arXiv subjects

Fu Liu

Publications and source records attributed to Fu Liu.

At least 37 records · Page 2Linked to original sources

arXiv2022

Reflectarrays and metasurface reflectors as diffraction gratings

Reconfigurable reflectors have a significant potential in future telecommunication systems, and approaches to the design and realization of full and tunable reflection control are now actively studied. Reflectarrays, being the classical approach to realization of scanning reflectors, are based on the phased-array theory (the so-called generalized reflection law) and the physical optics approximation of the reflection response. To overcome the limitations of the reflectarray technology, researchers actively study inhomogeneous metasurfaces, using the theory of diffraction gratings. In order to make these devices tunable and fully realize their potential, it is necessary to unify the two approaches and study reconfigurable reflectors from a unified point of view. Here, we offer a basic tutorial on reflectarrays and reflecting metasufaces, explaining their common fundamental properties that stem from the diffraction theory. This tutorial is suitable for graduate and post-graduate students and hopefully will help to develop more deeper understanding of both phased arrays and diffraction gratings.

physics.app-ph↗

arXiv2022

Geodesic photon coupling and non-Hermitian exceptional point of microcavities on topologically curved space

Asymmetric microcavities supporting Whispering-gallery modes (WGMs) are of great significance for on-chip optical information processing. We define asymmetric microcavities on topologically curved surfaces, where the geodesic light trajectories completely reconstruct the cavity mode features. The quality factors of the lossy chaotic and island modes in flat cavities can be increased by up to ~200 times by the space curvature. Strong and weak coupling between modes of very different origins occur when the space curvature brings them into resonance, leading to a fine tailoring of the cavity photon energy and lifetime. Finally, we prove that by varying the overall loss, an exceptional point can be clearly observed at which both the cavity photon energy and lifetime become degenerate. Our work is at the crosspoint of optical chaotic dynamics, non-Hermitian physics and geodesic optical devices, and would open the novel area of geodesic microcavity photonics.

physics.optics↗

arXiv2021

Angular-dependent Klein tunneling in photonic graphene

The Klein paradox consists in the perfect tunneling of relativistic particles through high potential barriers. As a curious feature of particle physics, it is responsible for the exceptional conductive properties of graphene. It was recently studied in the context of atomic condensates and topological photonics and phononics. While in theory the perfect tunneling holds only for normal incidence, so far the angular dependence of the Klein tunneling and its strong variation with the barrier height were not measured experimentally. In this work, we capitalize on the versatility of atomic vapor cells with paraxial beam propagation and index patterning by electromagnetically-induced transparency. We report the first experimental observation of perfect Klein transmission in a 2D photonic system (photonic graphene) at normal incidence and measure the angular dependence. Counter-intuitively, but in agreement with the Dirac equation, we observe that the decay of the Klein transmission versus angle is suppressed by increasing the barrier height, a key result for the conductivity of graphene and its analogues.

physics.optics↗

arXiv2021

Subwavelength Focusing by Engineered Power Flow-Conformal Metamirrors

Many advances in reflective metasurfaces have been made during the last few years, implementing efficient manipulations of wavefronts, especially for plane waves. Despite numerous solutions that have been developed throughout the years, a practical method to obtain subwavelength focusing without the generation of additional undesired scattering is a challenge to this day. In this paper, we introduce and discuss lossless reflectors for focusing incident waves into a point. The solution is based on the so-called power flow-conformal surfaces that allow theoretically arbitrary shaping of reflected waves. The metamirror shape is adapted to the power flow of the sum of the incident and reflected waves, allowing a local description of the reflector surface based on the surface impedance. In particular, we present a study of two scenarios. First, we study the scenario when the field is emitted by a point source and focused at an image point (in the considered example, with the λ/20 resolution). Second, we analyze a metasurface capable to focus the power of an illuminating plane wave. This work provides a feasible strategy for various applications, including detecting biological signals near the skin, sensitive power focusing for cancer therapy, and point-to-point power transfer.

