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Many nonlocal models have adopted Euclidean balls as the nonlocal interaction neighborhoods. When solving them numerically, it is sometimes convenient to adopt polygonal approximations of such balls. A crucial question is, to what extent such approximations affect the nonlocal operators and the corresponding solutions. While recent works have analyzed this issue for a fixed horizon parameter, the question remains open in the case of a small or vanishing horizon parameter, which happens often in many practical applications and has significant impact on the reliability and robustness of nonlocal modeling and simulations. In this work, we are interested in addressing this issue and establishing the convergence of the nonlocal solutions associated with polygonally approximated interaction neighborhoods to the local limit of the original nonlocal solutions. Our finding reveals that the new nonlocal solution does not converge to the correct local limit when the number of sides of polygons is uniformly bounded. On the other hand, if the number of sides tends to infinity, the desired convergence can be established. These results may be used to guide future computational studies of nonlocal models.

The piecewise quadratic polynomial collocation is used to approximate the nonlocal model, which generally obtain the {\em nonsymmetric indefinite system} [Chen et al., IMA J. Numer. Anal., (2021)]. In this case, the discrete maximum principle is not satisfied, which might be trickier for the stability analysis of the high-order numerical schemes [D'Elia et al., Acta Numer., (2020); Leng et al., SIAM J. Numer. Anal., (2021)]. Here, we present the modified (shifted-symmetric) piecewise quadratic polynomial collocation for solving the linear nonlocal diffusion model, which has the {\em symmetric positive definite system} and satisfies the discrete maximum principle. Using Faulhaber's formula and Riemann zeta function, the perturbation error for symmetric positive definite system and nonsymmetric indefinite systems are given. Then the detailed proof of the convergence analysis for the nonlocal models with the general horizon parameter $\delta=\mathcal{O}\left(h^\beta\right)$, $\beta\geq0$ are provided. More concretely, the global error is $\mathcal{O}\left(h^{\min\left\{2,1+\beta\right\}}\right)$ if $\delta$ is not set as a grid point, but it shall recover $\mathcal{O}\left(h^{\max\left\{2,4-2\beta\right\}}\right)$ when $\delta$ is set as a grid point. We also prove that the shifted-symmetric scheme is asymptotically compatible, which has the global error $\mathcal{O}\left(h^{\min\left\{2,2\beta\right\}}\right)$ as $\delta,h\rightarrow 0$. The numerical experiments (including two-dimensional case) are performed to verify the convergence., Comment: 23 pages

Reducing human reliance on energy-inefficient cooling methods such as air conditioning would have a large impact on the global energy landscape. By a process of complete delignification and densification of wood, we developed a structural material with a mechanical strength of 404.3 megapascals, more than eight times that of natural wood. The cellulose nanofibers in our engineered material backscatter solar radiation and emit strongly in mid-infrared wavelengths, resulting in continuous subambient cooling during both day and night. We model the potential impact of our cooling wood and find energy savings between 20 and 60%, which is most pronounced in hot and dry climates.

Reducing human reliance on energy-inefficient cooling methods such as air conditioning would have a large impact on the global energy landscape. By a process of complete delignification and densification of wood, we developed a structural material with a mechanical strength of 404.3 megapascals, more than eight times that of natural wood. The cellulose nanofibers in our engineered material backscatter solar radiation and emit strongly in mid-infrared wavelengths, resulting in continuous subambient cooling during both day and night. We model the potential impact of our cooling wood and find energy savings between 20 and 60%, which is most pronounced in hot and dry climates.

Optical spin-Hall effect (OSHE) is a spin-dependent transportation phenomenon of light as an analogy to its counterpart in condensed matter physics. Although being predicted and observed for decades, this effect has recently attracted enormous interests due to the development of metamaterials and metasurfaces, which can provide us tailor-made control of the light-matter interaction and spin-orbit interaction. In parallel to the developments of OSHE, metasurface gives us opportunities to manipulate OSHE in achieving a stronger response, a higher efficiency, a higher resolution, or more degrees of freedom in controlling the wave front. Here, we give an overview of the OSHE based on metasurface-enabled geometric phases in different kinds of configurational spaces and their applications on spin-dependent beam steering, focusing, holograms, structured light generation, and detection. These developments mark the beginning of a new era of spin-enabled optics for future optical components. © 2016, Xiaobo Yin, Jensen Li et al., published by De Gruyter 2016.

