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

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.

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 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 Outline

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

kk k1k1 k1k1 k2k2 k CARS Energy conservation Conservation of Momentum (phase matching)  Raman 11 11 22  AS  1 -  2 -  AS = 0  k = 2k 1 -k 2 -k AS = 0 Coherent Anti Stokes Raman Scattering (CARS)

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

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

F.T.

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

Experimental System (modified)

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

F.T Open band:

Limited Band Detection Summation over 500cm -1 window

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

Time Frequency Detection CHCl 3

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

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 !

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 Outline

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

Three pulses - Box-CARS geometry Time delays Spatial coordinates CCD k1k1 k1k1 k3k3 k3k3 k2k2 k2k2 ksks x z y

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

Single Pulse CARS Image CH 2 Cl 2

Time Resolved Signal and its Power Spectrum

CHBr 3 Several modes in the range

Time Resolved Signal and its Power Spectrum

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 Outline

Geometrical Effects CCD k1k1 k1k1 k3k3 k3k3 k2k2 k2k2 ksks x z y x y z

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

Measured and calculated tuning curve Measured Calculated

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

Phase matching tuned spectra

TFD Single Shot – Sum

Compare with scanned Results

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 Outline

CCD k1k1 k1k1 k3k3 k3k3 k2k2 k2k2 ksks x z y Single Shot Geometry: Parallel beams

Single Shot Geometry: Focused Beam k1k1 k2k2 k3k3 CCD L z x y

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

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

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

Time Frequency Detection: Multiplex single Shot Image τ [fs] Δ Focusing angle : δ = 3 mrad (CH 2 Br 2 )

TFD Single Shot – Fourier Transformed (CH 2 Br 2 )

TFD Scanned (CH 2 Br 2 )

Compare with scanned Results

TFD Single Shot – polarization dependence

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 Outline

+ 0 Detuning from a probe (k 3 ) carrier frequency k1k1 -k 2 k3k3 k1k1 k3k3 Time Frequency Detection

Detuning from a probe carrier frequency (Δ) 0 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

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

Identification of signals: Fundamental modes of frequency Ω 1 are spectrally peaked at Ω 1 /2 Intensity beats at frequency (Ω 1 ± Ω 2 ) spectrally peaked at [ (Ω 1 -Ω 2 )/2 ] Based on this result, it is now possible to directly and unambiguously identify the character of each peak

CCL 4

TFD analysis: CCL4 Lines at 99, 147, 246 cm -1

Homodyne beat : (Ω 1 -Ω 2 )=99cm -1 Detuning : (Ω 1 +Ω 2 ) /2=260 cm -1 Ω 1 = 210 cm -1 ; Ω 2 = 309 Homodyne beat : (Ω 3 -Ω 4 ) = 246cm -1 Detuning : (Ω 3 +Ω 4 )/2 =337 cm -1 Ω 4 = 214 cm-1 ; Ω 3 = 460 TFD analysis: CCL4

Homodyne beat : (Ω 5 -Ω 6 ) = 147cm-1 Detuning : (Ω 5 +Ω 6 ) /2 = 385 cm -1 Ω 5 = 317 cm -1 ; Ω 6 = 464 cm DERIVED fundamental frequencies KNOWN CCl 4 Modes TFD analysis: CCL4

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

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

The End Thank you