Steven A. Cummer

Full-wave simulations of electromagnetic cloaking structures

Pendry et al. have reported electromagnetically anisotropic and inhomogeneous shells that, in theory, completely shield an interior structure of arbitrary size from electromagnetic fields without perturbing the external fields. Neither the coordinate transformation-based analytical formulation nor the supporting ray-tracing simulation indicate how material perturbations and full-wave effects might affect the solution. We report fully electromagnetic simulations of the cylindrical version of this cloaking structure using ideal and nonideal (but physically realizable) electromagnetic parameters that show that the low-reflection and power-flow bending properties of the electromagnetic cloaking structure are not especially sensitive to modest permittivity and permeability variations. The cloaking performance degrades smoothly with increasing loss, and effective low-reflection shielding can be achieved with a cylindrical shell composed of an eight- (homogeneous) layer approximation of the ideal continuous medium. An imperfect but simpler version of the cloaking material is derived and is shown to reproduce the ray bending of the ideal material in a manner that may be easier to experimentally realize.

Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations

The technique of applying form-invariant, spatial coordinate transformations of Maxwell’s equations can facilitate the design of structures with unique electromagnetic or optical functionality. Here, we illustrate the transformation-optical approach in the designs of a square electromagnetic cloak and an omni-directional electromagnetic field concentrator. The transformation equations are described and the functionality of the devices is numerically confirmed by two-dimensional finite element simulations. The two devices presented demonstrate that the transformation optic approach leads to the specification of complex, anisotropic and inhomogeneous materials with well directed and distinct electromagnetic behavior.

One path to acoustic cloaking

A complete analysis of coordinate transformations in elastic media by Milton et al has shown that, in general, the equations of motion are not form invariant and thus do not admit transformation-type solutions of the type discovered by Pendry et al for electromagnetics. However, in a two-dimensional (2D) geometry, the acoustic equations in a fluid are identical in form to the single polarization Maxwell equations via a variable exchange that also preserves boundary conditions. We confirm the existence of transformation-type solutions for the 2D acoustic equations with anisotropic mass via time harmonic simulations of acoustic cloaking. We discuss the possibilities of experimentally demonstrating acoustic cloaking and analyse why this special equivalence of acoustics and electromagnetics occurs only in 2D.

Modeling electromagnetic propagation in the Earth-ionosphere waveguide

The ionosphere plays a role in radio propagation that varies strongly with frequency. At extremely low frequency (ELF: 3-3000 Hz) and very low frequency (VLF: 3-30 kHz), the ground and the ionosphere are good electrical conductors and form a spherical Earth-ionosphere waveguide. Many giants of the electromagnetics (EMs) community studied ELF-VLF propagation in the Earth-ionosphere waveguide, a topic which was critically important for long-range communication and navigation systems. James R. Wait was undoubtedly the most prolific publisher in this field, starting in the 1950s and continuing well into the 1990s. Although it is an old problem, there are new scientific and practical applications that rely on accurate modeling of ELF-VLF propagation, including ionospheric remote sensing, lightning remote sensing, global climate monitoring, and even earthquake precursor detection. The theory of ELF-VLP propagation in the Earth-ionosphere waveguide is mature, but there remain many ways of actually performing propagation calculations. Most techniques are based on waveguide mode theory with either numerical or approximate analytical formulations, but direct finite-difference time-domain (FDTD) modeling is now also feasible. Furthermore, in either mode theory or FDTD, the ionospheric upper boundary can be treated with varying degrees of approximation. While these approximations are understood in a qualitative sense, it is difficult to assess in advance their applicability to a given propagation problem. With a series of mode theory and FDTD simulations of propagation from lightning radiation in the Earth-ionosphere waveguide, we investigate the accuracy of these approximations. We also show that fields from post-discharge ionospheric currents and from evanescent modes become important at lower ELF (/spl lsim/500 Hz) over short distances (/spl lsim/500 km). These fields are not easily modeled with mode theory, but are inherent in the FDTD formulation of the problem. In this way, the FDTD solution bridges the gap between analytical solutions for fields close to and far from the source.

Ionospheric D region remote sensing using VLF radio atmospherics

Lightning discharges radiate the bulk of their electromagnetic energy in the very low frequency (VLF, 3–30 kHz) and extremely low frequency (ELF, 3–3000 Hz) bands. This energy, contained in impulse-like signals called radio atmospherics or sferics, is guided for long distances by multiple reflections from the ground and lower ionosphere. This suggests that observed sferic waveforms radiated from lightning and received at long distances (>1000 km) from the source stroke contain information about the state of the ionosphere along the propagation path. The focus of this work is on the extraction of nighttime D region electron densities (in the altitude range of ∼70–95 km) from observed VLF sferics. In order to accurately interpret observed sferic characteristics, we develop a model of sferic propagation which is based on an existing frequency domain subionospheric VLF propagation code. The model shows that the spectral characteristics of VLF sferics depend primarily on the propagation path averaged ionospheric D region electron density profile, covering the range of electron densities from ∼100 to 103 cm−3. To infer the D region density from observed VLF sferics, we find the electron density profile that produces a modeled sferic spectrum that most closely matches an observed sferic spectrum. In most nighttime cases the quality of the agreement and the uncertainties involved allow the height of an exponentially varying electron density profile to be inferred with a precision of ∼0.2 km.

