Abstract
A nonlinear analysis is made for a degenerate two-photon ring laser near its critical point corresponding to a self-pulsing instability by using the slaving principle and normal form theory. It turns out that the system undergoes two kinds of transitions, a usual Hopf bifurcation to a stable or unstable limit cycle and a co-dimension two Hopf bifurcation where the limit cycles disappear. An analytical criterion is given to distinguish the super-from the sub-critical bifurcation. We have also solved the equations numerically to confirm and to supplement our analytical results. In the case of super-critical bifurcation, a period-doubling bifurcation sequence to chaos is also observed with the decrease in pumping.
Original language | English (US) |
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Pages (from-to) | 163-174 |
Number of pages | 12 |
Journal | Zeitschrift für Physik B Condensed Matter |
Volume | 77 |
Issue number | 1 |
DOIs | |
State | Published - Feb 1 1989 |
Externally published | Yes |
ASJC Scopus subject areas
- Condensed Matter Physics