Paths of Least Time for Quantum Scale and a New Geometrical   Interpretation of Light Diffraction
  In this paper, a geometrical interpretation of light diffraction is given using an infinity of fluctuating geodesics that represent paths of least time in an homogeneous space. Without using the wave theory, we provide a geometrical explanation of the deviation of light's overall direction from rectilinear when light encounters edges, apertures and screens, which reconciles light particle-like nature with the interference phenomena. 
Faycal Ben Adda
physics.gen-ph physics.hist-ph