Do gravitational waves disperse/refract (like EM waves in a prism)?

Question

I have read this question:

What is the relationship between a gravitational wave and a graviton?

where kingledion says:

Gravitational waves were theorized a century ago and recently discovered, leading to the awarding of the 2017 Nobel Prize in Physics. According to Wikipedia: Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation.

Why do prisms work (why is refraction frequency dependent)?

where Ben Crowell says:

What is actually observed is the superposition of this wave with the incident wave. This superposition has two parts, a reflected wave and a transmitted one. In the limit of a low-density medium (such as a gas), the index of refraction is given by n2=1−ω2pf(ω), where ωp, called the plasma frequency, is given by ω2p=Ne2/mϵ0, where N is the number density of electrons. The plasma frequency has an e/m in it from the amplitude of the driven harmonic oscillator, and another factor of e because the amplitude of the reemitted wave is proportional to the amount of charge oscillating. In the case of silica glass, I think the 0.1 μm resonance is probably what is described by the above mechanism, while the other resonances are similar mathematically but involve other effects than oscillation of bound electrons. E.g., the Si-O-Si bridges would resonate at a lower frequency due to the greater inertia of the nuclei compared to electrons. The above does seem to suggest that there's some very universal behavior going on in the interaction of EM waves with matter.

where annav says:

A photon impinging on the surface of the lattice, finds not two slits , but a depth of slits all the way through. The observed effect of the different angular distribution according to the impinging frequency of the photon must be the result of the quantum mechanical interference of the photon, which must be constructive in the angle of refraction given by its frequency and index of refraction and destructive everywhere else, otherwise we would be seeing interference fringes ( actually we do get a second rainbow, but that is a different story :) , though should be similar). Then the problem is reduced to explaining the frequency dependence. I will hand wave again and say that the smaller the frequency the larger the distances in the interference pattern of the probability wave ; the photon will see the lattice gaps differently according to its wavelength, as is true for the double slit experiment, so a fanning out is to be expected.

Now there is a classical and a QM explanation both for dispersion/refraction of EM waves/photons through a prizm.

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.n optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light,2 as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses.The most familiar example of dispersion is probably a rainbow, in which dispersion causes the spatial separation of a white light into components of different wavelengths (different colors).

https://en.wikipedia.org/wiki/Dispersion_(optics)

Now even in the classical explanation of EM waves', it is easily explainable why the wavelength of different EM waves creates the dispersion we see in a prizm.

Now GW have been experimentally observed, they do exist.

I have not found anything about whether GWs do get dispersed based on their wavelength. Some GWs have their own specific wavelength, and some must be a combination of different wavelength waves (just like white light is a combination of all visible wavelength EM waves).

Now if we already observed GWs, did we observe their dispersion, they must obey the same physical laws, and they must undergo dispersion, as they change media.

The phase of gravitational waves in the dispersive case and non-dispersive case and dephasing between two waveforms. The total Mass M=106 M⊙, the symmetric mass ratio ν=10−5, e=0.5, p=12M and a=0.9. We set DL=1.00 Gpc, where Z≈0.20 and D≈0.83 Gpc. The Compton wavelength of graviton λg=1.6×1013 km. The cyan, orange and red curves represent the non-dispersive's, dispersion's phase and dephasing respectively.

In principle, gravitational waves could exist at any frequency. However, very low frequency waves would be impossible to detect and there is no credible source for detectable waves of very high frequency.

https://en.wikipedia.org/wiki/Gravitational_wave

http://inspirehep.net/record/1708562/plots

Question:

1. Do GWs disperse at the edge of different media (like EM waves in a prizm)?

2. Have we ever experimentally seen different wavelength GWs disperse at the edge of different media?

Answer 1

In physics we call waves to any physical perturbation of some quantity that propagates through space or time or or both and that obeys D'Alembert's wave equation or some generalization of it.

This equation doesn't care about the perturbation been on the water (ocean waves), on the pressure of air (sound waves), on the mechanical stresses of Earth's crust (sismic waves), on the field lines of the electromagnetic field (light) or on the curvature of space-time (gravitational waves). For a fixed number of dimensions this equation yields the same predictions for all of them. There can be polarization, difraction, refraction, coherence, reflection and other phenomena, the only major difference is what devices or physical systems should be the ones responsible for those.

Gravitational waves differ from electromagnetic waves in some fundamental aspects. For example; the straing of a gravitational wave depends on $r^{-1}$ while the intensity of light depends on $r^{-2}$ (where $r$ is the distance of the detector from the source). There is also the fact that matter is transparent to gravitational waves of any frequency. But still we can rescue some of the shared phenomenology.

We now know that gravitational waves with microwave frequencies (still as high for any known astrophysical phenomena) can be reflected from thin superconducting films. The gravitational waves move matter and matter that changes its motions generates gravitational waves, the over all effect can yield a coherent reflection from these films (just like electromagnetic waves reflect because the oscilating electric field moves charges in the mirror and in turn those generate their own electromagnetic waves).

See this research paper: Do Mirrors for Gravitational Waves Exist?

It is also known that light can move in non-straight paths on curved geometries of space-time. For example light can make a full circle around a black hole in what is known as the photon sphere. And it is also known that there are even solutions where a light ray can come back to the emmiting source after circling the black hole.

So, the surroundings of a black hole can act like a mirror (you can see yourself). The same goes for gravitational waves, they get diffracted so much that could go back to where it came. Thus black holes are mirrors for larger gravitational waves, just a very complicated mirror with a weird distorted image of yourself. By the way, the animation comes from a series of videos done by Viascience (highly recommended).

The search for echoes (like those of sound waves) by reflections of gravitational waves on certain space-times that could behave as "walls" has been investigated.

See this research paper: Gravitational wave sources: reflections and echoes

Diffraction of gravitational waves can happen in stellar clusters so maybe we could use those as your "prism"

See this research paper: Emission of gravitational waves from binary systems in the galactic center anddiffraction by star clusters

In fact the idea of diffracting gravitational waves can be extended to focus them. We can immagine some astrophysical objects as analogous to optical elements in an optical system. If we focus gravitational waves we can make gravitational telescopes (and not just observatories). In fact black holes not only can magnify light sources far away but also can magnify gravitational waves, this phenomenon is called gravitational lensing of gravitational waves and there are some papers exploring the subject.

See this research paper: Gravitational lensing of gravitational waves: wave natureand prospects for detection

See this research paper: Gravitational lensing of gravitational waves: A statisticalperspective

See this research paper: Effect of gravitational lensing on the distribution of gravitational waves from distant binary black hole mergers

See this research paper: Wave Effects in Gravitational Lensing of Gravitational Wavesfrom Chirping Binaries

Answer 2

Gravitational waves are a disturbance in space and time and move by penetrating space-time so no refraction occurs. The wavelength of gravity waves is much shorter than electron and protons.