Controlling refractive index of transformation-optics devices via optical path rescaling

Abstract

We present a general method of designing optical devices based on optical conformal mapping and rescaling the optical path along a given bunch of rays. It provides devices with the same functionality as those based purely on conformal mapping, but enables to manipulate the refractive index to a great extent—for instance, eliminate superluminal regions of space as well as reduce the refractive index in other regions significantly. The method is illustrated in two examples, a waveguide coupler and a plasmonic bump cloak, and numerical simulations confirm its functionality.

Directivity enhancement of a cylindrical wire antenna by a graded index dielectric shell designed using strictly conformal transformation optics

“…One requires dispersive narrowband metamaterial structures to realize the superluminal refractive index regions. Although there is no way to remedy this defect fully, we can significantly reduce it by employing the optical path rescaling method 9 , bringing the refractive index to a very moderate range.…”

“…The cloak of invisibility was the first and the most well-known application of TO 1 , 2 where an engineered material guides the electromagnetic wave around a hidden object. Inspired by the invisibility cloak idea, researchers began to adapt TO to various applications, providing interesting functionalities like carpet cloaking (also known as plasmonic bump cloaking) 3 – 9 , polarization splitting and transforming 10 – 14 , directivity enhancing 15 – 18 , 18 – 21 , beam expanding 22 , 23 , waveguide coupling 24 – 30 , and lens compression 31 – 34 .…”

Wide-Angle Ceramic Retroreflective Luneburg Lens Based on Quasi-Conformal Transformation Optics for Mm-Wave Indoor Localization

“…[GHz] [1] Van Atta array ± 52* no 200 [2] Van Atta array The transformation optics theory has gained popularity in the last two decades for providing a systematic approach to the design of invisible cloaks [27]- [31], conformal antenna arrays [32]- [33], directivity enhancers [34]- [35], waveguide bends and couplers [36]- [38]. TO has also been employed to modify the geometry of various dielectric lenses [39]- [53].…”

Design of a High-performance Flat Reflector Antenna Based on Conformal Transformation Optics

“…Multiplying the derivative of an increasing function by the structure's initial refractive index yields the refractive index with optimum values. In this method, the refractive index changes, but the wavefront does not change 33 .…”