First-order optical systems with unimodular eigenvalues

M.J. Bastiaans, T. Alieva

Research output: Contribution to journalArticleAcademicpeer-review

17 Citations (Scopus)


It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues, is similar to a separable fractional Fourier transformer in the sense that the ray transformation matrices of the unimodular system and the separable fractional Fourier transformer are related by means of a similarity transformation. Moreover, it is shown that the system that performs this similarity transformation, is itself a lossless first-order optical system. Based on the fact that Hermite-Gauss functions are the eigenfunctions of a fractional Fourier transformer, the eigenfunctions of a unimodular first-order optical system can be formulated and belong to the recently introduced class of orthonormal Hermite-Gaussian-type modes. Two decompositions of a unimodular first-order optical system are considered.
Original languageEnglish
Pages (from-to)1875-1883
Number of pages9
JournalJournal of the Optical Society of America A, Optics, Image Science and Vision
Issue number8
Publication statusPublished - 2006


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