Ultrafast Optical Physics II, SoSe 2014, May 16,
Lecture 6, Franz X. Kärtner
Review: Femtosecond Laser Frequency Combs
10.4 Noise in Modelocked Lasers
11 Amplifiers
11.1 Laser Amplifiers
1 Cavity Dumping
2 Laser Amplifier Rate Equations
2.1 Frantz-Nodvick Equation
2.2 B-Integral Scaling
2.3 Regenerative and Multipass Amplifiers
3 Chirped Pulse Amplification
3.1 Stretchers and Compressors
3.2 Gain Narrowing
3.3 Pulse Contrast
3.4 High Energy, Large Average Power Designs
1
Time-Domain Picture
t
t
t
2
Pulse Train from a Modelocked Laser
φ0
φ0 + 2ΔφCE
φ0 + ΔφCE
vg
t
TR
TR =
Frequency Comb
2L
vg
vp
f
0
f m = mf R + f CE
Carrier Frequency
fc
f
3
Measure carrier-envelope offset
frequency using 1f-2f Interferometer
power
beat
frequency
f ceo
2mFR + f ceo
mFR + f ceo
f
2mFR + 2 f ceo
4
Phillip Russel, Univ. of Bath, now Max-Planck
Institute for the Science of Light, Erlangen
http://nobelprize.org/nobel_prizes/physics/laureates/2005/hall-lecture.html
5
http://nobelprize.org/nobel_prizes/physics/laureates/2005/hall-lecture.html
6
Measure both repetition rate and carrierenvelope offset frequency
7
8
Bandwidth of Few-Cycle Optical Pulses!
Ti:sapphire Gain
Gain, a.u.
10 fs! ~ 4 cycles (Standard Optics)
Chirped Mirrors
2 Cycles = 5.4 fs!
One Octave!
Double-Chirped Mirror
Pairs
1 Cycle = 2.7 fs @ 800 nm!
0.6!
0.8!
1.0!
1.2!
Wavelength, µm!
1.4!
First demonstration of octave spanning Ti:Sapphire Laser:
U. Morgner, et al., PRL 86, 5462-5465, 2001.
9
9
Octave Spanning Oscillator!
10
Frequency Metrology
power
Frequency
to measure
Frequency
standard
f
11
What is a Clock?!
an oscillator
and
a clockwork
Pendulum - Christiaan Huygens 1656
Cesium atom - 1955 (10-10 ~ 1sec/300yrs)
Chronometer - John Harrison (H4) 1761 (10-6 ~ 1 sec/ 9 days )
Atomic fountain - NIST-F1 (1.7x10-15 ~ 1sec/20Myrs)
Quartz - W. Marrison, Bell Labs, 1928 (10-8 ~ 1 sec/3yrs )
Hg ion – 5x10-18 ~ 10sec since big bang
12
Optical Clock!
φCE = 0
φCE = 0
φCE = 0
φCE = 0
φCE = 0
φCE = 0
TR
Laser
CE-phase stabilized Femtosecond Pulse Train
Optical Ref.
f0 = m fR
fR = 1/TR : pulse repetition rate
fR
(n/m) f0
Each microwave cycle = M Optical Cycles
Low noise optical pulse train or microwaves
13
CH4-HeNe Based Frequency Comb and Clock
CH4/HeNe#1
Laser
PPLN
HeNe discharge tube
HeNe#2
Laser
3.39um
LF
~
DCMs
70MHz
LF
1 GHz
Ti:Sa
M. A. Gubin, Lebedev Institute
PZT
f/32
LBO
Pump Laser
570nm l/2
PBS
AOM
LF
A. Benedick, et al. Opt. Lett. 34, pp. 2168-2170, (2009)
14
Optical Arbitrary Waveform Generation
•  Require high repetition rate sources to ease (DE)MUX
fabrication requirements
15
Doppler-shift spectroscopy
NOT TO SCALE
spectrograph
Th-Ar lamp
Astro-comb
or I2 cell
C-H. Li, et al., Nature 452, 610-612 (2008).
