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TRANSCRIPT
Femtosecond pulse generation
Marc Hanna
Laboratoire Charles Fabry
Institut d’Optique, CNRS, Université Paris-Saclay
Outline
Introduction
1 Fundamentals of modelocking
2 Femtosecond oscillator technology
3 The carrier-envelope phase
Conclusion
Why ultrafast pulses?
MPQ
Laser matter interaction
- Multiphoton microscopy- Micromachining- XUV HHG sources
Shortest manmade events
- Ultrafast dynamics- Frequency metrology- Attophysics
MPQ GarchingLasik
t
EPpeak
Ultrashort pulses
t
I(t)
ω
I(ω)
ΔtΔω
Time – Bandwidth Product Kt
FourierTransform
Short pulses imply broad spectra
Ultrashort pulses
0.1
1
10
100
1000S
pectr
al B
andw
idth
(nm
)
2500200015001000500
Center wavelength
10 fs20 fs
50 fs100 fs
1 ps
20 fs @ 0.8 µm wavelength → 34 nm
100 fs @ 1 µm wavelength → 12 nm
Ultrafast sources are complex
Apollon project diagram
OscillatorStretchersAmplifiersNonlinear stages PostcompressionContrastOPA
Pulse shapingBeam shapingCompressor
Outline
Introduction
1 Fundamentals of modelocking
2 Femtosecond oscillator technology
3 The carrier-envelope phase
Conclusion
Longitudinal modes in a laser
cav
kL
ck
Lcav
Gain
Longitudinal modes in a laser
Lopt
Gain
Consider N modes that oscillate simultaneously
If the φn are all equal
Lcav/c0
Longitudinal modes in a laser
50 modes oscillating
In-phase modesRandom phase modes
For a 100 fs pulse, spectrum should be broader than 1500 GHz, typical free spectral range is 100 MHz → thousands of modes!
Modelocked laser
Gain Sat.Abs.
To operate in modelocked regime, we must favour pulsed mode vs CW mode i.e. favor large intensities: saturable absorption
Propagation effects: GVD
Propagating broadband pulses experience dispersion
PropagationMaterial n(λ)
Group velocity Group-velocity dispersion (GVD)
Propagation in a dispersive medium
• Field at the input of the medium : sum of monochromaticwaves
13
Propagation over z
Dispersion: Phase accumulates over distance z according to a different propagation constant for each frequency component
The field at z is given by
Phase velocityCEP
Group velocityPulse broadening
Frequency chirp
For a Gaussian pulse
with
Linear evolution of instantaneousfrequency
tt
pinst
Spectrogram : similar to music sheet
The spectrogram
Propagation effects: GVD
Effect of GVD on the spectrogram
Time (fs)
Fré
quency
(TH
z)
2nd order dispersion
Time (fs)
Fré
quency
(TH
z)
Spectrum
Temporal
profile
Fourier-transform limited
pulse
GVD Engineering
Materials – positive (normal, red ahead) GVD in visible and near IR
Negative GVD – prism pairs, grating pairs, chirped mirrors, GTI mirrors
The longer wavelengths traverse more glass
Propagation effects: SPM
Propagating intense pulses experience self-phase modulation
0 ck n(t)l
0 2n(t) n n I(t)
t
I
tinst
Propagation effects: SPM
Effect of SPM on the spectrogram
Temps (fs)
Fré
quence (
TH
z)
Self-phase modulation
Time (fs)
Fré
quency
(TH
z)
Spectrum Temporal
profile
Fourier-transform limited
pulse
20
Propagation effects: filtering
Even if no filter are inserted in the cavity, the gain medium has a finitebandwidth that limits spectral extension
Increasing gain
λ
Optical pow
er
Spectrum
Gain narrowing
Modelocked laser ingredients
Gain Sat.Abs.
β2 SPM
output
Predicting output pulse involves finding the stationary solution
Analytically – Master Equation of Mode Locking
Numerically – Solving propagation equation over large # roundtrips
Filter
Soliton modelocking
Small changes per roundtrip (low loss low gain)
Balance between anomalous GVD and SPM
Often used in bulk oscillators
Sat.Abs.
β2<0 SPM
Time (fs)
Fré
quency
(TH
z)
Soliton modelocking
Intensity profile
-5 -4 -3 -2 -1 0 1 2 3 4 50
0.2
0.4
0.6
0.8
1
t/ t
Inte
nsity p
rofile
(a
. u
.)
