1. Fundamentals of ultrafast optics and lasers

2. Laser-based static spectroscopy

3. Time-resolved spectroscopy

The birth of ultrafast optics, femtsecond pulse generation: case studies

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

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/

The Birth of Ultrafast ScienceThe Birth of Ultrafast Science

Leland Stanford Eadweard MuybridgeThe "Trotting Horse” ControversyPalo Alto, CA 1872

Time Resolution:1/60th of a second

Bar bet: Do all four hooves of a galloping horse ever simultaneously leave the ground?

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

Harold EdgertonMIT, 1942

“How to Make Apple sauce at MIT” 1964

Understanding and manipulating ultrafast dynamics in materials

Strobe PhotographyStrobe Photography

Femtoecond laser pulses

Time Resolution:few millisecond

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

Short laser pulsesShort laser pulses

Long pulse

Short pulse

The uncertainty principleTime-bandwidth product (The uncertainty principle) Bct πω 2≥∆⋅∆

Rule of thumb – 10fs needs 200 meV bandwidth

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

Time domain representationTime domain representationAny light field can be represented as:

[ ]ti pe ωΦ= ie (t)eERe[ ]Γ= i

e e (t)E Re)(tE

( )dt

dt

Γ=ωdt

dΦ+ω= p

Instantaneous frequency

dt

dΦ= 20 ωpt/tg

(up chirp)

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

Time vs. Frequency DomainTime vs. Frequency Domain• The frequency-domain equivalents of the intensity and

phase are the spectrum and spectral phase.• Fourier-transforming the pulse electric field:

yields: Note that φ and ϕ are different!

[ ] ccetE tit p .eI(t)2

1)( )(i += Φ ω

)(ie)S()( ωϕωω =E

ω0

laser gain profile

ω0

laser gain profile

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

Short pulse = ModeShort pulse = Mode--lockinglocking

exp( )( ) ( ) ( 2 / )mm

iE F m Tω ω ϕ δ ω π∞

=−∞

= −∑%

0=mϕ

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

Mode LockingMode LockingQ: How many different modes need to oscillate

simultaneously for 10 fs in a 1.5 meter Ti:sapphire laser?

A: bandwidth ∆l = 200 nm ∆ν = (c/λ2) ∆λ ~ 1014 Hz∆νbandwidth/∆νmode = 106 modes

Can this really happen?

ω0

laser gain profile

Yes, either actively or passively!

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

Case study (I) Case study (I) –– active mode lockingactive mode lockingTsunami Sub 30 fs Specifications

Average PowerMillennia Pro 5 W 400 mW

Pulse Width < 30 fsTuning Range 780 - 820 nm

Repetition Rate 80 MHz

Noise < 0.5%

Stability < 5%

Spatial Mode TEM 00

Beam Diameter at 1/e 2 points < 2 mmBeam Divergence, Full Angle < 1 mradPolarization > 500:1 vertical

Sub-30fsTsunami, Spectra-Physics, Inc

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

Case Study (I)Case Study (I)Active mode locking - acoustic optical modulator

Bragg diffractionDiving voltage V(t) cos[ωst]

skkk +='

sωωω +='Photon scattering away from a phonon

sλλθ

2sin =Bragg condition

Energy and momentum conservation

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

Case Study (I)Case Study (I)Active mode-lockinge.g., Acoustic optical modualtor in sub-30 fs Tsunami, Spectra-Physics, Inc

Modulates the amplitude and/or phase of the modes

Electric field of nth mode = En(t) = En cos(ωnt + φn) * [1 − η (1 − cos(Ωt + Φ)]

modulatortransmission

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

Case Study (I)Case Study (I)

frequency

ωn+Ωωn−Ω

En (t) = En (1− η) cos(ωnt + φn) + En (η/2) cos[(ωn−Ω)t + (φn− Φ)]

+ En (η/2) cos[(ωn+ Ω)t +(φn− Φ)]

If Ω = mode spacing by fine tuning AOM, so that ΩτRT = 2π:

Mode locking!!!

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

Case Study (II)Case Study (II)

Sub-30fs Mira, Coherent, Inc

Passive mode-lockinge.g., Kerr-lens in sub-30 fs Mira from Coherent, Inc

A type of saturable absorber

α(I) =α 0

1 + I Isat

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

Case Study (II)Case Study (II)Kerr-lens effect

x

L(x)n(x)

x

n(I) = n0 + n2I

Inside the medium

φ(x) = n k L(x) φ(x) = n(x) k L

Losses too high for a low-intensity cw mode to lase, but not for high-intensity fs pulse.

Cavity modeTi:sapp

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

Case Study (II)Case Study (II)Gain volume matching

High-intensity pulse

Low-intensity pulse

Ti:Sapph

Tuning slit width