Astro-comb => remove comb lines with
a stabilized Fabry-Perot cavity to
achieve line-spacing of 40 GHz
17
Th-Ar lamp versus Astro-Comb
(Whipple Obseratory, Arizona)
CCD array
Diffraction orders
Blue
ThAr
comb
Red
Echelle dispersion
18
10.4 Noise in Mode-Locked Lasers
19
Pulse train from a mode-locked laser
Figure 10.1: Pulse train from a mode-locked laser.
20
Optical spectrum of a mode-locked laser
Figure 10.2: Optical mode comb of a mode-locked laser output.
21
Perturbation theory
The dynamics of the pulse parameters due to the perturbed NLSE can be
projected out from the perturbation using the adjoint basis using the orthogonality
relation
22
Perturbation theory
Physics behind:
(10.15)à a change of soliton energy causes a cumulative change of phase since
the contribution from the Kerr effect has changed.
(10.14) & (10.16)à due to gain saturation, gain filtering, and saturable absorber
action, the pulse energy and center frequency fluctuations are damped with
decay constants
(10.17)à a change of carrier frequency causes a cumulative change of
displacement due to a change in group velocity.
23
Noise as a perturbation
Many noise sources: Fluctuations of the pump power
Mirror vibrations
Air currents, air pressure fluctuations
Temperature fluctuations
Here, we consider only fundamental noise sources:
Spontaneous emission noise from amplifier
Modeled as Gaussian white noise sources with autocorrelation function:
*
Power spectral density
of noise source
Noise energy added to intracavity field within one roundtrip:
Excess noise factor of amplifier
(non ideal amplifier)
Photon lifetime
24
Perturbations in amplitude, phase, carrier frequency and timing
Noise source
that generates
amplitude fluctuations
With:
25
Correlation functions of reduced noise sources
Noise sources are white and independent!
Define power spectra of amplitude, phase, frequency and timing fluctuations:
e.g. amplitude fluctuations:
26
Power spectral densities
Finite energy and center frequency fluctuations:
27
Phase noise and timing jitter
Undergo a diffusive motion with variances:
Causes fundamental linewidth of optical lines and the microwave
photo current spectrum
28
Phase Noise
Phase difference:
Gaussian random variable!
with probability density:
variance
Expectation value of phasor: exp(jϕ)
10.4.1 The Optical Spectrum
(Neglecting amplitude and frequency noise)
29
with
Fourier transform of pulse
c
m=0!
30
Noise close to line center is determined by correlation function for large T:
with:
31
Lorentzian lines at mode comb positions:
with HWHM
negligible at
line center
32
For cw-laser: Shawlow – Townes linewidth:
Typical numbers:
@1µm
2 l = 0.1
= 2.5x1011
fR = 100 MHz
Θ= 2
◊ Δfφ = 8 µHz X
Expected optical linewidth:
◊ Δfφ ∼ 1 mHz - 1 Hz
33
10.4.2 The Microwave Spectrum
10-fs laser: M=106
34
10.4.3 Example: Er-fiber laser
Figure 10.8: Schematic of soliton fiber laser mode-locked with a
semiconductor saturable Bragg reflector (SBR)
35
36
One often measures the phase noise of a harmonic of the photo current:
Single-Sideband Phase noise: SSB
37
Short Pulse Amplification
11 Amplifiers
11.1 Laser Amplifiers
1 Cavity Dumping
2 Laser Amplifiers
2.1 Frantz-Nodvick Equation
2.2 B-Integral Scaling
2.3 Regenerative and Multipass Amplifiers
3 Chirped Pulse Amplification
3.1 Stretchers and Compressors
3.2 Gain Narrowing
3.3 Pulse Contrast
3.4 High Energy, Large Average Power Designs
38
Pulse energies from different laser systems
103
Pulseenergy (J)
Regen + multipass amplifiers
1-100 W
average
power
100
Regenerative
amplifiers
10-3
Cavity-dumped
oscillators
10-6
Oscillators
10-9
10-3
100
103
106
109
Repetition Rate, Pulses per Second
39
1 Cavity Dumping
With Bragg cell
With Pockels cell
40
2 Laser Amplifier Rate Equations
3
2
Fast Relaxation
n: population density of upper laser level
τL
1
0
Fast Relaxation
gain : g(z,t) = σ ⋅ n(z,t)
: upper state lifetime
σ : interaction cross section
ω L : laser center frequency
ΔλL : FWHM laser gain bandwidth
ω L
: saturation fluence
Fsat =
σ
dI (z,t)
= g(z,t) ⋅ I (z,t)
dz
dn(z,t)
1
I (z,t)
pop. upper laser level :
= − n(z,t) − σ ⋅ n(z,t)
dz
τL
ω L
laser int ensity :
initial pop. upper laser level : n0 (z,t); small signal gain : g0 (z,t)
41
Laser Amplifiers
3
2
Pump pulse
Amplified
pulse
Seed
pulse
1
0
Energy levels of
amplifier medium
Laser
oscillator
Amplifier
medium
Laser amplifier: Pump pulse should be shorter than upper state
lifetime. Signal pulse arrives at medium after pumping and well within the
upper state lifetime to extract the energy stored in the medium, before it is
lost due to energy relaxation.
