Low-Cost Micromechanically Tunable Optical Devices: Strained Resonator Engineering, Technological Implementation and Characterization

The rapid growth of the optical communication branches and the enormous demand for more bandwidth require novel networks such as dense wavelength division multiplexing (DWDM). These networks enable higher bitrate transmission using the existing optical fibers. Micromechanically tunable optical microcavity devices like VCSELs, Fabry-Pérot filters and photodetectors are core components of these novel DWDM systems. Several air-gap based tunable devices were successfully implemented in the last years. Even though these concepts are very promising, two main disadvantages are still remaining. On the one hand, the high fabrication and integration cost and on the other hand the undesired adverse buckling of the suspended membranes. This thesis addresses these two problems and consists of two main parts: • PECVD dielectric material investigation and stress control resulting in membranes shape engineering. • Implementation and characterization of novel tunable optical devices with tailored shapes of the suspended membranes. For this purposes, low-cost PECVD technology is investigated and developed in detail. The macro- and microstress of silicon nitride and silicon dioxide are controlled over a wide range. Furthermore, the effect of stress on the optical and mechanical properties of the suspended membranes and on the microcavities is evaluated. Various membrane shapes (concave, convex and planar) with several radii of curvature are fabricated. Using this resonator shape engineering, microcavity devices such as non tunable and tunable Fabry-Pérot filters, VCSELs and PIN photodetectors are succesfully implemented. The fabricated Fabry-Pérot filters cover a spectral range of over 200nm and show resonance linewidths down to 1.5nm. By varying the stress distribution across the vertical direction within a DBR, the shape and the radius of curvature of the top membrane are explicitely tailored. By adjusting the incoming light beam waist to the curvature, the fundamental resonant mode is supported and the higher order ones are suppressed. For instance, a tunable VCSEL with 26 nm tuning range, 400µW maximal output power, 47nm free spectral range and over 57dB side mode suppresion ratio (SMSR) is demonstrated. Other technologies, such as introducing light emitting organic materials in microcavities are also investigated.

Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element

We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method.