One analytic form for four branches of the ABCD matrix

Abstract

It is not always possible to diagonalize the optical $ABCD$ matrix, but it can be brought into one of the four Wigner matrices by a similarity transformation. It is shown that the four Wigner matrices can be combined into one matrix with four branches. This result is illustrated in terms of optical activities, laser cavities, and multilayer optics.

21 pages, 3 figures, published in Special Issue: Festschrift in Memory of Lorenzo M. Narducci

References in corpus (3)

• Sliderule-like property of Wigner's little groups and cyclic S-matrices for multilayer optics
• ABCD Matrices as Similarity Transformations of Wigner Matrices and Periodic Systems in Optics
• Optical Activities as Computing Resources for Space-time Symmetries

Cited by in corpus (5)

• Wigner's Space-time Symmetries based on the Two-by-two Matrices of the Damped Harmonic Oscillators and the Poincaré Sphere
• Lens optics and the continuity problems of the ABCD matrix
• Poincaré Sphere and Decoherence Problems
• The O(3,2) Symmetry derivable from the Poincaré Sphere
• Internal Space-time Symmetries of Particles derivable from Periodic Systems in Optics