42
2.1 Franz-Nodvik Equations
Multi-pass gain and extraction
Fluence : F (z) = ∫ I (z,t) dt
∞
3
−∞
"L
%
Small signal gain : Go = exp $ ∫ g0 (z,t) dz '
#0
&
F / Fsat
Fluence after roundtrip i : Fi = Fsat ln !"1+ Go e i−1
−1 #$
)
1
0
−1
− F / Fsat
Gain after roundtrip i : Gi = !"1− e i−1
1−1 / Gi−1 #$
(
Fin
Amplifier
medium
G = Fout
Fext
/ Fin
F: Fluence =
Energy
Area
)
Fout
2.6
G0=3
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0
1
1
0.8
0.6
0.4
0.2
2
3
4
F = Fin / Fsat
extractable energy : Fext = Fpump ⋅
5
fL
⋅ pump efficiency
fp
0
η = Fout / Fext
(
2
43
2.2 B-integral scaling with pulse energy
K
go = 0.3cm-1
tp = 0.5 ns
n2 (cm2/W)
Jsat
K
Yb:YAG
1.03 µm
6.9x10-16
2.2 J/cm2
1.6
Yb:YLF
1.02 µm
1.3x10-16
10 J/cm2.
1.8
Yb:YLF
995 nm
1.3x10-16
7 J/cm2
2.6
For the same Bmax,
about 5 times more pulse
energy can be obtained
from YLF than YAG
*JSTQE, Konoplev V4,No2, pg 459,1998
44
2.3 Basic Amplifier Schemes
a) Multi-pass amplifier
pump
input
b) Regenerative amplifier
pump
output
gain
input/output
gain
polarizer
Pockels cell
45
Multipass amplifier pulse-growth/gain-extraction
Pulse growth dynamics
dictated by the system’s
GAIN and LOSS ratio
Fluence
0.2
( Fi/Fsat J')
0, n
0.1
DIODE
PUMP
0
0
0
4
4
8
8
12
12
n
16
20
24
16
20
24
16
20
24
Gain
Initial gain Go
0.2
( Gi )
g'⋅0 , n g'o
0.1
Round-trip transmission T
0
0
0
4
4
8
8
12
12
n
16
20
24
PASS NUMBER
Multipass amplifier: Theory and numerical analysis
Lowdermilk and Murray, JAP 51, No. 5 (1980)
46
Thermal Effects
Laser rod
er
w
o
p
Low
Pump
- Bulging of the surface
- Change of index of
refraction with pump
intensity distribution
Deformation of the material induces a thermal lens of strength f
-  What to care about in the design ?
