Regimes in astrophysical lensing: refractive optics, diffractive optics, and the Fresnel scale

TL;DR

This paper revises the understanding of astrophysical lensing regimes, showing that the true separation scale depends on the lens convergence and that refractive optics can apply at smaller scales than previously thought, with implications for scintillation studies.

Contribution

It introduces a generalized approach using Picard-Lefschetz theory to accurately evaluate diffraction integrals across all wave parameters, redefining the separation scale between lensing regimes.

Findings

The true separation scale is R_F / sqrt(κ), not R_F.

Refractive optics can apply at arbitrarily small scales for strong lenses.

Intensity variations in diffractive optics are generally small.

Abstract

Astrophysical lensing has typically been studied in two regimes: diffractive optics and refractive optics. Diffractive optics is characterized by a perturbative expansion of the Kirchhoff-Fresnel diffraction integral, while refractive optics is characterized by the stationary phase approximation. Previously, it has been assumed that the Fresnel scale, $R_F$ , is the relevant physical scale that separates these two regimes. With the recent introduction of Picard-Lefschetz theory to the field of lensing, it has become possible to generalize the refractive description of discrete images to all wave parameters, and, in particular, exactly evaluate the diffraction integral at all frequencies. In this work, we assess the regimes of validity of refractive and diffractive approximations for a simple one-dimensional lens model through comparison with this exact evaluation. We find that, contrary to previous assumptions, the true separation scale between these regimes is given by $R_F / \sqrt{\kappa}$, where $\kappa$ is the convergence of the lens. Thus, when the lens is strong, refractive optics can hold for arbitrarily small scales. We also argue that intensity variations in diffractive optics are generically small, which has implications for the study of strong diffractive scintillation (DISS).