Energy flow lines and the spot of Poisson–Arago

2009/09/12 by Michel Gondran, Alexandre Gondran
Mathematics · Physics and Astronomy · #Classical mechanics #Diffraction #Energy (signal processing) #Energy flow #Flow (mathematics) #Geometry #History and Developments in Astronomy #History and Theory of Mathematics #Line (geometry) #Mathematics #Mathematics and Applications #Mechanics #Monochromatic color #Opacity #Optics #Physics #Poisson distribution #Quantum mechanics #Shadow (psychology) #physics.optics

paper · pdf · doi:10.1119/1.3291215

arxiv created 2009/09/12 · openalex publication_date 2010/05/12 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show how energy flow lines answer the question about diffraction phenomena posed in 1818 by the French Academy: “Deduce by mathematical induction the movements of the rays during their crossing near the bodies.” The use of energy flow lines provides a complementary answer to Fresnel’s wave theory of light. A numerical simulation of the energy flow lines shows that they can reach the bright spot of Poisson–Arago in the shadow center of a circular opaque disk. For a monochromatic wave in vacuum, these energy flow lines correspond to the diffracted rays of Newton’s Opticks.

Citations

• II. The Bakerian Lecture. On the theory of light and colours
• Coherent and Incoherent States of the Radiation Field
• A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I
• Classical Electrodynamics