Transforming two-dimensional guided light using nonmagnetic metamaterial waveguides

Abstract

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...

Elliptical generalized Maxwell fish-eye lens using conformal mapping

“…The most notable one is the invisibility cloak [6,[63][64][65][66][67][68][69][70][71][72]. Furthermore, numerous devices have been designed using TO including polarization splitters [73][74][75][76][77][78], phase transformers [79][80][81], flat lenses [4,[82][83][84][85][86][87][88][89][90][91], field rotators [92,93], field concentrators [94][95][96], waveguide bends [97][98][99] and waveguide couplers [100][101][102][103][104][105][106][107].…”

Mitigating optical singularities in coordinate-based metamaterial waveguides

“…Unfortunately, several interesting coordinate-based designs of beam splitters [13,14,27] and invisibility cloaks [3,4,28] rely on singularities to achieve their functionality. These singularities result in extremely high or low material properties, which must be implemented with resonant metamaterials that are often lossy and have low bandwidth [11,[29][30][31].…”

“…These singularities result in extremely high or low material properties, which must be implemented with resonant metamaterials that are often lossy and have low bandwidth [11,[29][30][31]. Several research groups have tried to reduce these undesired effects by developing low-loss dielectric, active, and/or layered metamaterials [11,[30][31][32][33][34][35][36] and by developing optimized quasiconformal coordinate transformations [14,[37][38][39] or polarization-specific transformations [27,40,41]. Excitingly, transformation optics itself has also provided a valuable contribution [42][43][44].…”

Transformation optics for surface phenomena: Engineering the Goos-Hänchen effect

“…Transformation physics in combination with recent advances in artificial materials [26] has revolutionized nanomechanics, heat flow physics, acoustics, and fluid dynamics [27][28][29][30]. Until now, transformation optics was mainly used to modify the trajectory of light inside three-dimensional media [1][2][3] and to manipulate the path of surface waves [31][32][33][34][35]. Transformation optics is deemed unable to deal with surfaces; surfaces were rather seen as a hindrance causing unwanted reflections.…”