Four-Wave Mixing (FWM)

The theory of degenerate four-wave mixing (DFWM) involves the third-order susceptibility tensor. In spite of the fact that higher order polarizations responsible for nonlinear optical phenomena are small, the signal intensities in the FWM process can be large, due to its strong dependence on laser power, concentration and interaction length. Moreover, nonlinear susceptibilities can be greatly enhanced if one or more of the interacting frequencies are close to a single or multiphoton transition. Two color four-wave mixing (TC-FWM) may be thought of as a resonant variant of coherent anti-Stokes Raman spectroscopy (CARS). A qualitative explanation of the phenomenon is that two beams (pump) interfere in the medium inducing macroscopic variations in the ground and excited state density and/or polarization of the molecular species, forming a Bragg grating. When the probe beam is resonant with a second transition (same in degenerate case) in the upper (in stimulated emission pumping (SEP) spectroscopy) or lower state (UP transition), it gets reflected off the grating and its direction is given by the Bragg phase-matching condition. The diagram below shows energy level diagrams for the three spectroscopic techniques aforementioned.

Although similar to CARS, FWM is resonant in nature and as such allows for stronger non-linear effects. Unlike LIF, the coherent nature of the signal allows rejection of scattered light and plasma emission by detection at large distances.

The experimental arrangement used for double resonance four-wave mixing is displayed next. The two Nd:YAG lasers are triggered electronically by a pulse generator. R are broadband dielectric reflectors, P is a prism, BS is a 50% broadband beamsplitter, SP are spatial filters, L is a 1000 mm lens and M is a mask. The photodiode (PD) triggers the oscilloscope which sends data to a computer. Control of the timing between lasers, valve opening and high-voltage (HV) pulse applied on the source electrodes is done with a computer analogical card. The signal I_s travels through a 4-meter path consisting of spatial filters, resulting in efficient elimination of scattered light and emission from plasma.

FWM techniques have been used for the measurement of electronic transitions of cold transient species generated in a supersonic slit-jet discharge expansion, with a s/n ratio of as low as 10⁴, thus the setup proves to be a sensitive approach for the detection of transient molecules in a molecular beam discharge.

Selected publications:

• Fabio J. Mazzotti, Ranjini Raghunandan, Aaseef Muhammed Esmail, Marek Tulej, and John P. Maier
  J. Chem. Phys., 134(16), 164303/1–7, 2011.
  Characterization of C₄H in the A²Π and X²Σ⁺ states by double resonance four-wave mixing
  
• Richa Chauhan, Fabio J. Mazzotti, Ranjini Raghunandan, Marek Tulej, Peter P. Radi, and John P. Maier
  J. Phys. Chem. A, 114(9), 3329–3333, 2010.
  Rotationally Resolved Ground State Vibrational Levels of HC₂S Studied by Two-Color Resonant Four-Wave Mixing
  
• Ranjini Raghunandan, Fabio J. Mazzotti, Richa Chauhan, Marek Tulej, and John P. Maier
  J. Phys. Chem. A, 113(47), 13402–13406, 2009.
  Selective Detection of Radicals and Ions in a Slit-Jet Discharge by Degenerate and Two-Color Four-Wave Mixing
  
• Fabio J. Mazzotti, Elena Achkasova, Richa Chauhan, Marek Tulej, Peter P. Radi, and John P. Maier
  Phys. Chem. Chem. Phys., 10(1), 136–141, 2008.
  Electronic spectra of radicals in a supersonic slit-jet discharge by degenerate and two-color four-wave mixing