-  Heat in the amplifier medium due to
-  Quantum defect (~ 91% for Yb:YAG, ~ 76% for Nd:YVO4, ~ 67% for Ti:Sa)
-  Parasitic processes in 4-level systems, such as excited-state
absorption, upconversion or self quenching
47
Laser Material Choice
•  Wide emission bandwidth
•  Fsat that minimizes coating damage risk
•  Low non-linear index to avoid self focusing
•  Good thermo-optic coefficients, κ, α and dn/dT
•  High pump absorption (high doping possible), to
minimize material thickness
•  Low quantum defect, to minimize heat
48
Solid state laser materials for high average power / high peak power applications
Yb:YAG
300-K
Yb:YAG
CRYO
Yb:YLF
300-K
Yb:YLF
CRYO#1
Yb:YLF
CRYO#2
Yb:LuAG
300-K
Yb:CaF2
300-K
Ho:LuLF
300-K
Emission wavelength
(nm)
1030
Δλ=10
1029
Δλ=1.1
1020
Δλ=30
1020
Δλ=15
995
Δλ=5
1028
Δλ=1.3
1036
Δλ=30
2066
Δλ=75
Storage lifetime (ms)
1
1
2
2
2
1
2.4
15
Pump wavelength
(nm)
940
Δλ=17
940
Δλ=12
940
Δλ=10
960
Δλ=3
960
Δλ=3
940
Δλ=15
976
Δλ=5
1937
Δλ=30
Quantum defect (%)
9.5%
9.5%
9.5%
6.5%
3.5%
9.5%
5.8%
6.1%
Saturation fluence
12 J/cm2
2.2 J/cm2
90 J/cm2
11 J/cm2
6 J/cm2
7.4 J/cm2
76 J/cm2
80 J/cm2
Non linear index
(10-16 cm2/GW)
6.9
6.9
1.3
1.3
1.3
6.9
1.3
1.3
Birefringence
none
none
Uniaxial
Uniaxial
Uniaxial
none
none
None
Thermal cond. W/
m*K
8
40
4
30
30
8
5.2
5
Stress fracture (W/
cm)
88
88
1
50
50
88
1
1
Useful size (cm)
10
ceramic
10
ceramic
10
crystal
10
crystal
10
crystal
10
ceramic
40
crystal
40
crystal
Max Doping %
10%
10%
60%
60%
60%
50% ?
5%
5%
KEY:
Positive
Neutral
Caution
Negative
49
High Power Amplifier Technologies
Large Surface / Volume Ratio and Thermal Gradients along propagation
Innoslab, ILT Aachen
Thin Disc
Signal
Pump
Fiber
Cryogenic Laser
Improved thermal
conductivity,
thermal stress coeff.
pump absorption,
and
higher gain
Signal
Pump
50
3 Chirped-Pulse Amplification
Short
pulse
oscillator
G. Mourou and coworkers 1985
Dispersive delay line
Chirped-pulse
amplification involves stretching the
pulse before amplifying it,
and then compressing it later.
t
Solid state amplifier(s)
t
Stretching factors of up to 10,000 and
recompression for 30fs pulses can be
implemented.
Pulse compressor
51
Chirped Pulse Amplifier System
Oscillator – Stretcher – Multiple Amplifiers - Compressor Chain
Oscillator
Stretcher
Amplifier 1
Amplifier 2
Amplifier 3
Compressor
52
3.1 Stretchers and Compressors
3.1.1 Prism Pairs
3.1.2 Grating Pairs
3.1.3 Öffner Stretcher
3.1.4 Fiber or Volumne Bragg Gratings
3.1.5 Acousto-Optic Programable Filter (DAZZLER)
53
he following92expression (for single
pass) [55]:
CHAPTER
3. cos
NONLINEAR
PULSE PROP
(
)
(
)
=
e 3.16:
Prism
pair
for
dispersion
compensation.
The
3.1.1
Dispersion:
Prism
uces
to the
the distance
following
expression
(for
single
pass)
[55]:
the
expression
(for
single
pass)
is
between
prism
apices
and
( [55]:
) isPair
the angle between
e following
less
in(the
thethered
) light
(3.88)
( material
)=
efracted
ray atcos
frequency
and path
the linethen
joining
twowavelengths
apices. The
cos ( between
) can be prism
(3.88)
( order
)=
is) =
the
distance
apices
and
( )optical
is the a
ere
nd
and( third
dispersion
expressed
in terms
of the
engths
are
less
delayed
than
red
wavelength
cos ( )
(3.88)
C
(
)
=
cos
(
):
between
prism
apices
and
(
)
is
the
angle
between
Red joining the two
refracted
ray
at
frequency
and
the
line
rot
istance between prism apices and ( A) is
the
angle
between
3
2apices.
ß The
uency
and
the line joining
the
two
Optical
Pathlength
00dispersion
ond
and
third
order
can
be
expressed
in
terms
y
at
frequency
and
the
line
joining
the
two
apices.