ELF radiation produced by electrical currents in sprites

Measurements of ELF-radiating currents associated with sprite-producing lightning discharges exhibit a second current peak simultaneous in time with sprite luminosity, suggesting that the observed ELF radiation is produced by intense electrical currents flowing in the body of the sprite.

Wavefront modulation and subwavelength diffractive acoustics with an acoustic metasurface

Metasurfaces are a family of novel wavefront-shaping devices with planar profile and subwavelength thickness. Acoustic metasurfaces with ultralow profile yet extraordinary wave manipulating properties would be highly desirable for improving the performance of many acoustic wave-based applications. However, designing acoustic metasurfaces with similar functionality to their electromagnetic counterparts remains challenging with traditional metamaterial design approaches. Here we present a design and realization of an acoustic metasurface based on tapered labyrinthine metamaterials. The demonstrated metasurface can not only steer an acoustic beam as expected from the generalized Snells law, but also exhibits various unique properties such as conversion from propagating wave to surface mode, extraordinary beam-steering and apparent negative refraction through higher-order diffraction. Such designer acoustic metasurfaces provide a new design methodology for acoustic signal modulation devices and may be useful for applications such as acoustic imaging, beam steering, ultrasound lens design and acoustic surface wave-based applications.

Three-dimensional broadband omnidirectional acoustic ground cloak

The control of sound propagation and reflection has always been the goal of engineers involved in the design of acoustic systems. A recent design approach based on coordinate transformations, which is applicable to many physical systems, together with the development of a new class of engineered materials called metamaterials, has opened the road to the unconstrained control of sound. However, the ideal material parameters prescribed by this methodology are complex and challenging to obtain experimentally, even using metamaterial design approaches. Not surprisingly, experimental demonstration of devices obtained using transformation acoustics is difficult, and has been implemented only in two-dimensional configurations. Here, we demonstrate the design and experimental characterization of an almost perfect three-dimensional, broadband, and, most importantly, omnidirectional acoustic device that renders a region of space three wavelengths in diameter invisible to sound.

Measurement of charge transfer in sprite‐producing lightning using ELF radio atmospherics

Transient high altitude optical emissions referred to as “sprites” are believed to occur as a result of the transfer of large amounts of charge (∼100–300 C) from cloud altitudes of 5–10 km to the ground. Using a general subionospheric ELF propagation model, we quantitatively interpret magnetic field waveforms of ELF radio atmospherics originating in mid-western U.S. lightning discharges and observed at Stanford (∼1800 km range) to determine the temporal variation of the lightning current and thereby measure the charge transfer during the stroke. For 6 sprite-producing lightning current waveforms observed on July 24, 1996, we find that 25 to 325 coulombs of charge was transferred during the first 5 ms of the discharges, assuming a 10 km altitude for the initial charge.

Characteristics of Sprite-Producing Positive Cloud-to-Ground Lightning during the 19 July 2000 STEPS Mesoscale Convective Systems

During the summer of 2000, the Severe Thunderstorm Electrification and Precipitation Study (STEPS) program deployed a three-dimensional Lightning Mapping Array (LMA) near Goodland, Kansas. Video confirmation of sprites triggered by lightning within storms traversing the LMA domain were coordinated with extremely low frequency (ELF) transient measurements in Rhode Island and North Carolina. Two techniques of estimating changes in vertical charge moment (Mq) yielded averages of ;800 and ;950 C km for 13 sprite-parent positive polarity cloud-to-ground strokes (1CGs). Analyses of the LMA’s very high frequency (VHF) lightning emissions within the two mesoscale convective systems (MCSs) show that 1CGs did not produce sprites until the centroid of the maximum density of lightning radiation emissions dropped from the upper part of the storm (7‐11.5 km AGL) to much lower altitudes (2‐5 km AGL). The average height of charge removal (Zq) from 15 sprite-parent 1CGs during the late mature phase of one MCS was 4.1 km AGL. Thus, the total charges lowered by spriteparent 1CGs were on the order of 200 C. The regional 08C isotherm was located at about 4.0 km AGL. This suggests a possible linkage between sprite-parent CGs and melting-layer/brightband charge production mechanisms in MCS stratiform precipitation regions. These cases are supportive of the conceptual MCS spriteproduction models previously proposed by two of the authors (Lyons and Williams).