Single Shot Time and Frequency Resolved Four Wave Mixing Spectroscopy

  Time Resolved Four Wave Mixing (TR-FWM) is an excellent method for probing molecular vibrational dynamics on the femtosecond time scale.  Recently we discussed a 3-Dimensional forward propagating Boxcars geometry of three well collimated (unfocused) beams intersecting within a sample.  We have shown that the arrival time of each of the pulses to a particular location within the intersection region  determines the time delay between the pulses such that an image of the FWM signal generated in the different locations provides full information on the TR-FWM signal within a single laser shot [1].  Thus, each single shot experiment provides a time resolved signal, which in turn is Fourier Transformed to provide the frequency dependence of the FWM signal. We further showed [2] that the well collimated beams impose strict phase matching conditions on the generated FWM signal, thus enabling Phase Matching Spectral Filtering within the broad spectral width of the ultrashort pulses. Fig. 1a depicts the 3D geometry and the tuning of the Stokes angle δ and Fig.1b shows the observed (phase matched tuned) central frequency of the degenerate FWM signal.

Fig 1: a) 3-D forward propagating Box-CARS geometry b) Contour plot of Spectra of the signal taken as function of ,  Measured (circles) and calculated (solid line) central wavelengths c) Time resolved image of CHBr₃ taken at zero detuning  d) Multiplex power spectra at different center frequencies.  Each horizontal line is the Fourier Transform of a time resolved signal derived from a picture like part c

In order to obtain a full spectrally AND temporally resolved FWM signal, the experiment is repeated  for  different  angles.   For  each  angle,  an   image   is captured on the CCD  camera (such as Fig. 1c) from which the time resolved signal is derived and Fourier transformed.  Fig. 1d depicts a full two dimensional spectrogram over  a range of frequencies (Stokes angles). The horizontal axis is the Raman line frequency and the vertical axis is the Stokes angle δ calibrated in terms of the shift of the signal center frequency from the input laser frequency ( is equivalent to). A detailed analysis [2] shows that for CHBr₃ the combined time/frequency measurements allow unambiguous assignment of the observed lines and their identification as either fundamental modes or their beats.

The next step, presented here for the first time, is the amalgamation of these multiple experiments (each for a different tuning of the phase matched filter) into a single one. The experimental geometry was modified, such that instead of changing the input Stokes angle δ, now the Stokes beam (k₂) was gently focused by a cylindrical lens to the interaction region. Thus, the different directions (angles) were all present simultaneously, each giving rise to a signal centered at a different frequency and phase matched in a slightly different geometrical direction. The picture of the FWM signal as captured directly on the CCD camera (Fig. 2a) contains the entire range of input frequencies hitherto necessitating a series of different experiments with individually tuned input angles (compare to fig. 1c where a single input frequency is depicted). The method is demonstrated on liquid neat dibromomethane (CH₂Br₂). Fig 2b is equivalent to fig 1d, but this time it was obtained in a single laser shot.

Fig 2 a) Image of the captured signal. Different vibrational modes are spread out on the CCD camera. b) Power spectra of time and frequency  resolved images

Even for this relatively simple molecule, the data provides a wealth of information.  The symmetric double peak at  (peaking at  around zero detuning from the laser center frequency) points to two spectrally distinct spectroscopic pathways contributing to this signal. The double frequency signal at around zero detuning () is a result of the interference of these two pathways further supporting this interpretation [2].  The simultaneous observation of the entire spectrum allows not only the assignment of the observed beats to specific vibrational modes but also the identification of distinct contributions from various spectroscopic pathways.  As an example, the different modes on both sides of the line in Fig. 2a seem to suggest a well defined phase shift between these contributions.  The detailed interpretation will be discussed.

In conclusion, the ability to carry out fully time and frequency resolved measurement within a single laser shot opens the way to the addressing and spectral interpretation of complex molecules undergoing rapid photo-bleaching as is the case for many biological molecules.

 For further details please see:

[1] Y. Paskover, I. S. Averbukh Y. Prior, OE 15 (2007) 1700

[2] Y. Paskover, A Shalit Y. Prior, (2009) arxiv 0907.3625