No abstract

Orbital angular momentum densities in the astigmatic transformation of Lissajous geometric laser modes are originally and systematically investigated. The quantum theory of the coherent state is exploited to derive an analytical wave representation for the transformed output beams. The derived wave function is further employed to numerically analyze the propagation dependent orbital angular momentum densities. The parts of the negative and positive regions in the orbital angular momentum density are found to rapidly change in the Rayleigh range behind the transformation.

The quantum and classical dynamics of the SU(2) coupled oscillator model are systematically reviewed to provide the quantum eigenstates and stationary coherent states for characterizing laser transverse modes from the analogy with the quantum-classical connection. The integral formula for the representation of the stationary coherent states derived from the evolution of the time-dependent wave packet state is completely reviewed. Several calculated results for the stationary coherent states are illustratively presented to display the spatial distributions for the quantum-classical transition and the plentiful variations of phase singularities. The overall review is believed to provide a comprehensive insight into laser transverse modes characterized by the stationary coherent states of the SU(2) coupled oscillator model.