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