Generation of large orbital angular momentum from superposed Bessel beams corresponding to resonant geometric modes

We theoretically verify that a coherent superposition of nearly degenerate Bessel beams characterizes the family of resonant geometric modes in circular billiards. With the ray-wave correspondence, we experimentally exploit a large-aperture cylindrical waveguide to generate the resonant geometric modes with large orbital angular momentum. Furthermore, the free-space propagation of the geometric modes emerging from the cylindrical waveguide is demonstrated to display the transient dynamics of the coherent states released from a circular quantum billiard.