Observation of laser transverse modes analogous to a SU(2) wave packet of a quantum harmonic oscillator

We report the generation of a new type of laser transverse mode that is analogous to a SU(2) elliptical wave packet of a quantum harmonic oscillator. Experimental results show that using a doughnut pump profile to excite an isotropic microchip laser in a spherical cavity can generate the elliptical transverse modes. The formation of elliptical transverse modes is found to be a spontaneous locking process of Hermite-Gaussian modes within the same family. The chaotic relaxation oscillation caused by the interaction of two nearly degenerate elliptical modes is also observed.