Optical spin-Hall effect (OSHE) is a spin-dependent transportation phenomenon of light as an analogy to its counterpart in condensed matter physics. Although being predicted and observed for decades, this effect has recently attracted enormous interests due to the development of metamaterials and metasurfaces, which can provide us tailor-made control of the light-matter interaction and spin-orbit interaction. In parallel to the developments of OSHE, metasurface gives us opportunities to manipulate OSHE in achieving a stronger response, a higher efficiency, a higher resolution, or more degrees of freedom in controlling the wave front. Here, we give an overview of the OSHE based on metasurface-enabled geometric phases in different kinds of configurational spaces and their applications on spin-dependent beam steering, focusing, holograms, structured light generation, and detection. These developments mark the beginning of a new era of spin-enabled optics for future optical components. © 2016, Xiaobo Yin, Jensen Li et al., published by De Gruyter 2016.

Optical spin-Hall effect (OSHE) is a spin-dependent transportation phenomenon of light as an analogy to its counterpart in condensed matter physics. Although being predicted and observed for decades, this effect has recently attracted enormous interests due to the development of metamaterials and metasurfaces, which can provide us tailor-made control of the light-matter interaction and spin-orbit interaction. In parallel to the developments of OSHE, metasurface gives us opportunities to manipulate OSHE in achieving a stronger response, a higher efficiency, a higher resolution, or more degrees of freedom in controlling the wave front. Here, we give an overview of the OSHE based on metasurface-enabled geometric phases in different kinds of configurational spaces and their applications on spin-dependent beam steering, focusing, holograms, structured light generation, and detection. These developments mark the beginning of a new era of spin-enabled optics for future optical components. © 2016, Xiaobo Yin, Jensen Li et al., published by De Gruyter 2016.

Dark state physics has led to a variety of remarkable phenomena in atomic physics, quantum optics, and information theory. Here, we investigate interacting dark resonance type physics in multi-layered plasmonic meta-molecules. We theoretically demonstrate that these plasmonic meta-molecules exhibit sub-natural spectral response, analogous to conventional atomic four-level configuration, by manipulating the evanescent coupling between the bright and dark elements (plasmonic atoms). Using cascaded coupling, we show nearly 4-fold reduction in linewidth of the hybridized resonance compared to a resonantly excited single bright plasmonic atom with same absorbance. In addition, we engineered the geometry of the meta-molecules to realize efficient intramolecular excitation transfer with nearly 80%, on resonant excitation, of the total absorption being localized at the second dark plasmonic atom. An analytical description of the spectral response of the structure is presented with full electrodynamics simulations to corroborate our results. Such multilayered meta-molecules can bring a new dimension to higher quality factor plasmonic resonance efficient excitation transfer, wavelength demultiplexing, and enhanced non-linearity at nanoscale., Published in Applied Physics Letters, v105 article 111109, 2014.

We present axial plane optical microscopy (APOM) that can, in contrast to conventional microscopy, directly image a sample's cross-section parallel to the optical axis of an objective lens without scanning. APOM combined with conventional microscopy simultaneously provides two orthogonal images of a 3D sample. More importantly, APOM uses only a single lens near the sample to achieve selective-plane illumination microscopy, as we demonstrated by three-dimensional (3D) imaging of fluorescent pollens and brain slices. This technique allows fast, high-contrast, and convenient 3D imaging of structures that are hundreds of microns beneath the surfaces of large biological tissues.

