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