Title

Geometrical Representation Of Gaussian Beams Propagating Through Complex Paraxial Optical Systems

Abstract

Geometric relations are used to study the propagation environment of a Gaussian beam wave propagating through a complex paraxial optical system characterized by an ABCD ray matrix in two naturally linked complex planes. In the plane defined by beam transmitter parameters Ω0 and Ω, the propagation path is described by a ray line similar to the ray line in the Formula Presented diagram method, whereas the path in the plane of beam receiver parameters θ and Λ is described by a circular arc. In either plane the amplitude, phase, spot size, and radius of curvature of the Gaussian beam are directly related to the modulus and argument of the complex number designating a particular transverse plane along the propagation path. These beam parameters also lead to simple geometric relations for locating the beam waist, Rayleigh range, focal plane, and sister planes, which share the same radius of curvature but have opposite signs. Combined with the paraxial wave propagation technique based on a Huygens-Fresnel integral and complex ABCD ray matrices, this geometric approach provides a new and powerful method for the analysis and design of laser systems. © 1993 Optical Society of America.

Publication Date

10-20-1993

Publication Title

Applied Optics

Volume

32

Issue

30

Number of Pages

5918-5929

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1364/AO.32.005918

Socpus ID

0027672511 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0027672511

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