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  1. Femtosecond lasers István Robel Department of Physics and Radiation Laboratory University of Notre Dame June 22, 2005

  2. Outline • Basics of lasers • Generation and properties of ultrashort pulses • Nonlinear effects: • second harmonic generation • white light generation • Amplification of short laser pulses • Ultrafast laser spectroscopy

  3. Spontaneous emission Absorption Spontaneous emission Ground state Ground state • Characteristics of spontaneous emission • Random process • Photons from different atoms are not coherent • Random direction of emitted photon • Random polarization of emitted photon

  4. Bosons and fermions Two types of particles in nature: bosons and fermions • Bosons • Examples: photons, He4 atoms, Cooper pairs • A quantum state can be occupied by infinite many bosons • Bose-Einstein condensation: all bosons in a system will occupy the same quantum state (examples: supeconductivity, superfluid He, laser) • integer spin • Fermions • Examples are: electrons, protons, neutrons, neutrinos, quarks • Pauli exclusion principle: every quantum state can be occupied by 1 fermion at most • Half-integer spin

  5. Stimulated emission Ground state • The emitted photon is in the same quantum state as the incident photon: • same energy (or wavelength), • same phase (coherent) • same polarization • same direction of propagation

  6. Amplification of light Population Inversion “Negative temperature” Energy Molecules I0 I >I0 Light amplification by stimulated emission occurs when passing through gain medium Competing processes: Absorption: only possible if an atom is not in the excited state Spontaneous emission: important if the lifetime of the excited state is too short

  7. Four-level laser fast Molecules accumulate in this level, leading to an inversion with respect to this level. The four-level system is the ideal laser system. slow Laser transition fast

  8. Basic components of a laser I0 I1 I3 I2 Laser medium in excited state Mirror, R = 100% Mirror, R < 100% Ioutput • General characteristics of laser radiation: • Coherent (typical coherence length 1m) • Monochromatic (Dl/l=10-6) • Directional (mrad beam divergence ) • Polarized

  9. Time scales in nature • Shortest event ever measured (indirectly): decay of tau-lepton 0.4x10-24 s • Period of nuclear vibrations: 0.1x10-21s • Shortest event ever created: 250 attosecond (10-18s) x-ray pulse (2004) • Bohr orbit period in hydrogen atom: 150 attoseconds • Single oscillation of 600nm light: 2 fs (10-15s) • Vibrational modes of a molecule: ps timescale • Electron transfer in photosynthesis: ps timescale • Period of phonon vibrations in a solid: ps timescale • Mean time between atomic collisions in ambient air: 0.1 ns (10-9s) • Period of mid-range sound vibrations: ms

  10. Ultrashort laser pulses Irradiance vs. time Spectrum Long pulse time frequency Short pulse frequency time Heisenberg uncertainty principle: Dt*Dn≥1 e.g. for a 150fs pulse: Dn=7THz (e.g. n=600THz @ l=500nm) Dl=6nm wavelength spread @ l=500nm

  11. Frequency modes of the laser cavity Frequency modes of the laser cavity due to the spatial confinement: e.g. for a 1m long cavity: Dn=1.5GHz DE=0.6meV Dl=0.001A

  12. Generation of short pulses by mode-locking

  13. Mode-locking by non-linear polarization rotation • The polarization of very high intensity pulses is rotated when passing through a nonlinear medium • Using a polarizer low energy pulses can be filtered out, only the high energy mode-locked pulse gets amplified Nelson et al Appl. Phys. B65, 277-294 (1997)

  14. Group velocity dispersion: Chirp In a medium different frequencies propagate with different velocities

  15. Pulse compression • Spatial separation of different frequencies • Longer optical path for the frequencies that are “ahead” • Recombination of different frequencies in a short pulse

  16. Amplification of short laser pulses Energy levels pump Output Laser oscillator Amplifier medium R=100% R<100% • Difficulties: • beam only passes once through amplifier medium • Output intensity is changing in every roundtrip and intensity is lower than in cavity

  17. Pockels cell and cavity dumping V Polarizer R=100% R=100% Pockels cell The Pockels cell is a material that rotates the polarization of light if a voltage is applied on it If V = 0, the pulse polarization doesn’t change. If V = Vp, the pulse polarization switches to its orthogonal state.

