Controlling lightwave in Riemann space by merging geometrical optics with transformation optics

Yichao Liu,Sailing He,Fei Sun

doi:10.1038/s41598-017-19015-0

Yichao Liu, Sailing He + Show 1 more

Open Access

https://doi.org/10.1038/s41598-017-19015-0

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Abstract

In geometrical optical design, we only need to choose a suitable combination of lenses, prims, and mirrors to design an optical path. It is a simple and classic method for engineers. However, people cannot design fantastical optical devices such as invisibility cloaks, optical wormholes, etc. by geometrical optics. Transformation optics has paved the way for these complicated designs. However, controlling the propagation of light by transformation optics is not a direct design process like geometrical optics. In this study, a novel mixed method for optical design is proposed which has both the simplicity of classic geometrical optics and the flexibility of transformation optics. This mixed method overcomes the limitations of classic optical design; at the same time, it gives intuitive guidance for optical design by transformation optics. Three novel optical devices with fantastic functions have been designed using this mixed method, including asymmetrical transmissions, bidirectional focusing, and bidirectional cloaking. These optical devices cannot be implemented by classic optics alone and are also too complicated to be designed by pure transformation optics. Numerical simulations based on both the ray tracing method and full-wave simulation method are carried out to verify the performance of these three optical devices.

Highlights

Advancement of transformation optics (TO)[1,2] greatly enriches the connotation of optical design, and many optical devices with novel functions that were deemed impossible before have been designed and manufactured one after another, such as invisibility cloaks[3,4,5,6], super-lenses[7,8,9], concentrators[10,11], and rotators[12,13], etc
TO is a powerful optical design method which gives indirect control of light path by using complex materials that reflect the curved geometry from coordinate transformations
We propose a method which enriches the TO by adding some ray-optics designs in the reference space without producing more complex materials

Summary

Introduction

Advancement of transformation optics (TO)[1,2] greatly enriches the connotation of optical design, and many optical devices with novel functions that were deemed impossible before have been designed and manufactured one after another, such as invisibility cloaks[3,4,5,6], super-lenses[7,8,9], concentrators[10,11], and rotators[12,13], etc. Unlike classic geometrical optics (GO), which can control the light path by directly designing diverse permutations of some basic optical elements (prisms, lenses, and mirrors), TO has no particular basic optical elements. In our mixed design method, we first use TO to introduce a parallel Riemann space in reference space, design the light path on one Riemann space in the reference space with conventional optical elements (mirrors) by GO. By careful design of the shape and position of these conventional optical elements, novel optical devices with various fantastic functions can be obtained. All optical devices designed by our mixed method are impedance matched

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