The
(
)
=
(3.89)
between
prism
apices
and
(
)
is
the
angle
between
G
2
2 of the expression
dispersion
can
be
expressed
in
terms
optical
q.(3.83)
reduces
to
the
following
(for
single
2
can be( expressed
in terms of the optical
H
horder( dispersion
) =and cos
): joining
uency
the
line
the
two
apices.
The
¶
4 µ
os ( ):
2
3L
3
2
3 000 2 3
2
dispersion
can
be
expressed
in
terms
of
the
optical
E
3
(3.90)
(
)
=
+
00
00
2
3
00
2
3
( )= ( )=
(3.89)
4
cos
(
)
=
(3.89)2 (D ) F
(
)
=
22
2
2
2
2
2
2
¶ ¶
the following
derivatives
with respect to
2
B wavelength
4 2 3µ
2 of
4 µ
blau
3 the3 optical path
µ
¶
Blue (3.90)
000 00
4
2
3
3
(
)
=
+
) =43 2 3 2angle:
(3.89)
(3.90)
) = at
+ 000
22 3
3
2
is4(Brewster’s
the
between
prism
apices
eated
2 3 distance
2
3
( )=
+ and ( ) is t
2
3
2 3
µ
¶
4
g
of 00the at
optical
path
with
to wavelength
efracted
ray
and
the
the
4
2 frequency
30 2 respect
3 respect
0 2 line joining
tives
the
optical
path
with
to
wavelength
ULSEof
COMPRESSION
93
= 2[ + (2
)( ) ] sin
4( ) cos
(3.91)
2angle:
wster’s
3order
(3.90)
= following
and
third
be path
expressed
in term
angle:
2 +dispersion
3 of the can
2
3
hd)the
derivatives
optical
with
respect
4
3
2
derivatives
3 0 2 6 ( ):
4
2
00( ) =
30cos
02 2
=
[6(
)
(
+
2
+
4
luated
at
Brewster’s
angle:
[ + (23
)( ) ] sin
4( ) cos) + 12
3
0 2
0 2
0 00
3
(2
(3.91) )(3.92)
tives of)(the
to wavelength
3
) ]optical
sin path
4( 3)with
cosrespect
000
0 3
0 00 (3.91) 2
+2 Figure
] sin 3.16:
+ 12[(Prism pair
2 )(00for
) dispersion
] coscompensation.
(3.93) The blue w
angle: 2
( )=
2
2
00material in the light
3
0 2 2
54
have
less
path
then
The
0
00 the red000wavelengths.
= 2[index+of(2the prism material;
)( ) ] , sinand 4(are0 )2 cos
is the refractive
2delay line
15:
Optical
path
di
erence
in
a
two-element
dispersive
=
cos
(
)
ESSIONpath di
91
2
ptical
erence
in a two-element
dispersive
delay
3.1.2
Dispersion:
Grating
Pair
l
2
=
cos ( )
2
of the
di difference
raction angle
Phase
between is governed by the grating
hase
di erence
the reference
scattered
and the reference beam withscattered
beam
and
m-th-order
di by
raction
is given beam
by: Eqs.(3.84,3.85),
kout to obtain an
Using
Eq.(3.83)
and
it is possible
beam”
rating
is: ( ) =
k for
( )the
· l.GDD
Considering
free-space propagation
l terms wi
sions
and the
higher-order
dispersionbeam
for
iRESSION
erence
by
the
scattered
beam
and
the
reference
91
he two elements,through
we havethe
|kgrating
| = pair:
, and the accumulatedγ phase
γ is possible
Using
Eqs.(3.84,3.85),
it
to obtain
is: as( ) =
k Eq.(3.83)
( ) · l.and
Considering
free-space
propagati
α
itten
2 di raction
kin
sions
for
the
GDD
and
the
higher-order
dispersion terms
f
of the
angle
is
governed
by
the
grating
oe elements,
we
have
|k
|
=
,
and
the
pha
= [sin ( ) sin ]
(3.84) accumulated
D
through
the
pair: cos[
of m-th-order
dicos[
raction
is grating
given
by:
(
)
=
|l|
(
)]
=
(
)]
(3.83)
2
as
4
cos( )00
2
( )=
Grating: Bragg-Condition
3 2
cos3 ( )
is the angle between the incident wave vector and the normal
of the
grating.
