HRS Program FLS2010 Workshop March 4 th, 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

2 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)

3 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

4 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? Repetition rate determines drive power: Efficiency determines required drive pulse energy Efficiency:  Pulse energy 3 mJ // 3 J Rep. Rate 1kHz / 10MHz  Power: 3W / 30kW // 3 kW / 30MW

5 High Harmonic Generation Corkum, 1993 Cutoff formula ħω max = I p U p Electric Field, Position Time Ionization Three-Step Model Trajectories

6 Wavelength Scaling of HHG Efficiency Atomic units Field amplitude Drive pulse frequency Increase intensity Decrease frequency (increase wavelength) Ionization potential What is the impact on HHG conversion efficiency? 1.) Single-Atom Response 2.) Gas properties 3.) Phase matching

HHG efficiency for N-cycle flat top pulse Cutoff E. L. Falcão et al., Opt. Expr. 17, (June, 2009).

8 HHG Efficiency into Single Harmonic 800-nm (Xe) 400-nm driver (He) Conversion efficiency very sensitive to drive wavelength and interaction parameters 800-nm driver (He)

9 Experimental HHG Setup 800-nm Ti:S amplifier (1 kHz, 7 mJ) HHG chamber Telescope & Beam delivery Beam input port Beam transport Pulsed nozzle Soft-X-ray spectrometer

Pulse energy of 0.94 mJ for all gases Peak intensity: ~7.8x10 14 W/cm 2 (estimation) Nozzle length: 2 mm HHG spectra generated by 400-nm driver Ar: 0.05 mbar Ne: 0.3 mbar He: 1 bar

Ar: 0.05 bar Ne: 0.3 bar He: 1 bar Total HHG efficiency from 400-nm driver 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, (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

Peak intensity: ~1.6x10 15 W/cm 2 HHG spectra generated from 800-nm driver He: 1 bar Energy: 2 mJ Ne: 0.3 bar Energy: 2 mJ

Total HHG efficiency from 800-nm driver 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. Zr window ( eV) Al window (20-70 eV)

15 Comparison with previous results 800-nm driver (He) 400-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.

In final OPA stage: Yb:YAG pump replaces Nd:YLF BBO replaces MgO:PPSLT 2-µm drive laser based on cryo-Yb:YAG pump laser MgO:PPLN DFG MgO:PPLN OPA 1 = 2.0 µm 140µJ Si 2.5 mJ, 30 fs Suprasil MgO:PPSLT OPA 2 30 mJ BBO OPA 3 1 mJ 800-nm OPCPA seed 800-nm OPCPA pump Nd:YLF CPA system CFBG, 2 YDFA, Nd:YLF regen amp + 2 Nd:YLF multipass amp, grating stretcher 12 ps, 4 Ti:Sapphire oscillator Yb:YAG CPA system CFBG, YDFA, Yb:YAG regen amp + Yb:YAG multipass amp, grating stretcher 15 ps, 30 = 1.0 µm AOPDF

 2.2-  m drive wavelength extends HHG cutoff to 500 eV  Conversion efficiency of  Best current water-window experimental result: 300 eV cutoff,  ~ 5x10 -8, using multi-mJ 1.6-  m drive pulses E. J. Takahashi et al., PRL 101, (2008). Gaussian pulse,  FWHM = 6 cycles Ne gas, p = 3 bar, L = 2.5 mm, w 0 = 50  m, E ~ 1 mJ Theoretical Prediction Simulation parameters:

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

19 High Intensity Femtosecond Enhancement Cavities for High Repetition Rate FELs Use enhancement cavity to scale efficiency to ~ 10 -2

High-Power Enhancement Cavity 20  Requirements: optical beam access, high-intensity in interaction region, and low loss  1-MW intracavity power, 10 mJ, ~100 fs pulses circulating  Cavity Finesse > cm 2.6 mm patterned dielectric mirror Confocal cavity for high-intensity Bessel-Gauss beams – Cavity shown enables 1000 TW/cm TW/cm TW/cm 2

21 Preliminary Cavity Demonstration Single-mode HeNe source Beam Expander Pellicle CCD Photodiode Polarizer λ/2 R=91% R=99% 20μm Piezo 2μm Piezo LPF PI 42 kHz Lock-in Amp 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.

22 Cavity Results With One Patterned Mirror Pellicle (loss<1%) CCD R = 91% or 99% R = 99%  First cavity experiments done with single patterned mirror  Asymmetric modes seen, showing general structure of desired modes, but differing transverse profiles Transverse profiles at cavity center R=91% R=99%

23 ~30 modes with <1% loss only 2 modes (superposition modes in each direction) with 5% loss Cavity Results With One Patterned Mirror Loss Mode One Patterned Mirror Loss Mode Two Patterned Mirrors

24 Thank You Needs large average power Yb-doped Lasers!

25 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. Bessel-Gauss beam is a superposition of tilted Gaussian beams with wavevectors lying along the surface of a cone, Tilted Gaussian Beam

26 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. Bessel-Gauss Modified Bessel-Gauss Numerically computed mode Analytical Bessel- Gauss mode Field profile at focus: numerical versus analytical solution

Pump laser upgrade > 50 mJ, 2 kHz, 10 ps (c) Yb:YAG 4-pass amplifier fs, Yb-fiber oscillator CFBG stretcher /4 F1029 PBS 1 mW 400 ps /4 /2 FI Telescope 30-mW Yb-fiber preamplifier (1030 nm) >40 W Yb:YAG crystal PC TFP (b) Yb:YAG regenerative amplifier TFP FI seed Regen output 5 kHz Fiber-coupled LD /4 Telescope (a) Fiber seed >60 kHz Telescope 10 ps, >50 kHz (d) Multi-layer dielectric grating compressor LN 2 Dewar Yb:YAG crystals Fiber-coupled pump laser DM /4 DM L1 L2 L1 Telescope TFP Telescope 27

28 Summary kW-class cryogenically cooled Yb:YAG ps-lasers are ideal for  Inverse Compton Scattering Sources (direct use) -> 2 nd 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-  m OPCPA (200  J)  Initial results on 800 nm OPCPA

29 (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.

Efficiency Measurement using Calibrated XUV Photodiode At 40eV, Al transmission = 30%, photodiode response = 4 electrons/photon photodiode response