Soliton area theorem
with γ given by
)/(sech)( 2
0 tPtP
22E
effAc
n20 → Determines the achievable pulse
energy
The bestiary of stable pulse regimes
Intracavity pulse shaping mechanisms depend on: dispersion, SPM, spectral filtering, saturable gain / losses, and their locations and magnitude in the cavity
Andy Chong, William H. Renninger, and Frank W. Wise, "Properties of normal-dispersion femtosecond fiber lasers," J. Opt. Soc. Am. B 25, 140-148 (2008)
Pulse shaping mechanisms
Gain Sat.Abs.
β2 SPM
output
Filter
Example: ANDi lasers
All-normal dispersion lasers
Andy Chong, William H. Renninger, and Frank W. Wise, "Properties of normal-dispersion femtosecond fiber lasers," J. Opt. Soc. Am. B 25, 140-148 (2008)
Output
→ allow larger nonlinear phase shifts per roundtrip and energy scaling
Outline
Introduction
1 Fundamentals of modelocking
2 Femtosecond oscillator technology
3 The carrier-envelope phase
Conclusion
Gain media
1 Ti:Sapphire oscillators
2 Yb:bulk oscillators
3 RE:fiber oscillators
Ti:Sa is the best
absorption
émission
Inte
nsi
té (
u.a
.)
Longueur d’onde (nm)
absorption
émission
Inte
nsi
té (
u.a
.)
Longueur d’onde (nm)
Extremely broad gain bandwidth (5 fs @ 800 nm)
Large emission cross section (41×10-20 m2 @ 780 nm)
Fluorescence lifetime 3 µs
Thermal conductivity 35 W K-1 m-1
A standard Ti:Sa cavity
HR mirror
Tuning slit
Green pump laser
Ti:Sa crystal
Outputcoupler
KLM slit
Prisms for GVD control
Typical performances: 10 – 30 nJ pulse energy at 80 MHz (1 - 2 W) tunable from 700 to 1000 nm sub-100 fs pulses (down to 6 fs!)
Kerr lens saturable absorber
0 2n(x) n n I(x)
Usually requires additional perturbance to start modelocking
→ vibrating mirror
Commercial Ti:Sa oscillators
The Ti:Sa problem
Must be pumped in the green spectral region
Nd laser SHG
Large quantum defect, inefficient, complex, large footprint, expensive…
… but still used in many applications because of its extraordinaryproperties (extreme tunability and short pulsewidth)
Gain media
1 Ti:Sapphire oscillators
2 Yb:bulk oscillators
3 RE:fiber oscillators
Yb:bulk oscillators
Moderatly broad gain bandwidth (host-dependent)
Low emission cross section (host-dependent)
Fluorescence lifetime few 100s µs – few ms
Thermal conductivity 1 - 10 W K-1 m-1
Low quantum defect
Diode pumping @ 980 nm !
Yb-doped materials
Most used material Yb:YAG
But limited gain bandwidth: work on CaF2, CALGO, KYW
Properties are very host-dependent
σ
10-24 m2
∆λ
nm
τfluo
ms
κ
W/m/K
Yb:YAG 2.2 5 0.95 11
Yb:glass 0.05 40 1 0.8
Yb:KYW 3 10 0.7 3.3
Yb:CALGO 0.75 60 0.4 6.5
Yb:CaF2 0.25 30 2.5 9
A standard Yb:bulk cavity
Saturable absorption is usually implemented using a SESAM (SEmiconductor Saturable Absorber Mirror)
Crystal
Dichroic mirror
Prism
Laser diode
PrismSESAM
Typical performances: 10 – 30 nJ pulse energy at 50 MHz (1 - 2 W) at 1030 nm 300 fs pulses
SESAM
Design parameters:
modulation depthsaturation fluence recovery time nonsaturable losses
Often self-starting
Commercial Yb:bulk oscillators
Smaller footprint, less expensive thanTi:Sa…
… but longer pulses
Gain media
1 Ti:Sapphire oscillators
2 Yb:bulk oscillators
3 RE:fiber oscillators
RE:fiber oscillators
Large and broad gain bandwdith (~ 100 fs pulsewidth)
Monolithic integration, robutness, no spatial stability considerations
Large design freedom (nonlinearity dispersion etc)
Yb Er Th
Example of a modelocked oscillator
Erbium 50 pJ 50 MHz (2.5 mW) 1550 nm 150 fs
Ytterbium 100 pJ 50 MHz (5 mW) 1030 nm 150 fs
Thulium 100 pJ 10 MHz (1 mW) 2000 nm 500 fs
Nonlinear Amplifier Loop Mirror
Unbalanced Sagnac interferometer
Relative phase depends on pulse intensity
Commercial RE:fiber oscillators
Even smaller footprint, even lessexpensive than bulk
… but lower energies
Current research
1 Ti:Sapphire oscillators
2 Yb:bulk oscillators
3 RE:fiber oscillators
Selected current research – Ti:Sa
Selected current research – Ti:Sa
500 mW 50 fs @ 400 MHz
Both SESAM and KLM
« Low cost » Ti:Sa
48
Selected current research – Yb:bulk
242 W 1 ps 80 µJ 3 MHz soliton modelocking
HHG demonstrated with additional nonlinear compression
Selected current research – Yb:bulk
Selected current research – Yb:fiber
Selected current research – Yb:fiber
Step like saturable absorber, must be injected to start
Outline
Introduction
1 Fundamentals of modelocking
2 Femtosecond oscillator technology
3 The carrier-envelope phase
Conclusion
The carrier-envelope phase
• Influence of a constant phase term φCEP for a very short pulse
-20 -15 -10 -5 0 5 10 15 20-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (fs)
Ele
ctr
ic f
ield
(a.u
.)
