Wave propagation in metamaterials mimicking the topology of a cosmic string

Abstract

We study the interference and diffraction of light when it propagates through a metamaterial medium mimicking the spacetime of a cosmic string, -a topological defect with curvature singularity. The phenomenon may look like a gravitational analogue of the Aharonov-Bohm effect, since the light propagates in a region where the Riemann tensor vanishes being nonetheless affected by the non-zero curvature confined to the string core. We carry out the full-wave numerical simulation of the metamaterial medium and give the analytical interpretation of the results by use of the asymptotic theory of diffraction, which turns out to be in excellent agreement. In particular we show that the main features of wave propagation in a medium with conical singularity can be explained by four-wave interference involving two geometrical-optics and two diffracted waves.

Lensing of gravitational waves: universal signatures in the beating pattern

“…It is also interesting to note that the Fresnel number (2.21) for the PML is independent of the distance from the lens to the observer, while in case of lensing on a topological defect like a cosmic string, it does depend on the distance [77][78][79][80].…”

Lensing of gravitational waves: universal signatures in the beating pattern

“…It is also interesting to note that the Fresnel number (21) for the PML is independent of the distance from the lens to the observer, while in case of lensing on a topological defect like a cosmic string, it does depend on the distance [55][56][57][58].…”

“…The lines of local maxima and minima in the interference pattern can be easily understood if we regard them as constant-phase lines (nodal and antinodal lines [57,58]) which appear due to interference between two GO rays. Indeed, to have constructive or destructive interference, the maxima and minima occur when the "optical path difference" c∆t 21 between the GO rays can be written in terms of wavelength λ as follows…”

“…The bottom horizontal axis shows the frequency in units of the source frequency ω0, while the top axis maps into a physical GW frequency in the LIGO/Virgo band for a specific choice of lens mass M = 250M . The upper envelope line (purple dots) joins the maxima [Eq (58)(59)…”

“…Similar to Fig.12for Fresnel number ν0 = 5/4 and source locations: (a) y = 0.5; (b) y = 0.3, where in both cases ν0 > νG, so the GO oscillations overlap with the ringdown principal peak. The upper envelope line (purple dots) joins the maxima [Eq (58)…”