FLS2010 Workshop
March 4th, 2010
HHG based Seed Generation for X-FELs
Franz X. Kärtner, William S. Graves and David E. Moncton
and WIFEL Team
Department of Electrical Engineering and Computer Science
and Research Laboratory of Electronics,
Massachusetts Institute of Technology
Cambridge, MA, USA
HRS Program
Acknowledgement
Students:
Ch.-J. Lai, A. Benedick,
S.-W. Huang, S. Bhardwaj
A. Siddiqui, V. Gkortsas
B. Putnam, Li-Jin Chen
Research Scientists: K.-H. Hong, J. Moses
Postdocs and Visitors:
G. Cirmi (Politecnico Milano, Rocca Foundation)
A. Gordon (Technion, Israel)
O. Muecke (Techn. Univ. Vienna)
E. Falcao (Pernambuco, Brazil)
2
Outline
 Required Seed Power Levels
 Single Pass Efficiencies in High Harmonic Generation
 Wavelength Scaling of HHG
 Seed Generation for High Repetition Rate FELS
A High Average Power HHG Source for 13.5 nm
pumped by 515 nm Lasers (SHG of 1030nm), where
powerful Yb-doped lasers exist
3
Required Seed Power Levels
Direct Seeding: 100 kW (30fs)  3 nJ
Seeding for HGHG: 100 MW (30fs)  3 µJ
 Push direct seed wavelength as short as possible.
How does efficiency scale?
Efficiency determines required drive pulse energy
Repetition rate determines drive power:
Efficiency: 10-6  Pulse energy 3 mJ // 3 J
Rep. Rate 1kHz / 10MHz  Power: 3W / 30kW // 3 kW / 30MW
4
High Harmonic Generation
Trajectories
Three-Step Model
Electric Field, Position
Ionization
Time
Corkum, 1993
 XUV
Cutoff formula
1 2
 I p  mx
2
ħωmax = Ip+3.17 Up
5
Wavelength Scaling of HHG Efficiency
Atomic units
 m  e 1
max  I p
Field amplitude
2
00
2
Increase
intensity
E
E
 3.17

4
Ionization potential
Drive pulse frequency
Decrease
frequency
(increase
wavelength)
What is the impact on HHG conversion efficiency?
1.) Single-Atom Response
2.) Gas properties
3.) Phase matching
6
HHG efficiency for N-cycle flat top pulse
Cutoff
  0.0236
2 I p  50 arec
2
E016 / 3  cutoff
2
2
g (k , L) 1   4 ( N 1)
2
1


 0 w E (tbcutoff )
2
4
 ( cutoff ) (1   ) N

1


2
05 / E05 cutoff
~ U p 9 / 2 ~ 9
0.1
0.6
0.01
0.4
1E-3
1E-4
1E-5
0.2
He
Ne
Ar
Kr
Xe
200
arec
 (a.u.)

