Mathematics Colloquium : The Standard Model of Wave Interference - A slight detour along the journey

The wave theory of light owes its origins to the seminal work of Huygens, Young and Fresnel. Huygens proposed the principle of secondary waves as the mechanism underlying light propagation in his Treatise (1690). Young proposed the principle of wave interference as the basis for bright and dark fringe formation in his Natural Philosophy (1807). Fresnel developed both his predecessors’ ideas into a nice quantitative framework that also accounts for the transverse nature of light in his Memoirs (1815). Later workers like Stokes (1856), Kirchhoff (1882), Rayleigh & Sommerfeld (1900s) and Wolf & Marchand (1950s) helped further refine Fresnel’s original work by incorporating the wave equation into the formalism, but with varied degrees of success.

In this talk, I will dwell upon some very fertile ideas on the theory of wave interference that has largely gone unnoticed over the past 200 years. Starting from a reformulation of the classical double slit experiment using a highly versatile hyperbola theorem, the new analysis is then extended to encompass the multiple slit experiment and single slit experiment of the Fraunhofer class. The many advantages, implications and practical applications of the proposed treatment will be summed up in the closing remarks.