[Paper Review] Partially Coherent Optical Modelling of the Ultra-Low-Noise Far-Infrared Imaging Arrays on the SPICA Mission

S. Withington, Christopher N. Thomas+1 more|arXiv (Cornell University)|Jul 27, 2013

Superconducting and THz Device Technology2 references3 citations

TL;DR

This paper presents a partially coherent electromagnetic modeling framework for ultra-low-noise, multi-mode far-infrared Transition Edge Sensor (TES) detectors in the SPICA space telescope's SAFARI instrument. Using a hybrid Mattis-Bardeen-Drude model for superconducting Ta absorbers and mode-matching techniques in waveguides, the study demonstrates that a flat backshort at 0.375λ maximizes broadband throughput (up to 87%) and minimizes sensitivity to cavity shape, enabling high-fidelity, low-stray-light response across 210–34 μm.

ABSTRACT

We have developed a range of theoretical and numerical techniques for modeling the multi-mode, 210-34 micron, ultra-low-noise Transition Edge Sensors that will be used on the SAFARI instrument on the ESA/JAXA cooled-aperture FIR space telescope SPICA. The models include a detailed analysis of the resistive and reactive properties of thin superconducting absorbing films, and a partially coherent mode-matching analysis of patterned films in multi-mode waveguide. The technique allows the natural optical modes, modal responsivities, and Stokes maps of complicated structures comprising patterned films in profiled waveguides and cavities to be determined.

Motivation & Objective

• To develop accurate electromagnetic models for multi-mode, ultra-low-noise FIR TES detectors in the SPICA mission’s SAFARI instrument.
• To address the challenge of modeling complex optical responses in detectors sensitive to ~20 electromagnetic modes, unlike single-mode microwave horns or high-mode planar pixels.
• To optimize detector performance by minimizing stray light sensitivity and inter-pixel crosstalk through precise modeling of absorber and cavity geometry.
• To determine the optimal placement of a backshort in a waveguide to maximize modal throughput across a broad FIR band.
• To enable design of patterned superconducting absorbers with reduced impedance and enhanced filtering or shielding capabilities.

Proposed method

• Developed a composite conductivity model combining Mattis-Bardeen and Drude approaches to describe the complex, frequency-dependent sheet impedance of thin β-phase Ta films.
• Applied plane-wave and Green’s dyadic methods to compute sheet impedance, confirming consistency between two independent electromagnetic modeling techniques.
• Used mode-matching analysis in circular waveguides to calculate modal responsivities, Stokes maps, and throughput for patterned superconducting absorbers.
• Simulated waveguide systems with flat backshorts at varying distances (0.25λ to 0.375λ) to determine optimal placement for broadband performance.
• Evaluated throughput using geometric mode counting, 1/λ² fitting, and full electromagnetic simulations to compare idealized vs. realistic behavior.
• Assessed the impact of cavity shape and wall currents on optical response, advocating for flat backshorts to eliminate parasitic losses and reduce pixel-to-pixel variation.

Experimental results

Research questions

• RQ1 How can the optical response of multi-mode, superconducting TES detectors be accurately modeled in the partially coherent regime?
• RQ2 What is the optimal backshort position in a waveguide to maximize broadband modal throughput for FIR detectors?
• RQ3 To what extent do waveguide mode cutoffs and impedance variations degrade detector efficiency, and how can this be mitigated?
• RQ4 Can a planar, two-dimensional absorber achieve near-ideal absorption efficiency despite limited degrees of freedom compared to volumetric absorbers?
• RQ5 How does cavity geometry influence the spatial and modal response patterns of FIR detectors, and can this be minimized through design?

Key findings

• A flat backshort placed at 0.375λ from the absorber maximizes overall modal throughput across the 210–34 μm band, outperforming the conventional 0.25λ placement.
• The maximum achievable broadband efficiency for a planar superconducting absorber is capped at 87%, due to the two-dimensional nature of current dissipation.
• Full electromagnetic mode-matching simulations show smoother throughput variation than geometric mode counting, avoiding abrupt changes near mode cutoffs.
• The 1/λ² fit to mode count, when scaled by 87%, closely matches full simulation results, validating its use as a proxy for throughput estimation.
• Cavity walls with rough mechanical finishes induce parasitic ohmic losses; using a polished Si surface with sputtered Au coating eliminates these currents.
• Eliminating the cavity and using a flat backshort reduces pixel-to-pixel response variation and suppresses inter-pixel crosstalk by preventing wall currents.