  18. Regenerative amplifier M mirror TFP thin film polarizer FR Faraday rotator PC Pockels cell • Amplification of the seed pulse: • Seed pulse has to be injected when gain is maximal • Has to be ejected when pulse height and stability is maximal

  19. Chirped Pulse Amplification • Pulse is stretched first to avoid high intensity artifacts in the amplifier • Amplified pulse is compressed to obtain the short pulse duration Oscillator Stretcher Amplifier Compressor

  20. Nonlinear Optics Nonlinear polarization: P=e(c1E+c2E2+...) Phase matching condition ensures conservation of momentum: For a photon: Second harmonic! Higher frequencies occur due to the non-linear response of the material at high intensities

  21. Self phase modulation and white light continuum Intensity, au Wavelength, nm A wide range of frequencies is generated with a short, intense pulse 775 nm, 150 fs pulse in sapphire crystal

  22. The Clark CPA-2010 Laser System Parameters: Wavelength of fundamental: 775 nm Pulse duration: 150 fs Pulse energy: 1mJ Power per pulse: 7 GW Repetition rate: 1KHz Wavelength of second harmonic: 387 nm Pulse duration: 150 fs Pulse energy: 0.25mJ Er doped fiber oscillator 25KHz l=1.55mm Pumped with Cw diode laser l=1mm P=150mW Pulse compressor Second Harmonic Generation Pulse Stretcher First Level Ti:Sapphire Regenerative amplifier Pockels cell with HV supply and delay timer Pulse compressor Second and Third harmonic Output Nd:YAG pump laser Second Level

  23. Transient absorption spectroscopy Unexcited medium Excited medium Unexcited medium absorbs heavily at wavelengths corresponding to transitions from ground state. Excited medium absorbs weakly at wavelengths corresponding to transitions from ground state. • Varying the delay between excitation pulse and probe pulse results time-dependent measurement of phenomenon • Time resolution is limited by the length of the excitation pulse

  24. Experimental Setup: Pump-Probe configuration Chopper Sample Cell Filter Wheel CLARK -MXR CPA-2010 Pump Probe Optical Delay Rail Ocean Optics S2000 CCD Detector (7fs -1.6 ns) Ultrafast Systems Frequency Doubler 775 nm, 1 kHz 1 mJ/pulse To PC • Sample is excited by short laser pulse (pump) • Differential absorbance of the sample is measured by a delayed second pulse (probe) • Time dependence is measured by changing the delay of the probe pulse

  25. Femtosecond Transient Absorption Spectroscopy at NDRL

  26. Applications of pulsed lasers • Time dependent measurements of: • Thermalization of hot electron in a metal or semiconductor • Electron-phonon heat transfer • Decay of surface plasmon oscillations • Quantum beats • Electron transfer processes • Exciton lifetime in semiconductors • Charge carrier relaxation in semiconductors • Electron- and energy transfer in molecules • Photoinduced mutations in DNA

  27. Resources and References R. Trebino, Frequency-resolved Optical Gating: The Measurement of Ultrashort Laser Pulses, Book News Inc., (2002) R. Trebino, Lectures in Optics (Georgia Tech Lecture Notes) K. Ekvall, Time Resolved Laser Spectroscopy, Ph.D. Thesis, RIT Stockholm, (2000) B. B. Laud, Lasers and Non-Linear Optics, Wiley, (1991) CPA 2010 User’s Manual, Clark-MXR Inc, (2001) W. Demtröder, Laser spectroscopy, Springer, 1998 Ultrashort Laser Pulse Phenomena