Geodesic conformal transformation optics: manipulating light with continuous refractive index profile

TL;DR

This paper introduces a geodesic conformal transformation optics method that ensures continuous refractive index profiles, enabling highly effective light manipulation such as transparency, reflection, and cloaking with minimal discontinuities.

Contribution

It presents a novel approach using geodesic lenses for conformal transformation optics, overcoming previous discontinuity issues at Riemann sheet branch cuts.

Findings

Achieved conformal transparency and reflection with continuous refractive index profiles.

Demonstrated conformal invisible cloaks using perfect electromagnetic conductors.

Showed potential applications in other wave-based systems obeying the Helmholtz equation.

Abstract

Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual Riemann sheets, hence compromising the functionalities. To deal with that, we present a special method for conformal transformation optics based on the concept of geodesic lens. The requirement is a continuous refractive index profile of dielectrics, which shows almost perfect performance of designed devices. We demonstrate such a proposal by achieving conformal transparency and reflection. We can further achieve conformal invisible cloaks by two techniques with perfect electromagnetic conductors. The geodesic concept may also find applications in other waves that obey the Helmholtz equation in two dimensions.