Sensitivity of chaotic behavior to low optical frequencies of a double-beam torsional actuator

We investigate here how the optical properties at low frequencies affect the actuation dynamics and emerging chaotic behavior in a double-beam torsion actuator at nanoscale separations (<200nm), where the Casimir forces and torques play a major role. In fact, we take into account differences of the Casimir force due to alternative modeling of optical properties at low frequencies, where measurements are not feasible, via the Drude and plasma models, and repercussions by different material preparation conditions. For conservative autonomous actuation, bifurcation and phase portrait analysis indicate that both factors affect the stability of an actuating device in such a way that stronger Casimir forces and torques will favor increased unstable behavior. The latter will be enhanced by unbalanced application of electrostatic voltages in double-beam actuating systems. For the case of a time-periodic driving force, we use a Melnikov function and a phase plane analysis to study the emerging chaotic behavior with respect to the Drude and plasma modeling and material preparation conditions. We find indications that any factor that leads to stronger Casimir interactions will aid chaotic behavior and prevent long term prediction of the actuating dynamics. Moreover, in a double-beam actuator chaoticity will be amplified by the application of unbalanced electrostatic voltages. Therefore, the details of modeling of optical properties and the material preparations conditions must be carefully considered in the design of actuating devices at nanoscale because here Casimir forces are omnipresent and broadband type interactions.