The linear canonical transformations in classical optics

Tatiana Alieva, José A. Rodrigo, Alejandro Cámara, Martin J. Bastiaans

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

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Abstract

In this chapter we consider the application of the linear canonical transformations (LCTs) for the description of light propagation through optical systems. It is shown that the paraxial approximation of ray and wave optics leads to matrix and integral forms of the two-dimensional LCTs. The LCT description of the first-order optical systems consisting of basic optical elements: lenses, mirrors, homogeneous and quadratic refractive index medium intervals and their compositions is discussed. The applications of these systems for the characterization of the completely and partially coherent monochromatic light are considered. For this purpose the phase space beam representation in the form of the Wigner distribution (WD), which reveals local beam coherence properties, is used. The phase space tomography method of the WD reconstruction is discussed. The physical meaning and application of the second-order WD moments for global beam analysis, classification, and comparison are reviewed. At the similar way optical systems used for manipulation and characterization of optical pulses are described by the one-dimensional LCTs.
Original languageEnglish
Title of host publicationLinear Canonical Transforms: Theory and Applications
EditorsJ.J. Healy, M.A. Kutay, H.M. Ozaktas, J.T. Sheridan
Place of PublicationNew York
PublisherSpringer
Pages113-178
Number of pages66
ISBN (Electronic)978-1-4939-3028-9
ISBN (Print)978-1-4939-3027-2
DOIs
Publication statusPublished - 2016

Publication series

NameSpringer Series in Optical Sciences
PublisherSpringer
Volume198
ISSN (Print)0342-4111

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  • Cite this

    Alieva, T., Rodrigo, J. A., Cámara, A., & Bastiaans, M. J. (2016). The linear canonical transformations in classical optics. In J. J. Healy, M. A. Kutay, H. M. Ozaktas, & J. T. S. (Eds.), Linear Canonical Transforms: Theory and Applications (pp. 113-178). [5] (Springer Series in Optical Sciences; Vol. 198). Springer. https://doi.org/10.1007/978-1-4939-3028-9_5