ABCD-systems with unimodular eigenvalues

M.J. Bastiaans; T. Alieva

ABCD-systems with unimodular eigenvalues

M.J. Bastiaans
, T. Alieva

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

It is shown that a lossless first-order optical system (or ABCD-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.

Original language	English
Title of host publication	Proc. ICO Topical meeting on Optoinformatics/Information Photonics 2006, St. Petersburg, Russia
Editors	M.L. Calvo, A.V. Pavlov, J. Jahns
Place of Publication	St. Petersburg, Russia
Publisher	ITMO
Pages	239-241
ISBN (Print)	5-7921-0719-6
Publication status	Published - 2006

Cite this

@inproceedings{50f05ce9efc24549ab7ab60ccecf59d0,

title = "ABCD-systems with unimodular eigenvalues",

abstract = "It is shown that a lossless first-order optical system (or ABCD-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.",

author = "M.J. Bastiaans and T. Alieva",

year = "2006",

language = "English",

isbn = "5-7921-0719-6",

pages = "239--241",

editor = "M.L. Calvo and A.V. Pavlov and J. Jahns",

booktitle = "Proc. ICO Topical meeting on Optoinformatics/Information Photonics 2006, St. Petersburg, Russia",

publisher = "ITMO",

}

ABCD-systems with unimodular eigenvalues. / Bastiaans, M.J.; Alieva, T.
Proc. ICO Topical meeting on Optoinformatics/Information Photonics 2006, St. Petersburg, Russia. ed. / M.L. Calvo; A.V. Pavlov; J. Jahns. St. Petersburg, Russia: ITMO, 2006. p. 239-241.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - ABCD-systems with unimodular eigenvalues

AU - Bastiaans, M.J.

AU - Alieva, T.

PY - 2006

Y1 - 2006

N2 - It is shown that a lossless first-order optical system (or ABCD-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.

AB - It is shown that a lossless first-order optical system (or ABCD-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.

M3 - Conference contribution

SN - 5-7921-0719-6

SP - 239

EP - 241

BT - Proc. ICO Topical meeting on Optoinformatics/Information Photonics 2006, St. Petersburg, Russia

A2 - Calvo, M.L.

A2 - Pavlov, A.V.

A2 - Jahns, J.

PB - ITMO

CY - St. Petersburg, Russia

ER -

ABCD-systems with unimodular eigenvalues

Abstract

Fingerprint

Cite this