1. Purdue University Femtosecond CARS Spectroscopy of Gas-Phase Transitions: Theory and Experiments Prof. Robert P. Lucht School of Mechanical Engineering Purdue University and The Institute for Quantum Studies Texas A&M University TAMU/Princeton Summer School on Quantum Optics and Molecular Spectroscopy Casper, Wyoming July 16, 2007

2. Purdue University Acknowledgments Sukesh Roy, Innovative Scientific Solutions, Inc., Dayton, Ohio Terrence Meyer, Iowa State University Jim Gord, Air Force Research Laboratory, Wright-Patterson AFB Paul Kinnius, PhD Student, Purdue Funding Support from NSF, AFOSR, DOE/BES

3. Purdue University Fsec CARS for Gas-Phase Diagnostics Nsec CARS using (typically) a Q-switched Nd:YAG laser and broadband dye laser is a well- established technique for combustion and plasma diagnostics Fsec lasers have much higher repetition rates than nsec Q-switched Nd:YAG lasers: > 1 kHz versus ~10 Hz But can we obtain a sufficient signal on a single laser shot to make measurements in turbulent environments? And how do we extract temperature and concentration from the signal?

4. Purdue University Fsec CARS for Gas-Phase Diagnostics Fsec CARS for H 2 and N 2 has been demonstrated by Motzkus, Beaud, Knopp and colleagues primarily as a spectroscopic tool. For application as a diagnostic in turbulent flames, signal levels must be high enough to extract data on a single laser shot from a probe volume with maximum dimension ~ 1mm. How effectively can Raman transitions with line width ~ 0.1 cm -1 line width be excited by the fsec pump and Stokes beams (200 cm -1 bandwidth)?

5. Purdue University Potential Advantages of Fsec CARS Data rate of 1-10 kHz (yet to be demonstrated) would allow true time resolution, study of turbulent fluctuations Data rate of 1-10 kHz as opposed to 10 Hz would decrease test time considerably Fsec CARS, unlike nsec CARS, is insensitive to collision rates even up to pressure > 10 bars Fsec CARS signal increases with square of pressure

6. Purdue University Laser System for Fsec CARS

7. Purdue University Optical System for Fsec CARS

8. Purdue University Calculated Time Dependence of CARS Intensity with Time-Delayed Probe Beam

9. Purdue University Calculated Time Dependence of CARS Intensity with Time-Delayed Probe Beam At t = 0 psec, all Raman transitions oscillate in phase = giant coherence At t > 20 psec, Raman transitions oscillate with random phases

10. Purdue University Calculated Time Dependence of CARS Intensity with Time-Delayed Probe Beam

11. Purdue University Calculated Time Dependence of CARS Intensity with Time-Delayed Probe Beam

12. Purdue University Fs CARS Experimental Results: Flame Temperatures Equivalence ratio  is a measure of the actual fuel-air ratio to the stoichiometric fuel-air ratio.

13. Purdue University Fs CARS Experimental Results: Flame Temperatures

14. Purdue University Theory for Fitting Time-Delayed Probe Fs CARS Data Input parameters from spectroscopic database Fitting parameters

15. Purdue University Fs CARS Experimental Results: Flame Temperatures Fit temperatures are in excellent agreement with calculated adiabatic equilibrium temperatures.

16. Purdue University Fs CARS Experimental Results: Concentration Effects Nonresonant peak allows in-situ calibration of resonant CARS signal.

17. Purdue University Optical System for Single-Pulse Fs CARS with Chirped Probe Pulse Lang and Motzkus, 2002 Sukesh Roy (ISSI): High-Repetition Rate Gas-Phase Temperature Measurements in Reacting Flows Using Femtosecond CARS Spectroscopy (21:30)

18. Purdue University Numerical Model of Fs CARS in N 2 A model of the CARS process in nitrogen based on direct numerical integration of the time-dependent density matrix equations has been developed. Model is nonperturbative and is based on direct numerical integration of the time- dependend density matrix equations.

19. Purdue University Numerical Model of N 2 CARS CARS process is modeled using a fictitious electronic level as the intermediate level in the Raman process. The transition strengths are adjusted to give the correct Raman cross section.

20. Purdue University Time-Dependent Density Matrix Equations for the Laser Interaction Rate of change of population of state j: Time development of coherence between states i and j: Coupling of laser radiation and dipole moment for states j and m:

21. Purdue University Time-Dependent Density Matrix Equations for the Laser Interaction The off-diagonal density matrix elements are written in terms of slowly varying amplitude functions and a term that oscillates at the frequency or frequencies of interest for each term: The envelope functions and polarizations for the pump, Stokes, and probe beams are specified.

22. Purdue University Calculation of the Raman Coherence Time-dependent density matrix equations for coherence amplitudes (after application of the rotating wave approximation): The two-photon Raman coherence operates through intermediate states k. States e and g are not single-photon coupled. The laser interactions terms are defined by the following and similar equations:

23. Purdue University Numerical Results for 100 Fs Pulse J e = J g = 8  Raman = 0.05 cm -1 Stokes Irrad = 10xPump Irrad

24. Purdue University Numerical Results for 70 Fs Pulse J e = J g = 5  Raman = 0.05 cm -1 Stokes Irrad = Pump Irrad

25. Purdue University Comparison of Raman Excitation for 70 Fs Pulses, Peak Irradiance 2x10 18 W/m 2 J e = J g = 5  Raman = 0.05 cm -1 Stokes Irrad = Pump Irrad

26. Purdue University Comparison of Raman Excitation for 70 Fs Pulses, Peak Irradiance 10 19 W/m 2 J e = J g = 5  Raman = 0.05 cm -1 Stokes Irrad = Pump Irrad

27. Purdue University Comparison of CARS Signal for 70 Fs Pulses Stokes Irrad = Pump Irrad = 10 19 W/m 2 Stokes Irrad = Pump Irrad = 5x10 17 W/m 2

28. Purdue University Raman Excitation for 70 Fs Pulses Despite the drastic difference in laser bandwidth (200 cm -1 ) and Raman line width (0.05 cm -1 ), the 70-fsec laser pulse excites the Raman transition very effectively. The 70-fsec pulse couples very effectively with the Raman transition because the Raman coherence is established by a two- photon process. The Q-branch transitions are excited to the same extent with the same initial phase

29. Purdue University Coupling of 70-Fs Pump and Stokes Pulses with the Raman Coherence

30. Purdue University Phase of the Raman Coherence for Different Transitions Stokes Irrad = Pump Irrad is different for each of the different Q- branch transitions.

31. Purdue University Coupling of 70-Fs Pump and Stokes Pulses with the Raman Coherence Stokes Irrad = Pump Irrad

32. Purdue University Simultaneous Fs CARS for CO (2145 cm -1 ) and N 2 (2330 cm -1 ) The 180 fs spacing of the modulation in the probe delay scan corresponds to the 185 cm -1 frequency difference in the N 2 and CO Raman bands.

33. Purdue University Simultaneous Fs CARS for CO (2145 cm -1 ) and N 2 (2330 cm -1 ) The pump wavelengths for Raman resonance for N 2 and CO are 675 nm and 682 nm, respectively.

34. Purdue University Conclusions Initial fs CARS measurements show that temperature and concentration can be determined from temporal dependence of CARS signal in the first few fsec after “impulsive” pump-Stokes excitation. Measured flame temperatures appear to be very accurate. Fsec CARS offers some distinct (potential) advantages compared to nsec CARS  1 kHz data rate or greater  Impulsive excitation, strong coherence at short time delays  No effect of collisions for short time delays  You can see the fsec CARS signal from room air