0.0
-0.2
400
600
EnergyHHG (eV)
800
-0.4
-0.6
He
Ne
Ar
Kr
Xe
200
E. L. Falcão et al., Opt. Expr. 17, 11217 (June, 2009).
400
600
EnergyHHG (eV)
800
HHG Efficiency into Single Harmonic
400-nm driver (He)
800-nm driver (He)
800-nm
(Xe)
• Conversion efficiency very sensitive to
drive wavelength and
interaction parameters
8
Experimental HHG Setup
800-nm Ti:S amplifier
(1 kHz, 7 mJ)
Telescope &
Beam delivery
Soft-X-ray
spectrometer
Beam input port
Beam transport
Pulsed nozzle
HHG chamber
9
HHG spectra generated by 400-nm driver
45000
Ar
HH Intensity (Arb. U.)
30000
15000
0
12000
Ar: 0.05 mbar
Ne: 0.3 mbar
He: 1 bar
Ne
8000
4000
0
900
He
600
300
0
30
40
50
60
70
Photon Energy (eV)
• Pulse energy of 0.94 mJ for all gases
• Peak intensity: ~7.8x1014 W/cm2 (estimation)
• Nozzle length: 2 mm
Total HHG efficiency from 400-nm driver
Conversion Efficiency
1E-3
Calculation with Ar
Calculation with He
He
1E-4
Ar: 0.05
bar
Ne: 0.3 bar
He: 1 bar
1E-5
Ar
Ne
1E-6
0.0
0.2
Al window (20-70 eV)
0.4
0.6
0.8
1.0
400-nm pulse energy (mJ)
• Conversion efficiency of up to 2x10-4 from He over Al window
• “Good” agreement to analytic theory [1]
E. L. Falcão-Filho et al., Opt. Express 17, 11217 (June, 2009).
Efficiency per harmonic from 400-nm driver
• 8x10-5 at ~35 eV and 1x10-5 at ~60 eV for He
• 6x10-5 at ~27 eV for Ar
HH Intensity (Arb. U.)
HHG spectra generated from 800-nm driver
300
Ne: 0.3 bar
Energy: 2 mJ
200
100
0
HH Intensity (Arb. U.)
40
50
60
70
80
90
100
110
Photon Energy (eV)
100
80
He: 1 bar
Energy: 2 mJ
60
40
20
0
40
50
60
70
80
90
Photon Energy (eV)
Peak intensity: ~1.6x1015 W/cm2
100
110
Total HHG efficiency from 800-nm driver
Zr window
(60-100 eV)
Al window
(20-70 eV)
1E-5
Conversion
Efficiency
Ne
Zr window
1E-6
Al window
1E-7
• Conversion efficiency of up to 2x10-6 from He over Al and Zr window
• Efficiency per harmonic is one-to-two-order-of-magnitudes lower.
1E-5
Conversion
Efficiency
Calculation in Al window
Calculation in Zr window
He
Zr window
1E-6
Al window
1E-7
1.0
1.5
2.0
2.5
800-nm Pulse Energy (mJ)
3.0
Comparison with previous results
400-nm driver (He)
800-nm driver (He)
• Conversion efficiency very sensitive to the driving wavelength
• But predictable from our analytic theory that has shown a good agreement
to experimental results studied by 400-nm and 800-nm drivers.
15
2-µm drive laser based on cryo-Yb:YAG pump laser
Yb:YAG CPA system
CFBG, YDFA, Yb:YAG regen amp +
Yb:YAG multipass amp, grating stretcher
15 ps, 30 mJ @1kHz
800-nm
OPCPA
seed
Ti:Sapphire
oscillator
=
1.0 µm
DFG
MgO:PPLN
Nd:YLF CPA system
CFBG, 2 YDFA, Nd:YLF regen amp +
2 Nd:YLF multipass amp, grating stretcher
12 ps, 4 mJ @1kHz
 = 2.0 µm
OPA 1
Si
800-nm
OPCPA
pump
140µJ
MgO:PPLN
1 mJ
30 mJ
In final OPA stage:
• Yb:YAG pump replaces Nd:YLF
• BBO replaces MgO:PPSLT
AOPDF
OPA 2
OPA 3
MgO:PPSLT
BBO
2.5 mJ,
30 fs
Suprasil
Theoretical Prediction



2.2-mm drive wavelength extends HHG cutoff to 500 eV
Conversion efficiency of 10-7-10-8
Best current water-window experimental result:
300 eV cutoff,  ~ 5x10-8, using multi-mJ 1.6-mm drive pulses
E. J. Takahashi et al., PRL 101, 253901 (2008).
Simulation parameters:
Gaussian pulse, tFWHM = 6 cycles
Ne gas, p = 3 bar,
L = 2.5 mm, w0 = 50 mm,
E ~ 1 mJ
High-flux, High Repetition Rate 13.5-nm
(~93 eV) EUV source
• With 515-nm drive pulses generated from SGH of powerful 1µm lasers
 Efficiency into single harmonic: ~ 10-5
10
10
Efficiency (10 )
1
-6
-6
Efficiency (10 )
8
6
4
2
0
30 40 50 60 70 80 90 100 110
Energy (eV)
0.1
0.01
1E-3
515 nm
400 nm
1E-4
0.6
0.7
Pump Energy (mJ)
0.8
Use enhancement cavity to scale efficiency
to ~ 10-2
High Intensity Femtosecond
Enhancement Cavities for
High Repetition Rate FELs
19
High-Power Enhancement Cavity

Requirements: optical beam access, high-intensity in interaction region,
and low loss

