First-order optical systems with unimodular eigenvalues



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Bastiaans, Martin J. and Alieva, Tatiana Krasheninnikova (2006) First-order optical systems with unimodular eigenvalues. Journal of The Optical Society Of America A-Optics Image Science and Vision, 23 (8). pp. 1875-1883. ISSN 1084-7529

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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.

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© 2006 Optical Society of America. The Spanish Ministry of Education and Science is acknowledged for financial support: Ramon y Cajal grant and project TIC 2002-01846 (T. Alieva) and SAB2004-0018 (M. J. Bastiaans). Stimulating discussions with K. Bernardo Wolf (Universidad Nacional Autónoma de México, Cuernavaca) are gratefully acknowledged. The authors’ e-mail addresses are and

Uncontrolled Keywords:Fractional fourier-transforms, Integral transform, Implementation
Subjects:Sciences > Physics > Optics
ID Code:27647
Deposited On:11 Dec 2014 11:17
Last Modified:11 Dec 2014 11:17

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