Research Fellows Directory
Professor Mark Dennis
University of Bristol
Waves are a central, if somewhat intangible, feature of modern physics, describing phenomena such as light, sound, and matter on the nanoscale (through the waves of quantum mechanics). Their properties are unusual compared with matter: when multiple waves are added together, they can cancel out (destructive interference). My research is in the mathematical description and physical interpretation of interference. I am interested in two broad types of wave field: those that can be controlled (such as light manipulated by a hologram), and those that are deformed or random, such as light reflected from a rough surface, or sound dying away in an auditorium. Other natural fields I study are not random, such as the pattern of polarization in skylight. Often, my investigations give rise to new mathematical problems and their solution, such as approaching the problem of optical propagation using complex analytic functions.
This year, I have made progress in understanding several fundamental aspects of optical physics, particularly how a light beam, at the smallest (wavelength) scale, is deformed on reflection. We have discovered that this deformation is a classical analogue of the quantum-mechanical notion of ‘weak measurement’. This adds fundamental insight both to classical optics and quantum physics, and might help in creating more accurate imaging devices.
With my postdoc, I have applied the mathematical theory of superoscillation to develop new lenses for optical microscopes which beat the classical diffraction limit; colleagues in Southampton were able to implement this scheme experimentally to get a microscope with a resolution of better than a quarter wavelength.
In studying these phenomena, I am able to interact both with optical experimentalists as well as mathematicians interested in the underlying geometry of mathematical fields. Thus I am able to contribute both to the extremes of abstract mathematics and optical technologies.
Interests and expertise (Subject groups)