femtosecond lasers istván robel department of physics and radiation laboratory university of notre...
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Femtosecond lasers
István Robel
Department of Physics and Radiation LaboratoryUniversity of Notre Dame
June 22, 2005
• 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
Outline
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
Spontaneous emission
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
Bosons and fermions
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
Stimulated emission
En
erg
y
Population Inversion
Molecules
“Negative temperature”
Light amplification by stimulated emission occurs when passing
through gain medium
I0 I >I0
Competing processes:
Absorption: only possible if an atom is not in the excited stateSpontaneous emission: important if the lifetime of the excited state is too short
Amplification of light
The four-levelsystem is theideal lasersystem.
fast
fast
slow
Molecules accumulate in this level, leading to an inversion with respect to this level.
Lasertransition
Four-level laser
Mirror,R = 100%
Mirror,R < 100%
I0 I1
I2I3 Laser medium in excited state
Ioutput
General characteristics of laser radiation:• Coherent (typical coherence length 1m)• Monochromatic (/=10-6)• Directional (mrad beam divergence )• Polarized
Basic components of a laser
• 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
Time scales in nature
Long pulse
Short pulse
Irradiance vs. time
Spectrum
time
time
frequency
frequency
Heisenberg uncertainty principle:
t≥
e.g. for a 150fs pulse:=7THz (e.g. =600THz @ =500nm)=6nm wavelength spread @ =500nm
Ultrashort laser pulses
L
c
2
Frequency modes of the laser cavity due to the spatial confinement:
e.g. for a 1m long cavity:=1.5GHzE=0.6eV=0.001A
Frequency modes of the laser cavity
Generation of short pulses by mode-locking
• 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, 277-294 (1997)
Mode-locking by non-linear polarization rotation
In a medium different frequencies propagate with different velocities
v v / 1g phase
dn
n d
Group velocity dispersion: Chirp
• Spatial separation of different frequencies• Longer optical path for the frequencies that are “ahead”• Recombination of different frequencies in a short pulse
Pulse compression
Laser oscillato
r
Amplifier medium
pump
Energy
levels
Difficulties:• beam only passes once through amplifier medium• Output intensity is changing in every roundtrip and intensity is lower than in cavity
R=100% R<100%
Output
Amplification of short laser pulses
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.
V
Pockels cell
Polarizer
R=100% R=100%
Pockels cell and cavity dumping
M mirrorTFP thin film polarizerFR Faraday rotatorPC 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
Regenerative amplifier
Oscillator Stretcher Amplifier Compressor
• Pulse is stretched first to avoid high intensity artifacts in the amplifier
• Amplified pulse is compressed to obtain the short pulse duration
Chirped Pulse Amplification
Higher frequencies occur due to the non-linear response of the material at
high intensities
(2 ) ( )n n
Phase matching condition ensures conservation of
momentum:
Nonlinear polarization:P=()
tEtEP 20201 coscos
tt 2cos2
1
2
1cos2
tEE cos0For a photon:
Second harmonic!
Nonlinear Optics
0 2( , ) ( )z t k z n I t
0 2
( , ) ( )( )inst
z t I tt k z n
t t
775 nm, 150 fs pulse in sapphire crystal
A wide range of frequencies is generated with a short, intense pulse
Self phase modulation and white light continuum
Wavelength, nm
Inte
nsity
, au
Parameters:Wavelength of fundamental: 775 nmPulse duration: 150 fsPulse energy: 1mJPower per pulse: 7 GWRepetition rate: 1KHzWavelength of second harmonic: 387 nmPulse duration: 150 fsPulse energy: 0.25mJ
Er doped fiber oscillator
25KHz=1.55m
Pumped withCw diode laser
=1mP=150mW
Pulsecompressor
SecondHarmonic
Generation
PulseStretcher
First Level
Nd:YAG pump laser
Ti:SapphireRegenerative
amplifier
Pockels cellwith
HV supplyand delay timer
Pulsecompressor
Second and Third
harmonic
Second Level
Output
The Clark CPA-2010 Laser System
Unexcited medium Excited mediumUnexcited 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
Transient absorption spectroscopy
To PC
Optical Delay Rail
Frequency Doubler
Ocean OpticsS2000 CCD Detector
SampleCell
Filter Wheel
Chopper
CLARK-MXR
CPA-2010
775 nm, 1 kHz1 mJ/pulse
(7fs -1.6 ns)
Probe
Pump
Ultrafast Systems
• 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
Experimental Setup: Pump-Probe configuration
Femtosecond Transient Absorption Spectroscopy at NDRL
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
Applications of pulsed lasers
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
Resources and References