High resolution extended image near field optics

5. Creating arbitrarily accurate images

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Copyright (c) Malcolm Kemp 2010

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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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