Abstract
The effect of aberrations on the beam quality factor (M2) of Hermite-Gauss (HG) beams is examined. Using the method of moments, we derive closed-form analytical expressions of M2 due to astigmatism and spherical aberration. Our analysis reveals that the radius of the HG beams plays a significant role in determining the effect of the aberrations on M2. For each aberration, we establish a critical width that separates the region where M2 changes infinitesimally from the region where it changes sharply. The analytical results are validated through numerical simulations.
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