physics.optics↗

arXiv2021

Time-varying components for enhancing wireless transfer of power and information

Temporal modulation of components of electromagnetic systems provides an exceptional opportunity to engineer the response of those systems in a desired fashion, both in the time and frequency domains. For engineering time-modulated systems, one needs to thoroughly study the basic concepts and understand the salient characteristics of temporal modulation. In this paper, we carefully study physical models of basic bulk circuit elements -- capacitors, inductors, and resistors -- as frequency dispersive and time-varying components and study their effects in the case of periodical time modulations. We develop a solid theory for understanding these elements, and apply it to two important applications: wireless power transfer and antennas. For the first application, we show that by periodically modulating the mutual inductance between the transmitter and receiver, the fundamental limits of classical wireless power transfer systems can be overcome. Regarding the second application, we consider a time-varying source for electrically small dipole antennas and show how time modulation can enhance the antenna performance. The developed theory of electromagnetic systems engineered by temporal modulation is applicable from radio frequencies to optical wavelengths.

physics.app-ph↗

arXiv2021

Ehrhart positivity of Tesler polytopes and Berline-Vergne's valuation

For $\ba \in \R_{\geq 0}^{n}$, the Tesler polytope $\tes_{n}(\ba)$ is the set of upper triangular matrices with non-negative entries whose hook sum vector is $\ba$. Motivated by a conjecture of Morales', we study the questions of whether the coefficients of the Ehrhart polynomial of $\tes_n(1,1,\dots,1)$ are positive. We attack this problem by studying a certain function constructed by Berline-Vergne and its values on faces of a unimodularly equivalent copy of $\tes_n(1,1,\dots,1).$ We develop a method of obtaining the dot products appeared in formulas for computing Berline-Vergne's function directly from facet normal vectors. Using this method together with known formulas, we are able to show Berline-Vergne's function has positive values on codimension $2$ and $3$ faces of the polytopes we consider. As a consequence, we prove that the $3$rd and $4$th coefficients of the Ehrhart polynomial of $\tes_{n}(1,\dots,1)$ are positive. Using the Reduction Theorem by Castillo and the second author, we generalize the above result to all deformations of $\tes_{n}(1,\dots,1)$ including all the integral Tesler polytopes.

math.CO↗

arXiv2020

Ray dynamics of whispering-gallery modes in curved space

Microcavities supporting Whispering-gallery modes (WGMs) are of great significance for on-chip optical information processing, which is frequently analyzed using ray dynamics that conventionally involves straight light trajectories in flat space. We develop a novel mathematical model of ray dynamics that allows investigating photon movement in WGM-microcavities defined on curved surfaces, which consists of curved or twisted light trajectories following the geodesic lines of the space. We show that the resulting ray dynamics differs dramatically from those in flat microcavities, and in various manners depending on whether the curved surface can be unfolded to flat. Our methods suggest a redefinition of the WGM symmetry in curved space and provides a universal tool for analyzing three-dimensional (3D) photonic circuits containing curved structures with boundaries.

physics.optics↗

arXiv2020

A multi-functional reconfigurable metasurface: Electromagnetic design accounting for fabrication aspects

In this paper we present the theoretical considerations and the design evolution of a proof-of-concept reconfigurable metasurface, primarily used as a tunable microwave absorber, but also as a wavefront manipulation and polarization conversion device in reflection. We outline the design evolution and all considerations taken into account, from the selection of patch shape, unit cell size, and substrate, to the topology of the structure that realizes the desired tunability. The presented design conforms to fabrication restrictions and is co-designed to work with an integrated circuit chip for providing tunable complex loads to the metasurface, using a commercially available semiconductor process. The proposed structure can perform multiple tunable functionalities by appropriately biasing the integrated circuit: Perfect absorption for a wide range of incidence angles of both linear polarization states, accommodating a spectral range in the vicinity of 5 GHz, with potential also for wavefront control, exemplified via anomalous reflection and polarization conversion. The end vision is for such a design to be scalable and deployable as a practical HyperSurface, i.e., an intelligent multi-functional metasurface capable of concurrent reconfigurable functionalities: absorption, beam steering, polarization conversion, wavefront shaping, holography, and sensing.

