Single Shot Combined Time Frequency Four Wave Mixing

1. Single Shot Combined Time Frequency Four Wave Mixing Andrey Shalit, Yuri Paskover and Yehiam Prior Department of Chemical Physics Weizmann Institute of Science, Rehovot, Israel LPHYS 09 Barcelona July 17, 2009

2. Molecular spectroscopy can be performed either in the frequency domain or in the time domain. • In the frequency domain, we scan the frequency of excitation (IR 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.

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

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

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

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

7. 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

8. Ea Eb Ec Time delay Time Resolved Four Wave Mixing Phase matching ~ 50-100 femtosecond pulses ~ 0.1 mJ per pulse

9. Time Resolved Four Wave Mixing F.T.

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

11. Experimental System (modified)

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

13. F.T Open band:

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

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

16. Time Frequency Detection CHCl3

17. Spectral Distribution of the Observed Features 104 cm-1 365 cm-1 Observed frequency: 104 cm-1 Observed detuning : 310 cm-1 Observed frequency: 365 cm-1 Observed detuning : 180 cm-1

18. 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 !

19. Outline • Introduction, or “TFD: the best of both worlds” • Single Shot Four Wave Mixing • Tunable Single Shot Four Wave Mixing • Multiplex Single Shot Four Wave Mixing • TFD simplified analysis • Conclusions

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

21. k2 z k3 k1 k1 k3 x k2 ks y CCD Three pulses - Box-CARS geometry Time delays Spatial coordinates

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

23. CH2Cl2 Single Pulse CARS Image

24. Time Resolved Signal and its Power Spectrum

25. CHBr3 Several modes in the range

26. Time Resolved Signal and its Power Spectrum

27. Outline • Introduction, or “TFD: the best of both worlds” • Single Shot Four Wave Mixing • Tunable Single Shot Four Wave Mixing • Multiplex Single Shot Four Wave Mixing • TFD simplified analysis • Conclusions

28. k2 z k3 k1 k1 k3 x k2 ks y CCD x y z Geometrical Effects

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

30. Measured and calculated tuning curve Measured Calculated

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

32. Phase matching tuned spectra

33. TFD Single Shot – Sum

34. Compare with scanned Results

35. Outline • Introduction, or “TFD: the best of both worlds” • Single Shot Four Wave Mixing • Tunable Single Shot Four Wave Mixing • Multiplex Single Shot Four Wave Mixing • TFD simplified analysis • Conclusions

36. k2 z k3 k1 k1 k3 x k2 ks y CCD Single Shot Geometry: Parallel beams

37. Single Shot Geometry: Focused Beam z x y k1 k3 k2 CCD L

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

39. Intersection Region: y-z slice z -y +y k1 first k3 first

40. Intersection Region: y-z slice z -y +y Δ

41. τ [fs] Δ Time Frequency Detection:Multiplex single Shot Image Focusing angle : δ = 3 mrad (CH2Br2)

42. TFD Single Shot – Fourier Transformed (CH2Br2)

43. TFD Scanned (CH2Br2)

44. Compare with scanned Results

45. TFD Single Shot – polarization dependence

46. Outline • Introduction, or “TFD: the best of both worlds” • Single Shot Four Wave Mixing • Tunable Single Shot Four Wave Mixing • Multiplex Single Shot egenerate Four Wave Mixing • TFD simplified analysis • Conclusions

47. k3 k3 k1 -k2 + -k2 k1 Time Frequency Detection 0 Detuning from a probe (k3) carrier frequency

48. Spectral Distribution of the Signal Produced by a Fundamental Mode In TR-DFWM, we have shown that because of the quadratic dependence on the polarization, fundamental modes may be seen only after linearization of the signal, i.e. by heterodyne detection 0 Detuning from a probe carrier frequency (Δ)

49. Spectral Distribution of the Signal Produced by Intensity Beat 0 Detuning from a carrier (Δ)

50. Identification of signals: Fundamental modes of frequency Ω1 are spectrally peaked at Ω1/2 Intensity beats at frequency (Ω1 ± Ω2) spectrally peaked at [ (Ω1-Ω2)/2 ] Based on this result, it is now possible to directly and unambiguously identify the character of each peak