The most important note about the transmission of a Gaussian Beam [link] through various optical components [link] is that the beam will remain Gaussian, given that the system is paraxial. The shape of the Gaussian beam will change according to the components, however.

The complex amplitude of the Gaussian beam (width) is adjusted to the width of an optical component, for example.

The Gaussian beam that emerges from the above lens takes the following formulas:

Lenses may be used to focus the a Gaussian beam. This is achieved by positioning the lense appropriately according to the location of the beam waist. For applications such as laser scanning and compact-disk burning, it is desired to focus the beam to the smalles size possible.

The focused waist W0′ and the distance of the focused waist z’ are a function of the waist of the original beam and the focal length f of the lens.

Beams may also be relayed and expanded using lenses.

A Gaussian beam, as do rays and waves behave differently for a plane mirror (i.e. spherical mirror with infinite radius) and spherical mirrors.

As is the case with geometrical ray optics, beam properties through a system can be modeled using the ABCD matrix method.

B. E. A. Saleh and M. C. Teich, *Fundamentals of photonics*. Hoboken: Wiley, 2019.

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