physics.app-ph↗

arXiv2020

Limit linear series and ranks of multiplication maps

We develop a new technique for studying ranks of multiplication maps for linear series via limit linear series and degenerations to chains of genus-1 curves. We use this approach to prove a purely elementary criterion for proving cases of the Maximal Rank Conjecture, and then apply the criterion to several ranges of cases, giving a new proof of the case of quadrics, and also treating several families in the case of cubics. Our proofs do not require restrictions on direction of approach, so we recover new information on the locus in the moduli space of curves on which the maximal rank condition fails.

math.AG↗

arXiv2020

On the Todd Class of the Permutohedral variety

In the special case of braid fans, we give a combinatorial formula for the Berline-Vergne's construction for an Euler-Maclaurin type formula that computes number of lattice points in polytopes. Our formula is obtained by computing a symmetric expression for the Todd class of the permutohedral variety. By showing that this formula does not always have positive values, we prove that the Todd class of the permutohedral variety $X_d$ is not effective for $d\geq 24$. Additionally, we prove that the linear coefficient in the Ehrhart polynomial of any lattice generalized permutohedron is positive.

math.CO↗

arXiv2020

Deformation Cones of nested Braid fans

Generalized permutohedra are deformations of regular permutohedra, and arise in many different fields of mathematics. One important characterization of generalized permutohedra is the Submodular Theorem, which is related to the deformation cone of the Braid fan. We lay out general techniques for determining deformation cones of a fixed polytope and apply it to the Braid fan to obtain a natural combinatorial proof for the Submodular Theorem. We also consider a refinement of the Braid fan, called the nested Braid fan, and construct usual (respectively, generalized) nested permutohedra which have the nested Braid fan as (respectively, refining) their normal fan. We extend many results on generalized permutohedra to this new family of polytopes, including a one-to-one correspondence between faces of nested permutohedra and chains in ordered partition posets, and a theorem analogous to the Submodular Theorem. Finally, we show that the nested Braid fan is the barycentric subdivision of the Braid fan, which gives another way to construct this new combinatorial object.

math.CO↗

arXiv2020

Exploration of Intercell Wireless Millimeter-Wave Communication in the Landscape of Intelligent Metasurfaces

Software-defined metasurfaces are electromagnetically ultra-thin, artificial components that can provide engineered and externally controllable functionalities. The control over these functionalities is enabled by the metasurface tunability, which is implemented by embedded electronic circuits that modify locally the surface resistance and reactance. Integrating controllers within the metasurface cells, able to intercommunicate and adaptively reconfigure it, thus imparting a desired electromagnetic operation, opens the path towards the creation of an artificially intelligent (AI) fabric where each unit cell can have its own sensing, programmable computing, and actuation facilities. In this work we take a crucial step towards bringing the AI metasurface technology to emerging applications, in particular exploring the wireless mm-wave intercell communication capabilities in a software-defined HyperSurface designed for operation is the microwave regime. We examine three different wireless communication channels within the landscape of the reflective metasurface: Firstly, in the layer where the control electronics of the HyperSurface lie, secondly inside a dedicated layer enclosed between two metallic plates, and, thirdly, inside the metasurface itself. For each case we examine the physical implementation of the mm-wave transponder nodes, we quantify communication channel metrics, and we identify complexity vs. performance trade-offs.

