Optical scattering metrology using superoscillations

Abstract

This thesis reports on work in the field of optical scattering super-resolution metrology, whereby dimensional and positional parameters of nano/microscale objects are measured via analyses of the scattered light field from such objects. A major focus of this research is to better understand how the precision and accuracy of such a measurements task can be optimised, for which the concept of Fisher information is found to be an insightful and powerful tool.
- By applying scalar diffraction theory and the concept of Fisher information to the problem of an arbitrary structured field scattering by a sub-wavelength slit, I have derived new understanding of how, and why, superoscillatory light fields (and the phase singularities contained within) can provide a multi-fold enhancement in measurement precision.
- For the first time, I have shown how the advantages of superoscillatory illumination can be leveraged for the retrieval of complex, multi-parameter, dimensional profiles from the transmission scattering patterns of arbitrarily structured binary objects. In numerical studies, I show that feature sizes down to ~λ/10.5 can be consistently resolved in the profiles of random one-dimensional gratings – a factor of 2.2× smaller than is possible under plane wave illumination.
- I have conceived and developed a novel approach for optimising optical localisation measurement precision by structuring the surroundings of a measurement target to maximise the information content of the scattered light field over the finite aperture of a far-field detector. In supporting experiments (by my colleague Cheng-Hung Chi), this technique improves nanowire positional measurement precision by a factor of 6.5× - delivering a mean measurement standard deviation of just 61 pm (<λ/10400) in single-shot measurements under plane wave illumination.
- I show that the optimisation of object-plane structure yields a superoscillatory light field in the detection plane, demonstrating that the metrological advantage of such structured fields can be leveraged without the need to generate or precisely align complex incident fields.
- I have contributed to the development of new understanding of how material composition, nanostructural geometry, and environmental design can dictate (and thus be used to control) where information is generated, how it propagates, scatters and interferes, and that information flow can be strikingly, and importantly, different from energy flow in optical measurement systems.
Collectively, these works advance the field of optical scattering super-resolution metrology, based particularly upon the use of superoscillatory light fields. By applying the concept of Fisher information, a well-known metric from information theory, we can better understand and thereby optimise techniques for optical measurement at (sub)nanometric scales. Indeed, this work helps to reframe optical metrology as an exercise not only in measurement design but in “information field engineering".

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Identifiers

ORCID for Nikolay Zheludev: orcid.org/0000-0002-1013-6636

ORCID for Kevin Macdonald: orcid.org/0000-0002-3877-2976

ORCID for Eric Plum: orcid.org/0000-0002-1552-1840

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