Fig. 1: Fundamental modes of stable laser resonators.

Middle panel, the three families of modes of spherical stable laser resonators: Laguerre-Gaussian, Ince-Gaussian, and Hermite-Gaussian beams. The Ince-Gaussian modes converge to the Laguerre-Gaussian and Hermite-Gaussian when the focal distance tends to zero and infinity respectively. Left panel, the transition of the Gaussian beams to accelerating beams. The transformation occurs as the order, \(p\), and the waist size, \({w}_{0}\), go to infinity while keeping the ratio \(\kappa={w}_{0}/{p}^{1/6}\), which becomes the transverse scale of the accelerating beam, constant, and by shifting the coordinates to the left peak of the beam. Right panel, transmutation of the Gaussian beams to nondiffracting beams. The metamorphosis takes place when the order, \(p\), and the waist size, \({w}_{0}\), tend towards infinity, while maintaining the ratio \({k}_{t}=2\sqrt{p}/{w}_{0}\) constant, which becomes the transverse wavevector of the nondiffractive beam.