Focussing light in a bi-anisotropic slab with negatively refracting materials
We investigate the electromagnetic response of a pair of complementary bi-anisotropic media, which consist of a medium with positive refractive index ($+\ep$, $+μ$, $+ξ$) and a medium with negative refractive index($-\ep$, $-μ$, $-ξ$). We show that this idealized system has peculiar imaging properties in that it reproduces images of a source, in principle, with unlimited resolution. We then consider an infinite array of line sources regularly spaced in a one-dimensional photonic crystal (PC) consisting of 2n-layers of bi-anisotropic complementary media. Using coordinate transformation, we map this system into 2D corner chiral lenses of 2n heterogeneous anisotropic complementary media sharing a vertex, within which light circles around closed trajectories. Alternatively, one can consider corner lenses with homogeneous isotropic media and map them onto one dimensional PCs with heterogeneous bi-anisotropic layers. Interestingly, such complementary media are described by scalar, or matrix valued, sign-shifting parameters, which satisfy a generalized lens theorem, which can be derived using Fourier series solutions of the Maxwell's equations (in the former case), or from space-time symmetry arguments (in the latter case). Also of interest are 2D periodic checkerboards alternating rectangular cells of complementary media which are such that one point source in one cell gives rise to an infinite set of images with an image in every other cell. Such checkerboards can be mapped into a class of three-dimensional corner lenses of complementary bi-anisotropic media.