A novel technique for laser mode-matching in gravitational wave detectors

Current interferometric gravitational wave detectors were designed to be limited, in much of their sensitive band, by quantum noise in the form of shot noise (at high frequency) or quantum radiation pressure noise (at low frequency). In the current observation run (O3), a squeezed light source has been used to manipulate quantum noise and surpass the limits imposed by the circulating laser power by injecting nonclassical states of the electromagnetic field, called squeezed vacuum states, in the interferometer's dark port. Recent O3 results show that this technique was able to reduce the shot noise contribution to the noise spectral density by about one half. To surpass the so called standard quantum limit across the entire sensitivity band, an even more complex variation of this technique will be implemented, which requires the use of a so called “filter cavity” to reflect the squeezed quantum field and rotate the squeezing angle as a function of frequency. The performance of this techniques is however severely limited by light losses. One big contributor to optical losses is the mismatch between the squeezed vacuum beam, the beam circulating into the interferometer and, in the near future, the filter cavity fundamental transverse spatial mode. To be able to monitor and actively correct mode mismatch, an accurate, online sensing technique is needed. A possible solution consists in the introduction of an Electro-Optic Lens (EOL) that can induce radio-frequency sidebands in the Laguerre-Gauss 10 (LG10) transverse mode of the beam. If the modulation frequency is tuned in a way that one sideband is at the cavity LG10 frequency, then the resonance breaks the symmetry of the two sidebands and converts phase modulation into amplitude modulation, making it possible to retrieve an error signal directly from the cavity reflected electric field with the same single-element photodetector used for the Pound Drever Hall (PDH) locking technique. This error signal carries information about the magnitude and nature of the mismatch, providing all is needed to inform a dedicated feedback loop with a suitable actuator to maintain the mismatch at or below the 1% level. The goal of this thesis is to demonstrate the technique on a dedicated bench-top experiment employing an EOL prototype device. The EOL alignment and working point, as well as the cavity lock parameters were optimized in an already existing setup. Simulations and theoretical calculations of the cavity reflected field were performed to evaluate the system non-idealities: both Electro-Optic Modulator (for PDH technique) and EOL modulations effects and interactions, as well as some system imperfections were considered. The simulations confirm that this technique requires a stable cavity lock condition, and for this reason an accurate study and optimization of the feedback loop parameters was done. In conclusion, a characterization of the EOL error signal response to different mismatch conditions are presented.