Focussing light in a bi-anisotropic slab with negatively refracting materials

TL;DR

This paper explores the unique imaging capabilities of bi-anisotropic complementary media, demonstrating potential for unlimited resolution and novel lensing effects through coordinate transformations and photonic crystal configurations.

Contribution

It introduces a generalized lens theorem for bi-anisotropic media and maps complex systems into corner lenses, revealing new imaging phenomena and design principles for advanced optical devices.

Findings

Complementary bi-anisotropic media can reproduce images with unlimited resolution.

Coordinate transformations relate complex media arrangements to corner lenses.

Checkerboard structures produce infinite image sets from a single source.

Abstract

We investigate the electromagnetic response of a pair of complementary bi-anisotropic media, which consist of a medium with positive refractive index ($+\ep$, $+\mu$, $+\xi$) and a medium with negative refractive index($-\ep$, $-\mu$, $-\xi$). 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.