31 research outputs found
Focusing: coming to the point in metamaterials
The point of the paper is to show some limitations of geometrical optics in
the analysis of subwavelength focusing. We analyze 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 lambda/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
lambda/2 to nearly lambda/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 . In both cases,
the image resolution is about lambda/2.Comment: Version 2: 22 pages, 11 figures. More figures added, additional cases
discussed. Misprints corrected. Keywords: Maxwell fisheye, Eaton lens;
Non-Euclidean geometry; Stereographic projection; Transformation optics;
Metamaterials; Perfect lens. The last version appears at J. Modern Opt. 57
(2010), no. 7, 511-52