Modal interactions in resonant microscanners

The fast response of micromirrors and their ability to achieve large scanning angles and low wavelength sensitivity, has made them an appealing substitute for traditional scanning and display technologies. To achieve large rotation angles, while minimizing the voltage requirements, the microscanner is excited at its resonance frequency and then used to steer a light beam along a surface. In this work, we develop a comprehensive model of a torsional microscanner. Based on the eigenvalue problem, we reduce the model to a 2-DOF lumped-mass model that captures the significant dynamics of the microscanner. We use the method of multiple scales to derive an approximate analytical solution of the microscanner response to combined DC and resonant AC voltage excitation. We examined the characteristics of the solution and found that, for a range of DC voltage, a two-to-one internal resonance occurs between the first two modes. Therefore, the energy fed to the first (torsional) mode may be channeled to the second (bending) mode causing an undesirable steady-state response. This phenomenon results in significant degradation in the microscanner performance, therefore, the designer needs to identify it, design around it, or control it.