Pushing Fabry-Pérot etalons towards 100k spectral resolving power

Abstract

A significant focus of current and next-generation astronomical research is the study of exoplanets and the formation of habitable conditions in planetary systems. This requires high-performance spectrom- eters operating in the far-infrared (FIR) range, with the Fabry-Pérot etalon being the state-of-the-art solution. This thesis, a collaboration between TU Delft and the Netherlands Institute for Space Research (SRON), focused on identifying and overcoming the major performance limitations of the Fabry-Pérot. The performance metrics were spectral resolving power and transmission. The major performance lim- itation was identified to be diffraction, which is particularly relevant in the FIR range. A two-part model was developed based on Gaussian beam propagation and the Huygens-Fresnel principle. Gaus- sian beam propagation is a well-established method that takes diffraction effects into account but is limited to the paraxial approximation, which quickly breaks down in the FIR. The novel application of the Huygens-Fresnel principle to Fabry-Pérot propagation modeling accounts for diffraction effects and remains accurate with large beam divergence caused by diffraction. The Gaussian beam approach was used to validate initial results from the Huygens-Fresnel approach. The effect of diffraction on critical device dimensions, such as cavity length, beam waist, finite aperture, and mirror tilt was investigated. Additionally, an experiment design was proposed to further validate the model. This included research into the design of metal mesh mirrors and silicon-air distributed Bragg reflector mirrors using COMSOL and MATLAB simulations. The successful results of the Huygens-Fresnel model provide new insights into the constraints on critical dimensions of the Fabry-Pérot etalon due to diffraction effects. These insights can be used to propose high-performance Fabry-Pérots designs suitable for the exploration of exoplanets.