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

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

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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 1979 – Weizmann Institute (ever since) Where was I ?

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

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How does a laser work ?

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Incoherent Coherent

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Incoherent Coherent

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So, what can we do with these Coherent sources?

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Spontaneous Raman spectrum of CHCl 3 Direct spontaneous Raman spectrum (from the catalogue)

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k k1k1 k1k1 k2k2 k CARS Energy conservation Conservation of Momentum (phase matching) Raman AS AS = 0 k = 2k 1 -k 2 -k AS = 0 Four Wave Mixing (FWM) and Coherent Anti Stokes Raman Scattering (CARS)

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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 …….

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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.

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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

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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.

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

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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 Outline

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Time Resolved Four Wave Mixing F.T.

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

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Experimental System (modified)

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Time frequency Detection (CHCl 3 ) Summation over all frequencies (Δ) Open band:

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F.T Open band:

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Limited Band Detection Summation over 500cm -1 window

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

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Time Frequency Detection CHCl 3

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

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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 times faster, or in < 100 femtoseconds !

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Also A. Eckbreth, Folded BOXCARS configuration

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~ femtosecond pulses ~ 0.1 mJ per pulse EaEa EbEb EcEc Time delay Phase matching Time Resolved Four Wave Mixing

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Spatial Crossing of two short pulses: Interaction regions k3k3 k1k1 5mm Beam diameter – 5 mm 100 fsec = 30 microns Different regions in the interaction zone correspond to different times delays k 1 arrives first k 3 arrives first

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Three pulses - Box-CARS geometry Time delays Spatial coordinates

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+y-y k 1 firstk 3 first z k1k1 k2k2 k3k3 Pump-probe delay k1k1 k2k2 k3k3 Intersection Region: y-z slice

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Single Pulse CARS Image CH 2 Cl 2

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Time Resolved Signal and its Power Spectrum

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CHBr 3 Several modes in the range

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Time Resolved Signal and its Power Spectrum

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

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

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Measured and calculated tuning curve Measured Calculated

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Phase matching tuned spectra

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TFD Single Shot – Sum

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

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Compare with scanned Results

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Single Shot multiplexing: Focused Beam

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+y-y k 1 firstk 3 first z k1k1 k2k2 k3k3 Pump-probe delay k1k1 k2k2 k3k3 Intersection Region: y-z slice

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+y-y k 1 firstk 3 first z Intersection Region: y-z slice

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

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Time Frequency Detection: Single Shot Image Focusing angle : δ = 3 mrad (CH 2 Br 2 )

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Time Frequency Detection by Single Shot: Fourier Transformed (CH 2 Br 2 )

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TFD Scanned (CH 2 Br 2 )

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Taken by single shot Scanning method (10 min)

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Signal to noise comparison 150 pulses 1500 pulses 15,000 pulses 150,000 pulses

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Time Frequency Detection: Single Shot Image Focusing angle : δ = 3 mrad (CH 2 Br 2 )

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TFD Single Shot – polarization dependence

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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 Conclusions

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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

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