Large Phase Gradient Research Articles

Efficient Inverse Design of Large-Scale, Ultrahigh-Numerical-Aperture Metalens

Efficient design methods for large-scale metalenses are crucial for various applications. The conventional phase-mapping method shows a weak performance under large phase gradients, thus limiting the efficiency and quality of large-scale, high-numerical-aperture metalenses. While inverse design methods can partially address this issue, existing solutions either accommodate only small-scale metalenses due to high computational demands or compromise on focusing performance. We propose an efficient large-scale design method based on an optimization approach combined with the adjoint-based method and the level-set method, which first forms a one-dimensional metalens and then extends it to two dimensions. Taking fabrication constraints into account, our optimization method for large-area metalenses with a near-unity numerical aperture (NA = 0.99) has improved the focusing efficiency from 42% to 60% in simulations compared to the conventional design method. Additionally, it has reduced the deformation of the focusing spot caused by the ultrahigh numerical aperture. This approach retains the benefits of the adjoint-based method while significantly reducing the computational burden, thereby advancing the development of large-scale metalenses design. It can also be extended to other large-scale metasurface designs.

Wave-function reconstruction for large phase gradients based on optical differentiation

Wave-function reconstruction for large phase gradients based on optical differentiation

Ptychographic reconstruction with object initialization.

X-ray ptychography is a cutting edge imaging technique providing ultra-high spatial resolutions. In ptychography, phase retrieval, i.e., the recovery of a complex valued signal from intensity-only measurements, is enabled by exploiting a redundancy of information contained in diffraction patterns measured with overlapping illuminations. For samples that are considerably larger than the probe we show that during the iteration the bulk information has to propagate from the sample edges to the center. This constitutes an inherent limitation of reconstruction speed for algorithms that use a flat initialization. Here, we experimentally demonstrate that a considerable improvement of computational speed can be achieved by utilizing a low resolution sample wavefront retrieved from measured diffraction patterns as object initialization. In addition, we show that this approach avoids phase artifacts associated with large phase gradients and may alleviate the requirements on phase structure within the probe. Object initialization is computationally fast, potentially beneficial for bulky sample and compatible with flat samples. Therefore, the presented approach is readily adaptable with established ptychographic reconstruction algorithms implying a wide spread use.

A Network Optimized Ridge Estimator for Robust PSI Parameter Estimation and Its Application on Deformation Monitoring of Urban Area

Persistent scatterer (PS) interferometry (PSI) has the ability to achieve submeter-scale digital elevation model and millimeter-scale deformation. However, it is difficult to maintain good performance under long baseline and large phase gradient. In this article, we develop a network optimized ridge estimator for two-tier network PSI. Such a method can increase parameter estimation robustness and spatial continuity in single-prime mode and urban build environments. First, we construct an optimized first-tier network by outlier detection and subsets network construction. On this basis, we utilize the ridge estimator as a substitute for the weighted least squares (WLS) estimator to improve the estimation accuracy in network adjustment. In the second-tier network, we detect the remaining PSs by constructing local star networks, thus increasing the density of the measurements in the first-tier network. The effectiveness of the proposed method is demonstrated by using the 2016–2018 TerraSAR-X dataset acquired in Shenzhen Metropolis, China. In addition, the stress deformation of two typical buildings, i.e., Shenzhen CITIC Building and Shenzhen Convention and Exhibition Center, are monitored and analyzed.

Broad-angle refractive transmodal elastic metasurface

Achieving total mode conversion from longitudinal to shear waves for a broad incident angle has been a big scientific challenge in elastic fields, which was impossible to be achieved in classical elastic wave theory. In this paper, we propose and realize a refractive transmodal elastic metasurface that can convert an incident longitudinal wave to a shear wave for a broad incident angle. Here, the total mode conversion is achieved via a sufficiently large phase gradient, while the full transmission is achieved with the impedance-matched single-layered metasurface. Numerical and experimental investigations show that the proposed metasurface can provide almost total mode conversion for a broad incident angle from −20.4° to 22.3°. We expect that the proposed refractive transmodal metasurface can be applied in various ultrasonic systems.

