Conformal transformation optics

Xu, Lin; Chen, Huanyang

doi:10.1038/nphoton.2014.307

Cited by 247 publications

(147 citation statements)

References 97 publications

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“…These changes may occur at the interface of two homogeneous media or inside an anisotropic and inhomogeneous medium. So far, the concept of transformation optics was used to design different devices, mainly by focusing on the manipulation of the wave path of the electromagnetic waves [11,12]. Since transformation optics approach provides anisotropic and inhomogeneous media, capable to manipulate not only the wave paths but also the wave vectors, useful devices can be designed by targeting the manipulation of the wave vectors inside the medium.…”

Section: Introductionmentioning

confidence: 99%

Designing Devices for Wave-Vector Manipulation Using a Transformation-Optics Approach

Giloan¹

2017

Phys. Rev. Applied

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A transformation optics approach was used to derive a general method for designing electromagnetic devices able to manipulate the wave vectors in the specific manner required by the functionality of the device. While the wave paths inside the device remain of a secondary importance the wave vectors are gradually changed in the desired way by choosing the appropriate coordinate transformation. The proposed method was applied to design both converging and diverging flat lenses. Computer simulations revealed the focusing ability of a converging flat lens designed using the proposed technique.

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Section: Introductionmentioning

confidence: 99%

Designing Devices for Wave-Vector Manipulation Using a Transformation-Optics Approach

Giloan¹

2017

Phys. Rev. Applied

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“…Whereas transformation optics determines bulk optical properties by exploiting the relationship between a given coordinate system and the coordinate system that conforms to the travel of light [18][19][20][21][22][23][24][25][26][27][28], the proposed concept determines the optical properties of a metasurface of arbitrary geometry by exploiting the relationship between a given ambient coordinate system and the coordinate system that conforms to the geometry of the boundary. While a powerful concept in itself, the mathematical derivation associated with its analytical formulation -which we present in detail in the supplementary information -is highly non-trivial since it cannot be generalized from existing boundary conditions for generic surface geometries.…”

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Controlling electromagnetic fields at boundaries of arbitrary geometries

et al. 2016

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Rapid developments in the emerging field of stretchable and conformable photonics necessitate analytical expressions for boundary conditions at metasurfaces of arbitrary geometries. Here, we introduce the concept of conformal boundary optics: a design theory that determines the optical response for designer input and output fields at such interfaces.Given any object, we can realise coatings to achieve exotic effects like optical illusions and anomalous diffraction behaviour. This approach is relevant to a broad range of applications from conventional refractive optics to the design of the next-generation of wearable optical components. This concept can be generalized to other fields of research where designer interfaces with nontrivial geometries are encountered.In a bulk medium, a wave (e.g., optical, sound, seismic) accumulates phase gradually and propagates without experiencing abrupt variations. At the boundary with another material, however, the wave can experience large -although physically admissible-discontinuities in its reflected and transmitted fields [1,2] Here, we introduce the concept of conformal boundary optics, an analytical method -based on novel, firstprinciple derivations -that allows us to engineer transmission ( ) and reflection ( ) at will for any interface geometry and any given incident wave ( ). By resolving the boundary conditions between two materials at an interface of arbitrary geometry, this method addresses recent developments in nanophotonics with the general technique of differential geometry and coordinates transformation. Unlike transformation

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“…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 transformation optics to surface waves along graphene-dielectric [24,25] and metal-dielectric interfaces [26][27][28][29][30]. Indeed, at frequencies far away from the surface plasmon resonance of a metal-dielectric * Corresponding author.…”

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Transforming two-dimensional guided light using nonmagnetic metamaterial waveguides

et al. 2016

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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...

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Conformal transformation optics

Cited by 247 publications

References 97 publications

Designing Devices for Wave-Vector Manipulation Using a Transformation-Optics Approach

Designing Devices for Wave-Vector Manipulation Using a Transformation-Optics Approach

Controlling electromagnetic fields at boundaries of arbitrary geometries

Transforming two-dimensional guided light using nonmagnetic metamaterial waveguides

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