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Ultrafast Optics
Christoph Feest
December 10, 2007
Christoph Feest () Ultrafast Optics December 10, 2007 1 / 25
What are characteristic scales in quantum systems?
classical approach
v =
√2Ry
me=
c
137= α · c
virial-theorem
〈T 〉 = −1
2〈V 〉 = Ebinding
a0 = 0.53 · 10−10m
→ torbit ≈ 150 · 10−18s = 150as
Attosecond-scale means electron motion!
What are characteristic scales in quantum systems?
classical approach
v =
√2Ry
me=
c
137= α · c
virial-theorem
〈T 〉 = −1
2〈V 〉 = Ebinding
a0 = 0.53 · 10−10m
→ torbit ≈ 150 · 10−18s = 150as
Attosecond-scale means electron motion!
Contents
1 General ConsiderationsBeam PropertiesGain medium
2 fs-TechniquesChirpMode-lockingOptical Kerr-effect, SPM, SAM
3 as-TechniqueHigh Harmonic Generation
4 MeasurementTHz-SamplingThe Zoo: FROG, SPIDER, (CRAB, TIGER,) ...SEA-SPIDER
Christoph Feest () Ultrafast Optics December 10, 2007 3 / 25
Contents
1 General ConsiderationsBeam PropertiesGain medium
2 fs-TechniquesChirpMode-lockingOptical Kerr-effect, SPM, SAM
3 as-TechniqueHigh Harmonic Generation
4 MeasurementTHz-SamplingThe Zoo: FROG, SPIDER, (CRAB, TIGER,) ...SEA-SPIDER
Christoph Feest () Ultrafast Optics December 10, 2007 3 / 25
Contents
1 General ConsiderationsBeam PropertiesGain medium
2 fs-TechniquesChirpMode-lockingOptical Kerr-effect, SPM, SAM
3 as-TechniqueHigh Harmonic Generation
4 MeasurementTHz-SamplingThe Zoo: FROG, SPIDER, (CRAB, TIGER,) ...SEA-SPIDER
Christoph Feest () Ultrafast Optics December 10, 2007 3 / 25
Contents
1 General ConsiderationsBeam PropertiesGain medium
2 fs-TechniquesChirpMode-lockingOptical Kerr-effect, SPM, SAM
3 as-TechniqueHigh Harmonic Generation
4 MeasurementTHz-SamplingThe Zoo: FROG, SPIDER, (CRAB, TIGER,) ...SEA-SPIDER
Christoph Feest () Ultrafast Optics December 10, 2007 3 / 25
General Considerations Beam Properties
What do we want?
Confine energy in small spatial region!
Roundtrip:tRT = 2L
c
Longitudinal modes:δν = c
2L = 1tRT
time-bandwidth-product:∆t∆ν ≥ 0.441
Christoph Feest () Ultrafast Optics December 10, 2007 4 / 25
General Considerations Gain medium
Ti:Sapphire, (Ti3+ : Al2O3)
Ti:Sa parametersn = 1.76 τfluo = 3.2µs FWHM ≈ 200nm λmax ≈ 790nm
→ Issues: temporal & spatial coherence, dispersion
Christoph Feest () Ultrafast Optics December 10, 2007 5 / 25
fs-Techniques Mode-locking
Basic Ideas
Pulses:
emitted as trains tRT = 1δν
peak power P ∝ P0 · N2
∆t ≈ 1Nδν = 1
∆ν
key parameter: φn(t)
Christoph Feest () Ultrafast Optics December 10, 2007 7 / 25
fs-Techniques Mode-locking
Basic Ideas, visualised
Christoph Feest () Ultrafast Optics December 10, 2007 8 / 25
fs-Techniques Optical Kerr-effect, SPM, SAM
Optical Kerr-effect
high intensities > 1014 Wcm2 nnl = n0 + n2 · I
n2 ≈ +(10−16 . . . 10−15) cm2
Wnew wave vector knl = k(ω0) + ω0
cn2
A |g(t)|2
time-dependent response → Self-Phase-Modulation, SPM
Figure: RP Encyclopedia of Laser Physics and Technology
Christoph Feest () Ultrafast Optics December 10, 2007 9 / 25
fs-Techniques Optical Kerr-effect, SPM, SAM
+ Self-Amplitude-Modulation, SAM
beam intensity ∝ e−r2
Figure: Ferenc Krausz, Photonics II Lecture
Christoph Feest () Ultrafast Optics December 10, 2007 10 / 25
fs-Techniques Optical Kerr-effect, SPM, SAM
State of affairs
pulse rep. rate crystal energy/pulse e
commercial 7 fs 80 MHz Ti:Sa 2 · 10−9J 120.000commercial 25 fs 3 kHz Ti:Sa 7 · 10−4J 500.000
labs: single cycle regime reached
→ as-pulses require different technique
Christoph Feest () Ultrafast Optics December 10, 2007 11 / 25
as-Technique High Harmonic Generation
3-Step-Model
Figure: Corkum, Phys. Rev. Lett. 71, 1994 (1993)
Christoph Feest () Ultrafast Optics December 10, 2007 12 / 25
as-Technique High Harmonic Generation
Experimental setup
Figure: Cavalieri, New Journal of Physics 9 (2007) 242
Christoph Feest () Ultrafast Optics December 10, 2007 13 / 25
as-Technique High Harmonic Generation
HHG, results
Figure: Macklin, Phys. Rev. Lett. 70, 766 (1993)
Christoph Feest () Ultrafast Optics December 10, 2007 14 / 25
as-Technique High Harmonic Generation
3-Step-Model, Remarks
nonlinear response is not instantaneous
nonlinear response almost constant at high orders
maximum electron energy 3.17 UP = 3.17E 2
0
4ω2
up to 1000th order → keV
XUV pulses reach
E=90eV t=250as I = 1011 Wcm2
Christoph Feest () Ultrafast Optics December 10, 2007 15 / 25
Measurement THz-Sampling
fs-MIR-pulses, setup
Figure: Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 70 (14), 7 April 1997
I1−I2I1+I2
= sin(Γ) Γ ∝ EIR(t)
Christoph Feest () Ultrafast Optics December 10, 2007 16 / 25
Measurement THz-Sampling
THz Results
Figure: Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 70 (14), 7 April 1997
Christoph Feest () Ultrafast Optics December 10, 2007 17 / 25
Measurement THz-Sampling
Next Step: XUV Probe
Figures: E. Goulielmakis, et al., Science 305 1267 (2004)
Christoph Feest () Ultrafast Optics December 10, 2007 18 / 25
Measurement The Zoo: FROG, SPIDER, (CRAB, TIGER,) ...
