Scalings for diffraction-decorated caustics in gravitational lensing

Abstract

In the astronomically natural transitional approximations for waves near caustics in gravitational lensing, the familiar wavelength scalings associated with short-wave asymptotics are accompanied by a variety of dependences on disparate astronomical lengths, such as the Schwarzschild radius, separation of binary stars, and distance to the lens. These dependences are calculated analytically for spacings of interference fringes and the corresponding intensity amplifications, for two much-studied models: lensing of a distant source by an isolated star and near the fold and cusp caustics from a binary star lens. If the aperture of a telescope looking in the direction of the source is modelled by Gaussian apodization, the image is a complexification of the wave in the observation plane.

Einstein beams and the diffractive aspect of gravitationally-lensed light

“…The next outer complete ring from the previous set of parameters coalesces into a set of lattice points forming a diamond, while the internal set of interferences fades, as shown in figures 4(b) and (c). It is also seen that the ends of the diamond are cusps due to a caustic fold [14,36]. The coalescing of rings into lattices proceeds as we increase the ellipticity further.…”

“…The pattern that we see with symmetric lensing has an axial caustic, and the Bessel rings are symmetric interference fringes. The asymmetry of the lens produces crossings of gravitationally deflected light that results in two-dimensional interference lattice points, or decorations [14]. In figure 4(a) we see the smallest effect of the elliptical perturbation: the coalescence of the first ring into four interference maxima aligned with the axes of the asymmetry.…”

“…The SLM deflects the light by imparting phase shifts on an incoming light beam. Gravitational-like deflection following equation (1) can be imparted onto the light by encoding a position-dependent phase [14,27]…”

“…The earliest inquiry into this question found that monochromatic light produced by a symmetric lensing object should have the approximate form of a Bessel function [10], or more precisely expressed in terms of confluent hypergeometric functions [11][12][13]. Beam patterns of asymmetric lenses should yield astroid caustics [8] bearing diffractive decorations [14].…”

Lensing of gravitational waves: universal signatures in the beating pattern

“…Despite the fact that the PML model has been widely used for both EM [1,2] and GW lensing [34-39, 41-46, 48-60], some issues still need to be clarified. In particular, the customary condition for the transition from wave optics to geometrical optics (GO) regimes [31,34,36,37], λ R S , breaks down near the caustic [33,35,63,64]. Indeed, when the source approaches the line of sight (a caustic point for the PML), the time delay between the images becomes infinitesimally small, which means one needs infinite frequencies to reach the GO limit.…”