Symplectic algebra and Gaussian optics
type: Item
instance of: scholarly article
title: Symplectic algebra and Gaussian optics
zbMATH Open document ID: 0685.22011
DOI: 10.1007/BF00948964
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1988-01-01T00:00:00Z
review text: Optical systems at small angles are described by linear transformations of optical phase space; the group describing this Gaussian optical regime is the symplectic group Sp(4,R) and, when the system is invariant under rotations around its optical axis, \(Sp(2,R)=SL(2,R)\). Focusable systems relate a pair of conjugate planes as object and image. The author proves (Theorem 2) that generally non-axis-symmetric systems have besides a `touching' pair of planes, either a single other pair, or a one-parameter family of distinct conjugate planes. The latter case corresponds to Gaussian optics with axis-symmetric systems that constitute the generic case of interest. The author concludes stating that, in effect, Gaussian Sp(2,R)-transformation optics is sufficient for the purposes of description of focusable systems, the exceptions being isolated from the main manifold of Gaussian systems.
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 78A05
zbMATH DE Number: 4122253
zbMATH Keywords: linear transformations
zbMATH Keywords: optical phase space
zbMATH Keywords: Gaussian optical regime
zbMATH Keywords: symplectic group
zbMATH Keywords: non-axis-symmetric systems
zbMATH Keywords: conjugate planes
zbMATH Keywords: focusable systems
author: Heinz Helfenstein
MaRDI profile type: Publication
cites work: Q3696183
full work available at URL: https://doi.org/10.1007/bf00948964
OpenAlex ID: W2005650013
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description: scientific article; zbMATH DE number 4122253