ABCD Ray Matrices: Atmospheric Propagation

doi:10.1117/3.2643989.ch4

Book: Laser Beam Propagation in Random Media: New and Advanced Topics

Author(s): Larry C. Andrews, Melissa K. Beason

Published: 2023

https://doi.org/10.1117/3.2643989.ch4

Author Affiliations +

Abstract

In this chapter we introduce Gaussian-beam wave propagation through various optical structures such as lenses and aperture stops that are arbitrarily distributed along the propagation path but perfectly aligned with the optical axis. If we characterize the optical elements by 2x2 matrices, called ABCD ray matrices,^1–6 we can continue to use the paraxial approximation and Huygens–Fresnel integral. In free space this leads to a Gaussian-beam wave at the end of the path even though the beam passes through one or more of these optical elements. That is, the Gaussian nature of the beam model is preserved with the use of these matrices, unlike what actually occurs with hard-aperture structures. Fortunately, the ABCD ray matrix method also permits us to include the presence of optical turbulence along the path—over only a portion of the path or everywhere between input and output planes. The use of these matrices leads to generalizations of the spectral representations that arise in the Rytov approximation.