Four Wave Mixing Interferometry: Transient Grating and Two Dimensional

The previous sections have demonstrated how a femtosecond laser pulse is affected by the nonlinear parametric generation processes and transmission through dispersive media. Techniques used to reverse these effects and have all wavelengths arrive simultaneously at the sample were also introduced. This section will present the methods of four wave mixing interferometry which are used for pulse characterization and experimentation. First, the instrument used to undertake the two dimensional and transient grating spectroscopies in this dissertation will be presented since it is used for pulse characterization as well as experimentation on the samples. These experiments can be thought of as a more complicated version of pump-probe spectroscopy where a pump pulse excites a small fraction of molecules in an absorbing medium and then a probe pulse monitors the change in absorption induced by this excited state. The delay between pump and probe is scanned to observe how the system returns to equilibrium (steady state absorption). The key difference in these experiments is that the signal pulse is emitted in a background-free direction and there are two pump beams. A fourth beam (local oscillator, LO) is geometrically aligned (by the experiment) with the signal beam and allows for interferometric detection of emitted signal. A close-up picture of the view at the sample is shown in Figure 3.11

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Figure 3.11. The view of the nonlinear experiments employed in lab to highlight the differences with traditional pump probe spectroscopy. In pump probe spectroscopy, only two beams are utilized, a pump pulse and a probe pulse. Key features of this setup are background-free and interferometric signal detection. Three laser pulses (2 pump, 1 probe) induce signal emission.

There are a few approaches to Fourier transform 2DUV techniques. The first is a two-beam geometry based on pulse-shaping technology and is very similar to that shown in Figure 1.2(similar to pump probe geometry).49,69 The other is a passively-phase-

stabilized diffractive-optic-based interferometer employing four pulses, where one pulse is used as a reference for interferometric signal detection.52,70 The basic configuration of

the diffractive optics based interferometer is shown in Figure 3.12.

The key to interferometric stability is to generate pairs of phase-related pulses at the sample.71,72 Any instability in the reflections off of the spherical mirror cancel so the

setup is immune to noise associated with vibrations and thermal motion that would otherwise randomize the relative phase of the signal field and the laser pulse used as a reference beam. This geometry is preferred because in transient grating mode the setup can scan to hundreds of picoseconds delay between pump and probe pulses. Figure 2.11 in chapter 2 shows the standard method of pulse timing and naming of the delays.

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spectroscopy scans the delay between pulses 1 and 2, ττττ. Non-radiative transitions occur in T, the pump is absorbed in τ, and signal is radiated in

t

. Scanning τ is accomplished by inserting or removing glass in the path of the laser pulses through the

Figure 3.12. Basic schematic of the four wave mixing interferometer. Two pulses are sent into the setup with a mechanically controlled delay between them. The pulses are focused onto a diffractive optic to create the beam pattern shown on the mirror. The four beams are then sent to the sample (see Figure 3.11). Prism wedges are inserted into the paths of pulses 1 and 2 to control their relative delay. This delay is scanned in 2DUV experiments. All four beams are incident at the sample; pulses 1, 2, and 3 induce signal emission and pulse 4 is used as a reference field for interferometric detection of the signal. A typical interferogram is shown.

use of prism wedges as shown in Figure 3.12. The delay τ is typically scanned to 100 fs

τ < , as the signal decays with a time constant of roughly 50fs.52,70 The signal as a function of τ is then Fourier transformed at each detected pixel on the CCD detector to obtain the two dimensional spectra that are shown throughout this dissertation. 2D spectra can be taken at any pump-probe delay time T. Comparing the shape of 2D spectra (antidiagonal/diagonal line-width) as T varies reveals the timescale of solvent reorganization (solvation), vibrational cooling, and coherent vibrational motion.51,52,73,74

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Figure 3.13. Measured transient grating signal profiles as a function of pump probe delay. The left figure is taken with interferometric detection and the right with homodyne detection (i.e. collected without the local oscillator). The amplification of the signal with heterodyne detection is obvious. The observed modulation in the signal is due to coherent oscillation of the 800 cm-1 Raman active mode in cyclohexane.