We present axial plane optical microscopy (APOM) that can, in contrast to conventional microscopy, directly image a sample's cross-section parallel to the optical axis of an objective lens without scanning. APOM combined with conventional microscopy simultaneously provides two orthogonal images of a 3D sample. More importantly, APOM uses only a single lens near the sample to achieve selective-plane illumination microscopy, as we demonstrated by three-dimensional (3D) imaging of fluorescent pollens and brain slices. This technique allows fast, high-contrast, and convenient 3D imaging of structures that are hundreds of microns beneath the surfaces of large biological tissues.

Remotely manipulating a large number of microscopic objects is important to soft-condensed matter physics, biophysics, and nanotechnology. Optical tweezers and optoelectronic tweezers have been widely used for this purpose but face critical challenges when applied to nanoscale objects, including severe photoinduced damages, undesired ionic convections, or irreversible particle immobilization on surfaces. We report here the first demonstration of a lipid bilayer-integrated optoelectronic tweezers system for simultaneous manipulation of hundreds of 60 nm gold nanoparticles in an arbitrary pattern. We use a fluid lipid bilayer membrane with a 5 nm thickness supported by a photoconductive electrode to confine the diffusion of chemically tethered nanoparticles in a two-dimensional space. Application of an external a.c. voltage together with patterned light selectively activates the photoconducting electrode that creates strong electric field localized near the surface. The field strength changes most significantly at the activated electrode surface where the particles tethered to the membrane thus experience the strongest dielectrophoretic forces. This design allows us to efficiently achieve dynamic, reversible, and parallel manipulation of many nanoparticles. Our approach to integrate biomolecular structures with optoelectronic devices offers a new platform enabling the study of thermodynamics in many particle systems and the selective transport of nanoscale objects for broad applications in biosensing and cellular mechanotransductions., Published in Nano Letters, 2013. Prepared in collaboration with the Department of Mechanical Engineering, University of California Berkeley.

Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these spacetime crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter., Published in Physical Review Letters, v109 p163001-1/163001-5, 2012.

Plasmonics is considered as one of the most promising candidates for implementing the next generation of ultrafast and ultracompact photonic circuits. Considerable effort has been made to scale down individual plasmonic components into the nanometer regime. However, a compact plasmonic source that can efficiently generate surface plasmon polaritons (SPPs) and deliver SPPs to the region of interest is yet to be realized. Here, bridging the optical antenna theory and the recently developed concept of metamaterials, we demonstrate a subwavelength, highly efficient plasmonic source for directional generation of SPPs. The designed device consists of two nanomagnetic resonators with detuned resonant frequencies. At the operating wavelength, incident photons can be efficiently channeled into SPP waves modulated by the electric field polarization. By tailoring the relative phase at resonance and the separation between the two nanoresonators, SPPs can be steered to predominantly propagate along one specific direction. This novel magnetic nanoantenna paves a new way to manipulate photons in the near-field, and also could be useful for SPPbased nonlinear applications, active modulations, and wireless optical communications., Pub. in Nano Letters, 2012.

We report an invisibility carpet cloak device, which is capable of making an object undetectable by visible light. The cloak is designed using quasi conformal mapping and is fabricated in a silicon nitride waveguide on a specially developed nanoporous silicon oxide substrate with a very low refractive index (n is less than 1.25). The spatial index variation is realized by etching holes of various sizes in the nitride layer at deep subwavelength scale creating a local effective medium index. The fabricated device demonstrates wideband invisibility throughout the visible spectrum with low loss. This silicon nitride on low index substrate can also be a general scheme for implementation of transformation optical devices at visible frequencies., To be published in Nano Letters.

Indefinite optical properties, which are typically characterized by hyperbolic dispersion relations, have not been observed in naturally occurring materials, but can be realized through a metamaterial approach. We present here the design, fabrication and characterization of nanowire metamaterials with indefinite permittivity, in which all-angle negative refraction of light is observed. The bottom-up fabrication technique, which applies electrochemical plating of nanowires in porous alumina template, is developed and demonstrated in achieving uniform hyperbolic optical properties at a large scale. We developed techniques to improve the uniformity and to reduce the defect density in the sample. The non-magnetic design and the off-resonance operation of the nanowire metamaterials significantly reduce the energy loss of electromagnetic waves and make the broad-band negative refraction of light possible., Published in Philosophical Transactions of The Royal Society A, v369 p3434-3446, 2011.

