Abstract

Starting with the Iwasawa-type decomposition of a first-order optical system (or $\mathbf{A}\mathbf{B}\mathbf{C}\mathbf{D}$ system) as a cascade of a lens, a magnifier, and an orthosymplectic system (a system that is both symplectic and orthogonal), a further decomposition of the orthosymplectic system in the form of a separable fractional Fourier transformer embedded between two spatial-coordinate rotators is proposed. The resulting decomposition of the entire first-order optical system then shows a physically attractive representation of the linear canonical integral transformation, which, in contrast to Collins integral, is valid for any ray transformation matrix.

© 2005 Optical Society of America

Properties of the linear canonical integral transformation

Tatiana Alieva and Martin J. Bastiaans
J. Opt. Soc. Am. A 24(11) 3658-3665 (2007)

Synthesis of an arbitrary ABCD system with fixed lens positions

Martin J. Bastiaans and Tatiana Alieva
Opt. Lett. 31(16) 2414-2416 (2006)

Classification of lossless first-order optical systems and the linear canonical transformation

Martin J. Bastiaans and Tatiana Alieva
J. Opt. Soc. Am. A 24(4) 1053-1062 (2007)

Fast numerical algorithm for the linear canonical transform

Bryan M. Hennelly and John T. Sheridan
J. Opt. Soc. Am. A 22(5) 928-937 (2005)

Orthonormal mode sets for the two-dimensional fractional Fourier transformation

Tatiana Alieva and Martin J. Bastiaans
Opt. Lett. 32(10) 1226-1228 (2007)