Title: Directional Filter Design and Simulation for Superconducting On-chip Filter-banks

Abstract: Many superconducting on-chip filter-banks suffer from poor coupling to the detectors behind each filter. This is a problem intrinsic to the commonly used half wavelength filter, which has a maximum theoretical coupling of 50 %. In this paper we introduce a phase coherent filter, called a directional filter, which has a theoretical coupling of 100 %. In order to to study and compare different types of filter-banks, we first analyze the measured filter frequency scatter, losses, and spectral resolution of a DESHIMA 2.0 filter-bank chip. Based on measured fabrication tolerances and losses, we adapt the input parameters for our circuit simulations, quantitatively reproducing the measurements. We find that the frequency scatter is caused by nanometer-scale line-width variations and that variances in the spectral resolution is caused by losses in the dielectric only. Finally, we include these realistic parameters in a full filter-bank model and simulate a wide range of spectral resolutions and oversampling values. For all cases the directional filter-bank has significantly higher coupling to the detectors than the half-wave resonator filter-bank. The directional filter eliminates the need to use oversampling as a method to improve the total efficiency, instead capturing nearly all the power remaining after dielectric losses.