High resolution extended image near field optics

6. Understanding how the layout can circumvent the Rayleigh resolution criterion

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Copyright (c) Malcolm Kemp 2010

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Those in the field of optics who have grown up being taught the Rayleigh resolution criterion may take some convincing that such a device really would circumvent it, even though at no point did our argument introduce the wavelength of the light being focused (except implicitly in the sizes of some parts of the layout). The key points to note are:

-          The device we have described is an aplanatic optical layout, so would produce an arbitrarily accurate image if the Rayleigh resolution criterion didn’t apply.

-          The device is an extreme example of a ‘near field’ device, by which we mean a layout with an active component only fraction of a wavelength from the image. The introduction of the plane mirror positioned at the image plane makes it ‘near field’. Indeed, we see that it is precisely because there is such a mirror there that any inwardly radiating dipole centred on the image plane continues to increase in magnitude as we approach closer and closer to the dipole centre. Without such a mirror, the light waves would in effect refract/diffract away via the ‘gap’ in the boundary conditions created by the missing plane mirror. It is the lack of such a mirror (or equivalent optical element creating equivalent boundary conditions) that makes a device not ‘near field’ and hence ‘far field’.

Some might also argue that circumventing the Rayleigh resolution criterion in the manner being proposed is intrinsically objectionable from the perspective of quantum mechanics, given Heisenberg’s uncertainty principle. The argument would be that it ‘ought’ not to be possible to create an arbitrarily accurate image in this manner because doing seems to provide us with a way of simultaneously achieving an arbitrarily accurate measurement of the location of a light wave and of its momentum (given knowledge of the frequency of the light being used for imaging purposes).

To solution to this quantum mechanical paradox is to note that the device only transmits a fraction of the light incident on the image plane through to the image detector. The greater its accuracy the more light it ‘rejects’. It therefore corresponds to an example of ‘weak measurement’ as per Aharonov et al (1988) or Starling et al. (2009) as reported in Steinberg (2010). The greater its accuracy, the more it relies on ‘weak measurement’ as a means of apparently circumventing the Heisenberg uncertainty principle, i.e. the more photons it needs to use to achieve the required accuracy.

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