1. fundamentals of ultrafast optics and...

1. Fundamentals of ultrafast optics and lasers

2. Laser-based static spectroscopy

3. Time-resolved spectroscopy

Femtsecond pulse generation: active and passive mode-locking, ultrafast amplifiers

Laser Raman/Raleigh, multi-photon excitation spectroscopy; SWCNs

Ultrafast incoherent & coherent transient, magneto-optical, infrared & time-domain THz

SWCNs, (Ga,Mn)As, HTc superconductors

Today Today

Jigang Wang, Feb, 2009

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

A A femtosecondfemtosecond laser oscillator laser oscillator

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

Higher IntensitiesHigher Intensities

Rep rate (pps)

Puls

e en

ergy

(J)

10910610310010-3

10-9

10-6

100

10-3

Oscillator

Cavity-dumped oscillator

RegA

Regenerative

Regen + multipass

Regen + multi-multi-pass

1 W average power

Francois Salin, CELIA, France

Ultrafast am

plifiers

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

Ultrafast AmplifierUltrafast Amplifier

Pulse compressor

t

t

Solid state amplifiers

t

Dispersive delay linet

Short pulse

oscillator

Regenerative amplifier scheme

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

Regenerative Regenerative amplifieramplifier

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

Ultrafast AmplifiersUltrafast Amplifiers

PC1

PC2WP

Rod TFP

TFPSeed input

M1

M2

Before injection

Intra-cavity components:M1, M2 : End mirrors Rod : Ti:Sapphire rod WP : ¼ Waveplate TFP : Thin Film PolarizerPC2 : Pockels Cell

Only the pulse to be amplified enters the cavity

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

Ultrafast AmplifiersUltrafast Amplifiers

Intra-cavity components:M1, M2 : End mirrors Rod : Ti:Sapphire rod WP : ¼ Waveplate TFP : Thin Film PolarizerPC2 : Pockels Cell

PC1

PC2WP

Rod TFP

TFPSeed input

M1

M2

Regen operation: pulse injection

V1=Vλ/2

V2=Vλ/4

Pulse is injected using the external Pockels cell PC1.Pulse is trapped using the internal Pockels cell PC2.

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

Intra-cavity components:M1, M2 : End mirrors Rod : Ti:Sapphire rod WP : ¼ Waveplate TFP : Thin Film PolarizerPC2 : Pockels Cell

PC1

PC2WP

Rod TFP

TFPSeed input

M1

M2

Regen operation: pulse ejection

V2=Vλ/4

output

V2=0

:internal Pockels cell PC2 is turned off

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

The worldThe world’’s largest lasers largest laserAlmost 10 years journey, due next month!

192 shaped pulses; 1.8 MJ total energy

National Ignition Facility(LLNL)

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

Lasers as spectroscopy light sources Lasers as spectroscopy light sources

1. Static spectroscopy using CW lasers

2. Static spectroscopy using ultrashort pulsed lasersLaser Raman/Raleigh scattering, multi-photon excitation Spectroscopy; SWCNs

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

Laser scattering experiment Laser scattering experiment -- basics basics

Excitation laser

Scattered light

Basic Instrumentation:

– Illuminate a sample with laser light (e.g. 532nm, 780nm)

– Scattered (no absorbed) light in two forms – collection and spectrally resolved detection

• Elastic (Rayleigh) → λscattered = λincident

• Inelastic (Raman) → λscattered ≠ λincident

Photon energy ωp

0

30

50

60

Inte

nsity

I s

Spectrally-resolved detection

RayleighRaman Raman

ωe

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

Laser Rayleigh and Raman scatteringLaser Rayleigh and Raman scattering

tIRωααα sin10 +=

tEE eωααµ sin0==

])cos()[cos(2

1sin 010 ttEtE IReIRee ωωωωαωαµ +−−+=

Induces polarization P = N0µ oscillates at three frequencies!

Induced dipole Polarizability Incoming field

ωIR

ωe ωs

ωIR

ωe ωs

ωIR

ωs

E1

E2

VirtualState

Rayleigh Stokes Raman Anti-Stokes Raman

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

Signals from the scattering experimentsSignals from the scattering experiments

• Spectrum – ωIR can be molecular vibrationsand low energy collective excitations such as

phonons, magnons, plasmons, spin flip transitions…

• Scattered intensity – ~ 0.1 part per million photons

• Cross section – ~ 10-30 cm2

R

θ462

2

24

2

2

0 )2

()2

1()

2(

2

cos1 −∝+−+= λ

λπθ d

n

n

RII

22

2

4

65

)2

1(

3

2

+−=

n

nds λ

πσ ωσ h/0 sph IN =

Reman/Rayleigh scattering – a net change in polarizability

Absorption, FTIR – a net change in dipole moment,

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

The origin of polarizabilityThe origin of polarizability

Tendency of charge distribution or wave function of a dipole to be distorted by local E field, i.e.,

