Related papers: Conformal carpet and grating cloaks
We give a purely analytic construction of a self-similar local regular Dirichlet form on the Sierpi\'nski carpet using approximation of stable-like non-local closed forms which gives an answer to an open problem in analysis on fractals.
We complete the `paraxial' (small-angle) ray optics cloaking formalism presented previously [Choi and Howell, Opt. Express 22, 29465 (2014)], by extending it to the full-field of light. Omnidirectionality is then the only relaxed parameter…
We present the design, fabrication and performance test of a quasi three-dimensional carpet cloak made of normal dielectric in the microwave regime. Taking advantage of a simple linear coordinate transformation we design a carpet cloak with…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
Conformal prediction (CP) is a wrapper around traditional machine learning models, giving coverage guarantees under the sole assumption of exchangeability; in classification problems, for a chosen significance level $\varepsilon$, CP…
Fundamental bounds on the performance of monochromatic scattering-cancellation and field-zeroing cloaks made of prescribed linear passive materials occupying a predefined design region are formulated by projecting field quantities onto a…
In this paper, we bend a closed Riemannian manifold in the conformal class, through solving a fully nonlinear equation. As a result, we prove that each metric of quasi-negative Ricci curvature is conformal to a metric with negative Ricci…
An elliptic cylindrical wave expansion method by using Mathieu functions is developed to obtain the scattering field for a two-dimensional elliptic cylindrical invisibility cloak. The cloak material parameters are obtained from the spatial…
This paper introduces a conformal inference method to evaluate uncertainty in classification by generating prediction sets with valid coverage conditional on adaptively chosen features. These features are carefully selected to reflect…
We prove that, for arbitrary three-dimensional transformation-based invisibility cloaking of an object above a ground plane or of isolated object, there are practical constraints that increase with the object size. In particular, we show…
We present a theory for the cloaking of arbitrarily-shaped objects and demonstrate electromagnetic scattering-cancellation through designed homogeneous coatings. First, in the small-particle limit, we expand the dipole moment of a coated…
Conformal prediction constructs a confidence set for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal…
Transformation Acoustics emerged in the mid-2000s, initiating a new paradigm of metamaterial designs. One of the most compelling designs, the invisibility cloak, holds promise for stealth and noise reduction applications in aviation.…
We present the general theory of curves in conformal geometry using tractor calculus. This primarily involves a tractorial determination of distinguished parametrizations and relative and absolute conformal invariants of generic curves. The…
A near-perfect, non-singular cylindrical invisibility cloak with diamond cross section is achieved by a two-step coordinate transformation. A small line segment is stretched and then blown up into a diamond space, and finally the cloak…
We propose an analytical approach to the conformal mapping of (rectangular) polygons based on the theory of Riemann surfaces and theta functions.
Invisible cloak has long captivated the popular conjecture and attracted intensive research in various communities of wave dynamics, e.g., optics, electromagnetics, acoustics, etc. However, their inhomogeneous and extreme parameters imposed…
The governing equation for elastic waves in flexural plates is not form invariant, and hence designing a cloak for such waves faces a major challenge. Here, we present the design of a perfect broadband cloak for flexural waves through the…
We develop a very general theory on the regularized approximate invisibility cloaking for the wave scattering governed by the Helmholtz equation in any space dimensions via the approach of transformation optics.
The design rules of transformation optics generally lead to spatially inhomogeneous and anisotropic impedance-matched magneto-dielectric material distributions for, e.g., free-space invisibility cloaks. Recently, simplified anisotropic…