Multiple limit cycles in laser interference transduced resonators

Nanoscale resonators whose motion is measured through laser interferometry are known to exhibit stable limit cycle motion. Motion of the resonator through the interference field modulates the amount of light absorbed by the resonator and hence the temperature field within it. The resulting coupling of motion and thermal stresses can lead to self-oscillation, i.e. a limit cycle. In this work the coexistence of multiple stable limit cycles is demonstrated in an analytic model. Numerical continuation and direct numerical integration are used to study the structure of the solutions to the model. The effect of damping is discussed as well as the properties that would be necessary for physical devices to exhibit this behavior.

► We model resonators illuminated within an interference field.
► Resonators self-oscillate due to optical–thermal–mechanical feedback.
► Periodicity of the interference field leads to multiple stable limit cycles.
► Amplitude–frequency relationships and the role of damping are discussed.