## Measuring the universal synchronization properties of driven oscillators across a Hopf instability |

Optics Express, Vol. 22, Issue 7, pp. 7364-7373 (2014)

http://dx.doi.org/10.1364/OE.22.007364

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### Abstract

When a driven oscillator loses phase-locking to a master oscillator via a Hopf bifurcation, it enters a bounded-phase regime in which its average frequency is still equal to the master frequency, but its phase displays temporal oscillations. Here we characterize these two synchronization regimes in a laser experiment, by measuring the spectrum of the phase fluctuations across the bifurcation. We find experimentally, and confirm numerically, that the low frequency phase noise of the driven oscillator is strongly suppressed in both regimes in the same way. Thus the long-term phase stability of the master oscillator is transferred to the driven one, even in the absence of phase-locking. The numerical study of a generic, minimal model suggests that such behavior is universal for any periodically driven oscillator near a Hopf bifurcation point.

© 2014 Optical Society of America

**OCIS Codes**

(140.3520) Lasers and laser optics : Lasers, injection-locked

(140.3580) Lasers and laser optics : Lasers, solid-state

(190.3100) Nonlinear optics : Instabilities and chaos

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: January 21, 2014

Revised Manuscript: March 5, 2014

Manuscript Accepted: March 6, 2014

Published: March 24, 2014

**Virtual Issues**

Physics and Applications of Laser Dynamics (2014) *Optics Express*

**Citation**

M. Romanelli, L. Wang, M. Brunel, and M. Vallet, "Measuring the universal synchronization properties of driven oscillators across a Hopf instability," Opt. Express **22**, 7364-7373 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-7364

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