Lex ENE 00 /χεα = χ: electrical susceptibility0/ ≠dtdα

oC

o oC

o oC

o0/ ≠dtdµ

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

Selection rules: Raman vs. IRSelection rules: Raman vs. IR

ωe ωs

ωIR

ωe ωs

E1

Rayleigh Stokes Raman

V

)(),()( 0 ises EP ωωωχεω =

11),( EVVEse MM →→∝ωωχ

E2

E1

M is dipole transition element, e.g., where η is along E filed ><=→ irfM fi .η

21),( EVVEse MM →→∝ωωχ

ωe

IR absorptionE2

E1

One-photon

21)( EEe M →∝ωχ

Multi-photon, e.g., twophoton

1221

),(

EEEVVE

ee

MMM →→→∝ωωχ

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

SingleSingle--wall carbon nanotubeswall carbon nanotubes

Metallic Semiconducting

Ch = na + mb

n – m = 3M + ν

1) M = ν = 0

2) M ≠ 0, ν = 0

3) M ≠ 0, ν = ±1

Metal

Narrow Gap Semicond.

Large Gap Semicond.

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

Example: Laser Raman in SWCNsExample: Laser Raman in SWCNs

“Dark-field Spectroscopy”

1. Presence of nanotubes 2. Orientation of isolated tubes or aligned samples3. Diameters of carbon nanotubes:4. Mechanical strain

Raman Intensity vs. shift

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

Rayleigh scatterings in individual SWCNsRayleigh scatterings in individual SWCNs

In-situ CVD growthacross etched slit

Rayleigh Spectra

Energy (eV)

Heinz, Brus, Colombia Univ

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

MultiMulti--photon Excitation Spectroscopy in SWCNsphoton Excitation Spectroscopy in SWCNs

α

hν

1s

2p

Eg

Heinz, Brus, Colombia Univ

Motivations and basic schemes

Transient transmission and reflection spectroscopy

Ultrafast magneto-optical spectroscopy

Ultrafast mid-infrared/THz spectroscopy

Coherent transient spectroscopy

Examples

1. Time-resolved (ultrafast) laser spectroscopy

TodayToday’’s Lectures Lecture

Jigang Wang, Feb, 2009

Jigang Wang, http://www.cmpgroup.ameslab.gov/ultrafast/

TimeTime--resolved laser spectroscopy: whyresolved laser spectroscopy: why

Ultra-fast

Ultra-broadband

Ultra-intensive

Manipulation

Fundamental time scales for key microscopic interactions

Energy scales of important collective excitations

Searching for new regimes of condensed matter physics

A new paradigm for condensed matter physics

Fundamental time scales in condensed matterFundamental time scales in condensed matter

Jigang Wang, Feb, 2009

10-9 s = 1 ns

10-12 s = 1 ps

10-15 s = 1 fs

Time

carrier recombination(100ps-1ns)

carrier cooling (1-100ps)e-acoustic phonon (1-100 ps)

e-opitcal phonon scattering (<1 ps)e-hole scattering (<1 ps)

h-optical phonon scattering (100 fs)e-e scattering (10 fs)

e correaltion time (<1 fs)

Electronic Magnetic (Atomic) Structural

Spin precession, dampingin in FM(100 ps-10ns)

Spin-phonon (1-100ps)Spin precession in AFM (1-100ps)

Spin-orbit (10 fs)Spin-spin exchange(1 fs)

vibration period (100 fs)

ultrafast chemical/biological reactions

Ultrafast melting(1-100 ps)

Rotations of Molecules (1ns)

Fundamental energy scales in condensed matterFundamental energy scales in condensed matter

Jigang Wang, Feb, 2009

3 eV

Energy

1 eV

100 meV X

0 meV

Mott gap, charge-transfer gap (1-3 eV)

Interband transition in most semiconductors (400 meV – 2 eV)Multi-phonons and multi-magnons (50-500 meV)

Intra-exciton trainsiton in semiconducting SWCNs(150 meV - 300 meV)

Polarons (20-300 meV)

Pseudogap excitation (30-300 meV) Optical phonons (40-70 meV)Magnons (10- 40 meV)

Superconduting gap (1-40 meV)

Jigang Wang, Feb, 2009

Ultrafast laser spectroscopy: schemes Ultrafast laser spectroscopy: schemes

The most commonly used geometry is “pump and probe”.

It usually involves exciting the medium with one (or more) ultrashort laser pulse(s) and probing it a variable delay later with another.

