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.

An optical cloak made of dielectrics

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Regularization Of Inverse Problems

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.

Transformation optics and metamaterials

Invisibility or cloaking has captured human's imagination for many years. With the recent advancement of metamaterials, several theoretical proposals show cloaking of objects is possible, however, so far there is a lack of an experimental demonstration at optical frequencies. Here, we report the first experimental realization of a dielectric optical cloak. The cloak is designed using quasi-conformal mapping to conceal an object that is placed under a curved reflecting surface which imitates the reflection of a flat surface. Our cloak consists only of isotropic dielectric materials which enables broadband and low-loss invisibility at a wavelength range of 1400-1800 nm.

Dielectric Optical Cloak

Like their optical counterparts, acoustic metamaterials are capable of manipulating sound waves in unusual ways. An acoustic hyperlens is now demonstrated that is capable of magnifying subwavelength acoustic waves, and could therefore find applications in medical imaging or underwater sonar. Acoustic metamaterials can manipulate sound waves in surprising ways, which include collimation, focusing, cloaking, sonic screening and extraordinary transmission1,2,3,4,5,6,7,8,9,10,11,12,13,14. Recent theories suggested that imaging below the diffraction limit using passive elements can be realized by acoustic superlenses or magnifying hyperlenses15,16. 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.

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Experimental demonstration of an acoustic magnifying hyperlens.

We consider an invariant formulation of the system of Maxwell's equations for a general anisotropic medium on a compact orientable Riemannian three-manifold (M, g) with nonempty boundary. The system can be completed to a Dirac type first-order system on the manifold. We show that the Betti numbers of the manifold can be recovered from the dynamical response operator for the Dirac system given on a part of the boundary. In the case of the original physical Maxwell system, assuming that the entire boundary is known, all Betti numbers of the manifold can also be determined from the dynamical response operator given on a part of the boundary. Physically, this operator maps the tangential component of the electric field into the tangential component of the magnetic field on the boundary.

https://www.intlpress.com/site/pub/files/_fulltext/journals/cag/2010/0018/0005/CAG-2010-0018-0005-a004.pdf

Reconstruction of Betti numbers of manifolds for anisotropic Maxwell and Dirac systems

A wave propagation generated by a boundary source into a weakly lateral heterogeneous medium (WLHM) occupying a half-space is considered in the acoustic approximation. WLHM means that the velocity of the wave propagation depends weakly on the horizontal coordinates in comparison with the strong dependence on the vertical coordinate z. We consider the problem of the reconstruction of the velocity inside the half-space from the knowledge of the medium response measured at z=0. We obtain a recurrent system of 1D inverse problems to find...

/pdf/inverse-problem-of-velocity-reconstruction-in-weakly-lateral-35up6gdyuf.pdf

Inverse problem of velocity reconstruction in weakly lateral heterogeneous half-space

Cloaking devices are prescriptions of electrostatic, optical or electromagnetic parameter fields (conductivity $\sigma(x)$, index of refraction $n(x)$, or electric permittivity $\epsilon(x)$ and magnetic permeability $\mu(x)$) which are piecewise smooth on $\mathbb R^3$ and singular on a hypersurface $\Sigma$, and such that objects in the region enclosed by $\Sigma$ are not detectable to external observation by waves. Here, we give related constructions of invisible tunnels, which allow electromagnetic waves to pass between possibly distant points, but with only the ends of the tunnels visible to electromagnetic imaging. Effectively, these change the topology of space with respect to solutions of Maxwell's equations, corresponding to attaching a handlebody to $\mathbb R^3$. The resulting devices thus function as electromagnetic wormholes.

Electromagnetic wormholes via handlebody constructions

We consider a Dirac-type operator $D_P$ on a vector bundle $V$ over a compact Riemannian manifold $(M,g)$ with a nonempty boundary. The operator $D_P$ is specified by a boundary condition $P(u|_{\p M})=0$ where $P$ is a projector which may be a non-local, i.e. a pseudodifferential operator. We assume the existence of a chirality operator which decomposes $L^2(M, V)$ into two orthogonal subspaces $X_+ \oplus X_-$. Under certain conditions, the operator $D_P$ restricted to $X_+$ and $ X_-$ defines a pair of Fredholm operators which maps $X_+\to X_-$ and $X_-\to X_+$ correspondingly, giving rise to a superstructure on $V$. In this paper we consider the questions of determining the index of $D_P$ and the reconstruction of $(M, g), V$ and $D_P$ from the boundary data on $\p M$. The data used is either the Cauchy data, i.e. the restrictions to $\p M \times \R_+$ of the solutions to the hyperbolic Dirac equation, or the boundary spectral data, i.e. the set of the eigenvalues and the boundary values of the eigenfunctions of $D_P$. We obtain formulae for the index and prove uniqueness results for the inverse boundary value problems. We apply the obtained results to the classical Dirac-type operator in $M\times \C^4$, $M \subset \R^3$.

Yaroslav Kurylev

Papers

Reconstruction of Betti numbers of manifolds for anisotropic Maxwell and Dirac systems

Inverse problem of velocity reconstruction in weakly lateral heterogeneous half-space

Electromagnetic wormholes via handlebody constructions

Inverse Problems and Index Formulae for Dirac Operators

One-dimensional inverse problem