Inversion and Analysis of Mining Subsidence by Integrating DInSAR, Offset Tracking, and PIM Technology

High-intensity underground mining generates considerable surface subsidence in mining areas, including ground cracks and collapse pits on roads and farmland, threatening the safety of buildings. Large-amplitude subsidence (e.g., >2 m) is usually characterized by a large phase gradient in interferograms, leading to severe phase decorrelation and unwrapping errors. Therefore, the subsidence on the surface cannot be well derived simply using conventional differential interferometric synthetic aperture radar (DInSAR) or other geodetic measurements. We propose a new method that combines both DInSAR and subpixel offset-tracking technology to improve mine subsidence monitoring over large areas. We utilize their respective advantages to extract both the spatial boundaries and the amplitude of displacements. Using high-resolution RADARSAT-2 SAR images (5 m) acquired on February 13, 2012, and November 27, 2012, in the Shendong Coalfield located at the border between Shaanxi Province and Inner Mongolia Province, China, we obtain the subcentimetre-level subsidence of the mine boundary by DInSAR and resolve the metre-level mine subsidence centre based on subpixel offset tracking. The whole subsidence field is obtained by combining and analyzing the subcentimetre-level and the metre-level subsidence. We use the probability integral method (PIM) function model to fit the boundary and central mine subsidence to reconstruct the spatial distribution of the mine subsidence. Our results show that the maximum central subsidence reaches ~4.0 m (beyond the monitoring capabilities of DInSAR), which is generally in agreement with the maximum subsidence of ~4.0-5.0 m from field investigation. We also model the boundary and the central subsidence (the final fitting coefficient is 0.978). Our findings indicate that the offset-tracking method can compensate for the deficiency of DInSAR in large-amplitude subsidence extraction, and the inclusion of the PIM technique helps reconstruct the whole subsidence field in mining areas.

Plasmonic Metasensors Based on 2D Hybrid Atomically Thin Perovskite Nanomaterials.

In this work, we have designed highly sensitive plasmonic metasensors based on atomically thin perovskite nanomaterials with a detection limit up to 10−10 refractive index units (RIU) for the target sample solutions. More importantly, we have improved phase singularity detection with the Goos–Hänchen (GH) effect. The GH shift is known to be closely related to optical phase signal changes; it is much more sensitive and sharp than the phase signal in the plasmonic condition, while the experimental measurement setup is much more compact than that of the commonly used interferometer scheme to exact the phase signals. Here, we have demonstrated that plasmonic sensitivity can reach a record-high value of 1.2862 × 109 µm/RIU with the optimum configurations for the plasmonic metasensors. The phase singularity-induced GH shift is more than three orders of magnitude larger than those achievable in other metamaterial schemes, including Ag/TiO2 hyperbolic multilayer metamaterials (HMMs), metal–insulator–metal (MIM) multilayer waveguides with plasmon-induced transparency (PIT), and metasurface devices with a large phase gradient. GH sensitivity has been improved by more than 106 times with the atomically thin perovskite metasurfaces (1.2862 × 109 µm/RIU) than those without (918.9167 µm/RIU). The atomically thin perovskite nanomaterials with high absorption rates enable precise tuning of the depth of the plasmonic resonance dip. As such, one can optimize the structure to reach near zero-reflection at the resonance angle and the associated sharp phase singularity, which leads to a strongly enhanced GH lateral shift at the sensor interface. By integrating the 2D perovskite nanolayer into a metasurface structure, a strong localized electric field enhancement can be realized and GH sensitivity was further improved to 1.5458 × 109 µm/RIU. We believe that this enhanced electric field together with the significantly improved GH shift would enable single molecular or even submolecular detection for hard-to-identify chemical and biological markers, including single nucleotide mismatch in the DNA sequence, toxic heavy metal ions, and tumor necrosis factor-α (TNFα).

