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 transformationoptical
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.