Allan Greenleaf

Bio: Allan Greenleaf is an academic researcher from University of Rochester. The author has contributed to research in topics: Fourier integral operator & Cloaking. The author has an hindex of 31, co-authored 90 publications receiving 4040 citations.

On nonuniqueness for Calderón’s inverse problem

Abstract: We construct anisotropic conductivities with the same Dirichlet-to-Neumann map as a homogeneous isotropic conductivity. These conductivities are singular close to a surface inside the body.

Anisotropic conductivities that cannot be detected by EIT.

Abstract: We construct anisotropic conductivities in dimension 3 that give rise to the same voltage and current measurements at the boundary of a body as a homogeneous isotropic conductivity. These conductivities are non-zero, but degenerate close to a surface inside the body.

Full-Wave Invisibility of Active Devices at All Frequencies

Abstract: There has recently been considerable interest in the possibility, both theoretical and practical, of invisibility (or “cloaking”) from observation by electromagnetic (EM) waves. Here, we prove invisibility with respect to solutions of the Helmholtz and Maxwell’s equations, for several constructions of cloaking devices. The basic idea, as in the papers [GLU2, GLU3, Le, PSS1], is to use a singular transformation that pushes isotropic electromagnetic parameters forward into singular, anisotropic ones. We define the notion of finite energy solutions of the Helmholtz and Maxwell’s equations for such singular electromagnetic parameters, and study the behavior of the solutions on the entire domain, including the cloaked region and its boundary. We show that, neglecting dispersion, the construction of [GLU3, PSS1] cloaks passive objects, i.e., those without internal currents, at all frequencies k. Due to the singularity of the metric, one needs to work with weak solutions. Analyzing the behavior of such solutions inside the cloaked region, we show that, depending on the chosen construction, there appear new “hidden” boundary conditions at the surface separating the cloaked and uncloaked regions. We also consider the effect on invisibility of active devices inside the cloaked region, interpreted as collections of sources and sinks or internal currents. When these conditions are overdetermined, as happens for Maxwell’s equations, generic internal currents prevent the existence of finite energy solutions and invisibility is compromised.

Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics

Abstract: We describe recent theoretical and experimental progress on making objects invisible to detection by electromagnetic waves. Ideas for devices that would once have seemed fanciful may now be at least approximately implemented physically using a new class of artificially structured materials called metamaterials. Maxwell's equations have transformation laws that allow for the design of electromagnetic material parameters that steer light around a hidden region, returning it to its original path on the far side. Not only would observers be unaware of the contents of the hidden region, they would not even be aware that something was being hidden. An object contained in the hidden region, which would have no shadow, is said to be cloaked. Proposals for, and even experimental implementations of, such cloaking devices have received the most attention, but other designs having striking effects on wave propagation are possible. All of these designs are initially based on the transformation laws of the equations that govern wave propagation but, due to the singular parameters that give rise to the desired effects, care needs to be taken in formulating and analyzing physically meaningful solutions. We recount the recent history of the subject and discuss some of the mathematical and physical issues involved.

Electromagnetic wormholes and virtual magnetic monopoles from metamaterials.

Abstract: We describe new configurations of electromagnetic (EM) material parameters, the electric permittivity $ϵ$ and magnetic permeability $\ensuremath{\mu}$, which allow one to construct devices that function as invisible tunnels These allow EM wave propagation between the regions at the two ends of a tunnel, but the tunnels themselves and the regions they enclose are not detectable to lateral EM observations Such devices act as wormholes with respect to Maxwell's equations and effectively change the topology of space vis-\`a-vis EM wave propagation We suggest several applications, including devices behaving as virtual magnetic monopoles, invisible cables, and scopes for MRI-assisted surgery

Metamaterial Electromagnetic Cloak at Microwave Frequencies

Abstract: A recently published theory has suggested that a cloak of invisibility is in principle possible, at least over a narrow frequency band. We describe here the first practical realization of such a cloak; in our demonstration, a copper cylinder was "hidden" inside a cloak constructed according to the previous theoretical prescription. The cloak was constructed with the use of artificially structured metamaterials, designed for operation over a band of microwave frequencies. The cloak decreased scattering from the hidden object while at the same time reducing its shadow, so that the cloak and object combined began to resemble empty space.

An optical cloak made of dielectrics

Abstract: Invisibility devices have captured the human imagination for many years. Recent theories have proposed schemes for cloaking devices using transformation optics and conformal mapping. Metamaterials, with spatially tailored properties, have provided the necessary medium by enabling precise control over the flow of electromagnetic waves. Using metamaterials, the first microwave cloaking has been achieved but the realization of cloaking at optical frequencies, a key step towards achieving actual invisibility, has remained elusive. Here, we report the first experimental demonstration of optical cloaking. The optical 'carpet' cloak is designed using quasi-conformal mapping to conceal an object that is placed under a curved reflecting surface by imitating the reflection of a flat surface. The cloak consists only of isotropic dielectric materials, which enables broadband and low-loss invisibility at a wavelength range of 1,400-1,800 nm.

Controlling sound with acoustic metamaterials

Abstract: Acoustic metamaterials can manipulate and control sound waves in ways that are not possible in conventional materials. Metamaterials with zero, or even negative, refractive index for sound offer new possibilities for acoustic imaging and for the control of sound at subwavelength scales. The combination of transformation acoustics theory and highly anisotropic acoustic metamaterials enables precise control over the deformation of sound fields, which can be used, for example, to hide or cloak objects from incident acoustic energy. Active acoustic metamaterials use external control to create effective material properties that are not possible with passive structures and have led to the development of dynamically reconfigurable, loss-compensating and parity–time-symmetric materials for sound manipulation. Challenges remain, including the development of efficient techniques for fabricating large-scale metamaterial structures and converting laboratory experiments into useful devices. In this Review, we outline the designs and properties of materials with unusual acoustic parameters (for example, negative refractive index), discuss examples of extreme manipulation of sound and, finally, provide an overview of future directions in the field. Acoustic metamaterials can be used manipulate sound waves with a high degree of control. Their applications include acoustic imaging and cloaking. This Review outlines the designs and properties of these materials, discussing transformation acoustics theory, anisotropic materials and active acoustic metamaterials.

Transformation optics and metamaterials

Abstract: Transformation optics describes the capability to design the path of light waves almost at will through the use of metamaterials that control effective materials properties on a subwavelength scale. In this review, the physics and applications of transformation optics are discussed.