The aligning of frequencies on an equidistant spectral grid, known as mode locking, is a necessary feature for generating ultrashort laser pulses. Existing phase models aim to explain how different frequencies generated in a nonlinear microresonator self-synchronize to make a short optical pulse. One particular model, based on a variant of the nonlinear Schrödinger equation called the Lugiato-Lefever equation, has gained attention because it describes coupled phases occurring in triplets rather than pairs. Recent work probing this model with nonlinear dynamics has helped draw new conclusions about how these new laser devices self-synchronize.

DeTal et al. report findings on the transition to partial and complete synchronization in the presence of quenched disorder in the ternary model for general coupled-oscillator systems. The group observed first-order transitions with hysteresis, a feature not usually found in other synchronizing phase models.

“One surprise was that the hysteresis width, determining where desynchronization appears, grows with the number of oscillators,” said author Hossein Taheri. “Usually more neighbors simplifies establishing global synchronized behavior.”

The first-order transition with hysteresis was found in both Gaussian and uniform disorder, and the group found that the transitions were characteristically different from those found in the classic Kuramoto model, which is prevalent in the study of paired phase oscillators.

The group hopes their work will inspire further work on the model and its variants and looks to use the theory as a guiding strategy for enhanced performance of robust nonlinear microresonator applications.

Source: “Synchronization behavior in a ternary phase model,” by N. DeTal, H. Taheri, and K. Wiesenfeld, Chaos: An Interdisciplinary Journal of Nonlinear Science (2019). The article can be accessed at