E

K

Ultrafast excitation –Highly non-equilibrium state

Time-delayed probe –build-up of transient state

and recovery of the ground state

Jigang Wang, Feb, 2009

Ultrafast laser spectroscopy: how Ultrafast laser spectroscopy: how

∆t

10 fs – 100 fs

k2

DetectorSpectrometer

k1TimeTime

SignalSignal

∆∆tt = = --100 fs100 fs ∆∆tt = 0 fs= 0 fs ∆∆tt = 100 fs= 100 fs

λλ λλλλ

Sub-10 fs, sub-1 nm, B field up to 10T, Low temperature

down to 1.2K

Jigang Wang, Feb, 2009

Ultrafast laser spectroscopy: types Ultrafast laser spectroscopy: types

∆t

T

2k2-k1

k1

R

EEUltrafast incoherent Spectroscopy: Transient reflection/transmission

Ultrafast mid-infrared

Ultrafast THz Spectroscopy

Ultrafast magneto-optical

Coherent transient spectroscopy

Jigang Wang, Feb, 2009

Ultrafast laser spectroscopy: signalsUltrafast laser spectroscopy: signals

TransmissionTransmission

ReflectionReflection

EmissionEmission

Signals -> M, p, σ, χ(2) , χ(3) ...

Absorption

magnetization, conductivity, electrical polarization, 2nd and 3rd order nonlinearity……

Let the unexcited medium have an absorption coefficient, α0.Immediately after excitation, the absorption decreases by ∆α0.

∆α(τ) = ∆α0 exp(–τ /τex) for τ > 0

where τ is the delay after excitation, and τex is the excited-state lifetime.

So the transmitted probe-beam intensity—and hence pulse energy and average power—will depend on the delay, τ, and the lifetime, τex:

Itransmitted(τ) = Iincident exp–[α0 – ∆α0exp(–τ /τex)]L where L = sample length

= Iincident exp–α0L exp∆α0exp(–τ /τex)L

≈ [ Iincident exp–α0L] 1+∆α0exp(–τ /τex)L assuming ∆α0 L << 1

≈ Itransmitted(0−) 1+∆α0exp(–τ /τex)L

Jigang Wang, Feb, 2009

Ultrafast laser spectroscopy: modelingUltrafast laser spectroscopy: modelingExample: transient transmission

Jigang Wang, Feb, 2009

Ultrafast laser spectroscopy: modelingUltrafast laser spectroscopy: modelingExample: transient transmission

∆T(τ) /T0 = [Itransmitted(τ) – Itransmitted(0−)] /Itransmitted(0−)

The relative change in transmitted intensity vs. delay, τ, is:

Cha

nge

in p

robe

-be

am in

tens

ity

Delay, τ0

Itransmitted(τ) ≈ Itransmitted(0−) 1+∆α0exp(–τ /τex)L

∆T(τ) /T0 ≈ ∆α0 exp(–τ /τex)L

⇒

InGaAs

Jigang Wang, Feb, 2009

Example: transient transmission in LT InGaAs

-0.8

-0.4

0.0

0.4

0.8

∆R/R

(%

)

20016012080400

Time Delay (ps)

-0.8

-0.4

0.0

0.4

∆R/R

(%

)

100Time Delay (ps)

InGaMnAs/InGaAsT= 20K

Ultrafast carrier dynamicsUltrafast carrier dynamics

Pump: 2 µmProbe: 775 nm

1. Initial drop in reflectivity

2. Very rapid rise (~2 ps) + sign change

3. Periodic oscillations(~ 23 ps)

4. Very slow decay(100’s of ps)

Jigang Wang, Feb, 2009

Carrier trapping: two regimesCarrier trapping: two regimes

V.B

C.B

As+Ga

Antisite

Ga Vacancies

As0Ga

Antisite

(1) carrier trapping by mid- bandgapdefects (~2 ps)

(2) reexcitation and recombination of trapped carriers

-6

-4

-2

0

2

103 *∆

R/R

3210-1Time delay [ps]

(1)

(2)

Jigang Wang, Feb, 2009

-1.0

-0.5

0.0

0.5

1.0

∆R/R

(%

)

1208040Time Delay (ps)

650nm

775nm

850nm

Propagating coherent acoustic phonons Propagating coherent acoustic phonons

EF

~100 fs

Phonon package

Cs

InAs GaSb

Jigang Wang, Feb, 2009

Ultrafast MagnetoUltrafast Magneto--optical Spectroscopyoptical Spectroscopy

Magnetic IonsMagnetic Ions

CarriersCarriers

ExcitationExcitation

Detection Detection kθ

kη

M

fs- & vectorially resolved Magnetization dynamics at H < 8.0 T and T > 1.5K

Jigang Wang, Feb, 2009

Transient Demagnetization in Transient Demagnetization in InMnAsInMnAs

0.4

0.2

0.0

− ∆θ

K /θ

K

1 10 100 1000Time Delay (ps)

