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We report what is to our best knowledge the first observation of Mathieu-Gauss modes directly generated in an axicon-based stable resonator. By slightly breaking the symmetry of the cavity we were able to generate single lowest and high-order Mathieu-Gauss modes of high quality. The observed transverse modes have an inherent elliptic structure and exhibit remarkable agreement with theoretical predictions.

The three dimensional distribution of focused vector Mathieu-Gauss beams (vMG) is studied in the vicinity of the geometrical focus of an unapertured thin lens. We adopt two different intensity based criteria for defining the actual focus. Our analysis confirms the existence of a focal shift towards the lens for this type of beams. The dependence of the focal shift on the different parameters of the beams is discussed in detail. Beams with different states of polarization are studied as well, and it is shown that the focal shift is independent of the polarization.