physics.app-ph↗

arXiv2020

Pulsed Self-Oscillating Nonlinear Systems for Robust Wireless Power Transfer

While wired-power-transfer devices ensure robust power delivery even if the receiver position or load impedance changes, achieving the robustness of wireless power transfer (WPT) is challenging. Conventional solutions are based on additional control circuits for dynamic tuning. Here, we propose a robust WPT system in which no additional tuning circuitry is required for robust operation. This is achieved by our systematically designing the load and the coupling link to be parts of the feedback circuit. Therefore, the WPT operation is automatically adjusted to the optimal working condition under a wide range of load and receiver positions. In addition, pulsed oscillations instead of single-harmonic oscillation are adopted to increase the overall efficiency. An example system is designed with the use of a capacitive coupling link. It realizes a virtual, nearly-ideal oscillating voltage source at the load site, giving efficient power transfer comparable to that of the ideal wired-connection scenario. We numerically and experimentally verify the robustness of the WPT system under the variations of load and coupling, where coupling is changing by our varying the alignment of aluminum plates. The working frequency and the transferred power agree well with analytical models. The proposed paradigm can have a significant impact on future high-performance WPT devices. The designed system can also work as a smart table supporting multiple receivers with robust and efficient operation.

physics.app-ph↗

arXiv2019

Active Metasurfaces as a Platform for Capacitive Wireless Power Transfer Supporting Multiple Receivers

As wireless power transfer (WPT) repeaters, metasurfaces can enhance field coupling, improving the WPT operation. In this paper, we show that metasurfaces can also be used as transmitters of capacitive WPT systems. Such a metasurface-based WPT system can feed multiple receivers and provide robust operation against load or position variations. We formulate an analytical model of such WPT systems. We also discuss the exact solution of a particular example with $N$ identical receivers.

physics.app-ph↗

arXiv2019

Omnidirectional Wireless Power Transfer with Automatic Power Flow Control

We present an omnidirectional wireless power transfer (WPT) system capable of automatic power flow control using three orthogonal transmitter (Tx)-repeater (Rp) pairs. The power drawn from each transmitter is automatically adjusted depending on the mutual inductance between the receiver and the Tx-Rp pair. The proposed approach enables the receiver to harvest almost uniform power with high efficiency (90\%) regardless of its position.

eess.SY↗

arXiv2019

The Software-Defined Metasurfaces Concept and Electromagnetic Aspects

We present the concept and electromagnetic aspects of HyperSurFaces (HSFs), artificial, ultrathin structures with software controlled electromagnetic properties. The HSFs key unit is the metasurface, a plane with designed subwavelength features whose electromagnetic response can be tuned via voltage-controlled continuously-tunable electrical elements that provide local control of the surface impedance and advanced functionalities, such as tunable perfect absorption or wavefront manipulation. A nanonetwork of controllers enables software defined HSFs control related to the emerging Internet of Things paradigm.

physics.app-ph↗

arXiv2019

Self-Oscillating Capacitive Wireless Power Transfer with Robust Operation

We show that a capacitive wireless power transfer device can be designed as a self-oscillating circuit using operational amplifiers. As the load and the capacitive wireless channels are part of the feedback circuit of the oscillator, the wireless power transfer can self-adjust to the optimal condition under the change of the load resistance and the transfer distance. We have theoretically analyzed and experimentally demonstrated the proposed design. The results show that the operation is robust against changes of various parameters, including the load resistance.

physics.app-ph↗

arXiv2019

Intelligent Metasurfaces with Continuously Tunable Local Surface Impedance for Multiple Reconfigurable Functions

Electromagnetic metasurfaces can be characterized as intelligent if they are able to perform multiple tunable functions, with the desired response being controlled by a computer influencing the individual electromagnetic properties of each metasurface inclusion. In this paper, we present an example of an intelligent metasurface which operates in the reflection mode in the microwave frequency range. We numerically show that without changing the main body of the metasurface we can achieve tunable perfect absorption and tunable anomalous reflection. The tunability features can be implemented using mixed-signal integrated circuits (ICs), which can independently vary both the resistance and reactance, offering complete local control over the complex surface impedance. The ICs are embedded in the unit cells by connecting two metal patches over a thin grounded substrate and the reflection property of the intelligent metasurface can be readily controlled by a computer. Our intelligent metasurface can have significant influence on future space-time modulated metasurfaces and a multitude of applications, such as beam steering, energy harvesting, and communications.

physics.app-ph↗