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Polarization rotation through differential transmission in refractive CMB telescopes identified using a hybrid physical optics method

Xiaodong Ren, Rustam Balafendiev, Jon E. Gudmundsson

TL;DR

This work identifies a polarization-rotation systematic in refractive CMB telescope beams caused by polarization-dependent AR-coating transmission. It introduces a hybrid physical-optics framework that embeds full-wave AR-coating simulations as Jones matrices within the PO propagation, enabling accurate, efficient modeling of polarization response. The study finds that differential AR-coating transmission can produce polarization offsets up to about $0.3^ {\circ}$ in the 90/150 GHz bands (and up to $0.15^ {\circ}$ on-axis at 120 GHz), leading to temperature-to-polarization leakage of order $0.5\%$ in Mueller-beam analysis, especially near band edges. These results highlight critical design and calibration considerations for AR coatings in future CMB refractive optics to control systematic polarization rotation and leakage.

Abstract

We identify a polarization rotation systematic in the far field beams of refractive cosmic microwave background (CMB) telescopes caused by differential transmission in anti-reflection (AR) coatings of optical elements. This systematic was identified following the development of a hybrid physical optics method that incorporates full-wave electromagnetic simulations of AR coatings to model the full polarization response of refractive systems. Applying this method to a two-lens CMB telescope with non-ideal AR coating, we show that polarization-dependent transmission can produce a rotation of the far-field polarization angle that varies across the focal plane with a typical amplitude of 0.05-0.5 degrees. If ignored in analysis, this effect can produce temperature to polarization leakage and Stokes Q/U mixing.

Polarization rotation through differential transmission in refractive CMB telescopes identified using a hybrid physical optics method

TL;DR

This work identifies a polarization-rotation systematic in refractive CMB telescope beams caused by polarization-dependent AR-coating transmission. It introduces a hybrid physical-optics framework that embeds full-wave AR-coating simulations as Jones matrices within the PO propagation, enabling accurate, efficient modeling of polarization response. The study finds that differential AR-coating transmission can produce polarization offsets up to about in the 90/150 GHz bands (and up to on-axis at 120 GHz), leading to temperature-to-polarization leakage of order in Mueller-beam analysis, especially near band edges. These results highlight critical design and calibration considerations for AR coatings in future CMB refractive optics to control systematic polarization rotation and leakage.

Abstract

We identify a polarization rotation systematic in the far field beams of refractive cosmic microwave background (CMB) telescopes caused by differential transmission in anti-reflection (AR) coatings of optical elements. This systematic was identified following the development of a hybrid physical optics method that incorporates full-wave electromagnetic simulations of AR coatings to model the full polarization response of refractive systems. Applying this method to a two-lens CMB telescope with non-ideal AR coating, we show that polarization-dependent transmission can produce a rotation of the far-field polarization angle that varies across the focal plane with a typical amplitude of 0.05-0.5 degrees. If ignored in analysis, this effect can produce temperature to polarization leakage and Stokes Q/U mixing.
Paper Structure (10 sections, 7 equations, 7 figures)

This paper contains 10 sections, 7 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Optical Modeling Methods
  3. Hybrid Physical Optics Analysis for Refractive Optics
  4. Effective Polarization Angle of Far-field Beams
  5. A Two-lens CMB Telescope
  6. Simulations
  7. Accuracy of the hybrid PO method
  8. Spurious optical polarization
  9. Conclusions
  10. acknowledgment

Figures (7)

  • Figure 1: Schematic showing critical parameters used in a hybrid PO calculation for a lens with anti-reflection coating on both sides.
  • Figure 2: Optical schematic of the two-lenses telescope gudmundsson2020geometrical. The two lenses have a diameter of 300 mm and are constructed of HDPE. $C_{\mathrm{fp}}$ is the coordinate system on the focal plane. $C_{\mathrm{beam}}$ indicates the far-field coordinate system.
  • Figure 3: Transmission of the quarter-wave AR coating on HDPE for $s-$ (top) and $p$-polarization (bottom). Each panel shows the transmission as a function of frequency for incidence angles from $0^{\circ}$ (normal incidence) to $30^{\circ}$. The curve color indicates the incidence angle according to the colorbar. The coating has an effective refractive index of $n_\mathrm{AR}=1.23$ and a physical thickness of 0.51mm.
  • Figure 4: Far-field beam comparison of the two-lens optics at 120GHz obtained using hybrid-PO and MoM. Top panel shows the co- and cross-polarization beams for a feed at the focal-plane center. Bottom panel shows the corresponding co- and cx-polarization beams for a feed located at $x = 120mm$ in the focal planes.
  • Figure 5: Far-field beam polarization offsets of the HDPE two-lens optical system as a function of feed position for the 75-100 GHz and 130-180 GHz bands, and at 120 GHz. In the optical setup, the feed is rotated by $45^{\circ}$ about its symmetry axis to evaluate the polarization response.
  • ...and 2 more figures