Minisymposia Abstracts

Speaker: Matti Lassas
University of Helsinki
Title: Degenerate elliptic equations and the appearance of hidden boundary conditions in invisibility cloaking
Abstract: We consider the invisibility cloaking for the Helmholtz and Schrodinger equations and Maxwell's systems. We concentrate on the transformation optics cloaking which is based on the use of a singular coordinate transformation that pushes isotropic material parameters forward into singular, anisotropic ones [1,2,3]. The obtained cloaking constructions are related to degenerate elliptic equations. We review various existence and non-existence results for solutions of these degenerate elliptic equations. In particular, we consider the "hidden" boundary conditions which can appear at the surface separating the cloaked and uncloaked regions [4-8].

Speaker: Daniel Onofrei
University of Utah
Title: Mathematical analysis of the active exterior cloaking
Abstract: The quasistatics active exterior cloaking proposed by Guevara Vasquez, Milton and Onofrei is studied rigorously with a new approach based on first kind integral equations associated to boundary layer operators. This new approach permits us to extend the previous results to three dimensions and to the finite frequency regime. The existence of a unique minimal energy solution for the model will be showed and numerically supported.

Speaker: Kui Ren
University of Texas, Austin
Title: On feasibility of active exterior cloaking
Abstract: We perform a systematic investigation (mainly numerically) on the feasibility of active exterior cloaking in quasistatic and low-frequency regimes. We evaluate the impact of various media properties on the cloaking scheme. This is a joint work with Daniel Onofrei (University of Utah)

Speaker: Ting Zhou
University of California, Irvine
Title: On Approximate Electromagnetic Cloaking by Transformation Media
Abstract: We give a comprehensive study on regularized approximate electromagnetic cloak- ing in the spherical geometry via the transformation optics approach. The following aspects are investigated: (i) near-invisibility cloaking of passive media as well as active/radiating sources; (ii) the existence of cloak-busting inclusions without lossy medium lining; (iii) overcoming the cloaking-busts by employing a lossy layer out- side the cloaked region; (iv) the frequency dependence of the cloaking performances. We address these issues and connect the obtained asymptotic results to singular ideal cloaking. Numerical verications and demonstrations are provided to show the sharp- ness of our analytical study.This is a joint work with Dr. Hongyu Liu.

Speaker: Andrea Alu
University of Texas
Title: Metamaterial cloaking using passive metamaterials and metasurfaces
Abstract: We discuss here the properties and functionalities of a variety of cloaking techniques involving passive metamaterials and metasurfaces. In particular, we describe the concepts of plasmonic cloaking and of mantle cloaking, showing that a single frequency-selective metasurface or a uniform thin metamaterial cover may be able to provide drastic scattering reduction for all polarizations and incidence angles, with significant advantages compared to other cloaking techniques in terms of reduced thickness, low weight, simplicity, and possibly enhanced bandwidth of operation. We provide physical insights into this cloaking mechanism and into its application to camouflaging, non-invasive probing, imaging, and lowinterference communications. In addition, we will discuss the general limitations of cloaking using passive devices, deriving fundamental bounds that any passive cloak has to obey in terms of bandwidth and overall performance.

Speaker: Xudong Chen
National University of Singapore
Title: Cloaking a Sensor for 2D and 3D Maxwell equations
Abstract: The sensor effects for two-dimensional and three-dimensional Maxwell equations are presented. Ideal cloaking is accompanied by shielding: There is a decoupling of the fields inside and outside of the cloaked region, so that external observations do not provide any indication of the presence of a cloaked object, nor is any information about the fields outside detectable inside the cloaked region. In comparison, the sensor effect breaks this connection between cloaking and shielding, allowing the former without the latter, showing that sensors can be cloaked. Recently, Greenleaf (in PRE, 2011) analyzed the sensor effect for acoustic equations, and the approach was different from Alu and Enghet's one (in PRL, 2009). In this presentation, the sensor effect for two-dimensional and three-dimensional Maxwell equations are investigated via an approach that is similar to, yet different from, Greenleaf\u2019s one.

Speaker: Fernando Guevara Vasquez
University of Utah
Title: Active exterior cloaking for the Helmholtz equation
Abstract: We present a cloaking method that hides objects using active sources. The sources generate waves that cancel a known incident field inside a region with destructive interference. Since very little waves reach the object, the scattered field from the object is virtually zero. Moreover the radiated waves from the sources are close to zero far away from the sources, so the object and sources are for all practical purposes invisible. We recall how to construct such a cloak with a monopole and dipole density on a surface (Green's formulas) and then show how to achieve a similar effect without completely surrounding the object with sources, i.e. leaving the object connected with the exterior.

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