Abstract

Duality principles are derived that apply to any first-order system. Both symplectic and nonsymplectic duality transformations are studied. Duality permits a significant simplification for classifying first-order systems as well as proving operator relations for such systems. As an example of this technique operator relations for three dimensions are analyzed. Laplacian and Fourier duals are defined, and the completeness of this approach is explicitly proved for two-dimensional first-order systems; this approach yields the first complete classification to our knowledge of ISP(4, C), the complex, inhomogeneous four-dimensional, symplectic group.

© 1990 Optical Society of America

Full Article  |  PDF Article
More Like This
Fourier-optics approach to the symplectic group

Mark Kauderer
J. Opt. Soc. Am. A 7(2) 231-239 (1990)

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)

First-order optical systems with unimodular eigenvalues

Martin J. Bastiaans and Tatiana Alieva
J. Opt. Soc. Am. A 23(8) 1875-1883 (2006)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Tables (1)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (83)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription