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One of the key challenges in current research into electromagnetic cloaking is to achieve invisibility at optical frequencies and over an extended bandwidth. There has been significant progress towards this using the idea of cloaking by sweeping under the carpet of Li and Pendry. Here, we show that we can harness surface plasmon polaritons at a metal surface structured with a dielectric material to obtain a unique control of their propagation. We exploit this control to demonstrate both theoretically and experimentally cloaking over an unprecedented bandwidth (650-900 nm). Our non-resonant plasmonic metamaterial is designed using transformational optics extended to plasmonics and allows a curved reflector to mimic a flat mirror. Our theoretical predictions are validated by experiments mapping the surface light intensity at a wavelength of 800 nm.

The design of hybrid systems controllers requires one to handle both discrete and continuous functionalities in a single development framework. In this paper, we propose the design and verification of such controllers using a correct-by-construction approach. We use proof-based formal methods to model and verify the required safety properties of the given controllers. Both Event-B with Rodin, and hybrid programs and dynamic differential logic with KeYmaera are experimented on a common case study related to the modelling of a car controller. Finally, we discuss the lessons learnt from these experiments and draw the first steps towards a generic method for modelling hybrid systems in Event-B.

We numerically study the focusing and bending effects of light and sound waves through heterogeneous isotropic cylindrical and spherical devices. We first point out that transformation optics and acoustics show that the control of light requires spatially varying anisotropic permittivity and permeability, while the control of sound is achieved via spatially anisotropic density and isotropic compressibility. Moreover, homogenization theory applied to electromagnetic and acoustic periodic structures leads to such artificial (although not spatially varying) anisotropic permittivity, permeability and density. We stress that homogenization is thus a natural mathematical tool for the design of structured metamaterials. To illustrate the two-step geometric transform-homogenization approach, we consider the design of cylindrical and spherical electromagnetic and acoustic lenses displaying some artificial anisotropy along their optical axis (direction of periodicity of the structural elements). Applications are sought in the design of Eaton and Luneburg lenses bending light at angles ranging from 90 • to 360 • , or mimicking a Schwartzchild metric, i.e. a black hole. All of these spherical metamaterials are characterized by a refractive index varying inversely with the radius which is approximated by concentric layers of homogeneous material. We finally propose some structured cylindrical metamaterials consisting of infinitely conducting or rigid toroidal channels in a homogeneous bulk material focusing light or sound waves. The functionality of these metamaterials is demonstrated via full-wave threedimensional computations using nodal elements in the context of acoustics, and finite edge-elements in electromagnetics.