Phase anholonomy in dissipative optical systems with periodic oscillations

We show that some lasers and nonlinear optical devices with dissipation have in common certain characteristics that lead to a kind of phase anholonomy when such dissipative systems undergo a periodic motion with some frequency, say. The amount of the phase anholonomy accumulated in a period of 2/ is defined generally for such systems and further calculated for a subclass of such systems near the Hopf-bifurcation point. It turns out that the phase accumulation is generally determined by the size of the periodic orbit. By constructing a simple Hamiltonian, we show precisely that the phase anholonomy in these dissipative sytems can indeed be interpreted as Berrys phase.