Extraction of main elements from a TEM composite laser pattern

We examined the atypical formation and superposition of transverse electromagnetic modes (TEM) of high order in a commercial He-Ne laser (@543.5 nm). The competence of the dominant modes exhibits a periodic and stable dynamic, uncommon in industrialized systems. Also, the intensity shows a smooth transition. The origin of the phenomenon is only a product of intra-cavity diffractive components. We found the promotors are a stable optical cavity but quasi-degenerated, with large transversal section (the Fresnel number is irregular), and a breaking the axial symmetry (producing astigmatism). The analysis of the average intensity patterns, and a correlation algorithm — via bi-orthogonal decomposition based on Hermite-Gauss polynomials — expose the five principal TEM elements. These results could be meaningful and inspiring both in courses of optics, laser engineering as in image processing. (paper)