Broadband and high-efficiency accelerating beam generation by dielectric catenary metasurfaces

Abstract Self-accelerating beams show considerable captivating phenomena and applications owing to their transverse acceleration, diffraction-free and self-healing properties in free space. Metasurfaces consisting of dielectric or metallic subwavelength structures attract enormous attention to acquire self-accelerating beams, owing to their extraordinary capabilities in the arbitrary control of electromagnetic waves. However, because the self-accelerating beam generator possesses a large phase gradient, traditional discrete metasurfaces suffer from insufficient phase sampling, leading to a low efficiency and narrow spectral band. To overcome this limitation, a versatile platform of catenary-inspired dielectric metasurfaces is proposed to endow arbitrary continuous wavefronts. A high diffraction efficiency approaching 100% is obtained in a wide spectral range from 9 to 13 μm. As a proof-of-concept demonstration, the broadband, high-efficiency and high-quality self-accelerating beam generation is experimentally verified in the infrared band. Furthermore, the chiral response of the proposed metasurfaces enables the spin-controlled beam acceleration. Considering these superior performances, this design methodology may find wide applications in particle manipulation, high-resolution imaging, optical vortex generation, and so forth.

Sharp Small-Scale Perturbations of Fringes at the Interference of Dispersed Broad-Spectrum Laser Beams

The interference of two dispersed laser speckle-fields with a great spectrum width has been studied by numerical modeling. Local small-scale perturbations of interference fringes with an abrupt drop of contrast in the interference picture have been revealed. It has been shown that these perturbations occur in the region of a large phase gradient and a small module of the mutual coherence function of coinciding interfering fields. The analytical description of small-scale perturbations is given, and the probability of their appearance is estimated.

Experimental study of vibration isolation in thin-walled structural assemblies with embedded total-internal-reflection metasurfaces

The concept of total-internal-reflection elastic metasurface (TIR-MS) was recently proposed [1] and employed within flexible planar waveguides in order to create highly subwavelength sound-hard barriers impenetrable to low frequency elastic waves. The underlying physical mechanism relies on the design of engineered interfaces exhibiting extreme phase gradients such that any incoming wave at, approximately, any incidence will experience total-internal-reflection conditions. At the design frequency, the metasurface exhibits a large phase gradient such that, in accordance with the generalized Snell's law, the first critical angle is virtually always exceeded. It is worth noting that in practical realizations, the actual total reflection performance might vary depending on the angle of incidence. This dependence is due to the discrete implementation of the metasurface which results in diffraction effects. This paper presents the results of an experimental study that explores the vibration isolation performance of TIR-MS when applied to structures made of complex combinations of different elastic waveguides (e.g. bolted assemblies of beams, plates, and shells). Such system can be seen as a prototypical structure emulating mechanical assemblies of practical interest for many engineering applications. Experimental results confirm that, when the TIR-MS is embedded in the host waveguide, significant vibration isolation capabilities are achieved under quasi-omnidirectional incidence and highly subwavelength excitation conditions (i.e. the ratio of the operating wavelength to the width of the TIR-MS is approximately 5.25). These experimental results suggest new interesting directions to achieve vibration isolation and mechanical energy filtering for practical engineering systems.

Shaping the wavefront of light with high-order and short-period mode metasurfaces

We numerically investigate metasurfaces based on the well-known V-shaped antennas operating in high-order modes and short-period modes for shaping the wavefront of light. By careful arrangement of the V-shaped antennas, we design two novel super cells with large phase gradients. As a proof of concept, we design two novel metasurfaces by simulation to operate in high-order modes and short-period modes. In particular, the short-period combination can be equivalent to a metasurface operating in the second-order mode. Based on the new concept, we further arrange two azimuthal phase gradient metasurfaces to generate optical vortex beams with topological charges n = 3 and n = 2. Our results will further extend photonic research and new applications of metasurfaces.

Controlling the Dynamics and Optical Binding of Nanoparticle Homodimers with Transverse Phase Gradients.

While transverse phase gradients enable studies of driven nonequilibrium phenomena in optical trapping, the behavior of electrodynamically interacting particles in a transverse phase gradient has not been explored in detail. In this Letter we study electrodynamically interacting pairs of identical nanoparticles (homodimers) in transverse phase gradients. We establish that the net driving force on homodimers is modulated by a separation-dependent interference effect for small phase gradients. By contrast, large phase gradients break the symmetry of the interaction between particles and profoundly change the electrodynamic interparticle energy landscape. Our findings are particularly important for understanding multiparticle dynamics during the self-assembly and rearrangement of optical matter.