theoutgoing
grating condition
) element;
= 2 |l|
cos[
( From
)]
=
cos[ vector,
)] is2 (3.8
4 2 ( which
stspacing
is
the
angle
of
the
wave
00
= [sin ( ) sin ]
( ) = (3.84)
cos(
3 2 cos3elements
n of frequency;
is the spacing between the scattering
( )
rection
parallel to their normal. In the case of a grating pair the
Derivative:
µ
¶
e angle between2 the incident
wave
2 vector and the norm
12
2 sin ( )
000
3
( )= 4 2
1
+
=
(3.85)
cos
(
)
3 ( wave
2
ve
spacing ofisthe
From
the grating
condition
ment;
thegrating.
angle
of the
outgoing
vector,
cos
)
cos2 ( which
)
equency;
is the spacing between the µscattering eleme
¶
2
12 case of a grating
2 sin (pair
) t
000
n parallel to their normal.
In
the
Loss:
~
25%
for
metals,
~
5%
for
dielectrics
55
( )=
1+
evidenttofrom
Eq.(3.86)
4 2 that
3 grating pairs give 2negative d
qs.(3.84,3.85), it Itis ispossible
obtain
analytic
expres-
3.1.3 4f - Pulse Shaper
0 - Dispersion Stretcher (4f-Imaging)
grating
grating
f
2f
f
Andrew Weiner: Pulse shaper
Phase Mask
grating
grating
f
2f
f
Generates dispersion for pulse shaping
56
3.1.3 Öffner Stretcher und Compressor
positive dispersion
grating
grating
f
2f
f-d
negative dispersion
Phase Mask
grating
grating
f
2f
f+d
57
3.1.4 Fiber Bragg Grating or Volume Bragg Grating
http://www.teraxion.com
Pros and Cons
BragGrate™ Mirror
BragGrate™ Pulse
http://www.optigrate.com
BragGrate™ Mirror
Reflecting Bragg Grating (RBG) for laser m
laser wavelength locking
Pros and Cons
BragGrate™ Deflector
BragGrate™ Combiner
• 
•  Large stretching up to 10ns (1m grating)
BragGrate™ Notch Filter
• 
•  Compensate for higher
BragGrate™ Bandpass Filter
• 
order dispersion
BragGrate™ Spatial Filter
• 
•  Compact
Wavelength and
Bandwidth Calculator
• 
•  Low peak power handling
•  .....
• 
Transmitting BG
Reflecting BG
The BragGrate™ Mirror is a reflecting volume Brag
silicate
2 glass. BragGrate™ Mirrors are placed in a
management of the laser radiation. The laser mo
selection with the bandwidth down to 10 GHz and
of 0.1-0.5 nm. BragGrate™ Mirrors have a record
5 x 5 mm cross section
medium peak power handling
X 100 withstand
ps delay
record high optical densities of up to 1
shift
reduction
of up to 5 pm/K at 532 nm.
Compact
Compensate
for higher
Specifications
order dispersion
Diffraction Efficiency (DE): 3-99.7%
Spectral Bandwidth: 20 pm to 20 nm
.....
Wavelength Range: 320-2700 nm
Grating Thickness: 0.50-20 mm
Apertures: up to 35×35 mm2
Angular Selectivity: 1-100 mrad
58
3.1.5 Acousto-Optic Programmable Dispersive Filter
al
Bire
yst
r
C
nt
e
g
frin
Acousto-Optic Programable Dispersive Filter (AOPDF or DAZZLER)
59
3.2 Gain Narrowing
10-fs sech2 pulse in
Ti:sapphire gain
cross section
3
2
0.6
65-nm FWHM
0.4
1.5
32-nm FWHM
1
longer
pulse out
0.2
0
650
to a pulse with input bandwidth
2.5
0.8
700
750
800
850
900
950
0.5
0
1000
Wavelength (nm)
Normalized Gain)
Normalized spectral intensity
1
In general when applying gain
ΔλFluo
G with bandwidth
Δλ0
the output bandwidth is
Δλ =
Δλ0
" Δλ0 %
1+ ln(G) $
'
# ΔλFluo &
2
Rouyer et al.,
Opt. Lett. 18, 214 (1993).
