Measurement of M(2)-Curve for Asymmetric Beams by Self-Referencing Interferometer Wavefront Sensor

For asymmetric laser beams, the values of beam quality factor [Formula: see text] and [Formula: see text] are inconsistent if one selects a different coordinate system or measures beam quality with different experimental conditionals, even when analyzing the same beam. To overcome this non-uniqueness, a new beam quality characterization method named as M(2)-curve is developed. The M(2)-curve not only contains the beam quality factor [Formula: see text] and [Formula: see text] in the x-direction and y-direction, respectively; but also introduces a curve of [Formula: see text] versus rotation angle α of coordinate axis. Moreover, we also present a real-time measurement method to demonstrate beam propagation factor M(2)-curve with a modified self-referencing Mach-Zehnder interferometer based-wavefront sensor (henceforth SRI-WFS). The feasibility of the proposed method is demonstrated with the theoretical analysis and experiment in multimode beams. The experimental results showed that the proposed measurement method is simple, fast, and a single-shot measurement procedure without movable parts.