Laser and Gaussian Beam Propagation and Transformation

Optical engineers and researchers working on optics deal with laser beams and optical systems as usual tools in their specific areas. The knowledge of the special characteristics of the propagation of laser beams through optical systems has to be one of the keystones of their actual work, and the clear definition of their characteristic parameters has an important impact in the success of the applications of laser sources. In this article, we will provide some basic hints about the characterization and transformation of laser beams that also deserve special attention in basic and specific text books (e.g., see Refs. [7–13]). The Gaussian beam case is treated in the first place because of its simplicity. Besides, it allows to introduce some characteristic parameters whose definition and meaning will be extended along the following sections to treat any kind of laser beam. In between, we will show how the beam is transformed by linear optical systems. These systems are described by using the tools of matrix optics. In the following, we will assume that laser beams have transversal dimensions small enough to consider them as paraxial beams. What it means is that the angular spectrum of the amplitude distribution is located around the axis of propagation, allowing a parabolic approximation for the spherical wavefront of the laser beam. In the paraxial approach, the component of the electric field along the optical axis is neglected. The characterization of laser beams within the nonparaxial regime can be done, but it is beyond the scope of this presentation. We will take the amplitudes of the beams as scalar quantities. This means that the polarization effects are not considered, and the beam is assumed to be complete and homogeneously polarized. A proper description of the polarization dependences needs an extension of the formalism that is not included here. Pulsed laser beams also need a special adaptation of the fundamental description presented here.