)(
2
0
2
0
)(
2exp)( CEPpti
et
tEtE
0CEP
The carrier-envelope phase
• Influence of a constant phase term φCEP for a very short pulse
-20 -15 -10 -5 0 5 10 15 20-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (fs)
Ele
ctr
ic f
ield
(a.u
.)
)(
2
0
2
0
)(
2exp)( CEPpti
et
tEtE
2/ CEP
The carrier-envelope phase
• Influence of a constant phase term φCEP for a very short pulse
-20 -15 -10 -5 0 5 10 15 20-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (fs)
Ele
ctr
ic f
ield
(a.u
.)
)(
2
0
2
0
)(
2exp)( CEPpti
et
tEtE
CEP
The carrier-envelope phase
• Influence of a constant phase term φCEP for a very short pulse
-20 -15 -10 -5 0 5 10 15 20-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (fs)
Ele
ctr
ic f
ield
(a.u
.)
)(
2
0
2
0
)(
2exp)( CEPpti
et
tEtE
2/3 CEP
The carrier-envelope phase
• Influence of a constant phase term φCEP for a very short pulse
-20 -15 -10 -5 0 5 10 15 20-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (fs)
Ele
ctr
ic f
ield
(a.u
.)
)(
2
0
2
0
)(
2exp)( CEPpti
et
tEtE
0CEP
CEP vs propagation
Field after propagation in a dispersive material
02
After propagation over z, maximum of the envelope for tmax=z/vg
At this point the phase is equal to
CEP
p
g
p
CEPL
zzk
v
zz
2)(
nnL
g
CEP
CEP vs propagation
CEP phase is accumulated upon propagation due to differencebetween phase and group velocity
CEP
p
g
p
CEPL
zzk
v
zz
2)(
nnL
g
CEP
Fused silica Air
Consequence of CEP evolution in a cavity?
Gain Sat.Abs.
β2 SPM
output
Filter
Steady state condition for a mode-locked laser
• For a mode-locked laser with repetition rate equal to T, the steady state condition is on the pulse shape, not on the roundtrip phase like in CW
• Stationnary if R(ω)=1, leading to perfectly regular frequencycomb spacing
CEP phase slip
The angular frequency ωCEO represents the rate at which the CEP phase drifts at the output of a mode-locked laser
Fourier
Transform
CEP: summary
CEP: Carrier-envelope phase
Phase of the carrier at the pulse maximum
CEO: Carrier-envelope offset
Frequency shift of the comb, induces a continuous drift of the CEP for successive pulses
Outline
Introduction
1 Fundamentals of modelocking
2 Femtosecond oscillator technology
3 The carrier-envelope phase
Conclusion
Conclusion
Femtosecond oscillators – large variety concepts, technologies, and performance, almost exclusively based on modelocking
Often used as a subsystem in a larger source setup (MOPA, OPCPA) so that few characteristics are retained at the end
Some properties e. g. repetition rate stability are carried over
Ti:Sa oscillators are still widely used for some applications (high field physics, nonlinear microscopy), but are not predominant anymore
66
Bonus: Non modelocked fs sources
67
Bonus: Non modelocked fs sources
140 fs 2.4 µJ pulses @ 1030 nm… without modelocking!
Thank you
Other gain media
Other notable gain media at different wavelengths
Nd:glass (1053 nm)
Cr:LiCAF, Cr:LiSAF (800 nm)
Cr:ZnSe (2.4 µm)
Cr:fosterite (1.25 µm)
Ho:YAG (2 µm)
70
NPE SA