Studying the properties of gravitational waves under the lens of Photonics

Gravity and Electromagnetism share many similarities: the particle responsible for the force obey the wave equation, are massless, and have 2 degree of polarisations. The main difference is their spin: the photon is spin 1, whilst the graviton is spin 2.
The project of the PhD is to understand which electromagnetism results holds for linearised gravity and vice versa. So far, we have studied:
a) The properties of spin from a more theoretical perspective, with a decomposition motivated by electromagnetism.
b) The equivalent of polarisation singularities for gravitational waves. Polarisation singularities happen when the polarisation takes a more "symmetric" shape, like linear or circular polarisation. These singularities are sturdy to deformation because of their topological nature.
A future direction would be to understand the sum of polychromatic gravitational waves, more precisely the fact that polarisation draws Lissajous type figure, in analogy with the paper "Knotting fractional-order knots with the polarization state of light" by Emilio Pisanty, currently working at Kings College. We also aim to understand the underlying rotation symmetry in the case of gravitational waves.
c) The polarisation of the CMB. The Cosmic Microwave Background is comprised of photons from the last scattering surface, which have an intensity but also polarisation information. As of the last 15 years, there have been a massive effort in the scientific communities to measure precisely the polarisation of the CMB. A big issue is the calibration of polarimeters, and we are proposing a new method to calibrate precisely instruments without relying on external sources. So far, results are promising, it seems like our method of calibration is a cost-free, model-independent way of recalibrating older instruments using the current flagship of calibration (Simons observatory).