1. Four Wave Mixing – a Mirror in Time Suzdal NLO-50(+) September 2011
Yehiam Prior
Weizmann Institute of Science, Rehovot, Israel
Suzdal NLO-50(+) September 2011

4. It took a long time….
And in 1960 the LASER was invented: Soon to be described as a “solution looking for a problem”

5. Where was I ?
th grade student in Jerusalem, deciding to continue my studies in the US Berkeley, looking for a Thesis advisor Options: Shen, Townes, Hahn post doc position: Nico Bloembergen – Weizmann Institute (ever since)

6. How does a laser work ?
Monochromatic, Directional, Intense, Coherent

7. How does a laser work ?

8. Incoherent
Coherent

9. Incoherent
Coherent

10. So, what can we do with these
Coherent sources?

11. Spontaneous Raman spectrum of CHCl3
Direct spontaneous Raman spectrum (from the catalogue)

12. Conservation of Momentum
Four Wave Mixing (FWM) and Coherent Anti Stokes Raman Scattering (CARS)
Conservation of Momentum
(phase matching)
Energy conservation
WRaman w1 w2
wAS
2w1- w2- wAS = 0 Dk k1 k2
kCARS
Dk = 2k1-k2-kAS= 0

13. FWM Applications included:
Molecular spectroscopy
Rotational and vibrational dynamics
Solid state fast relaxation phenomena
Photon echoes
Combustion diagnostics
Surface diagnostics
Biological applications
Microscopy
Remote sensing
…….

14. Spectroscopy can be performed either in the frequency domain or in the time domain.
In the frequency domain, we scan the frequency of excitation (absorption), or the frequency of observation (Spontaneous Raman spectroscopy), etc.
Alternatively, we can capture the time response to impulse excitation, and then Fourier Transform this signal to obtain a frequency domain spectrum.
We are always taught that the choice of one or the other is a matter of convenience, instrumentation, efficiency, signal to noise, etc. but that the derived physical information is the same, and therefore the measurements are equivalent.

15. Time Resolved Four Wave Mixing
A pair of pulses (Pump and Stokes) excites coherent vibrations in the ground state
A third (delayed) pulse probes the state of the system to produce signal
The delay is scanned and dynamics is retrieved

16. However, practically ALL CARS and Four Wave Mixing experiments were/are performed in the frequency domain.
i.e. one is not directly measuring the molecular polarization (wavefunction) which is oscillating at optical frequencies.

17. Combined Time Frequency Detection of Four Wave Mixing
With:
Dr. Yuri Paskover (currently in Princeton)
Andrey Shalit

18. Outline Time Frequency Detection (TFD) : the best of both worlds
Single Shot Degenerate Four Wave Mixing
Tunable Single Shot Degenerate Four Wave Mixing
Multiplex Single Shot Degenerate Four Wave Mixing
TFD simplified analysis
Conclusions

19. Time Resolved Four Wave Mixing
F.T.

20. Time Domain vs. Frequency Domain
In this TR-FWM the signal is proportional to a (polarization)2 and therefore beats are possible

21. Experimental System (modified)

22. Time frequency Detection (CHCl3)
Open band:
Summation over all
frequencies (Δ)

23. F.T
Open band:

24. Limited Band Detection
Summation over
500cm-1 window

25. Open vs. Limited Detection
F.T
Open band:
F.T
Limited band:

26. Time Frequency Detection CHCl3

27. Spectral Distribution of the Observed Features
104 cm-1
365 cm-1
Observed frequency: cm-1
Observed detuning : cm-1
Observed frequency: cm-1
Observed detuning : cm-1

28. 1015 times faster, or in < 100 femtoseconds !
However, this is a long measurement, it takes approximately 10 minutes, or >> 100 seconds.
In what follows I will show you how this same task can be performed much faster.
1015 times faster, or in < 100 femtoseconds !

29. Also
A. Eckbreth, Folded BOXCARS configuration

30. Time Resolved Four Wave MixingEa Eb Ec
Time delay
Phase matching
~ femtosecond pulses ~ 0.1 mJ per pulse

31. Spatial Crossing of two short pulses: Interaction regionsk3 k1
k1 arrives first
k3 arrives first
100 fsec = 30 microns
5mm
Beam diameter – 5 mm
Different regions in the interaction zone correspond to different times delays

32. Three pulses - Box-CARS geometry
Time delays Spatial coordinates 32

34. Intersection Region: y-z slice
k1 first
k3 first z k1 k2 k3
Pump-probe delay

35. Single Pulse CARS Image
CH2Cl2

36. Time Resolved Signal and its Power Spectrum

37. Several modes in the range
CHBr3

38. Time Resolved Signal and its Power Spectrum

39. Geometrical Effects : Phase mismatchingx y z
Calculated
Measured
Shalit et al. Opt. Comm. 283, 1917 (2010) 39

40. Spectrum of the central frequency (coherence peak) as a function of the Stokes beam deviation

41. Measured and calculated tuning curve

42. Phase matching tuned spectra

43. TFD Single Shot – Sum

44. For each time delay, a spectrally resolved spectrum was measured.

45. Compare with scanned Results

46. Single Shot multiplexing: Focused Beam

47. Intersection Region: y-z slice
k1 first
k3 first z k1 k2 k3
Pump-probe delay

48. Intersection Region: y-z slice
k1 first
k3 first

49. Intersection Region: y-z sliceΔ

50. Time Frequency Detection: Single Shot Image
Focusing angle : δ = 3 mrad
(CH2Br2)

51. Time Frequency Detection by Single Shot: Fourier Transformed
(CH2Br2)

52. TFD Scanned (CH2Br2)

53. Scanning method (10 min)
Taken by single shot

54. Signal to noise comparison
150 pulses pulses
15,000 pulses ,000 pulses

55. Time Frequency Detection: Single Shot Image
Focusing angle : δ = 3 mrad
(CH2Br2)

56. TFD Single Shot – polarization dependence

57. Conclusions
Time Frequency combined measurements offer advantages over either domain separately
Specific advantages in spectroscopy of unknown species, by the ability to identify the character of observed lines (fundamental or beat modes)
Advantages in cleaning up undesirable pulse distortions
Single mode FWM measurements
Tunable single mode FWM measurements
Multiplex single mode FWM measurements
Significant theoretical foundation (not discussed here)
More work needed to improve resolution, bandwidth, accuracy, reproducibility, etc

58. Thank you Acknowledgements
Dr. Alexander Milner, Dr. Riccardo Castagna, Dr. Einat Tirosh, Sharly Fleischer, Andrey Shalit, Atalia Birman, Omer Korech, Dr. Mark Vilensky, Dr. Iddo Pinkas
Thank you