Development of a stabilized Ti:Sa frequency comb for frequency comparisons at high stability in the optical region

This dissertation describes the development of a self-referenced optical frequency comb (OFC) based on a Ti:Sa femtosecond (fs) laser, to be employed in frequency comparisons between a strontium optical lattice clock and other frequency references, both in the radio-frequency (RF) and in the optical domain. The Ti:Sa mode-locked laser, which employs external fiber broadening (EB) for the generation of octave-spanning spectrum, has been stabilized by locking an OFC tooth to a clock laser with high spectral purity, operating at 698 nm and resonant with the clock transition $^1$S$_0$-$^3$P$_0$ in neutral strontium atoms. The frequency stability of this EB OFC has been tested both in the RF domain by comparison with a high-quality quartz oscillator slaved to the global positioning system (GPS) signal, and in the optical domain with a second stabilized diode laser at 689 nm slaved at long term to the intercombination transition $^1$S$_0$-$^3$P$_1$ in atomic strontium. We perform a frequency noise and intensity-related dynamics characterization of the free-running fs Ti:Sa EB OFC and implement these results for optimizing the phase--lock of the OFC to a Hz-wide 698 nm semiconductor laser. Based on the frequency noise of the beatnote between the clock laser and corresponding EB OFC tooth $f_{b698}$ we expect that the short term frequency stability of the 698 nm clock laser is then transferred to each tooth of the octave-spanning EB OFC. Moreover, the noise transfer processes between the pump laser and the Ti:Sa laser have been studied in detail, both comparing the resulting frequency noise of the EB OFC output spectrum with a single-mode Coherent Verdi V5 and a multi-mode Spectra Physics Millennia Xs 532 nm pump lasers. In particular, in the latter case we demonstrate that the implementation of an additional control loop for the stabilization of carrier-envelope offset (CEO) frequency $f_{CEO}$ allowed us to stabilize this signal at mHz level, that is compatible with $f_{CEO}$ stabilization results with the single-mode pump laser case. Moreover, we show that, with our optical standard operated at a wavelength 698 nm the impact of $f_{CEO}$ frequency noise on the frequency noise of any EB OFC tooth is negligible when compared with the frequency noise of the $f_{b698}$. Despite the OFCs are used typically for precision frequency measurements, we demonstrate an approach to perform an absolute frequency measurement of unstable frequency by the EB OFC. Most of this thesis is devoted to the EB OFC. However, I also present characteristics and our first stabilization results of the OFC working at quasi octave-spanning regime