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

E. C. G. Sudarshan; R. Simon; N. Mukunda

doi:10.1103/PhysRevA.28.2921

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

E. C. G. Sudarshan, R. Simon, and N. Mukunda

Phys. Rev. A 28, 2921 – Published 1 November 1983

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 Poincaré 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.

Received 20 December 1982

DOI:https://doi.org/10.1103/PhysRevA.28.2921

Authors & Affiliations

E. C. G. Sudarshan^*

Institute of Theoretical Physics, S-41296 Göteborg, Sweden

R. Simon^†

Department of Physics, Indian Institute of Science, Bangalore 560012, Karnataka, India

N. Mukunda^‡

Institute of Theoretical Physics, S-41296 Göteborg, Sweden

^*Permanent address: Department of Physics, Center for Particle Theory, University of Texas at Austin, Austin, Texas 78712.
^†On leave of absence from the Department of Physics, The American College, Madurai, Tamil Nadu, India.
^‡Permanent address: Centre for Theoretical Studies and Department of Physics, Indian Institute of Science, Bangalore 560012, Karnataka, India.

Paraxial-wave optics and relativistic front description. II. The vector theory

N. Mukunda, R. Simon, and E. C. G. Sudarshan

Phys. Rev. A 28, 2933 (1983)

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Vol. 28, Iss. 5 — November 1983

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