The variational principle in transformation optics engineering and some applications

Transformation optics specializes in the engineering of advanced optical devices, and in combination with differential geometry it allows to control electromagnetic fields with artificial media in an unprecedented manner. In this work, we model transformation optics in an inherently covariant fashion starting with a fundamental Lagrangian function. As an application, we present the construction of a flat reflectionless immersion lens whose superior performance is important to applications in bio- and nano-technology.