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Frequency combs in the extreme UV

Frequency combs in the extreme UV. Johann G. Danzl, 2005/11/09. Frequency combs – What for?. Measurement/synthesis of optical frequencies Measure frequencies rather than wavelengths Optical atomic clocks Subcycle physics High resolution spectroscopy Test fundamental theories

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Frequency combs in the extreme UV

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  1. Frequency combs in the extreme UV Johann G. Danzl, 2005/11/09

  2. Frequency combs – What for? • Measurement/synthesis of optical frequencies • Measure frequencies rather than wavelengths • Optical atomic clocks • Subcycle physics • High resolution spectroscopy • Test fundamental theories • Fundamental constants • Technological applications of metrology

  3. Harmonic Frequency Chains Complex, delicate and expensive Designed to measure just one single optical frequency Very few put in operation

  4. time Fourier transform (sin(1.5*t)+sin(1.6*t))^2 Mode separation = fr= (sin(1.5*t)+sin(1.6*t)+sin(1.7*t))^2 Spectral width of the comb Δω↑ ↨ Shorter pulses (sin(1.5*t)+sin(1.6*t)+sin(1.7*t)+sin(1.8*t))^2 Frequency combs 10 ns 10 fs

  5. t fc optical carrier frequency A(t) … periodic envelope function (amplitude and phase modulation) A(t)strictly periodic with periodicity => Fourier series in fr fc= nc fr + f0

  6. Cundiff & Ye, Rev Mod Phys, 75, 325-342 (2003) vg≠vφ Phaseshift determines position of the comb

  7. Udem et al., Nature, Vol 416, 14 March 2002, p 233-237 Determining the frequencies in the comb used in feedback to stabilize the position of the comb

  8. Femtosecond mode locked lasers Working horse: Ti-Sapphire Kerr-lens mode locked laser Gain bandwidth ~ 128 THz (300nm) Repetition rate ~ 100 MHz – 1 GHz Central λ ~ 800 nm Octave spanning combs Pulse durations down to 5 fs Pumped with green cw diode laser www.wikipedia.org

  9. U. Keller, Nature 424, 831-838 (2003) Kerr lens + effective aperture → Gain for pulsed mode n, I n, I effective aperture: overlap with pump laser C.w. Pulse High peak intensity Kerr effect Mode locking C.w. operation: No fixed phase relation between the modes Phase locking or Mode locking:Fixed phase relationship between the modes of the laser resonator cavity →interference → pulses

  10. measured via beat as described before, stabilized with feedback loop to pump-laser intensity nTiSa = n(T) movable mirror 2 n fr + f0 n fr + f0 beat f0 2 x 2 n fr + 2 f0 TiSa mode locked fs laser Compensating the dispersion of the crystal: prisms or chirped mirrors

  11. Jones et al., Science, 288, Issue 5466, 635-639, (2000) Photonic crystal fiber Dispersion and Nonlinearity can be designed Increases comb bandwidth 4-wave mixing process Band structure (crystal)

  12. Gohle et al., Nature, 436, 234-237 (2005) 20 fs @ 112 MHz chirped mirrors Sapphire windows Brewster angled Full repetition rate of the laser! • Time domain: coherent pulse addition • Round trip time of pulse = period of laser • Pulse envelope does not change shape during one round trip • Carrier envelope phase shift is the same for laser and resonator XUV HHG Xenon jet

  13. Gohle et al., Nature, 436, 234-237 (2005) Interferometric Autocorrelation: used to estimate pulse duration: Intensity of 2ω light scales with square of incident intensity filter to block the fundamental wavelength www.wikipedia.org Spectrum inside the resonator TiSa laser Resonator Chirp free pulse of 28 fs duration Average power in resonator: 38 W Peak power: 12 MW Intensity in the focus: 5*1013 W/cm2

  14. Jones et al., PRL, 94, 193201 (2005) effective cavity finesse: 2500 Repetition rate 100 MHz frequency resolved optical gating (FROG): pulse duration 48 fs (incident), 60 fs (transmitted) pulse energy 4.8 µJ enhancement factor 600 vs. incident pulse peak intracavity intensity: > 3 x 1013 W/cm2

  15. Lindner et al., PRA 68, 013814 (2003) High harmonic generation in rare gases

  16. Distance from nucleus E(t) time Corkum, PRL, 71, 1994-1997 (1993) very high intensities > 1013 W/cm2 ponderomotive energy Ip atomic ionization potential Lewenstein et al., PRA, 49, 2117-2132 (1994) Baltuska et al., Nature, 421, 611-615 (2003)

  17. Gohle et al., Nature, 436, 234-237 (2005) Coherence? XUV comb structure of the k-th laser harmonic: Widely spaced comb (112 MHz) Link to Cs atomic clock Jones et al., PRL, 94, 193201 (2005) XUV output 23 eV Comb of odd laser harmonics that stem from the periodicity of carrier wave Nested comb with frequency spacing given by laser repetition rate

  18. Jones et al., PRL, 94, 193201 (2005) Coherence High frequency roll-off:photomultiplier amplifier BBO: beta barium-borate optical crystal

  19. Gohle et al., Nature, 436, 234-237 (2005) Coherence 3rd harmonic of Nd:YVO4 laser repetition rate phase locked to 2nd harmonic of TiSa repetition rate

  20. Gohle et al., Nature, 436, 234-237 (2005) Power of the spectral features Feature at 103 nm: Rydberg levels of the atom Stark shifted into 8 or 9 photon Resonance during pulse? Presently: > 1 nW in the range 120 nm – 60 nm → 10-8 of laser power (Gohle) 10 µW in the 3rd harmonic → 10-8 conversion efficiency (Jones) Spacial coherence Divergence angles 14, 11, 10 mrad for 7th, 9th, 11th harmonic, resp. Approximately diffraction limit: tight focusing

  21. Future precision dispersion characterization: enhancement factors of 1000 high energy oscillators (extended cavity Ti:sapphire, Yb:YAG) - 1µJ pulses intracavity pulses: 100 µJ (but nonlinear effects) XUV output in the mW range High resolution spectroscopy in the XUV New tests of fundamental physical theories XUV interferometry holography nanolithography microscopy X-ray atomic clocks

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