First-order optical systems with real eigenvalues

M.J. Bastiaans, T. Alieva

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)


It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only real eigenvalues, is similar to a separable hyperbolic expander in the sense that the respective ray transformation matrices are related by means of a similarity transformation. Moreover, it is shown how eigenfunctions of such a system can be determined, based on the fact that simple powers are eigenfunctions of a separable magnifier. As an example, a set of eigenfunctions of a hyperbolic expander is determined and the resemblance between these functions and the well-known Hermite–Gauss modes is exploited.
Original languageEnglish
Pages (from-to)52-55
Number of pages4
JournalOptics Communications
Issue number1
Publication statusPublished - 2007


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