ABSTRACT
There are several approaches to the spatial characterization of laser beams. One of the simplest characterization techniques is probably the measurement of beam power, which is often recorded over time to reveal potential instabilities. However, spatial resolution is lost here and is only achieved using a camera to record the power density in a transverse plane instead of integration. Although this approach gives a more detailed picture, there is still a crucial beam characteristic missing: its propagation. Two beams can exhibit exactly the same power density distribution but completely differ in propagation. A simple and commonly used measure to evaluate laser beam propagation is the beam propagation ratio M2, which compares the propagation properties of the beam to those of a perfect diffraction-limited Gaussian beam. Moreover, laser light has a certain phase and wave front distribution, as well as a certain polarization. While the former is commonly measured with interferometers or Shack-Hartmann sensors (SHS) the latter can be obtained from recording the Stokes parameters of the beam. Amplitude, phase, and polarization completely describe a laser beam and are traditionally measured by various experiments. A modern and comprehensive approach that enables to gather the complete information on an optical field at once is given by modal decomposition using an
inner-product measurement. Since intensity, phase, wave front, polarization distribution, and even orbital angular momentum density can be inferred from that approach, we will focus on this technique in the next sections and show how it can be applied to measure the above-mentioned fundamental beam quantities.