High‐Efficiency, Extreme‐Numerical‐Aperture Metasurfaces Based on Partial Control of the Phase of Light

AbstractHigh‐quality flat optical elements require efficient light deflection to large angles and over a wide wavelength spectrum. Although phase gradient metasurfaces achieve this by continuously adding phase shifts in the range of 0–2π to the electric field with subwavelength‐sized scatterers, their performance is limited by the spatial resolution of phase modulation at the interface. Here, a new class of metasurfaces is introduced, where the phase shifts cover less than the full 0–2π range, offering significant advantages. This approach allows the realization of metasurfaces with more compact and less mutually‐interacting scatterers, and thus more precise phase modulation, and advances the performance limits of metasurfaces to domains significantly beyond those of the full coverage phase gradient approach. Applying this concept to both plasmonic and dielectric surfaces, large phase gradients resulting in high‐numerical‐aperture immersion metalenses (NA = 1.4) with near diffraction‐limited resolution (≈0.32λ) at visible wavelengths are demonstrated. This concept enables added functionalities such as broadband performance and wavelength de‐multiplexing on a single layer, surpassing the theoretical cross‐polarization transmission efficiency limit for single‐layer plasmonic metasurfaces, and yields 67% efficiency for dielectric metasurfaces. This work paves the way toward realizing high‐resolution flat optical elements and efficient plasmonic metadevices.

Transmodal elastic metasurface for broad angle total mode conversion

It has been long believed that a total mode conversion between longitudinal and shear elastic waves can only be achieved at a certain incidence angle. Here, we show that a total mode conversion can be achieved for a broad range of incidence angles by a specially designed elastic metasurface, namely, transmodal metasurface. From the generalized reflection law, we found that the incident longitudinal wave can be totally converted to a reflected shear wave over a broad range of incidence angles if a sufficiently large phase gradient is introduced at the boundary. Numerical and experimental investigations with a specially engineered transmodal metasurface showed that the total mode conversion can be achieved for wide incidence angles from 19° to 90°, which was impossible to be achieved previously. The proposed idea of the transmodal metasurface can open up an advanced avenue for tailoring elastic wave modes as an outstanding alternative to generating shear waves.

Elevation Extraction and Deformation Monitoring by Multitemporal InSAR of Lupu Bridge in Shanghai

Monitoring, assessing, and understanding the structural health of large infrastructures, such as buildings, bridges, dams, tunnels, and highways, is important for urban development and management, as the gradual deterioration of such structures may result in catastrophic structural failure leading to high personal and economic losses. With a higher spatial resolution and a shorter revisit period, interferometric synthetic aperture radar (InSAR) plays an increasing role in the deformation monitoring and height extraction of structures. As a focal point of the InSAR data processing chain, phase unwrapping has a direct impact on the accuracy of the results. In complex urban areas, large elevation differences between the top and bottom parts of a large structure combined with a long interferometric baseline can result in a serious phase-wrapping problem. Here, with no accurate digital surface model (DSM) available, we handle the large phase gradients of arcs in multitemporal InSAR processing using a long–short baseline iteration method. Specifically, groups of interferometric pairs with short baselines are processed to obtain the rough initial elevation estimations of the persistent scatterers (PSs). The baseline threshold is then loosened in subsequent iterations to improve the accuracy of the elevation estimates step by step. The LLL lattice reduction algorithm (by Lenstra, Lenstra, and Lovász) is applied in the InSAR phase unwrapping process to rapidly reduce the search radius, compress the search space, and improve the success rate in resolving the phase ambiguities. Once the elevations of the selected PSs are determined, they are used in the following two-dimensional phase regression involving both elevations and deformations. A case study of Lupu Bridge in Shanghai is carried out for the algorithm’s verification. The estimated PS elevations agree well (within 1 m) with the official Lupu Bridge model data, while the PS deformation time series confirms that the bridge exhibits some symmetric progressive deformation, at 4–7 mm per year on both arches and 4–9 mm per year on the bridge deck during the SAR image acquisition period.

Broadband spoof surface plasmon polariton couplers based on transmissive phase gradient metasurface

In this paper, we propose the design of broadband spoof surface plasmon polariton (SSPP) couplers based on transmissive phase gradient metasurfaces (TPGMs). Due to the large parallel phase gradient, transmitted waves through the TPGM are converted to driven surface waves (DSW). By placing the TPGM above a square patch array, the DSW can be coupled to an eigenmode SSPP in a broadband. High efficiency can be achieved since there is no initial reflection and SSPP decoupling effect in such SSPP couplers. A SSPP coupler was demonstrated in a microwave regime. Both the simulated and measured results show that the SSPP coupler can operate effectively in 7.0–9.9 GHz under normal incidence. Our finding may pave the way for broadband applications of SSPP.

