If Quantum Mechanics is the Paraxial Optics, then …

Axel Lubk

Gerard Nienhuis

Roberto Ortega-Martı́nez, Carlos Moreno, Ana Leonor Rivera

The paraxial regime of scalar wave optics has the same structure as non-relativistic quantum mechanics, with wavelength taking the place of the Planck constant. The Wigner function is a central tool to explore the phase space of a system; in optics, moreover, it can be produced by purely optical means. In this first part, we present a matrix-based formalism for the study of paraxial optical systems, and apply it to the description of a setup that, as will be seen in the second part, produces the Wigner function.

E. C. G. Sudarshan, R. Simon, Narasimhaiengar Mukunda

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 Poincar\'e 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.

Ángel S. Sanz, Salvador Miret-Artés

J. I. Cirac, Harry J. Kimble