CF1L.2.pdf
CLEO Technical Digest © OSA 2012
Unified Microscopic-Macroscopic Picture of High Harmonic Generation from the VUV to the keV X-ray Region T. Popmintchev1, D. Popmintchev1, M.-C. Chen1, J. P. Siqueira2, C. Hernández-García3, J. A. PérezHernández4, L. Plaja3, A. Becker1, A. Jaron-Becker1, S. Ališauskas5, G. Andriukaitis5, A. Pugžlys5, A. Baltuška5, M. M. Murnane1, H. C. Kapteyn1 1
JILA, University of Colorado at Boulder, Boulder, CO 80309-0440 USA Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, Brazil 3 Grupo de Investigación en Óptica Extrema, Universidad de Salamanca, Salamanca E37008, Spain 4 Centro de Láseres Pulsados, CLPU, Salamanca E37008, Spain 5 Photonics Institute, Vienna University of Technology, Vienna, 1040, Austria
[email protected] 2
Abstract: We present a unified picture of phase matching of high harmonic upconversion spanning the electromagnetic spectrum from the VUV to keV, combining both microscopic and macroscopic physics. We validate this picture with experiment and theory. ©2010 Optical Society of America OCIS codes: (140.7240) UV, EUV, and X-ray lasers; (190.7220) Upconversion; (320.7110) Ultrafast nonlinear optics.
Using the nonlinear-optical process of high harmonic generation (HHG), light from an ultrafast Ti:Sapphire laser can be coherently upconverted under phase matching conditions to generate fully spatially and temporally coherent light in the extreme ultraviolet (EUV) region of the spectrum. The grand challenge for extending bright HHG to higher photon energies is the development of phase matching and quasi-phase matching techniques that enable efficient nonlinear upconversion. In the past few years, we have demonstrated that full phase matching of HHG scales with the wavelength of the driving laser as ~λL(1.6-1.7) [1,2], almost as strongly as the single-atom cutoff ~λL2. This makes it possible to generate bright coherent supercontinua in the soft X-ray region around 0.33 keV using a 1.3 µm driver [1], 0.52 keV using 2 µm driver [3], and here, 1.6 keV (7.7 Å), or harmonic order >5001th using a 3.9 µm driver [4,5]. This rapid progress allows us to generalize the phase-matched HHG upconversion throughout the electromagnetic spectrum.
Fig. 1 Unified picture of phase-matched HHG including microscopic and macroscopic effects. Counter-intuitively, experiment and theory show that the order of the nonlinearity must dramatically increase from 3-11 in the vacuum UV using vacuum UV driving laser wavelengths, to >5001 in the keV X-ray region using mid-IR driving lasers. The HHG emission evolves from a single harmonic, to a harmonic comb or a supercontinuum, to an ultra broad supercontinuum in the X-ray region that can support few attosecond pulse durations, and possibly even zeptosecond time scales. The driving and the upconverted wavelengths merge in the vacuum UV region close to the valence ionization potentials of atoms and molecules.
Here we present for the first time a unified picture of phase-matched upconversion of laser light from the vacuum UV to the keV X-ray region, that combines microscopic single-atom quantum physics with macroscopic
CF1L.2.pdf
CLEO Technical Digest © OSA 2012
extreme nonlinear optics, and is validated by theory and experiment (see Fig. 1). We also present a physically intuitive, analytical, phase-matching cutoff rule that predicts the maximum photon energy that can be fully phase matched. Counterintuitively, to efficiently generate higher-energy high harmonic beams, the order of the nonlinearity must dramatically increase from ~3-11 in the vacuum UV, to >5001 in the keV X-ray region. The bright phase matched HHG spectra therefore evolve from a single harmonic in the VUV, to combs or supercontinua of tens of harmonics in the EUV, to a broad X-ray supercontinua spanning thousands of harmonics in the soft X-ray region. In a generalized picture in the time domain, the HHG pulses scale from pulse durations of 100s of attoseconds in the VUV-EUV, from 10s to few attosecond pulse durations in the soft X-ray region, to zeptosecond time scales in the multi-keV X-ray region. Also surprisingly, we uncover that the generalized macroscopicmicroscopic phase-matched upconversion favors tunnel ionization everywhere, and the phase-matched upconversion is non-perturbative process even in the VUV. Experimentally, the VUV, EUV, and X-ray harmonics are generated by focusing ultrafast, 4.5-10 mJ, 0.267 