## 5 Modulation of a Femtosecond Ti:sapphire Oscillator  
One of the main motivations for extending molecular modulation to the CW domain is that it would allow combining this technique with femtosecond Ti:sapphire laser technology. The idea is that the modulator can be used to efficiently generate sidebands on a femtosecond oscillator to produce a broad spectrum with a large number of spectral components. This scheme was first suggested by [PERSON] _et al._[53], and was later experimentally demonstrated with Q-switched pulsed lasers by [PERSON] and colleagues [54; 55; 56]. Consider a broadband laser with power spectral density \(F(\
u)\). If this laser goes through a molecular medium that is prepared in a highly coherent state, modulation produces sideband \"replicas\" of the spectrum spaced from the original by the modulation frequency. The first Stokes and anti-Stokes sidebands will produce replicas \(F(\
u-\
u_{M})\) and \(F(\
u+\
u_{M})\), the second orders will produce \(F(\
u-2\
u_{M})\) and \(F(\
u+2\
u_{M})\), and this process could continue until the spectrum fills the full optical  
Figure 5: The power of the 807 nm anti-Stokes beam as a function of two-photon Raman detuning, \((\
u_{pump}-\
u_{Stokes})-\
u_{ab}\), at a D\({}_{2}\) gas pressure of 0.01 atm. At these low pressures, Doppler broadening is the dominant contribution to the linewidth. The two-photon detuning is varied by locking either the pump or the Stokes beam to a different cavity mode. As a result, the data points are spaced in frequency by the free spectral range of the cavity, which is 200 MHz. range. Figure 6 shows how the scheme works for a typical broadband Ti:sapphire laser oscillator with a spectrum that spans from about 700 nm to 900 nm in wavelength. In this qualitative calculation, we use the vibrational transition in D\({}_{2}\) (\(\
u_{M}=90\) THz) to produce sidebands and broaden the Ti:sapphire spectrum. To show the effect more clearly, we assume 60% conversion efficiency to each sideband, although as mentioned above, in the near future, we will aim for about 10% conversion efficiency with \(|\rho_{ab}|\approx 0.01\). Intensity spectra (in linear scale) for the incident Ti:sapphire beam and for first, second, and third order modulation are shown. A key advantage of this approach, and the feature that sets it apart from similar previous work, is that since the molecules are prepared with two CW lasers, the linewidth of the molecular oscillations can be made very narrow. When the two driving lasers are locked to the high-finesse cavity, their linewidths can be narrowed to values much smaller than 1 kHz. This also sets the linewidth of the molecular oscillations (_i.e._, the precision in the value of \(\
u_{M}\)). As a result, the mixing process will not significantly affect the spectral characteristics of the individual comb lines of the Ti:sapphire oscillator. Many of the ideas and experiments that use stable Ti:sapphire comb lines may be performed with the much broader spectrum of Figure 6. We also note that the broad output spectrum of Figure 6 can form a phase-stabilized frequency comb. This can be accomplished by adjusting the modulation frequency \(\
u_{M}\) to be an exact integer multiple of the comb-spacing of the Ti:sapphire laser. The modulation frequency is precisely set by the frequencies of the pump and the Stokes laser beams, \(\
u_{M}=\
u_{pump}-\
u_{Stokes}\). The pump and Stokes laser beams can, for example, be locked to two teeth of a separate phase-stabilized frequency-comb oscillator. We note that throughout this section, we have assumed the Ti:sapphire laser to be sufficiently weak such that it does not interfere with the molecular state preparation. This assumption is satisfied for a  
Figure 6: Broadening the spectrum of a Ti:sapphire laser using the vibrational transition in D\({}_{2}\) with \(\
u_{M}=90\) THz. Starting with a typical broadband laser with power spectral density, \(F(\
u)\), replicas of the spectrum spaced by the Raman transition frequency are produced.