Single Shot Combined Time Frequency Four Wave Mixing

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.

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

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

Coherent Anti Stokes Raman Scattering (CARS) Energy conservation w 1 Dk w 1 w 2 Conservation of Momentum (phase matching) w. AS k 2 k 1 k. CARS WRaman 2 w 1 - w 2 - w. AS = 0 Dk = 2 k 1 -k 2 -k. AS= 0

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

Time Resolved Four Wave Mixing Ea Eb Ec Time delay Phase matching ~ 50 -100 femtosecond pulses ~ 0. 1 m. J per pulse

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) Open band: Summation over all frequencies (Δ)

Open band: F. T

Limited Band Detection Summation over 500 cm-1 window

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

Time Frequency Detection CHCl 3

Spectral Distribution of the Observed Features 104 cm-1 Observed frequency: 104 cm-1 Observed detuning : 310 cm-1 365 cm-1 Observed frequency: Observed detuning : 365 cm-1 180 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. 1015 times faster, or in < 100 femtoseconds !

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

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

Three pulses - Box-CARS geometry z k 2 k 3 k 2 Time delays y k 1 ks Spatial coordinates CCD k 1 x k 3

Intersection Region: y-z slice k 2 k 3 k 1 Pump-probe delay -y z +y k 1 first k 3 k 2 k 1 Pump-probe delay

Single Pulse CARS Image CH 2 Cl 2

Time Resolved Signal and its Power Spectrum

Several modes in the range CHBr 3

Time Resolved Signal and its Power Spectrum

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

Geometrical Effects z k 1 k 2 x k 3 y x y z k 1 ks CC D k 2

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

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

Single Shot Geometry: Parallel beams z k 2 x k 1 k 3 k 2 y ks CCD k 1 k 3

Single Shot Geometry: Focused Beam z x y k 1 k 3 CC L D k 2

Intersection Region: y-z slice k 2 k 3 k 1 Pump-probe delay -y z +y k 1 first k 3 k 2 k 1 Pump-probe delay

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

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

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

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

Time Frequency Detection k 3 k 1 -k 2 k 1 + 0 Detuning from a probe (k 3) carrier frequency

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)

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

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

TFD analysis: CCL 4 Lines at 99, 147, 246 cm-1

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

TFD analysis: CCL 4 DERIVED fundamental frequencies 210 309 317 464 214 460 Homodyne beat : (Ω 5 -Ω 6) = 147 cm-1 KNOWN CCl 4 Modes Detuning : (Ω 5+Ω 6) /2 = 385 cm-1 Ω 5 = 317 cm-1 ; Ω 6= 464 cm-1 214 313 460

Outline • 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

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

The End Thank you