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
I >I0
Light amplification by stimulated emission occurs when passing through gain medium
Energy
Population Inversion
Molecules
“Negative temperature”
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 The four-level system is the ideal laser system. fast
Molecules accumulate in this level, leading to an inversion with respect to
this level.
slow
Laser
transition
fast

8. Basic components of a laser
Mirror,
R = 100%
R < 100% I0 I1 I2 I3
Laser medium in excited state
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
Heisenberg uncertainty principle:
Dt*Dn≥1
e.g. for a 150fs pulse:
Dn=7THz (e.g. l=500nm)
Dl=6nm wavelength l=500nm
Long pulse
Short pulse
Irradiance vs. time
Spectrum
time
frequency

11. 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. B 65, (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
pump
Output
Laser oscillator
Amplifier medium
R=100%
R<100%
Energy levels
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
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. V
Pockels cell
Polarizer
R=100%
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
Higher frequencies occur due to the non-linear response of the material at high intensities
Nonlinear polarization:
P=e(c1E+c2E2+...)
For a photon:
Second harmonic!
Phase matching condition ensures conservation of momentum:

21. Self phase modulation and white light continuum
Wavelength, nm
Intensity, au
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 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
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
To PC
Optical Delay Rail
Frequency Doubler
Ocean Optics
S2000 CCD Detector
Sample
Cell
Filter Wheel
Chopper
CLARK
-MXR
CPA-2010
775 nm, 1 kHz
1 mJ/pulse
(7fs -1.6 ns)
Probe
Pump
Ultrafast Systems

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