Beam tube boundary effects in stray light modeling of long Fabry-Perot arm cavities for third-generation gravitational-wave detectors

TL;DR

This paper introduces a waveguide-like mode description to incorporate beam tube boundary conditions in modeling stray light in long Fabry-Perot cavities, validating FFT-based tools for third-generation gravitational-wave detectors.

Contribution

It develops a mode-based approach to include boundary effects, providing a benchmark for FFT tools and analyzing the impact of boundary conditions on stray light coupling.

Findings

Boundary effects are suppressed with increased baffle density.

Strain coupling from defects is small in dense baffling regimes.

FFT-based models remain valid for 3G detector design.

Abstract

Next-generation gravitational-wave detectors such as Cosmic Explorer and the Einstein Telescope will operate 10-40 km Fabry-Perot arm cavities inside vacuum beam tubes. FFT-based paraxial tools treat propagation in free space and therefore do not explicitly enforce beam tube boundary conditions. We introduce a waveguide-like mode description of the optical field that incorporates an imposed beam tube boundary condition and enables an independent benchmark of free-space FFT tools We derive the associated modal-mixing matrices for mirrors and baffles, including a closed-form series for axisymmetric circular apertures. We quantify the strain-equivalent couplings from baffle miscentering and from a localized near-wall tube defect, and show that they are suppressed as baffle density increases. In the relevant regime of densely baffled cavities and small perturbations, beam tube boundary effects are subdominant, which supports the continued use of FFT-based codes to guide the design of 3G detectors.