Paraxial-wave optics and relativistic front description. I. The scalar theory

Abstract

The scalar wave equation is analyzed in the relativistic front form, appropriate for paraxial-wave optics. The group-theoretical basis for this treatment is uncovered. The formal similarity of the propagation of paraxial beams through optical systems to the quantum mechanics of particles in two dimensions subject to harmonic impulses, and the role of the metaplectic group of Bacry and Cadilhac, are both traced back to the structure of the Poincare group. Light rays are defined in this context as in statistical-wave optics, and the laws for their free propagation as well as transmission through lenses are derived.