High resolution extended image near field
5. Creating arbitrarily accurate images
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Copyright (c) Malcolm
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Why have we analysed the relatively contrived optical layout
described in Section 4?
We cannot in practice create mirrors with this level of perfection, and even if
we could the light would bounce arbitrarily often between, ,
the source (destination) of the outwardly (inwardly) radiating (magnetic)
dipole and the hemispherical mirror placed at .
The point is that the optical layout we have contrived has
an unusual and potentially desirable feature. The light coming back towards the
plane mirror at at is entirely concentrated onto .
In short, we have created a device that arbitrarily accurately focuses
light onto , even if we needed a rather
contrived way of generating the relevant oncoming wavefronts to do so.
The key additional insight is to realise that the elongated
confocal and coaxial optical layout described at the start of Section 2 has ‘essentially’
the same optical characteristics as going two times round the the hemispherical
and plane mirror optical layout described in Section 4. By
‘essentially’ the same we mean that if the ellipsoids in Section 2 were
elongated enough (so that the hole near their joint axis subtended an
arbitrarily small solid angle on each end mirror) and large enough relative to
the size of the image at roughly the centre of the image plane then the optical
characteristics of exhibited by the layout in the vicinity of the centre of the
object plane would be the same as that created by the layout in Section 4.
Any outwardly radiating (magnetic) dipole coming from a
given point in the object plane near its centre is thus converted to an
inwardly radiating (magnetic) dipole that concentrates onto the corresponding
point in the image plane, completely circumventing the Rayleigh resolution
limit. This is the case for all points sufficiently near the centre of
the object/image plane, and hence involves an entire extended image, as long as
design feature (f) of Section
2 applies, and as long as the mirror in the image plane is sufficiently
well mirrored that as far as any individual incoming dipole is concerned, the
plane mirror is essentially fully mirrored (hence the need for design feature
(a) of Section 2).
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