352
E. Khan and E. Narimanov
Fig. 14.5 The dielectric
permittivity components of
the planar silver-silica
hyperbolic metamaterial (see
Fig. 14.4a) calculated using
effective medium approach
of (14.5) and (14.6). Note
that this composite has
Re [ τ ] Re [ n ] < 0 and
relatively small loss
(Im [] Re []) in the
entire visible range
14.5 The Hyperlens
With the wavenumber no longer limited by the frequency, the hyperbolic media are
no longer subject to the conventional diffraction limit of optical imaging [39–41].
However, a simple slab of a hyperbolic (meta)material, with its translation symmetry
in the object plane, will not allow image magnification. Furthermore, a propagating
wave with a large wavenumber that can be supported by the hyperbolic medium, will
immediately become evanescent once it escapes into the surrounding dielectric. The
hyperlens allows to resolve both of these issues.
14.5.1 Hyperlens: The Concept
The main purpose of the hyperlens is to “convert” the evanescent fields that carry the
subwavelength information, to propagating waves (see Fig. 14.1b), which would then
allow for their processing with standard optical components. This “conversion” however must be accomplished without any loss of information, as this would otherwise
prevent the accurate image recovery.
In other words, this means that the new waves that were formed by the hyperlens
from the incident evanescent field, must not “mix” with the “original’ propagating
components of the incident signal. As a result, a straightforward approach based on
a subwavelength grating on the surface or in the bulk of the hyperbolic medium,
[42–44] cannot be a basis for the hyperlens.
To understand how one can avoid the “mixing” of the outgoing waves that originate from the incident propagating waves and the incident evanescent field that was
“converted” by the hyperlens, optical imaging should be considered as a scattering
experiment in the angular momentum basis. The incident plane wave that illuminates
the object, can then be expressed as
E. Khan and E. Narimanov
Fig. 14.5 The dielectric
permittivity components of
the planar silver-silica
hyperbolic metamaterial (see
Fig. 14.4a) calculated using
effective medium approach
of (14.5) and (14.6). Note
that this composite has
Re [ τ ] Re [ n ] < 0 and
relatively small loss
(Im [] Re []) in the
entire visible range
14.5 The Hyperlens
With the wavenumber no longer limited by the frequency, the hyperbolic media are
no longer subject to the conventional diffraction limit of optical imaging [39–41].
However, a simple slab of a hyperbolic (meta)material, with its translation symmetry
in the object plane, will not allow image magnification. Furthermore, a propagating
wave with a large wavenumber that can be supported by the hyperbolic medium, will
immediately become evanescent once it escapes into the surrounding dielectric. The
hyperlens allows to resolve both of these issues.
14.5.1 Hyperlens: The Concept
The main purpose of the hyperlens is to “convert” the evanescent fields that carry the
subwavelength information, to propagating waves (see Fig. 14.1b), which would then
allow for their processing with standard optical components. This “conversion” however must be accomplished without any loss of information, as this would otherwise
prevent the accurate image recovery.
In other words, this means that the new waves that were formed by the hyperlens
from the incident evanescent field, must not “mix” with the “original’ propagating
components of the incident signal. As a result, a straightforward approach based on
a subwavelength grating on the surface or in the bulk of the hyperbolic medium,
[42–44] cannot be a basis for the hyperlens.
To understand how one can avoid the “mixing” of the outgoing waves that originate from the incident propagating waves and the incident evanescent field that was
“converted” by the hyperlens, optical imaging should be considered as a scattering
experiment in the angular momentum basis. The incident plane wave that illuminates
the object, can then be expressed as