Computing focused beam transmissions of photonic crystals using angular spectrum field synthesis

Recently novel types of imaging spectrometers have been successfully demonstrated, where photonic crystals filters are placed onto a detector. For focused beams, it is however unclear how numerical aperture (NA), aperture shape and aberrations affect the transmission of these filters and there is currently no established and computational efficient method to assess this. In this work we present an angular spectrum method to reconstitute focused beam fields and transmissions based on plane wave simulations. Once these plane wave simulations have been performed, the transmission of arbitrary pupils, aberrations and NA can be directly computed. We investigate the accuracy of this method by comparing the synthesized transmission and Poynting vectors with a fully simulated focused Gaussian beam. These results show that an angular sampling between 0.5° and 0.8° is required to achieve an accurate result depending on the mesh sampling of the simulation. Lastly, we demonstrate how this method can be used to investigate the effect of the pupil shape and aberrations on the transmission profiles. This analysis enables the identification of spectral regions which are sensitive to the instrument design but also regions which appear robust. We believe that the method described in this work can provide scientists and optical engineers a tool to perform detailed performance studies on these promising new instruments.