1-MW intracavity power, 10 mJ, ~100 fs pulses circulating

Cavity Finesse > 3000
patterned dielectric
mirror
0.1 TW/cm2
1000 TW/cm2
2.6 mm
15 cm
Confocal cavity for high-intensity Bessel-Gauss beams
– Cavity shown enables 1000 TW/cm2
20
Preliminary Cavity Demonstration
First demonstration of cavity operation is carried out with CW laser.
Also, axicon coupling optics excluded. Instead, collimated beam is
used allowing measurement of intrinsic suppression of higher modes.
Single-mode
HeNe source
λ/2
Polarizer
Beam Expander
R=99%
Pellicle
Photodiode
R=91%
42 kHz
20μm Piezo
2μm Piezo
LPF
CCD
PI
Lock-in Amp
21
Cavity Results With One Patterned Mirror


Transverse profiles at cavity center
First cavity experiments done
with single patterned mirror
Asymmetric modes seen,
showing general structure of
desired modes, but differing
transverse profiles
R=91%
Pellicle
R = 99%
(loss<1%)
R = 91% or 99%
R=99%
CCD
22
Cavity Results With One Patterned Mirror
Two Patterned Mirrors
Loss
Loss
One Patterned Mirror
Mode
Mode
only 2 modes (superposition modes
in each direction) with <1% loss, next
higher mode >5% loss
~30 modes
with <1% loss
23
Thank You
Needs large average power Yb-doped Lasers!
24
Analytical Bessel-Gauss Form of Modes
The cavity modes have been analyzed numerically with custom paraxial
wave optics software package. They can also be understood from an
analytical perspective as Bessel-Gauss beams.
Tilted Gaussian Beam
Bessel-Gauss beam is a superposition of tilted
Gaussian beams with wavevectors lying along the
surface of a cone,
25
Analytical Bessel-Gauss Form of Modes
Bessel-Gauss beams traversing paraxial optical systems transform with
an ABCD matrix similar to a Gaussian beam. Bessel-Gauss beams can
then be shown to be modes of the confocal resonator, and the dominant
modes of our special cavity.
Field profile at focus:
numerical versus analytical
solution
Numerically
computed mode
Analytical BesselGauss mode
26
Bessel-Gauss
Modified Bessel-Gauss
Pump laser upgrade > 50 mJ, 2 kHz, 10 ps
(b) Yb:YAG regenerative amplifier
(c) Yb:YAG 4-pass amplifier
LN2 Dewar
L1
L2 DM
Yb:YAG
crystals
DM L2
Yb:YAG crystal
>40 W
Fiber-coupled
pump laser
L1
Fiber-coupled LD
PC
TFP
/4
TFP
FI
TFP
Telescope
TFP
/4
Telescope
Telescope
Regen output
5 mJ@2 kHz
seed
Telescope
fs, Yb-fiber
oscillator
>60 mJ@2 kHz
FI
Telescope
PBS
/4
10 ps, >50 mJ@2 kHz
CFBG
stretcher
(d) Multi-layer dielectric
grating compressor
(a) Fiber seed
27
1 mW
400 ps
F1029
/2
/4
30-mW Yb-fiber
preamplifier (1030 nm)
Summary
kW-class cryogenically cooled Yb:YAG ps-lasers are ideal for
 Inverse Compton Scattering Sources (direct use)
-> 2nd generation synchrotron like laboratory sources with
exceptional beam properties
 micron sized source ideal for phase contrast imaging
 fs-pulse durations ideal for time resolved x-ray diffraction
 Pumping of few cycle OPCPAs covering the visible to MID IR range
 Analytic HHG efficiency formulas and wavelength scaling
 Development of few-cycle 2-mm OPCPA (200 mJ)
 Initial results on 800 nm OPCPA
28
(a) For a 5-cycle-driver-pulse,
k = 0, L = 5 mm at 1 bar.
(b) Same as (a) including
plasma and neutral atom
phase mismatching.
29
Efficiency Measurement using Calibrated XUV
Photodiode
At 40eV, Al transmission = 30%,
photodiode response = 4 electrons/photon
EHH 
I ph  40eV
30%  4 1.6 1019 1000

I ph
30 A

J
pulse
photodiode response
