Transforming guided waves with metamaterial waveguide cores

Paper in proceeding, 2016

Metamaterials make use of subwavelength building blocks to enhance our control on the propagation of light. To determine the required material properties for a given functionality, i.e., a set of desired light flows inside a metamaterial device, metamaterial designs often rely on a geometrical design tool known as transformation optics. In recent years, applications in integrated photonics motivated several research groups to develop two-dimensional versions of transformation optics capable of routing surface waves along graphene-dielectric and metal-dielectric interfaces. Although guided electromagnetic waves are highly relevant to applications in integrated optics, no consistent transformation-optical framework has so far been developed for slab waveguides. Indeed, the conventional application of transformation optics to dielectric slab waveguides leads to bulky three-dimensional devices with metamaterial implementations both inside and outside of the waveguide's core. In this contribution, we develop a transformation-optical framework that still results in thin metamaterial waveguide devices consisting of a nonmagnetic metamaterial core of varying thickness [Phys. Rev. B 93.8, 085429 (2016)]. We numerically demonstrate the effectiveness and versatility of our equivalence relations with three crucial functionalities: a beam bender, a beam splitter and a conformal lens. Our devices perform well on a qualitative (comparison of fields) and quantitative (comparison of transmitted power) level compared to their bulky counterparts. As a result, the geometrical toolbox of transformation optics may lead to a plethora of integrated metamaterial devices to route guided waves along optical chips.