We present the experimental generation and characterization of each one of the four fundamental families of Helmholtz-Gauss beams: cosine-Gauss beams, stationary and helical Mathieu-Gauss beams, stationary and traveling parabolic-Gauss beams, and Bessel-Gauss beams. Both the transverse intensity profile and power spectrum that each one of the beams exhibits upon propagation is observed and compared to the theoretical model with good quantitative agreement. Emphasis is made on the fact that each of the four families of HzG beams is complete and orthogonal, and thus of fundamental relevance.
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