Daniel G. Schuster Jr., Mario W. Gomes, Alexandra B. Artusio-Glimpse, Grover A. Swartzlander Jr.
In this paper, the response is found for a semi-cylindrical rod rocking on a level surface while subjected to forces from radiation pressure and gravity. Changes in the oscillation frequency of the rod as a function of light intensity are determined for both a mirrored and non-mirrored rod. The simulation results show that the equilibrium positions for the mirrored and non-mirrored rod exhibit a classic pitchfork and cusp catastrophe type bifurcation at critical laser intensities, respectively. By linearizing the systems equations of motion and sinusoidally modulating the laser intensity, the mathematical model for the rocking semi-cylinder could be transformed in the standard form of Mathieu’s equation. Inspired by the stability regions of the vertically oscillating inverted pendulum, a region of laser modulation parameters was determined, which could stabilize orientations of the lens which were unstable with constant laser intensity. Lastly, a comparison between the bifurcation point and change in natural frequency as functions of intensity between a previous analytical derivation and the full nonlinear model also showed that they agree closely for laser intensities near and below the critical intensity.
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