Considering that the signal is interferometrically detected, it is necessary to separate the contribution of the reference field from the detected field so that only the third-order signal of interest remains. This method of signal collection is known as optical heterodyne detection (OHD). The measured interferogram is given by

2 2

( ) 2 ( ) cos( )

ref S ref S ref S

I = E + E t + E E t φ −φ (3.19)

where E_ref is the reference field, E_S( )t is the time dependent signal field, and φ_ref and φ_S are the phases of the reference and signal fields, respectively. 71,75 In the experiments

discussed herein, the reference field term is numerically removed through a Fourier transform/apodization routine. This routine Fourier transforms the measured interferogram into the time domain, selects the signal via a Gaussian apodization function, then Fourier transforms this signal back into the frequency domain. In the limit of the reference field intensity being much greater than the signal intensity (i.e.,

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2 2

( )

ref S

E E t ) the term E t_S( )2can be neglected, this is a typical case in the laboratory,. This reduces the measured signal intensity to the following

2 _{ref S}( ) cos( _{ref S})

I = E E t φ −φ (3.20)

Equation 3.20 shows that the measured interferogram is linear with respect to the signal field and the components of the phase of the reference field and signal are present. These components allow for full characterization of the signal field (i.e. separation into real and imaginary components). The real component of the measured signal is identical to the measured signals in pump-probe spectroscopy. Furthermore OHD amplifies the signal by a factor of 2 E_ref /E t compared to the homodyne signal (signal collected _S( ) without interferometric detection).75 Figure 3.13 demonstrates this by plotting the

acquired signal for cyclohexane as the pump-probe delay is scanned. The observed oscillations in time are due to coherent motion of the 800 cm-1 Raman active vibrational

mode of cyclohexane. The only change made between the two measurements was the reference field was blocked for homodyne signal collection. It is quite obvious that the observed signal-to-noise ratio in the case of interferometric detection is much better. Being able to resolve this particular vibrational coherence with such deep modulation requires a laser pulse with a duration that is at most half of the vibration period. The period of oscillation for this mode in cyclohexane is 42fs which is a strong internal check to ensure that the laser pulses are on the order of 20fs.

Now that the experimental setup and signal detection have been introduced, samples are ready to be studied and new physics explored. However, before measuring signals that carry information on relaxation dynamics of UV absorbent materials, the

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experimentalist must ensure that the laser pulse is properly compressed, well behaved, and ready for experimentation. The process of Frequency Resolved Optical Gating (FROG) allows the phase of the laser pulse to be determined by using the pump pulses as a ‘gate’ which induce signal generation in the four wave mixing experiment only when all three pulses are temporally overlapped in the sample.66 This process simply involves

placing a transparent medium at the sample position and scanning the pump-probe delay. When all pulses are overlapped in time and space in the sample, signal generation occurs. The signal profile as a function of delay is given by the spectrogram

(

)

( ) (

)

(

)

2 2 , exp TG FROG I ω T E t E t T i t dtω ∞ −∞ =

_∫

− − (3.21)

where the delay between pulses is given by T and it is assumed that all pulses are the same wavelength. Two pulses, E t

(

−T

)

2, act as a gating function for the third field, the probe pulse in Figure 3.11. Since the spectrogram is resolved in frequency and time, the phase of the pulse can easily be observed. A chirped laser pulse will show tilt in the spectrogram where a compressed pulse shows all wavelengths arriving simultaneously at the sample position. Measuring a FROG spectrogram allows the experimenter to determine is the laser pulse is compressed. Figure 3.14(a) shows a spectrogram of the compressed third harmonic pulse. Panel (b) is another plot of the interferometrically detected oscillations from cyclohexane.

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Figure 3.14. (a) Compressed third harmonic FROG spectrogram measured in the experimental setup with homodyne detection. All wavelengths arriving simultaneously (vertically aligned spectrogram) indicates proper pulse compression. (b) View of vibrational coherence of cyclohexane over a larger delay range than in Figure 3.13.

All of these studies utilize dynamic sample volumes to avoid damage from UV excitation. Studies on the DNA nucleobases presented in Chapter 4, 5, and 6 implement a low-noise rotating sample holder, modeled after that described in Reference76. The

sample holder enables the use of small sample volumes and can be adapted to the cryostat, which is useful for measurements at cryogenic temperatures. The transient grating measurements shown in Figure 4.4 demonstrate that motion of the sample causes fairly little noise in the signal phase. For example, with a peak power of 1.4GW/cm2,

signal-to-noise ratios of 350:1 at T=0.5ps and 38:1 at T=100ps in the absorptive transient grating signal component are obtained (the absorptive signal component is sensitive to phase noise). A gravity fed jet is utilized in Chapters 7 and 8. Section 7.2B contains background on this setup.

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