Observation of quantum-classical correspondence from high-order transverse patterns

We experimentally observe the formation of high-order transverse patterns in a laser resonator with a high degree of frequency degeneracy. It is found that the transverse patterns are well localized on the Lissajous orbits. The connection between the wave functions and the classical periodic orbits is analytically constructed by using the representation of SU(2) coherent states. With this connection, the observed transverse patterns are reconstructed very well. The nice reconstruction suggests that the laser resonators can be deliberately designed to attain a more thorough understanding of the quantum-classical connection.