High Harmonic Generation
When a very intense light pulse is focused into a gas (usually at reduced pressure), strong nonlinear interactions can lead to the generation of very high odd harmonics of the optical frequency of the pulse, i.e., to an extreme form of nonlinear frequency conversion. This typically occurs at optical intensities of the order of 1014 W/cm2 or higher. Although only a tiny fraction of the laser power can be converted into higher harmonics, the frequency-upconverted output can still be useful for measurements down to wavelengths in the hard ultraviolet or even the X-ray spectral region. Such high harmonics may be used instead of synchrotron radiation. They are also used for generating ultrashort pulses with attosecond durations in the extreme ultraviolet spectral region [4, 10, 11, 13, 12, 22]. Such attosecond pulses are now used for various fundamental studies e.g. of electronic motion in various kinds of materials. Even zeptosecond pulses (i.e., with durations well below one attosecond) might be possible .
In most cases, the pump source used contains a passively mode-locked laser and a regenerative amplifier based on titanium–sapphire crystals as the gain media. The repetition rate is then between a few hertz and a few kilohertz. Recently, however, a resonant cavity (enhancement resonator) has been used instead of an amplifier to increase the pulse energy to the level required for high harmonic generation . This allowed for a much higher repetition rate of more than 100 MHz.
Although a detailed description of the physical processes behind high harmonic generation is complicated (and often relies on computationally intensive numerical quantum simulations), a number of basic aspects can be grasped with the “simple man's model” , describing how an electron under the influence of a strong electromagnetic field can leave its atom, be accelerated and later collide with the atom, thereby emitting harmonic radiation. More sophisticated models describe the quantum dynamics of the involved electrons.
For further dealing with the generated ultraviolet light, special ultraviolet optics are required. For the shorter wavelengths, the choice of available components is very restricted, and one can essentially use only reflective optics.
The RP Photonics Buyer's Guide contains ten suppliers for high harmonic generation equipment. Among them:
|||F. Brunel, “Harmonic generation due to plasma effects in a gas undergoing multiphoton ionization in the high-intensity limit”, J. Opt. Soc. Am. B 7 (4), 521 (1990); https://doi.org/10.1364/JOSAB.7.000521|
|||A. L’Huillier, X. F. Li and L. A. Lompré, “Propagation effects in high-order harmonic generation in rare gases”, J. Opt. Soc. Am. B 7 (4), 527 (1990); https://doi.org/10.1364/JOSAB.7.000527|
|||P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization”, Phys. Rev. Lett. 71 (13), 1994 (1993) https://doi.org/10.1103/PhysRevLett.71.1994 (simple man's model)|
|||P. Antoine et al., “Attosecond pulse trains using high-order harmonics”, Phys. Rev. Lett. 77 (7), 1234 (1996); https://doi.org/10.1103/PhysRevLett.77.1234|
|||D. M. Mittleman et al., “High-field harmonic generation in the tight-focusing limit”, J. Opt. Soc. Am. B 13 (1), 170 (1996); https://doi.org/10.1364/JOSAB.13.000170|
|||Ch. Spielmann et al., “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses”, Science 278, 661 (1997); https://doi.org/10.1126/science.278.5338.661|
|||T. Brabec and F. Krausz, “Intense few-cycle laser fields: frontiers of nonlinear optics”, Rev. Mod. Phys. 72 (2), 545 (2000); https://doi.org/10.1103/RevModPhys.72.545|
|||P. Salieres and M. Lewenstein, “Generation of ultrashort coherent XUV pulses by harmonic conversion of intense laser pulses in gases: towards attosecond pulses”, Meas. Sci. Technol. 12, 1818 (2001); https://doi.org/10.1088/0957-0233/12/11/309|
