Dressed mode description of optical bistability. II. Analytical treatment of self-pulsing
Abstract
We start from the dressed mode formulation of optical bistability, given in a previous paper. By performing an exact adiabatic elimination of the atomic modes, we derive a closed system of time evolution equations for the field modes, that play the role of order parameters. In particular in the simplest setting of two unstable modes the problem is reduced to a set of only two differential equations in time, that fully include both nonlinearity and propagation. Thus we can describe self-pulsing in terms of a simple two-dimensional phase space, which allows for treating cw and pulsing states on the same footing. We determine the full domain of existence of the self-pulsing state and describe how this state varies with the control parameters. In particular we find hysteresis cycles of novel type, that involve both cw and pulsing states, thereby enriching the phenomenology of Optical Bistability. A part of the boundary of the domain of existence of the self-pulsing state is found to be a line of Hopf bifurcations, which points out the existence of a higher order bifurcation in our system. In conclusion, our procedure exploits and develops in the best way Haken's theory of generalized Ginzburg-Landau equations for phase-transition-like phenomena in systems far from thermal equilibrium.
- Publication:
-
Zeitschrift fur Physik B Condensed Matter
- Pub Date:
- March 1982
- DOI:
- 10.1007/BF01686187
- Bibcode:
- 1982ZPhyB..47...79B