Protoplanetary disks (PPDs) have gained substantial attention due to their crucial role in planet formation. Observing their features in the far-infrared (FIR) spectrum has been challenging due to limitations in current optics and detectors, with proposed missions requiring a spectrometer with a spectral resolving power on the order of magnitude of 100,000. A promising solution is the virtually imaged phased array (VIPA), which could surpass the commonly used Fabry-Perot etalon and diffraction grating spectrometers. However, due to their novelty, VIPAs have seen limited applications in space and lack a numerically efficient model, preventing confi- dent recommendation for FIR spectroscopy. In this project, a one-dimensional (1D) analytical VIPA model with a numerically efficient implementation using Gaussian beam formalism was developed, showing close alignment with an advanced 2D model by Hu et al. (2015) based on the angular spectrum of plane waves. The new model demonstrated potential for VIPAs to meet the spectral resolving power required for space missions and showed the possibility to be further expanded to 2D for higher accuracy, while retaining high efficiency. An experimental setup for verifying the simulation results was proposed. The interplay between various device parameters, coupled with the numerous degrees of freedom required for aligning the optical setup, presented significant experimental challenges. Additionally, investigations into the design of inductive metal mesh mir- rors, supported by simulations in COMSOL and MATLAB, uncovered several difficulties that were thoroughly explored. The analytical VIPA model based on Gaussian beam propagation shows promise as a method for optimizing a VIPA for high-resolution far-infrared spectroscopy but further research and experimental validation are necessary to fully establish its efficiency and effectiveness. The project was a collaboration between TU Delft and the Netherlands Institute for Space Research (SRON).

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.