Mathematical and Computational Methods in Photonics
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Course Overview
This course provides an introduction to the analytical and computational mathematics underpinning modern photonics. Photonics studies the propagation and control of light in complex micro- and nano-structured media, with applications ranging from high-resolution imaging and advanced sensing to energy-efficient devices and metamaterial design.
Recent progress in nanoscience has created new challenges in modelling electromagnetic waves at subwavelength scales, where conventional technologies reach their limits. The course explores how sophisticated mathematical tools — including asymptotic analysis, spectral theory, mathematical imaging, layer potentials, stochastic modelling, and optimal design — enable breakthroughs in diffractive optics, plasmonics, photonic crystals, super-resolution, and electromagnetic cloaking.
Throughout the course, we emphasize the interplay between rigorous analysis and computation, and show how mathematical insight guides the design of nanostructures capable of light confinement, enhancement, and manipulation far below the wavelength scale.