Wave Geometry & Optical Field Theory

In nature, one never finds the ideal plane waves described in textbooks. Real physical waves, such as light beams, spread, diffract, scatter and interfere, in ways that can be studied with mathematical methods such as vector calculus, Fourier analysis, and complex integration. We are interested in describing the geometry of propagating waves, often focusing on 'singular' features, such as optical vortices (wave dislocations), which are lines in three dimensions around which optical energy circulates. Problems we are currently interested in include the structure of reflected light beams, the structure of diffraction catastrophes, quantum chaology, optical weak measurement, knotted optical vortices and vortices in electron waves.

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