Abstract

Recently, a synchronization regime of frequency locking without phase locking (referred to also as “bounded phase”, “phase entrainment” or “phase trapping”) has been experimentally isolated in laser oscillators [1,2], and afterwards in hydrodynamics [3] and in nanomechanical oscillators [4]. In this regime, two interacting systems keep oscillating at the same mean frequency, but their phase difference is not constant in time. It is well known that this behavior occurs whenever a driven system loses phase-locking via a Hopf bifurcation. However, in our opinion the bounded-phase regime has not been fully understood yet. Indeed, at first sight the bounded-phase regime is a kind of intermediate regime between locking and unlocking: on one hand, frequency locking is preserved; on the other hand, the RF spectrum and the phasor plots (Fig. 1 (a)) are qualitatively the same as in the unlocked regime. Furthermore, the system passes from bounded to unbounded phase smoothly, without a bifurcation. In the present work, we provide for the first time a full quantitative characterization of the synchronization in the bounded phase regime, by measuring the spectra of the phase fluctuations of a driven opto-radiofrequency oscillator, based on a dual-frequency laser submitted to optical feedback [5].

© 2015 IEEE