Femtosecond CARS Spectroscopy of Gas-Phase Transitions: Theory and Experiments

1. 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. 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. 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. Fsec CARS for Gas-Phase Diagnostics • Fsec CARS for H2 and N2 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 widthbe excited by the fsec pump and Stokes beams (200 cm-1 bandwidth)?

5. 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. Laser System for Fsec CARS

7. Optical System for Fsec CARS

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

9. 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. Calculated Time Dependence of CARS Intensity with Time-Delayed Probe Beam

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

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

13. Fs CARS Experimental Results: Flame Temperatures

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

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

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

17. 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. Numerical Model of Fs CARS in N2 • 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. Numerical Model of N2 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. 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. 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. Calculation of the Raman Coherence The two-photon Raman coherence operates through intermediate states k. States e and g are not single-photon coupled. Time-dependent density matrix equations for coherence amplitudes (after application of the rotating wave approximation): The laser interactions terms are defined by the following and similar equations:

23. Numerical Results for 100 Fs Pulse Je = Jg = 8 DwRaman = 0.05 cm-1 Stokes Irrad = 10xPump Irrad

24. Numerical Results for 70 Fs Pulse Je = Jg = 5 DwRaman = 0.05 cm-1 Stokes Irrad = Pump Irrad

25. Comparison of Raman Excitation for 70 Fs Pulses, Peak Irradiance 2x1018 W/m2 Je = Jg = 5 DwRaman = 0.05 cm-1 Stokes Irrad = Pump Irrad

26. Comparison of Raman Excitation for 70 Fs Pulses, Peak Irradiance 1019 W/m2 Je = Jg = 5 DwRaman = 0.05 cm-1 Stokes Irrad = Pump Irrad

27. Comparison of CARS Signal for 70 Fs Pulses Stokes Irrad = Pump Irrad = 5x1017 W/m2 Stokes Irrad = Pump Irrad = 1019 W/m2

28. 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. Coupling of 70-Fs Pump and Stokes Pulses with the Raman Coherence

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

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

32. Simultaneous Fs CARS for CO (2145 cm-1) and N2 (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 N2 and CO Raman bands.

33. Simultaneous Fs CARS for CO (2145 cm-1) and N2 (2330 cm-1) The pump wavelengths for Raman resonance for N2 and CO are 675 nm and 682 nm, respectively.

34. 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