First-order optical systems with unimodular eigenvalues

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 s...

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Detalles Bibliográficos
Autores: Bastiaans, Martin J., Alieva Krasheninnikova, Tatiana
Tipo de recurso: artículo
Fecha de publicación:2006
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/51272
Acceso en línea:https://hdl.handle.net/20.500.14352/51272
Access Level:acceso abierto
Palabra clave:535
Fractional fourier-transforms
Integral transform
Implementation
Óptica (Física)
2209.19 Óptica Física
Descripción
Sumario: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.