FLS 2010 Workshop March 4 th 2010 HHG

FLS 2010 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 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 1030 nm), where powerful Yb-doped lasers exist 3

Required Seed Power Levels Direct Seeding: 100 k. W (30 fs) 3 n. J Seeding for HGHG: 100 MW (30 fs) 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 m. J // 3 J Rep. Rate 1 k. Hz / 10 MHz Power: 3 W / 30 k. W // 3 k. W / 30 MW 4

High Harmonic Generation Trajectories Three-Step Model Electric Field, Position Ionization Time Corkum, 1993 Cutoff formula ħωmax = Ip+3. 17 Up 5

Wavelength Scaling of HHG Efficiency Atomic units Field amplitude Ionization potential Drive pulse frequency Increase intensity 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 E. L. Falcão et al. , Opt. Expr. 17, 11217 (June, 2009).

HHG Efficiency into Single Harmonic 400 -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 k. Hz, 7 m. J) Telescope & Beam delivery Soft-X-ray spectrometer Beam input port Beam transport Pulsed nozzle HHG chamber 9

HHG spectra generated by 400 -nm driver Ar: 0. 05 mbar Ne: 0. 3 mbar He: 1 bar • Pulse energy of 0. 94 m. J for all gases • Peak intensity: ~7. 8 x 1014 W/cm 2 (estimation) • Nozzle length: 2 mm

Total HHG efficiency from 400 -nm driver Ar: 0. 05 bar Ne: 0. 3 bar He: 1 bar • Conversion efficiency of up to 2 x 10 -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 • 8 x 10 -5 at ~35 e. V and 1 x 10 -5 at ~60 e. V for He • 6 x 10 -5 at ~27 e. V for Ar

HHG spectra generated from 800 -nm driver Ne: 0. 3 bar Energy: 2 m. J He: 1 bar Energy: 2 m. J Peak intensity: ~1. 6 x 1015 W/cm 2

Total HHG efficiency from 800 -nm driver Zr window (60 -100 e. V) Al window (20 -70 e. V) • Conversion efficiency of up to 2 x 10 -6 from He over Al and Zr window • Efficiency per harmonic is one-to-two-order-of-magnitudes lower.

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 m. J @1 k. Hz 800 -nm OPCPA seed Ti: Sapphire oscillator l = 1. 0 µm DFG Mg. O: PPLN Nd: YLF CPA system CFBG, 2 YDFA, Nd: YLF regen amp + 2 Nd: YLF multipass amp, grating stretcher 12 ps, 4 m. J @1 k. Hz l = 2. 0 µm OPA 1 Si 800 -nm OPCPA pump 140µJ Mg. O: PPLN 1 m. J 30 m. J In final OPA stage: • Yb: YAG pump replaces Nd: YLF • BBO replaces Mg. O: PPSLT AOPDF OPA 2 Mg. O: PPSLT OPA 3 BBO 2. 5 m. J, 30 fs Suprasil

Theoretical Prediction § § § 2. 2 -mm drive wavelength extends HHG cutoff to 500 e. V Conversion efficiency of 10 -7 -10 -8 Best current water-window experimental result: 300 e. V cutoff, h ~ 5 x 10 -8, using multi-m. J 1. 6 -mm drive pulses E. J. Takahashi et al. , PRL 101, 253901 (2008). Simulation parameters: Gaussian pulse, t. FWHM = 6 cycles Ne gas, p = 3 bar, L = 2. 5 mm, w 0 = 50 mm, E ~ 1 m. J

High-flux, High Repetition Rate 13. 5 -nm (~93 e. V) EUV source • With 515 -nm drive pulses generated from SGH of powerful 1µm lasers Efficiency into single harmonic: ~ 10 -5

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 m. J, ~100 fs pulses circulating § Cavity Finesse > 3000 patterned dielectric mirror 0. 1 TW/cm 2 1000 TW/cm 2 2. 6 mm 15 cm Confocal cavity for high-intensity Bessel-Gauss beams – Cavity shown enables 1000 TW/cm 2 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 He. Ne source Polarizer λ/2 Beam Expander Photodiode R=99% Pellicle R=91% 42 k. Hz 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 One Patterned Mirror 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 Bessel. Gauss mode 26 Bessel-Gauss Modified Bessel-Gauss

Pump laser upgrade > 50 m. J, 2 k. Hz, 10 ps (b) Yb: YAG regenerative amplifier (c) Yb: YAG 4 -pass amplifier LN 2 Dewar L 1 L 2 DM Yb: YAG crystals DM L 2 Yb: YAG crystal >40 W Fiber-coupled pump laser L 1 Fiber-coupled LD PC TFP FI l/4 TFP Telescope l/4 Regen output 5 m. J@2 k. Hz seed Telescope fs, Yb-fiber oscillator >60 m. J@2 k. Hz Telescope FI PBS l/4 10 ps, >50 m. J@2 k. Hz CFBG stretcher (d) Multi-layer dielectric grating compressor (a) Fiber seed 27 1 m. W 400 ps F 1029 l/2 l/4 30 -m. W Yb-fiber preamplifier (1030 nm)

Summary k. W-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 -mm OPCPA (200 m. J) § Initial results on 800 nm OPCPA 28

(a) For a 5 -cycle-driver-pulse, Dk = 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 40 e. V, Al transmission = 30%, photodiode response = 4 electrons/photon photodiode response