Regional Academic in Applied Mathematics

The School of Mathematics and Statistics, The Open University

k.s.rogers@open.ac.uk

I am a lecturer in the Applied Mathematics group at the Open University. As a regional academic, I manage associate lecturers in addition to my teaching and research. My primary research interests are in optimisation of optical systems.

Before joining the OU, I was a postdoctoral researcher at the Institute for Vibration Research (ISVR), and a PhD student in Astrophysics, at the University of Southampton. In both cases I was applying maths to real problems: modelling structural vibrations at the ISVR, and in Astrophysics I was modelling the interactions between photons and electrons in the vicinity of black holes.

This followed on from my MMath (Hons) at the University of Bath.

Superoscillatory functions are bandlimited functions which oscillate locally much faster than their fastest Fourier component. These superoscillations are counter-intuitive, and come at a cost: their amplitude is very small.

It has long been thought that the resolution of optical systems is fundamentally limited by their bandlimited nature. However, it is possible to beat this diffraction limit by carefully engineering the interference of light to create superoscillatory spots of light -- in theory achieving perfect resolution. However, the cost of superoscillations means that most of the energy of the system is diverted into high-energy sidebands. This limits the practical use of superoscillations for high-resolution imaging.

Using mathematical modelling and numerical optimisation techniques, I am exploring the trade-off between achieving high resolution (very small superoscillations) and maintaining sufficient energy in the superoscillations for practical use. This is more widely relevant to applications beyond optics.

I am currently a supervisor on the following PhD projects:

Most of my teaching is on final year applied maths modules. I am module team chair of M373 Optimization, and contribute to MS327 Deterministic and Stochastic Dynamics. I am also contributing to a new module on mathematical and scientific computing, which is aimed at mathematics students as well as students on other degrees, such as Data Science.