sub-10-fs-Methods
Figure: Stibenz, Steinmeyer et al., Appl. Phys. B 83, 511-519 (2006)
Christoph Feest () Ultrafast Optics December 10, 2007 19 / 25
Measurement SEA-SPIDER
Sea-Spider, schematic
Spatially Encoded Arrangement forSpectral Phase Interferometry for Direct Electric-field Reconstruction
Figure: A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, Opt. Lett. 31,1914-1916 (2006)
S(x , ω) = |E (x , ω + ω0)|2 + |E (x , ω + ω0 + Ω)|2 +
2|E (x , ω + ω0)| · |E (x , ω + ω0 + Ω)|cos(φ(x , ω + ω0)− φ(x , ω + ω0 + Ω) + Kx)|
Christoph Feest () Ultrafast Optics December 10, 2007 20 / 25
Measurement SEA-SPIDER
Sea-Spider, schematic
Spatially Encoded Arrangement forSpectral Phase Interferometry for Direct Electric-field Reconstruction
Figure: A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, Opt. Lett. 31,1914-1916 (2006)
S(x , ω) = |E (x , ω + ω0)|2 + |E (x , ω + ω0 + Ω)|2 +
2|E (x , ω + ω0)| · |E (x , ω + ω0 + Ω)|cos(φ(x , ω + ω0)− φ(x , ω + ω0 + Ω) + Kx)|
Christoph Feest () Ultrafast Optics December 10, 2007 20 / 25
Measurement SEA-SPIDER
Sea-Spider, results
Figure: A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, Opt. Lett. 31,1914-1916 (2006)
Christoph Feest () Ultrafast Optics December 10, 2007 21 / 25
Measurement SEA-SPIDER
Sea-Spider, processing the results
Figure: Ellen M. Kosik, Aleksander S. Radunsky, Ian A. Walmsley, and ChristopheDorrer, Opt. Lett., 30 (3), 326-328, (2005)
Christoph Feest () Ultrafast Optics December 10, 2007 22 / 25
Measurement SEA-SPIDER
Sea-Spider, enjoying the results
Figure: A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, Opt. Lett. 31,1914-1916 (2006))
Christoph Feest () Ultrafast Optics December 10, 2007 23 / 25
Applications & Conclusions
Applications
communications (1, 4µm gap)
THz-Imaging & -Sampling (low absorption)
medical & biological microscopy (increased resolution)
structuring & cutting (no heat diffusion)
ultrafast metrology (exiting and probing with short pulses, dynamics)
control of chemical reactions (valence electrons, shaped pulses)
Conclusion
Ultrafast optics breaks new ground in
high-field science
frequency and time metrology
industrial, medical and biological technologies
Applications & Conclusions
Applications
communications (1, 4µm gap)
THz-Imaging & -Sampling (low absorption)
medical & biological microscopy (increased resolution)
structuring & cutting (no heat diffusion)
ultrafast metrology (exiting and probing with short pulses, dynamics)
control of chemical reactions (valence electrons, shaped pulses)
Conclusion
Ultrafast optics breaks new ground in
high-field science
frequency and time metrology
industrial, medical and biological technologies
Sources
A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, Opt. Lett. 31,1914-1916 (2006)
Stibenz, Steinmeyer et al., Appl. Phys. B 83, 511-519 (2006)
Corkum, Phys. Rev. Lett. 71, 1994 (1993)
E. Goulielmakis, et al., Science 305 1267 (2004)
Ellen M. Kosik, Aleksander S. Radunsky, Ian A. Walmsley, and ChristopheDorrer, Opt. Lett., 30 (3), 326-328, (2005)
Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 70 (14), 7 April (1997)
Macklin, Phys. Rev. Lett. 70, 766 (1993)
Cavalieri, New Journal of Physics 9 (2007) 242
Springer Handbook of Lasers and Optics, 2007
RP Encyclopedia of Laser Physics and Technology(http://www.rp-photonics.com/)