Negative refraction in 2D checkerboards related by mirror anti-symmetry and 3D corner lenses

Guenneau, Sébastien; Vutha, Amar C.; Ramakrishna, S. Anantha

doi:10.1088/1367-2630/7/1/164

Cited by 36 publications

(36 citation statements)

References 27 publications

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“…Using such transformation optics tools, it was also shown that two corners of NIM combined in a checkerboard fashion can act as a unique resonator [23,24,25,26]. Such checkerboards and can be themselves mapped onto three dimensional corner reflectors [27] and they actually exhibit some form of extraordinary transmission [28].…”

Section: Introductionmentioning

confidence: 99%

Focusing: coming to the point in metamaterials

Guenneau¹,

Diatta²,

McPhedran³

2010

Journal of Modern Optics

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This paper reviews some properties of lenses in curved and folded optical spaces. The point of the paper is to show some limitations of geometrical optics in the analysis of subwavelength focusing. We first provide a comprehensive derivation for the equation of geodesics in curved optical spaces, which is a tool of choice to design metamaterials in transformation optics. We then analyse the resolution of the image of a line source radiating in the Maxwell fisheye and the Veselago-Pendry slab lens. The former optical medium is deduced from the stereographic projection of a virtual sphere and displays a heterogeneous refractive index n(r) which is proportional to the inverse of 1 + r 2 . The latter is described by a homogeneous, but negative, refractive index. It has been suggested that the fisheye makes a perfect lens without negative refraction [Leonhardt, Philbin arXiv:0805.4778v2]. However, we point out that the definition of super-resolution in such a heterogeneous medium should be computed with respect to the wavelength in a homogenized medium, and it is perhaps more adequate to talk about a conjugate image rather than a perfect image (the former does not necessarily contains the evanescent components of the source). We numerically find that both the Maxwell fisheye and a thick silver slab lens lead to a resolution close to λ/3 in transverse magnetic polarization (electric field pointing orthogonal to the plane). We note a shift of the image plane in the latter lens. We also observe that two sources lead to multiple secondary images in the former lens, as confirmed from light rays travelling along geodesics of the virtual sphere. We further observe resolutions ranging from λ/2 to nearly λ/4 for magnetic dipoles of varying orientations of dipole moments within the fisheye in transverse electric polarization (magnetic field pointing orthogonal to the plane). Finally, we analyse the Eaton lens for which the source and its image are either located within a unit disc of air, or within a corona 1 < r < 2 with refractive index n(r) = 2/r − 1. In both cases, the image resolution is about λ/2.

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Section: Introductionmentioning

confidence: 99%

Focusing: coming to the point in metamaterials

Guenneau¹,

Diatta²,

McPhedran³

2010

Journal of Modern Optics

View full text Add to dashboard Cite

show abstract

“…This covers the case of perfect corner reflectors of 2n-fold skew-symmetry, and we are therefore ensured of the cancellation of the optical path. It is worth noting that the generalized lens theorem was also applied to infinite checkerboards of skew-symmetry in [5]. Let us now derive this theorem using the powerful tool of geometric transformations.…”

Section: A Generalized Lens Theorem For Electromagnetic Complementarymentioning

confidence: 99%

“…It has been shown in [5] that a source placed in one cell of a rectangular checkerboard produces an image in every other cell. This straightforwardly applies to triangular checkerboards as well, since they meet the property of mirror antisymmetry of the Generalized lens theorem, as can be observed in the lower panel of Fig.…”

Section: Plasmonic Resonances In Infinite Checkerboardsmentioning

confidence: 99%

“…It is clear that a single source generates a point image inside every other block of the checkerboard. This can be easily shown by considering a singly periodic set of oblique slabs in either direction and using the generalized lens theorem [4,5] whereby the condition of complementarity is satisfied for the layers along the imaging direction with varying refractive index n in the direction transverse to the imaging direction.…”

Section: Mapping Homogeneous Isotropic Checkerboards Onto Icosahedralmentioning

confidence: 99%

“…We note that for rectangular checkerboards, the previous analysis simplifies since in that case T ij |u 1 · (u 2 × u 3 )| = δ ij [5]. We can build upon the previous algorithm and generate a checkerboard structure with as many complementary phases as we wish, provided that they respect mirror symmetries along the main diagonals, thereby generating multiphase 3D corner reflectors.…”

Section: Mapping Homogeneous Isotropic Checkerboards Onto Icosahedralmentioning

confidence: 99%

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