(1) (2) (4)(3)

-∆M

/MSpin-spin Spin-phonon Heat diffusion

Jigang Wang, Feb, 2009

Ultrafast Rotation in Ultrafast Rotation in GaMnAsGaMnAs

-80

-60

-40

-20

0

20

∆θ k

(µr

ad)

8006004002000Time Delay (ps)

30

20

10

0

∆θ k

(µr

ad)

3.02.01.00.0-1.0Time Delay (ps)

Y+(0)

|B|=0T, T = 5K

Jigang Wang, Feb, 2009

-10

1

-8-6

-4-2

02

-1

0

1

∆Mz (10 -5

rad)

∆My (10

-5 )

∆Mx (10

-5 )

Z (001)

X (110)

Y (1-10)

(100)MHA

3.1 eV ~ 120 fs

Ultrafast Rotation in Ultrafast Rotation in GaMnAsGaMnAs

-10

-8

-6

-4

-2

0

∆M

z (1

0-5 ra

d)

-1.0 0.0 1.0

∆My (10-5 )

-1.5

-1.0

-0.5

0.0

0.5

1.0 ∆

My

(10-5

)

-1.5 -1.0 -0.5 0.0 0.5 1.0

∆Mx (10-5 )

-10

-8

-6

-4

-2

0

∆M

z (1

0-5 ra

d)

-1.5 -1.0 -0.5 0.0 0.5 1.0

∆Mx (10-5 )

9.3 ps

Amplitude Amplitude andand Phase informationPhase informationReal & Imaginary Part of Real & Imaginary Part of σσ((ωω), ), εε((ωω))

( ) ωωω σ ω

≡ ≈+ + 0

( ) 2( ) 1 ( )

OUT

IN S

Et

E n d Z

Complex transmission coefficientComplex transmission coefficient

( )tE t( )iE t

thin filmthin film

FieldField--resolved Detectionresolved Detection

1 THz = 300 µm = 33 cm-1 = 4.1 meV

ZnTe

ETHz(t) ∝dt2

d2P(t)

near-IR pulse

nonlinear crystal(ZnTe)

Jigang Wang, Feb, 2009

Optical Pump and THz probeOptical Pump and THz probe

Jigang Wang, Feb, 2009

THz probes of THz probes of excitonexciton formation and ionization formation and ionization ∆σ

1(Ω

-1cm

-1) 20

10

∆t (ps)

0

100

200

300

Photon Energy (meV)

0

4 8 4 8

4 8

TL = 6 K 30 K 60 K

T = 6 K T = 6 K ⇒⇒ recombinativerecombinativepopulation decaypopulation decay

High THigh TLL: : ee--hh pairs become conductingpairs become conducting

ExcitonicExcitonic component remainscomponent remains

⇒⇒ excitonexciton ionization (via phonons)ionization (via phonons)

Quantum beatQuantum beat detected by 3detected by 3--Pulse fourPulse four--wavewave--mixingmixing

k2

k3

k1

k1+k2- k3

Δt12

Coherent transient Spectroscopy Coherent transient Spectroscopy

LL0

LL1ћωcE

ner

gy

Optical excitation mostly on LL1

The LL0 signal is small in comparison to LL1, but with strong oscillations

LL1 signal – no clear oscillations.

Quantum Beats of 2D MagnetoQuantum Beats of 2D Magneto--excitonsexcitons

Coherent Quantum Beats Coherent Quantum Beats

+k2 +k1-k3

∆t12

ks

ω1 phase accumulated

+k2+k1

-k3

∆t12

ks

ω0 phase accumulated

•• k2 create dipole k2 create dipole coherence , k1 & k3 coherence , k1 & k3 probesprobes

•• The oscillations of The oscillations of ΩΩ00--ΩΩ1 will decay as 1 will decay as ΓΓ0+0+ΓΓ1 1

Jigang Wang, Feb, 2009

Other ultrafast spectroscopic techniquesOther ultrafast spectroscopic techniques

Photon Echo, three pulse photon-echo peak shift

Heterodyne detected four-wave mixing

Transient grating spectroscopy,

Transient Coherent Raman Spectroscopy

Ultrafast electron scattering,

ultrafast X-ray scattering/absorption

Transient Surface SHG Spectroscopy

Transient photo-emission Spectroscopy

Time-resolved fluoresce spectroscopy

Heterodyned ultrafast polarization spectroscopy

……

Almost any physical effect that can be induced and thereby

probed by ultrashort light pulses!