Gravitational lensing of waves: Novel methods for wave-optics phenomena

Abstract

Wave-optics phenomena in gravitational lensing occur when the signal’s wavelength is commensurate to the gravitational radius of the lens. Although potentially detectable in lensed gravitational waves, fast radio bursts and pulsars, accurate numerical predictions are challenging to compute. Here we present novel methods for wave-optics lensing that allow the treatment of general lenses. In addition to a general algorithm, specialized methods optimize symmetric lenses (arbitrary number of images) and generic lenses in the single-image regime. We also develop approximations for simple lenses (point-like and singular isothermal sphere) that drastically outperform known solutions without compromising accuracy. These algorithms are implemented in (o); an accurate, flexible, and fast code. o efficiently computes the frequency-dependent amplification factor for generic lens models and arbitrary impact parameters in O(1ms) to O(10 ms) depending on the lens configuration and complexity. o is readily applicable to model lensing diffraction on gravitational-wave signals, offering new means to investigate the distribution of dark-matter and large-scale structure with signals from ground and space detectors. Published by the American Physical Society 2025