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**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

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

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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)

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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 CHCl3**

Direct spontaneous Raman spectrum (from the catalogue)

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**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

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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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**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

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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 (CHCl3)**

Open band: Summation over all frequencies (Δ)

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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**

F.T Open band: F.T Limited band:

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**Time Frequency Detection CHCl3**

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**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

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**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 !

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Also A. Eckbreth, Folded BOXCARS configuration

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**Time Resolved Four Wave Mixing**

Ea Eb Ec Time delay Phase matching ~ femtosecond pulses ~ 0.1 mJ per pulse

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**Spatial Crossing of two short pulses: Interaction regions**

k3 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

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**Three pulses - Box-CARS geometry**

Time delays Spatial coordinates 32

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**Intersection Region: y-z slice**

k1 first k3 first z k1 k2 k3 Pump-probe delay

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**Single Pulse CARS Image**

CH2Cl2

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**Time Resolved Signal and its Power Spectrum**

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**Several modes in the range**

CHBr3

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**Time Resolved Signal and its Power Spectrum**

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**Geometrical Effects : Phase mismatching**

x y z Calculated Measured Shalit et al. Opt. Comm. 283, 1917 (2010) 39

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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**

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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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**Intersection Region: y-z slice**

k1 first k3 first z k1 k2 k3 Pump-probe delay

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**Intersection Region: y-z slice**

k1 first k3 first

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**Intersection Region: y-z slice**

Δ

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**Time Frequency Detection: Single Shot Image**

Focusing angle : δ = 3 mrad (CH2Br2)

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**Time Frequency Detection by Single Shot: Fourier Transformed**

(CH2Br2)

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TFD Scanned (CH2Br2)

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Scanning method (10 min) Taken by single shot

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**Signal to noise comparison**

150 pulses pulses 15,000 pulses ,000 pulses

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**Time Frequency Detection: Single Shot Image**

Focusing angle : δ = 3 mrad (CH2Br2)

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**TFD Single Shot – polarization dependence**

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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

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**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

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