Critical analysis of in-plane free-space light beam coupling using photonic curved micromirrors

Abstract

Free-space coupling of Gaussian light beams using flat and curved photonic microelectromechanical systems mirrors was analyzed in detail. The theoretical background and the non-ideal effects, such as limited micromirror extent, asymmetry in the curvature of spherical micromirrors, misaligned axes, and micromirror surface irregularities, were analyzed. The derived formulas were used to study and compare theoretically and experimentally the behavior of flat (one-dimensional), cylindrical (two-dimensional), and spherical (three-dimensional) micromirrors. The analysis focused on the regime of dimensions in which the curved micromirrors radius of curvature is comparable to the incident beam Rayleigh range, also corresponding to a reference spot size. A transfer matrix-based field and power coupling coefficients were derived for general micro-optical systems accounting for different matrix parameters in the tangential and sagittal planes of the microsystem taking into account the possible non-idealities. The results were presented in terms of normalized quantities such that the findings are general and can be applied to different situations. In addition, silicon micromirrors were fabricated with controlled shapes and used to experimentally analyze the coupling efficiency at the visible and near-infrared wavelengths.