Localization of wave patterns on classical periodic orbits in a square billiard

The connection between wave functions and classical periodic trajectories in a square billiard is analytically constructed by using the representation of SU(2) coherent states. The analytical function form is modified to show that the wave patterns can be apparently localized on the classical periodic trajectories by superposing a few nearly degenerate eigenfunctions. Based on the analogy between the Schrödinger and Helmholtz equations, the features of wave functions are experimentally studied from the transverse pattern formation in a laterally confined microcavity laser. The experimental transverse pattern in a square-shaped microcavity agrees very well with the constructed wave pattern concentrated along classical periodic orbits.