Electro-optical lensing devices for RF sensing of cavity-laser mode-matching

Both current (Virgo, LIGO, KAGRA) and future (eg. ET, Cosmic Explorer) interferometric gravitational-wave detectors are designed to be limited in most of their sensitivity band by quantum noise, which occurs at low frequencies in the form of quantum radiation pressure noise and at high frequencies as shot noise. The state-of-the-art of gravitational-wave interferometers makes use of nonclassical states of the electromagnetic field, called squeezed vacuum states, injecting them in the interferometer's dark port. To fully exploit this technique and overcome the so-called standard quantum limit, these squeezed states must be controlled by reflecting them off detuned optical resonators, called filter cavities, which allow to optimize the squeezing angle as a function of frequency. The ultimate reduction in quantum noise is however severely limited by light losses, for which one of the main contributions is represented by the imperfect matching between the mode of the squeezed and bright beams, and the various cavities present in the interferometer, including the filter cavities. To be able to monitor and actively correct this issue, an accurate, online mode-matching sensing technique is needed. A sensing technique based on fast modulation of the Laguerre-Gauss 10 (LG10) mode is being developed by the ET-Virgo group in Padova, and it is based on an electro-optical lens (EOL), a device capable of changing its focal length at radio frequency. Similarly to the Pound-Drever-Hall locking technique, this generates sidebands whose beat signal with the carrier field reflected by the cavity contains information on the amount and type of mismatch. The aim of this thesis is to characterize and study the performance of different EOL designs on a dedicated bench-top experiment. In particular we will compare two different approaches: one is the direct modulation of LG10 modes; the other is the modulation of the Hermite-Gauss 02 and 20 modes and their subsequent conversion in LG10 mode by an appropriate cylindrical telescope.