µm, 0.4 µm, 0.8 µm, 1.3 µm, 2.0 µm and 3.9 µm laser beams into a gas-filled hollow waveguide. We implement pressure-tuned phase matching to optimize the HHG flux, under optimal laser intensity at each laser wavelength, dictated by a so-called critical ionization of the medium ηCR above which phase matching is not possible. Bright phase matched HHG reach conversion efficiencies of 10-3-10-4 in the VUV region, compared to 10-5 in the EUV using Ti:Sapp lasers. Such unprecedented efficiency in the VUV results from a of combination of a 103x higher micro-yield (single-atom scaling of λL-6.5 under phase matching condition), allowed by a ~10x higher critical ionization for macroscopic phase matching, compared to using Ti:Sapp lasers. Interestingly, we can also isolate a single phase-matched VUV harmonic. Moreover, VUV HHG fully phase-matches at relatively high levels of ionization – tens of percent – showing that phase-matched HHG is non-perturbative process even in the VUV. The required optimal pressures and interaction lengths evolve from 40 atm) and multi-cm lengths in the X-ray region. Tunnel ionization dominates in all phase-matched regimes illustrated in Fig. 1. As a result, since the physics of ionization does not change, we can use a simple tunneling ionization model to derive an analytic phase matching cutoff rule that is generalized for any HHG upconversion process above the ionization potential Ip: ℎ𝜈!" !"#$%% = 𝐼! +
ln!
𝛼𝐼!! 𝜆!! 𝛽𝐼! 𝜏! −ln 1 − 𝜂!" (𝜆! )
Here τL is the laser pulse duration, and α and β are constants that depend on the laser pulse shape and the state from which the electron wavepacket is tunnel ionized. Clearly, the small deviation of λL(1.6-1.7) from the λL2 scaling of the ponderomotive energy physically arises mainly from the strong scaling of the critical ionization ηCR ~λL2 which increases by 4 orders of magnitude from the vacuum VUV to the mid-IR laser wavelengths. Short, few cycle laser pulses make it possible to generate a slightly higher-energy photons of only percents, before the critical ionization level is exceeded. However, the most significant HHG enhancement - by orders of magnitude - arises when the right combination of laser wavelengths and laser intensity are used. In summary, we present a unified picture of HHG phase matching throughout the electromagnetic spectrum from the VUV to the keV X-ray region, by combining both microscopic and macroscopic physics. Counterintuitively, to efficiently generate higher-energy high harmonic beams, the order of the nonlinearity must dramatically increase from ~3-11 in the vacuum UV, to >5001 in the keV region. We also uncovered some general microscopic and macroscopic features of efficient HHG nonlinear frequency upconversion. Interestingly, tunnel ionization dominates everywhere and the fully phase-matched upconversion is a non-perturbative process even in the VUV. Our unified upconversion picture allows us to predict a straightforward route to generate zeptosecond X-ray flashes that are comparable to the times scales of processes inside the nucleus. In the future, a bright, tabletop, fully coherent light source, widely tunable from the vacuum UV to the multi-keV X-ray region, is feasible to capture and image function at the space-time in bio-, nano-, and materials systems, or to use as a seed for free-electron lasers. This work was supported by the NSSEFF program and by the NSF ERC in EUV Science and Technology. AJB and AB acknowledge support from the US Air Force Office of Scientific Research (Grant no. FA9550-10-1-0561). [1] T. Popmintchev et al., “Phase matched upconversion of coherent ultrafast laser light into the soft and hard x-ray regions of the spectrum.” PNAS 106 (26), 10516 (2009). [2] T. Popmintchev et al., “The attosecond nonlinear optics of bright coherent X-ray generation“, Nature Photonics 4, 822 (2010). [3] M.-C. Chen et al., “Bright, Coherent, Ultrafast Soft X-Ray Harmonics Spanning the Water Window from a Tabletop Light Source”, Phys. Rev. Lett. 105, 173901 (2010). [4]T. Popmintchev et al.,” Bright Coherent Attosecond-to-Zeptosecond Kiloelectronvolt X-ray Supercontinua”, OSA Conference on Lasers and Electro-optics/ Quantum Electronics and Laser Science (CLEO/QELS), Baltimore, MD, Postdeadline paper: PDPC12 (2011). [5] G. Andriukaitis et al., “90 GW Peak-Power Few-Cycle Mid-IR Pulses from an Optical Parametric Amplifier”, Opt. Lett. 36, 2755 (2011).
