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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 29, Iss. 9 — Sep. 1, 2012
  • pp: 1860–1869

Propagation of Gaussian-apodized paraxial beams through first-order optical systems via complex coordinate transforms and ray transfer matrices

T. Graf, D. N. Christodoulides, M. S. Mills, J. V. Moloney, S. C. Venkataramani, and E. M. Wright  »View Author Affiliations


JOSA A, Vol. 29, Issue 9, pp. 1860-1869 (2012)
http://dx.doi.org/10.1364/JOSAA.29.001860


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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

OCIS Codes
(000.3860) General : Mathematical methods in physics
(080.2730) Geometric optics : Matrix methods in paraxial optics
(140.0140) Lasers and laser optics : Lasers and laser optics
(260.1960) Physical optics : Diffraction theory
(260.2030) Physical optics : Dispersion
(080.4295) Geometric optics : Nonimaging optical systems

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: March 21, 2012
Revised Manuscript: July 17, 2012
Manuscript Accepted: July 17, 2012
Published: August 15, 2012

Citation
T. Graf, D. N. Christodoulides, M. S. Mills, J. V. Moloney, S. C. Venkataramani, and E. M. Wright, "Propagation of Gaussian-apodized paraxial beams through first-order optical systems via complexcoordinate transforms and ray transfer matrices," J. Opt. Soc. Am. A 29, 1860-1869 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-9-1860


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