Frequency locking without phase locking of two coupled nonlinear oscillators is experimentally demonstrated. This synchronization regime is found for two coupled laser modes, beyond the phaselocking range fixed by Adler's equation, because of a resonance mechanism. Specifically, we show that the amplitudes of the two modes exhibit strong fluctuations that produce average frequency synchronization, even if the instantaneous phases are unlocked. The experimental results are in good agreement with a theoretical model.

We propose an experimental and theoretical study of the dynamical regimes observed when the two modes of a two-frequency solid-state laser are coupled by frequency-shifted optical feedback. The detuning associated to the feedback is close to the frequency of the laser relaxation oscillations. Special attention is devoted to the dynamics of the phase of the beat note between the modes relative to the phase of an external radio-frequency reference. In particular, we analyze in detail the transition from phase locking to the external reference to phase drift. This transition occurs through a window of frequency locking without phase locking [Thévenin, Romanelli, Vallet, Brunel, and Erneux, Phys. Rev. Lett. 107, 104101 (2011)]. Furthermore, a large variety of dynamical behaviors, such as weak intensity modulation, self-pulsing, and chaos, are experimentally found. These results are successfully reproduced by a theoretical model based on coupled rate equations. The extension of the model to the description of other active media such as semiconductor lasers is briefly outlined.

International audienceWe derive a delay-differential equation model that describes continuous-wave (cw) or passively Q-switched (PQS) two-frequency solid-state lasers submitted to frequency-shifted feedback (FSF). The study focuses on the locking of the beat note between the two free-running laser frequencies to a reference external frequency. The locking domain is obtained analytically in the cw regime. The PQS regime is treated by adding a saturable absorber population in the model equations. In this case, numerical simulations permit us to evaluate a locking range that is smaller than in the cw case. We find good agreement between the theoretical predictions and experiments carried out with a cw diode-pumped dual-polarization Nd:YAG laser as well as with previously published experimental results obtained with cw Er:Yb:glass [ Opt. Lett. 32, 1099 (2007)] and PQS Nd:YAG [ Opt. Lett. 33, 2524 (2008)] lasers. Applications of the FSF locking technique include the lidar-radar technique, for which a highly coherent beat note is required

A mode-locked solid-state laser containing a birefringent element is shown to emit synchronously two frequency combs associated to the two polarization eigenstates of the cavity. An analytical model predicts the polarization evolution of the pulse train, which is determined by the adjustable intracavity birefringence. Experiments realized with a Nd:YAG laser passively mode locked by a semiconductor saturable absorber mirror are in perfect agreement with the model. Locking between the two combs arises for particular values of their frequency difference, e.g., half the repetition rate, and the pulse train polarization sequence is then governed by the relative overall phase offset of the two combs.