Acoustic metasurfaces with rapid change profiles

Acoustic metasurfaces with subwavelength unit cells modulating the phase of sound wave were developed to realize beam forming, steering, focusing, and recently carpet cloaking. However, these metasurfaces were used for small phase gradient applications and the ability to cloak or mimic reflection surfaces with rapid change profiles remained unexplored. Here, we analytically and experimentally investigate the effect of rapid change in-plane phase gradient on the design of acoustic metasurfaces for carpet cloaking and diffusing applications. Helmholtz resonators with different neck radii are used to form the ultrathin metasurface in our study. The variation of neck radius of the Helmholtz resonator results in different reflection phase of acoustic wave. In both analytical and experimental results, the large in-plane phase gradient does not affect the carpet cloak design, which is solely depending on the phase correction of the local profile height. On the contrary, the impedance mismatch resulted from the rapid change profile yields additional scattering to the reflection from such rapid change profiles. The recreation of the reflection pattern of rapid change profiles from a flat surface using metasurface needs to consider this multiple scattering, which requires additional amplitude modulation from the metasurface.

A thin and conformal metasurface for illusion acoustics of rapidly changing profiles

Recently developed metasurfaces have been used for surface engineering applications. However, the ability to cloak or mimic reflective surfaces with a large in-plane phase gradient remains unexplored. One major challenge is that even with a small incidence angle, the strong acoustic impedance variation induced by the random height profile creates additional scattering and increases the complexity of the analysis and design of the metasurface. Here, we introduce an acoustic metasurface with 1/12 wavelength thickness to realize an acoustic carpet cloak for a randomly rapid-change surface and a virtual acoustic diffuser from a flat surface using a set of Helmholtz resonators. The limitation of the metasurface for large phase gradient application is explored based on a nonlocal model that considers the contributions from neighboring surface profiles. This study extends the integration of smart acoustic surface and may find applications of surface engineering such as in architectural acoustics.

In-Plane Feed Antennas Based on Phase Gradient Metasurface

We propose the design of in-plane feed antennas (IPFA) based on phase gradient metasurface (PGM). The in-plane feed is realized using PGM with large in-plane phase gradient, which can couple normally incident waves efficiently into surface waves along the surface. This is different from conventional reflector antennas and reflectarray antennas, where the focus lies above the reflector. As an example, an IPFA is demonstrated, which is composed of a superthin PGM and a waveguide feeding structure. Due to the large phase gradient of the PGM toward the feeding waveguide, incident waves can be coupled as surface waves into the waveguide; whereas transmitted waves can be radiated out along the normal of the PGM. Both the simulated and experimental results verify the high gain and high efficiency of the IPFA with in a broad band in 3.0–3.2 GHz.

Vortex waves in sunspots

Context. Waves in the magnetized solar atmosphere are one of the favourite means of transferring and depositing energy into the solar corona. The study of waves brings information not just on the dynamics of the magnetized plasma, but also on the possible ways in which the corona is heated. Aims. The identification and analysis of the phase singularities or dislocations provide us with a complementary approach to the magnetoacoustic and Aflven waves propagating in the solar atmosphere. They allow us to identify individual wave modes, shedding light on the probability of excitation or the nature of the triggering mechanism. Methods. We use a time series of Doppler shifts measured in two spectral lines, filtered around the three-minute period region. The data show a propagating magnetoacoustic slow mode with several dislocations and, in particular, a vortex line. We study under what conditions the different wave modes propagating in the umbra can generate the observed dislocations. Results. The observed dislocations can be fully interpreted as a sequence of sausage and kink modes excited sequentially on average during 15 min. Kink and sausage modes appear to be excited independently and sequentially. The transition from one to the other lasts less than three minutes. During the transition we observe and model the appearance of superoscillations inducing large phase gradients and phase mixing. Conclusions. The analysis of the observed wave dislocations leads us to the identification of the propagating wave modes in umbrae. The identification in the data of superoscillatory regions during the transition from one mode to the other may be an important indicator of the location of wave dissipation.