Mathematical Shape Evaluation of a Concave MEMS Mirror

Abstract

A mirror is a key component of microcavity lasers. We developed a tunable laser with a microelectromechanical system (MEMS) movable mirror and a vertical cavity surface emitting laser (VCSEL), called MEMS-VCSEL. A concave shape for the MEMS mirror is fabricated to reduce diffraction loss by applying a chemical mechanical polishing process to the Si surface of a MEMS chip. Because the shape of the cavity in VCSELs affects the beam profile or the polarization of laser light, it should be evaluated quantitatively to investigate the characteristics of the laser. In this study, we demonstrate that the concave shape measured in three dimensions complies with Euler's theorem in differential geometry at the bottom area of the concave. The principal curvatures and directions of the MEMS mirror are estimated and revealed to agree with the actual concave shape. Our quantitative evaluation helps estimate not only the principal curvatures and directions, but also the normal curvature of the concave shape in any direction. These estimations are valuable for investigating the characteristics of MEMS-VCSELs such as the mode profile and the polarization state.