Abstract

Based on non-Euclidean transformation optics, we design a thin metamaterial lens that can achieve wide-beam radiation by embedding a simple source (a point source in the three-dimensional (3D) case or a line current source in the 2D case). The scheme is performed on a layer-by-layer geometry to convert curved surfaces in the virtual space into flat sheets, which pile up and form the entire lens in the physical space. Compared to previous designs, the lens does not have extreme material parameters. Simulation results confirm its functionality.

Highlights

  • Achievements in metamaterials in the past decade have enabled unconventional control of electromagnetic fields, such as perfect imaging [1] and directive emission [2]

  • Besides the fascinating prospect in perfect imaging and invisibility, many practical instruments, for example, lenses to collimate, bend, split or shift beams have been proposed as the applications of metamaterials

  • It is demonstrated that a point source embedded in a slab of near-zero index material radiates energy only in a narrow cone [2]

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Summary

Introduction

Achievements in metamaterials in the past decade have enabled unconventional control of electromagnetic fields, such as perfect imaging [1] and directive emission [2]. Transformation optics utilizes the form-invariance property of Maxwell’s equations, which ensures a spatial coordinate transformation can be interpreted as (or equivalent to) the effect of a substitution of media This fact provides a bright way to manipulate electromagnetic fields on both wave and ray scales, facilitating the design of new materials and advanced devices [5]. The design of metamaterial lenses seems to face a natural dilemma, that when the lens is tuned to be relatively thin (compared to the width of lens or beam), the material parameters always require extreme values [2, 6,7,8,9,10] and sometimes a wide source [9], while the devices will become thick if the singularities are removed [11]. Holding the same geometry in cross section, this scheme should be valid for two-dimensional case, and numerical simulations confirm this deduction

Non-Euclidean Transformation
Discussion
Conclusion

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