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It does look like that, but that spot could also be a result of resonator design and a missing or unfocused collimating lens. An uncollimated TEMn0 beam will look much like the pictures shown.
Found this physics paper on "Intensity Correlation Functions for 'Thermalised' TEMn0 laser beams." The HeNe laser used was 'thermalised' by shining it on a rotating ground glass disc. The authors presented calculations of the intensity correlation functions of the TEM10, TEM20, TEM30, TEM40 Gaussian-Hermite beams.
Pretty interesting. https://www.researchgate.net/public...Functions_for_'Thermalised'_TEMn0_Laser_Beams
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