The law of refraction first derived by Snellius and later introduced as the Huygens-Fermat principle, states that the incidence and refracted angles of a lightwave at the interface of two different materials are related to the ratio of the refractive indices in each medium. Whereas all natural materials have a positive refractive index and therefore exhibit refraction in the positive direction, artificially engineered negative index metamaterials have been shown capable of bending lightwaves negatively. Such a negative refractive index is the key to achieving a perfect lens that is capable of imaging well below the diffraction limit. However, negative index metamaterials are typically lossy, narrow band, and require complicated fabrication processes. Recently, an alternative approach to obtain negative refraction from a very thin nonlinear film has been proposed and experimentally demonstrated in the microwave region. However, such approaches use phase conjugation, which makes optical implementations difficult. Here, we report a simple but different scheme to demonstrate experimentally nonlinear negative refraction at optical frequencies using four-wave mixing in nanostructured metal films. The refractive index can be designed at will by simply tuning the wavelengths of the interacting waves, which could have potential impact on many important applications, such as superlens imaging., Published in Nature Materials, 30 Oct 2011.

Acoustic metamaterials can manipulate sound waves in surprising ways, which include collimation, focusing, cloaking, sonic screening and extraordinary transmission. Recent theories suggested that imaging below the diffraction limit using passive elements can be realized by acoustic superlenses or magnifying hyperlenses. These could markedly enhance the capabilities in underwater sonar sensing, medical ultrasound imaging and non-destructive materials testing. However, these proposed approaches suffer narrow working frequency bands and significant resonance-induced loss, which hinders them from successful experimental realization. Here, we report the experimental demonstration of an acoustic hyperlens that magnifies subwavelength objects by gradually converting evanescent components into propagating waves. The fabricated acoustic hyperlens relies on straightforward cutoff-free propagation and achieves deep-subwavelength resolution with low loss over a broad frequency bandwidth. © 2009 Macmillan Publishers Limited. All rights reserved.

Acoustic metamaterials can manipulate sound waves in surprising ways, which include collimation, focusing, cloaking, sonic screening and extraordinary transmission. Recent theories suggested that imaging below the diffraction limit using passive elements can be realized by acoustic superlenses or magnifying hyperlenses. These could markedly enhance the capabilities in underwater sonar sensing, medical ultrasound imaging and non-destructive materials testing. However, these proposed approaches suffer narrow working frequency bands and significant resonance-induced loss, which hinders them from successful experimental realization. Here, we report the experimental demonstration of an acoustic hyperlens that magnifies subwavelength objects by gradually converting evanescent components into propagating waves. The fabricated acoustic hyperlens relies on straightforward cutoff-free propagation and achieves deep-subwavelength resolution with low loss over a broad frequency bandwidth. © 2009 Macmillan Publishers Limited. All rights reserved.

Acoustic metamaterials can manipulate sound waves in surprising ways, which include collimation, focusing, cloaking, sonic screening and extraordinary transmission. Recent theories suggested that imaging below the diffraction limit using passive elements can be realized by acoustic superlenses or magnifying hyperlenses. These could markedly enhance the capabilities in underwater sonar sensing, medical ultrasound imaging and non-destructive materials testing. However, these proposed approaches suffer narrow working frequency bands and significant resonance-induced loss, which hinders them from successful experimental realization. Here, we report the experimental demonstration of an acoustic hyperlens that magnifies subwavelength objects by gradually converting evanescent components into propagating waves. The fabricated acoustic hyperlens relies on straightforward cutoff-free propagation and achieves deep-subwavelength resolution with low loss over a broad frequency bandwidth. © 2009 Macmillan Publishers Limited. All rights reserved.