First-order optical systems with real eigenvalues

M.J. Bastiaans, T. Alieva

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)

Abstract

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
Volume272
Issue number1
DOIs
Publication statusPublished - 2007

Fingerprint

Eigenvalues and eigenfunctions
Optical systems
eigenvectors
eigenvalues
rays
magnification

Cite this

Bastiaans, M.J. ; Alieva, T. / First-order optical systems with real eigenvalues. In: Optics Communications. 2007 ; Vol. 272, No. 1. pp. 52-55.
@article{35e97ac01d564aa5a77af6230bd583dd,
title = "First-order optical systems with real eigenvalues",
abstract = "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.",
author = "M.J. Bastiaans and T. Alieva",
year = "2007",
doi = "10.1016/j.optcom.2006.11.003",
language = "English",
volume = "272",
pages = "52--55",
journal = "Optics Communications",
issn = "0030-4018",
publisher = "Elsevier",
number = "1",

}

First-order optical systems with real eigenvalues. / Bastiaans, M.J.; Alieva, T.

In: Optics Communications, Vol. 272, No. 1, 2007, p. 52-55.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - First-order optical systems with real eigenvalues

AU - Bastiaans, M.J.

AU - Alieva, T.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

U2 - 10.1016/j.optcom.2006.11.003

DO - 10.1016/j.optcom.2006.11.003

M3 - Article

VL - 272

SP - 52

EP - 55

JO - Optics Communications

JF - Optics Communications

SN - 0030-4018

IS - 1

ER -