Harmonics of femtosecond and continuous-wave radiation for precision spectroscopy: generation efficiency and spectral line shape
Precision spectroscopy in the UV and VUV ranges, including spectroscopy of the thorium-229 nuclear transition (148.4 nm), requires narrow-band sources obtained by frequency multiplication of stabilized lasers. Upon harmonic generation, the radiation intensity drops and the phase noise grows. In this work, both factors are analyzed for two types of primary sources: a continuous-wave single-frequency laser and a femtosecond optical frequency comb. It is shown that in the weak-conversion regime for equal average input powers, the power of the central mode in the spectrum of the Kth harmonic of femtosecond radiation matches the harmonic power of continuous-wave radiation for K=2 and noticeably exceeds it for K>2. Within the first-order dispersion approximation, group-velocity mismatch reduces the total conversion efficiency without affecting the power of the exactly phase-matched central mode. The transformation of the phase noise of an ultrastable laser upon harmonic generation leads to two effects that depend on K: the harmonic linewidth grows linearly, whereas the power fraction in the carrier decreases as a Gaussian function and is determined by the high-frequency noise of the stabilization loop (the servo bumps). Measurements of the phase-noise spectra of a laser stabilized to a Fabry-Perot cavity show that for a typical rms phase excursion of ~100 mrad the carrier loses about half of its power already at the eighth harmonic, while for a non-optimal stabilization-loop gain carrier collapse occurs at the second-third harmonic.