BACKGROUND

The diffraction limit has been thought to impose a fundamental limit on the resolution of focusing and imaging for over a century. However, research over the last decade has explored methods to overcome this limitation. Significant attention has focused on near field strategies to recover non-propagating evanescent waves whose range of k vectors are required to reduce the size of a focal spot below the diffraction limit. Near-field techniques such as scanning near-field optical microscopy (SNOM) and the use of field concentrators have been explored. The concept of a super-lens is still visionary being based on suitable bulk metamaterials which are still to be developed. Whilst the near field has seen most activity, in general, concepts to beat the diffraction limit in the far-field are still rare and have only recently been realized in the optical domain using either a lens-less angular spectrum synthesis approach or nanohole arrays. The latter split and re-interfere light fields to sub-diffraction-limited hot spots at a typical distance of 10 nm from the array. Nanohole arrays exploit the fundamental concept of super-oscillations which states that a band- limited function may oscillate faster than its highest Fourier component. This is achieved through a redistribution of intensity from high-frequency to low-frequency modes. In the case of optical fields, this means that the size of a focal spot may arbitrarily be reduced at the expense of the spot intensity and the emergence of sidebands which contain the vast majority of the optical intensity. It would be immensely advantageous to show how we may squeeze light in the far field to beat the diffraction limit whilst retaining a useable working distance. Indeed, even a factor of two resolution improvement greatly enhances the imaging capabilities in microscopy. The advantages would be further enhanced if we were able to achieve this using readily available technology.

OPTICAL EIGENMODES

We have developed the optical eigenmode technique to determine the minimum spot size achievable in the focal plane of a microscope objective and for a given region of interest. This is a powerful, far-field" method and constitutes a significant step forward towards the successful application of sub-wavelength spots in super-resolving imaging and lithographic devices. A spatial light modulator (SLM) was used to create the optical eigenmode beam which allows us to generate the sub-diffractive spot as a optimization superposition of Bessel beams (BBs). Moreover, we remark that the optimization procedure, as implemented here, is compatible with any optical microscope system bringing sub-diffractive focal spots readily within reach of numerous applications.

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