title: First-order optical systems with unimodular eigenvalues.
abstract: 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, and one of them is used to derive an easy optical realization in more detail.
authors.affiliation: Faculteit Elektrotechniek, Technische Universiteit Eindhoven, Eindhoven, Netherlands. m.j.bastiaans@tue.nl
authors.forename: Martin J
authors.initials: MJ
authors.lastname: Bastiaans
authors.forename: Tatiana
authors.initials: T
authors.lastname: Alieva