|||M. Drescher et al., “X-ray pulses approaching the attosecond frontier”, Science 291, 1923 (2001); https://doi.org/10.1126/science.1058561|
|||P. M. Paul et al., “Observation of a train of attosecond pulses from high harmonic generation”, Science 292, 1689 (2001); https://doi.org/10.1126/science.1059413|
|||A. Baltuška et al., “Attosecond control of electronic processes by intense light fields”, Nature 421, 611 (2003); https://doi.org/10.1038/nature01414|
|||R. Kienberger et al., “Atomic transient recorder”, Nature 427, 817 (2004); https://doi.org/10.1038/nature02277|
|||P. Agostini and L. F. DiMauro, “The physics of attosecond light pulses”, Rep. Prog. Phys. 67, 813 (2004); https://doi.org/10.1088/0034-4885/67/6/R01|
|||J. Seres et al., “Laser technology: source of coherent kiloelectronvolt X-rays”, Nature 433, 596 (2005); https://doi.org/10.1038/433596a|
|||R. J. Jones et al., “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity”, Phys. Rev. Lett. 94 (19), 193201 (2005); https://doi.org/10.1103/PhysRevLett.94.193201|
|||C. Gohle et al., “A frequency comb in the extreme ultraviolet”, Nature 436, 234 (2005); https://doi.org/10.1038/nature03851|
|||F. Krausz et al., “Attosecond pulse generation and detection”, http://www.mpq.mpg.de/lpg/research/attoseconds/attosecond.html|
|||C. Winterfeldt, C. Spielmann, and G. Gerber, “Colloquium: optimal control of high-harmonic generation”, Rev. Mod. Phys. 80, 117 (2008); https://doi.org/10.1103/RevModPhys.80.117|
|||D. C. Yost et al., “Efficient output coupling of intracavity high-harmonic generation”, Opt. Lett. 33 (10), 1099 (2008); https://doi.org/10.1364/OL.33.001099|
|||H. Ren et al., “Quasi-phase-matched high harmonic generation in hollow core photonic crystal fibers”, Opt. Express 16 (21), 17052 (2008); https://doi.org/10.1364/OE.16.017052|
|||O. H. Heckl et al., “High harmonic generation in a gas-filled hollow-core photonic crystal fiber”, Appl. Phys. B 97, 369 (2009); https://doi.org/10.1007/s00340-009-3771-x|
|||F. Krausz and M. Ivanov, “Attosecond physics”, Rev. Mod. Phys. 81, 163 (2009); https://doi.org/10.1103/RevModPhys.81.163|
|||S. Hädrich et al., “Generation of μW level plateau harmonics at high repetition rate”, Opt. Express 19 (20), 19374 (2011); https://doi.org/10.1364/OE.19.019374|
|||T. Witting, “Technology for attosecond science” (review article), Rev. Sci. Instrum. 83, 071101 (2012); https://doi.org/10.1063/1.4731658|
|||C. Hernández-García et al., “Zeptosecond high harmonic keV X-ray waveforms driven by midinfrared laser pulses”, Phys. Rev. Lett. 111 (3), 033002 (2013); https://doi.org/10.1103/PhysRevLett.111.033002|
|||I. Pupeza et al., “Compact high-repetition-rate source of coherent 100 eV radiation”, Nature Photonics 7, 608 (2013); https://doi.org/10.1038/nphoton.2013.156|
|||M. Chini, K. Zhao and Z. Chang, “The generation, characterization and applications of broadband isolated attosecond pulses”, Nature Photon. 8, 178 (2014); https://doi.org/10.1038/nphoton.2013.362|
|||J. Fischer et al., “Intra-oscillator high harmonic generation in a thin-disk laser operating in the 100-fs regime”, Opt. Express 29 (4), 5833 (2021); https://doi.org/10.1364/OE.414444|
|||B. Major et al., “Compact intense extreme-ultraviolet source”, Optica 8 (7), 960 (2021); https://doi.org/10.1364/OPTICA.421564|
|||T. Severt et al., “Enhancing high-order harmonic generation by controlling the diffusion of the electron wave packet”, Optica 8 (8), 1113 (2021); https://doi.org/10.1364/OPTICA.422711|
|||L. Yue and M. B. Gaarde, “Introduction to theory of high-harmonic generation in solids: tutorial”, J. Opt. Soc. Am. B 39 (2), 535 (2022); https://doi.org/10.1364/JOSAB.448602|
|||E. Goulielmakis and T. Brabec, “High harmonic generation in condensed matter” (review article), Nature Photonics 16, 411 (2022); https://doi.org/10.1038/s41566-022-00988-y|
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