# Generation of Ultrafast Optical Pulses via Molecular Modulation in Ambient Air
## 1 Introduction  
Broadband pulse light sources, such as a Ti:Sapphire laser and other femtosecond (fs) laser systems, enable a range of important applications, such as nonlinear and time-resolved spectroscopic studies of molecular dynamics and chemical reactions [1; 2; 3; 4], coherent anti-Stokes Raman scattering spectroscopy [5], and even laser annealing [6]. In addition, ultrashort optical pulses in the deep ultraviolet (DUV) region can be used for the resonant and non-resonant multi-photon ionization of molecules in mass spectrometry, which can be applied to improve reliability in forensic science [7; 8]. However, for studying fast processes in atoms and molecules, such as electron movement [9], one needs a source of coherent radiation producing pulses on the order of several fs or even beyond that [10].  
Production of ever-shorter light pulses requires generation of an emission with an ever-wider coherent bandwidth and careful control of the phases. One of the methods for generating ultrabroadband spectrum is termed molecular modulation [11; 12; 13]. Several demonstrations of the ultrabroadband light source have been reported, i.e., the generation of more than 40 emission lines with a picosecond laser in hydrogen gas [14] and more than one-octave spanning spectrum of carrier-envelope controlled Raman sidebands [15]. Such multi-emissions can be employed not only as an ultrabroadband laser system, but also as a source of ultrashort optical pulses if the phases of the multiple molecular modulation sidebands can be properly controlled. Manipulation of the relative phases is typically possible with a spatial light modulator (SLM) [16] or a spatial phase controller [17]. Then, the resultant temporal waveform can be measured by, for example, cross-correlation signals in Xe gas [18].  
In this work, we used a picosecond laser system to demonstrate molecular modulation in ambient air. We utilized a collinearly focused pump and Stokes beams with the optical frequencydifference matching a vibrational transition of nitrogen molecules. In a relatively simple experimental configuration we produced a broad spectrum of multiple mutually-coherent narrow-band components, and demonstrated control over the spectral phases of these components. The adjustment of the spectral phases was done without separating the spectral components spatially, but rather by adjusting an overall dispersion via varying the optical path in glass. Furthermore, the diagnostics of the resultant pulsed waveform was performed by refocusing the multi-component beam into the second interaction region and utilizing molecular modulation in air the second time.  
In the following we describe the procedure for generating multiple coherent Raman sidebands in air using the vibrational mode of the nitrogen molecule at 2331 cm\({}^{-1}\). We then demonstrate how the relative phases of the sidebands can be controlled by a pair of rotating glass plates. Finally, we determine the phases of the Raman sidebands and estimate the temporal waveform of the generated ultrashort pulses by monitoring the optical spectrum of the third anti-Stokes sideband (AS3) with a spectrometer.