Transition from eigenmodes to geometric modes characterized by the quantum SU(2) coupled oscillator model: A review

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.