Revisiting 2x2 matrix optics: Complex vectors, Fermion combinatorics, and Lagrange invariants

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dc.creatorSugon Jr., Quirino M.
dc.creatorMcNamara, Daniel J.
dc.date2008-12-03
dc.date.accessioned2026-07-07T12:08:44Z
dc.date.available2026-07-07T12:08:44Z
dc.descriptionWe propose that the height-angle ray vector in matrix optics should be complex, based on a geometric algebra analysis. We also propose that the ray's 2x2 matrix operators should be right-acting, so that the matrix product succession would go with light's left-to-right propagation. We express the propagation and refraction operators as a sum of a unit matrix and an imaginary matrix proportional to the Fermion creation or annihilation matrix. In this way, we reduce the products of matrix operators into sums of creation-annihilation product combinations. We classify ABCD optical systems into four: telescopic, inverse Fourier transforming, Fourier transforming, and imaging. We show that each of these systems have a corresponding Lagrange theorem expressed in partial derivatives, and that only the telescopic and imaging systems have Lagrange invariants.
dc.description10 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/0812.0664
dc.identifierhttp://arxiv.org/abs/0812.0664
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/209423
dc.subjectOptics
dc.titleRevisiting 2x2 matrix optics: Complex vectors, Fermion combinatorics, and Lagrange invariants
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