M² and High-order Modes
M² is a measurement that was originally designed to determine the quality of a real beam in comparison to a theoretically perfect fundamental mode Gaussian beam (Siegman 1990). Although many lasers are designed to output a fundamental mode Gaussian beam, imperfections and/or cavity design in the laser will often cause superimposed higher-order transverse modes. M² provides an excellent metric for determining the higher-order mode content. In his original paper introducing M², Siegman gives mathematical expressions for the theoretical value of M² based on the weighted content of the various modes in a beam. In this blog post, we will programmatically generate Gaussian beams with multi-mode content and then analyze the M² value of these artificial beams calculated by the DataRay software in order to confirm the accuracy of our algorithms.