Almost a decade ago, transformation optics established a geometrical perspective to describe the interaction of light with structured matter, enhancing our understanding and control of light. However, despite their huge technological relevance in applications such as optical circuitry, optical detection, and actuation, guided electromagnetic waves along dielectric waveguides have not yet benefited from the flexibility and conceptual simplicity of transformation optics. Indeed, transformation optics inherently imposes metamaterials not only inside the waveguide's core but also in the surrounding substrate and cladding. Here we restore the two-dimensional nature of guided electromagnetic waves by introducing a thickness variation on an anisotropic dielectric core according to alternative two-dimensional equivalence relations. Our waveguides require metamaterials only inside the core with the additional advantage that the metamaterials need not be magnetic and, hence, our purely dielectric waveguides are low loss. We verify the versatility of our theory with full wave simulations of three crucial functionalities: beam bending, beam splitting, and lensing. Our method opens up the toolbox of transformation optics to a plethora of waveguide-based devices.DOI: 10.1103/PhysRevB.93.085429Geometrical reasoning played a crucial role in the historical development of optics as a scientific discipline, and its successes are associated with the names of great scientists like Snell, de Fermat, Huygens, Newton, and others. To this day, the design of many optical components, e.g., microscopes, displays, and fibers, is based on the ray picture of light, valid for electromagnetic waves inside media with slowly varying refractive index distributions [1]. Through the advent of metamaterials and photonic crystals [2-8]-artificial materials whose electromagnetic properties are determined by subwavelength unit cells-light may be manipulated by enhanced optical properties at the micro-and nanoscale. As a result, there is a growing need for analytical tools to model and design metamaterial devices that act upon the electric and magnetic components of light [9].With the design and experimental demonstration of invisibility cloaks [10][11][12][13][14], transformation optics proved to be an adequate geometrical tool to explore the full potential of metamaterials. Succinctly, transformation optics relies on the form invariance of Maxwell's equations to determine appropriate material properties, i.e., permittivity and permeability distributions, that materialize unconventional light flows based on the deformation of a coordinate system. Using this geometrical perspective of the interaction of light with structured matter, researchers have discovered and reconsidered many optical phenomena in three-dimensional metamaterials with regard to wave propagation [15][16][17] To enhance control on the propagation of surface waves confined to a single interface [21][22][23], several research groups successfully applied the existing framework of transfor...

The enhancement of optical forces has enabled a variety of technological applications that rely on the optical control of small objects and devices. Unfortunately, optical forces are still too small for the convenient actuation of integrated switches and waveguide couplers. Here we show how the optical gradient force can be enhanced by an order of magnitude by making use of gauge materials inside two evanescently coupled waveguides. To this end, the gauge materials inside the cores should emulate imaginary vector potentials for photons pointing perpendicularly to the waveguide plane. Depending on the relative orientation of the vector potentials in neighboring waveguides, i.e., pointing away from or towards each other, the conventional attractive force due to an even mode profile may be enhanced, suppressed, or may even become repulsive. This and other new features indicate that the implementation of complex-valued vector potentials with non-Hermitian waveguide cores may further enhance our control over mode profiles and the associated optical forces.

Transformation optics has revolutionized our approach to material design in several scientific disciplines by determining the material properties that implement the desired effects of a coordinate transformation. Unfortunately, the performance of several coordinate-based devices, such as beam splitters and invisibility cloaks, suffers from the necessary implementation of singularities with extreme material parameters. Here, we make use of transformation optics to eliminate these singularities in an isotropic way for the improvement of coordinate-based metamaterial waveguides. In particular, singularities that lead to vanishing material properties are softened with a global rescaling of the coordinates, while singular terms that lead to infinite material properties are strategically replaced by well-behaved curve factors. Detailed full-wave simulations confirm that the resulting waveguide devices are as efficient as their singular counterparts despite the fact that they consist of materials with much more moderate optical properties.