Seminar 25, Tuesday 19 January 2021, 14:00 (London Time)
Speaker: Ross McPhedran (School of Physics, University of Sydney, Australia)
Title: Resonant States for Scattering Problems: Killing Mie Softly
Abstract: This talk deals with issues common to those addressed by David Bergman, in that the topic is certain difficulties associated with complex resonant states encountered in scattering problems. These difficulties arise when one wishes to evaluate normalisation integrals and inner products for these states, which have rapid oscillations and diverging amplitudes at large dis- tances from the scatterer. Rather than using numerical treatments, the method presented here is analytic in nature, and relies on results of distri- bution theory. The method can yield closed form expressions for integrals over an infinite range involving the product of two Bessel functions of the same or different types, combined with a power of the radial distance. The essential point is that for rapidly oscillating functions with mean zero, the contribution to the integrals from the infinite upper limit is zero, despite the diverging amplitudes (equivocation trumps exaggeration).
Biography: Ross McPhedran is an Emeritus Professor at the University of Sydney, a Fellow of the Australian Academy of Science and the Optical Society of America, the Institute of Physics UK and the Australian Institute of Physics and doctor honoris causa of Aix-Marseille University.He works on problems in mathematical physics and wave science. Notably, he has many contributions to the theory of composite materials, the theory of diffraction gratings, and the theory of photonic, phononic, and platonic crystals, the latter name being chosen by Ross, and he codiscovered anomalous localized resonance. He has published over 300 articles in offered scientific journals, has an h index of 64 and around 17,000 citations on Google Scholar. He is the founding president of the ETOPIM association. The topic will include plasmonic resonances of particles, and the mathematical background to effective medium theories (particularly Bergman-Milton bounds and multipole theories).