Frequency pushing in lasers with injected signal

Abstract
Suitable equations for lasers with injected signal are derived in the case of a population decay much slower than the other damping processes. A perturbative approach for a small input field ɛ shows evidence of anomalous pushing of the laser frequency away from the external reference one. A threshold for the appearance of antisynchronized solutions is analytically found and numerically checked. A double-point bifurcation explains the switch from pulled- to pushed-frequency solutions as an exchange with a second branch of auto-Q-switched periodic trajectories. The final analysis of locking threshold allows us to relate the small- and large-ɛ behavior.

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