## 2 Molecular Modulation
### Molecular Modulation with CW Lasers  
Despite these exciting experiments, molecular modulation technique as demonstrated in these experiments has significant limitations and has not yet made a big impact on other research areas. The required laser intensities for preparing the molecules into a maximally coherent state is quite high, exceeding 100 MW/cm\({}^{2}\). As a result, all of those molecular modulation experiments described in the previous paragraph have been performed using Q-switched pulsed lasers, which have important limitations. The duty cycle of these lasers is low, less than 1 part in \(10^{7}\), which severely restricts data rates. Furthermore, each sideband has a minimum linewidth that is determined by the duration of the Q-switched pulse, 1/(10 ns) \(\approx\) 100 MHz. This is an important limitation for precision spectroscopy experiments where the transitions studied may have linewidths on the Hz level. To overcome these limitations, it is important to extend the molecular modulation technique to the CW domain.  
For extending the technique to the CW domain, two approaches are promising. One approach is to utilize the tight confinement of hollow-core photonic crystal fibers, an approach that has been studied by [PERSON] and colleagues [46]. In contrast, our approach is to place the molecules inside a cavity with high finesse at the pump and at the Stokes wavelengths, as shown in Figure 1b. When the cavity resonance condition is simultaneously satisfied for both laser beams, high intensities build up inside the cavity and the molecules are driven to a highly coherent state. If the pump and the Stokes beams are  
Figure 1: **(a)** Simplified energy level diagram. Two intense lasers, the pump and the Stokes, drive the Raman transition and establish the molecular coherence, \(\rho_{ab}\). The molecules can then be used to modulate any other mixing laser with frequency \(\
u_{0}\) to produce frequency upshifted or downshifted sidebands at frequencies \(\
u_{0}+\
u_{M}\) and \(\
u_{0}-\
u_{M}\), respectively. With the polarization configuration as shown, only a frequency upshifted sideband is produced. **(b)** Molecular modulation with CW laser beams. The molecules are placed inside a cavity with a high finesse at the pump and at the Stokes wavelengths. For a sufficiently large molecular coherence, any mixing laser incident on the cavity will be modulated. The mixing beam does not need to be resonant with the cavity as the modulation is produced in a single pass through the system.  
linearly polarized, higher-order Stokes and anti-Stokes beams from the driving lasers will be produced. A separate weaker mixing laser can also be modulated in a single pass through the system. Our scheme was motivated by the recent pioneering experiments of [PERSON] and colleagues that have demonstrated CW Raman lasing of the Stokes beam inside a high-finesse cavity [21; 22; 23; 24; 25; 26; 35]. We have extended these experiments to the regime of sufficiently high coherence such that significant modulation can be produced in a single pass through the system. As a result, the mixing beam does not need to be resonant with the cavity, and any optical wavelength can be modulated. This broadband modulation capability is critical, as it may allow for the broadening of the already broad spectrum of a Ti:sapphire oscillator.