Selective excitation and detection of higher-order doughnut laser modes as an incoherent superposition of two petals modes in a digital laser resonator

Higher-order Laguerre-Gaussian beams with zero radial index and nonzero azimuthal index are known to carry orbital angular momentum (OAM), and they are routinely created external and internal to laser cavities. Previous reports on the generation of such modes from laser cavities suffer from inconclusive evidence of the real electromagnetic field. In this paper we demonstrate a simple method of selectively generating higher-order doughnut modes using a digital laser and we show that an observed doughnut beam from a laser cavity may not be a pure Laguerre-Gaussian azimuthal mode but can be an incoherent sum of petal modes, which do not carry OAM. We also demonstrate a method that could be used for future analysis of such fields from laser resonators.