Mathematical analysis of the two dimensional active exterior cloaking in the quasistatic regime

We design a device that generates fields canceling out a known probing field inside a region to be cloaked while generating very small fields far away from the device. The fields we consider satisfy the Laplace equation, but the approach remains valid in the quasistatic regime in a homogeneous medium. We start by relating the problem of designing an exterior cloak in the quasistatic regime to the classic problem of approximating a harmonic function with harmonic polynomials. An explicit polynomial solution to the problem was given earlier in [Phys. Rev. Lett. 103 (2009), 073901]. Here we show convergence of the device field to the field needed to perfectly cloak an object. The convergence region limits the size of the cloaked region, and the size and position of the device.Comment: submitted to Analysis and Mathematical Physic

Green's functions and relative local density of states in two-dimensional lossy structured systems

The local density of states (LDOS) is a function of spatial position and frequency which governs the radiation properties of sources placed within structured optical systems. We show how the enhancement or suppression of the relative LDOS, comparing two-dimensional systems, may be computed from Green's tensors obeying the two-dimensional Helmholtz equation and electromagnetic boundary conditions, both around and within a coated, lossy, non-magnetic cylinder. We illustrate the spatial and spectral variation of this relative LDOS with numerical results for both principal cases of polarization, with either the magnetic or the electric field of the Green's function source along the cylinder axis