Abstract

We investigate the linear propagation of Gaussian-apodized solutions to the paraxial wave equation in free-space and first-order optical systems. In particular, we present complex coordinate transformations that yield a very general and efficient method to apply a Gaussian apodization (possibly with initial phase curvature) to a solution of the paraxial wave equation. Moreover, we show how this method can be extended from free space to describe propagation behavior through nonimaging first-order optical systems by combining our coordinate transform approach with ray transfer matrix methods. Our framework includes several classes of interesting beams that are important in applications as special cases. Among these are, for example, the Bessel–Gauss and the Airy–Gauss beams, which are of strong interest to researchers and practitioners in various fields.

© 2012 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Accumulated Gouy phase shift in Gaussian beam propagation through first-order optical systems

M. Fatih Erden and Haldun M. Ozaktas
J. Opt. Soc. Am. A 14(9) 2190-2194 (1997)

Airy-Gauss beams and their transformation by paraxial optical systems

Miguel A. Bandres and Julio C. Gutiérrez-Vega
Opt. Express 15(25) 16719-16728 (2007)

Hermite–sinusoidal-Gaussian beams in complex optical systems

Lee W. Casperson and Anthony A. Tovar
J. Opt. Soc. Am. A 15(4) 954-961 (1998)

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

Figures (6)

You do not have subscription access to this journal. Figure files 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 (59)

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