Influence of gain narrowing in a Ti:sapphire
amplifier on a 10 fs seed pulse
60
3.3 Contrast Ratio
If a pulse has a relativistic peak intensity ( 1018 W/cm2 @ 800 nm) a “little”
satellite pulse, a million times weaker, it is still 1 TW/cm2. This can do
some serious damage!
Ionization sets in at 1011 W/cm2 : so at 1021 W/cm2 we need a 1010 contrast
ratio!
Major sources of poor contrast
Nanosecond scale:
pre-pulses from oscillator
pre-pulses from amplifier
ASE from amplifier
Picosecond scale:
reflections in the amplifier
spectral phase or amplitude distortions
61
Log(Energy)
Amplified pulses often have poor contrast
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Spectral phase
aberrations
FWHM
Pre-pulses
Back
Front
ASE
10 ns
ns
ps 0
time
Pre-pulses can degrade a medium before desired interaction with strong field.
62
3.4 High Energy, Large Average Power Design
Multipass Composite Thin-Disc (CTD) Amplifier
Cryogenic CTD
Main Features:
•  High laser energy: ~J,
•  High laser Power: ~ 100 W,
•  ns pulse-duration
Angled
kaleidoscope
•  (Cryo-) Composite Thin-Disc
with improved ASE rejection
Vacu
um te
lesco
pe / s
patia
l
filter
Mirror
switchyard
Out !
63
Image relayed, 12-pass optical architecture
64
Face Pumping of CTD
• 
• 
• 
• 
• 
• 
Uniformity (ray-trace)
Homogeneous pumping "
1-D thermal distribution
Low wavefront distortion
Special shape mitigates ASE
92% absorption in double pass
Simple gain-element fabrication
Heat
inde
x
Laser
65
Cryogenic operation - spectroscopy
Energy Levels in Yb:YAG
Pump:
940 nm
3kBT @ 300K,
9kBT @ 100K
§ 
§ 
§ 
§ 
Absorption Coefficient (cm–1)
Energy
Laser:
1030 nm
Yb:YAG Absorption Spectrum*
10
8
77 K
6
Laser
Wavelength
Pump
Array
4
2
300 K
0
900 920
940 960 980 1000 1020 1040
Wavelength (nm)
4-level laser with small quantum defect
Direct diode-pumping with standard diode-bars
Higher absorption coefficient " ease of pumping
Lower saturation fluence (~1.8 J/cm2) " efficiency and low damage
risk
CRYOGENIC OPERATION
Enables efficient high-power lasers
with near-ideal beam quality
66
Cryogenic operation – thermal wavefront
45
8
UNDOPED YAG
7
40
6
35
5
30
4
25
3
20
2
15
1
10
100
150
200
250
0
300
CTE(ppm/K), dn/dT
dn/dT (ppm/K)
CTE (ppm/K),
(ppm/K)
THERMAL CONDUCTIVITY (W/m K)
Thermal
Conductivity (W/m K)
Properties of Undoped YAG *
50
•  Thermo-optic material properties
improve at low temperature
•  Modest LN2 requirements
(requires ~ 6 l /hr at 1 kW )
Wavefront (OPD) figure of merit
TEMPERATURE
Temperature
(K)(K)
100 K
Yb:YAG
100 K
Yb:YLF
300 K
Nd:YAG
FOM (rel. Nd:YAG)
97
187
1
quantum-limited thermal load χQL
9.6%
5.9%
32%
1.0
17
0.6
bandwidth
Δλ (nm)
67
Yb:YAG Pre-amplifier operation at 130 K
•  Operation a multi-pass Yb:YAG pre-amplifier at
130 K is a good choice to mitigate gain narrowing
130K Yb:YAG
Pre Amplifier
" 100 mJ, 1nm output after 12 passes
100 mJ, 4.4 mm
1 nm, 1.6 ns
100 Hz
(n
FWHM
m)
Amplified bandwidth (nm)
G:= 1 , 1.1 .. 50
3
3 nm KYW input seed
2
at 130 K
1
at 77 K
0
Temperature (K)
Analytic formula (Gaussian Model)
Rouyer et al., Opt. Lett. 18, 214 (1993)
10
20
30
40
50
Gain
68
Hardware
Quasi-cw at 20 Hz
69
What if there is no laser material at your
operating wavelength?
What if there is no laser material that allows
for few-cycle pulses?
Use Nonlinear Optics!
70