They achieve generations of deflection, single-focusing, dual-focusing, and orbital angular momentum with and . It is noteworthy that metasurfaces assembled by these isotropic meta-atoms are polarization-insensitive. Our models are numerically verified, and all results are consistent with theoretical predictions. Different from reflective metasurfaces that sometimes encounter feeding blockage, transmissive metasurfaces are feasible for the realization of a more compact terahertz system.

Specular Surface Shape Measurement with Orthogonal Dual-Frequency Fourier Transform Deflectometry

Three-dimensional (3D) shape measurement for specular surfaces is becoming increasingly important in various applications. A novel orthogonal dual-frequency fringe is proposed in the specular surface shape measurement to overcome the phase jumping and discontinuities in spatial phase unwrapping. The fringe recalibrated high-accuracy phase information from its high-frequency fringe component with low-ambiguity phase information from its low-frequency fringe component. An improved Fourier transform deflectometry method based on the orthogonal dual-frequency fringe is proposed to measure 3D specular surface shapes. Simulation results showed that the orthogonal dual-frequency Fourier transform deflectometry (ODD) method could precisely reconstruct flat surfaces with an error of 2.16 nm rms, and concave surfaces with an error of 1.86 μm rms. Experimental results showed that the reconstructed shapes of both the flat mirror and the concave mirror measured by the ODD measurement system were highly comparable to those obtained by the phase-measuring deflectometry (PMD) method. This new fringe provides a distinctive approach to structured pattern construction and reduces the phase unwrapping ambiguities in specular surface shape measurement. The ODD method can achieve accurate 3D shape measurement for specular surfaces by sampling only one fringe, providing a possible basis for future real-time measurement of specular surfaces.

Active terahertz beam steering based on mechanical deformation of liquid crystal elastomer metasurface

Active metasurfaces are emerging as the core of next-generation optical devices with their tunable optical responses and flat-compact topography. Especially for the terahertz band, active metasurfaces have been developed as fascinating devices for optical chopping and compressive sensing imaging. However, performance regulation by changing the dielectric parameters of the integrated functional materials exhibits severe limitations and parasitic losses. Here, we introduce a C-shape-split-ring-based phase discontinuity metasurface with liquid crystal elastomer as the substrate for infrared modulation of terahertz wavefront. Line-focused infrared light is applied to manipulate the deflection of the liquid crystal elastomer substrate, enabling controllable and broadband wavefront steering with a maximum output angle change of 22° at 0.68 THz. Heating as another control method is also investigated and compared with infrared control. We further demonstrate the performance of liquid crystal elastomer metasurface as a beam steerer, frequency modulator, and tunable beam splitter, which are highly desired in terahertz wireless communication and imaging systems. The proposed scheme demonstrates the promising prospects of mechanically deformable metasurfaces, thereby paving the path for the development of reconfigurable metasurfaces.

Absolute Phase Unwrapping for Objects With Large Depth Range

This paper presents a method for unwrapping the phase using only the geometric constraints and photometric information of the structured light system, which can cope with objects in a large depth range without the need for additional image acquisition or other cameras. Following the minimum phase method, this paper also establishes an artificial plane and generates an initial unwrapped phase map from the absolute phase map of the plane. Starting from the reference plane, we divide the space into several 2π intervals pixel by pixel. The boundaries at phase discontinuities in the initial unwrapped phase map are then used to segment the object into independent regions. Regarding the projector as a point light source, synthetic images of each region corresponding to different spatial 2π intervals are generated sequentially according to Lambert’s cosine law. The interval in which the region corresponds is identified by comparing the similarity of these synthetic images with the modulation image, leading to the acquisition of an entire absolute phase map of the object. Experiments are conducted to evaluate the performance of the proposed method.

High-Efficiency Dynamic Terahertz Deflector Utilizing a Mechanically Tunable Metasurface.

Terahertz (THz) wave manipulation, especially the beam deflection, plays an essential role in various applications, such as next-generation communication, space exploration, and high-resolution imaging. Current THz optical components and devices are hampered by their large bulk sizes and passive responses, limiting the development of high-performance, miniaturized THz microsystems. Tunable metasurfaces offer a powerful dynamic optical platform for controlling the propagation of electromagnetic waves. In this article, we presented a mechanically tunable metasurface (MTM), which can achieve terahertz beam deflection and vary the intensity of the anomalous reflected terahertz wave by changing the air gap between the metallic resonator (MR) array with phase discontinuities and Au ground plane. The absence of lossy spacer materials substantially enhances deflection efficiency. The device was fabricated by a combination of the surface and bulk-micromachining processes. The THz beam steering capability was characterized using terahertz time domain spectroscopy. When the air gap is 50 μm, the maximum deflection coefficient reaches 0.60 at 0.61 THz with a deflection angle of ~44.5°, consistent with theoretical predictions. We further established an electrically tunable miniaturized THz device for dynamic beam steering by introducing a micro voice coil motor to control the air gap continuously. It is shown that our designed MTM demonstrates a high modulation depth of deflection coefficient (~ 62.5%) in the target steered angle at the operating frequency. Our results showcase the potential of the proposed MTM as a platform for high-efficiency THz beam manipulation.

Phase Cost Indicator-Guided Central Difference Information Filter 2-D Phase Unwrapping Approach

Phase unwrapping (PU) as an ill-posed inverse scientific problem has invariably been the significant difficulty in interferometric synthetic aperture radar (InSAR) technique for topographic mapping. Conventional PU approaches may produce a local or global unwrapping bias in severe phase changes caused by noise and large gradient terrain because the phase continuity assumption is not satisfied. To address this issue, we have created a novel phase quality-guided integrated filtering and unwrapping process for PU. In particular, the PU path is guided by an innovative phase cost indicator, which can automatically coordinate contributions from several phase quality estimation methods so that the unwrapping path can circumvent phase discontinuity regions and delay unwrapping these pixels. Since the central difference transform is another extra effective nonlinear transformation mode based on sigma points and only has one regulation parameter, we have employed the central difference information filter (CDIF) for the first time to realize the dynamic estimation of the unwrapped phase in the PU process. We tested the proposed approach using two real datasets with different mountainous areas. The results demonstrate that the PU accuracy of the proposed approach based on these two datasets is improved by 25.2% and 40.4% compared to the unscented information filtering (UIF) PU method, and the anti-noise capacity and unwrapping efficiency of the CDIF are both slightly superior to the UIF.

Micronization as a solution for enhancing the thermal insulation of nanocellular poly(methyl-methacrylate) (PMMA)

This work shows a route to reduce the thermal conductivity of nanocellular poly(methyl-methacrylate) (PMMA). This approach is based on micronizing to replace the continuous solid phase by a discontinuous one. PMMA powders with densities of 147–195 kg/m3, formed by particles of 100 μm with nanometric cells inside them, are produced by milling. Micronization allows increasing the overall porosity maintaining the cell size. Results prove that after milling it is possible to obtain open cell nanoporous PMMA powders with thermal conductivity below that of the bulk materials (15% reduction). The reduction is not only due to a density decrease, but a result of the new structure of the powder material. The discontinuity of the solid phase and the increase in radiation extinction are the key factors allowing this improvement. This route is confirmed as a promising alternative to enhance the performance of nanocellular polymers.