High harmonic generation

Last updated November 12, 2024

High-harmonic generation (HHG) is a non-linear process during which a target (gas, plasma, solid or liquid sample) is illuminated by an intense laser pulse. Under such conditions, the sample will emit the high order harmonics of the generation beam (above the fifth harmonic). Due to the coherent nature of the process, high-harmonics generation is a prerequisite of attosecond physics.

Perturbative harmonic generation

Perturbative harmonic generation is a process whereby laser light of frequency ω and photon energy ħω can be used to generate new frequencies of light. The newly generated frequencies are integer multiples nω of the original light's frequency. This process was first discovered in 1961 by Franken et al.,^[1] using a ruby laser, with crystalline quartz as the nonlinear medium.

Harmonic generation in dielectric solids is well understood and extensively used in modern laser physics (see second-harmonic generation). In 1967 New et al. observed the first third harmonic generation in a gas.^[2] In monatomic gases it is only possible to produce odd numbered harmonics for reasons of symmetry. Harmonic generation in the perturbative (weak field) regime is characterised by rapidly decreasing efficiency with increasing harmonic order.^[3] This behaviour can be understood by considering an atom absorbing n photons then emitting a single high energy photon. The probability of absorbing n photons decreases as n increases, explaining the rapid decrease in the initial harmonic intensities.

Development

The first high harmonic generation was observed in 1977 in interaction of intense CO₂ laser pulses with plasma generated from solid targets.^[4] HHG in gases, far more widespread in application today, was first observed by McPherson and colleagues in 1987,^[5] and later by Ferray et al. in 1988,^[6] with surprising results: the high harmonics were found to decrease in intensity at low orders, as expected, but then were observed to form a plateau, with the intensity of the harmonics remaining approximately constant over many orders.^[7] Plateau harmonics spanning hundreds of eV have been measured which extend into the soft X-ray regime.^[8] This plateau ends abruptly at a position called the high harmonic cut-off.

Properties

High harmonics have a number of interesting properties. They are a tunable table-top source of XUV/soft X-rays, synchronised with the driving laser and produced with the same repetition rate. The harmonic cut-off varies linearly with increasing laser intensity up until the saturation intensity I_sat where harmonic generation stops.^[9] The saturation intensity can be increased by changing the atomic species to lighter noble gases but these have a lower conversion efficiency so there is a balance to be found depending on the photon energies required.

High harmonic generation strongly depends on the driving laser field and as a result the harmonics have similar temporal and spatial coherence properties.^[10] High harmonics are often generated with pulse durations shorter than that of the driving laser.^[11] This is due to the nonlinearity of the generation process, phase matching and ionization. Often harmonics are only produced in a very small temporal window when the phase matching condition is met. Depletion of the generating media due to ionization also means that harmonic generation is mainly confined to the leading edge of the driving pulse.^[12]

High harmonics are emitted co-linearly with the driving laser and can have a very tight angular confinement, sometimes with less divergence than that of the fundamental field and near Gaussian beam profiles.^[13]

Semi-classical approach

The maximum photon energy producible with high harmonic generation is given by the cut-off of the harmonic plateau. This can be calculated classically by examining the maximum energy the ionized electron can gain in the electric field of the laser. The cut-off energy is given by:^[14]

E_{\mathrm {max} }=I_{p}+3.17\ U_{p}

where U_p is the ponderomotive energy from the laser field and I_p is the ionization potential.

This cut-off energy is derived from a semi-classical calculation, often called the three-step model. The electron is initially treated quantum mechanically as it tunnel ionizes from the parent atom, but its subsequent dynamics are treated classically. The electron is assumed to be born into the vacuum with zero initial velocity, and to be subsequently accelerated by the laser beam's electric field.

The three-step model ThreeStep.png — The three-step model

Half an optical cycle after ionization, the electron will reverse direction as the electric field changes sign, and will accelerate back towards the parent nucleus. Upon return to the parent nucleus it can then emit bremsstrahlung-like radiation during a recombination process with the atom as it returns to its ground state. This description has become known as the recollisional model of high harmonic generation.^[15]

Since the frequency of the emitted radiation depends on both the kinetic energy and on the ionization potential, the different frequencies are emitted at different recombination times (i.e. the emitted pulse is chirped). Furthermore, for every frequency, there are two corresponding recombination times. We refer to these two trajectories as the short trajectory (which are emitted first), and the long trajectory.

In the semiclassical picture, HHG will only occur if the driving laser field is linearly polarised. Ellipticity on the laser beam causes the returning electron to miss the parent nucleus. Quantum mechanically, the overlap of the returning electron wavepacket with the nuclear wavepacket is reduced. This has been observed experimentally, where the intensity of harmonics decreases rapidly with increasing ellipticity.^[16] Another effect which limits the intensity of the driving laser is the Lorentz force. At intensities above 10¹⁶ W·cm⁻² the magnetic component of the laser pulse, which is ignored in weak field optics, can become strong enough to deflect the returning electron. This will cause it to "miss" the parent nucleus and hence prevent HHG.

Phase matching

As in every nonlinear process, phase matching plays an important role in high harmonic generation in the gas phase. In free-focusing geometry, the four causes of wavevector mismatch are: neutral dispersion, plasma dispersion, Gouy phase, and dipole phase.^[17]^[18]

The neutral dispersion is caused by the atoms while the plasma dispersion is due to the ions, and the two have opposite signs. The Gouy phase is due to wavefront phase jump close to the focus, and varies along it. Finally the dipole phase arises from the atomic response in the HHG process.^[19] When using a gas jet geometry, the optimal conditions for generating high harmonics emitted from short trajectories are obtained when the generating gas is located after the focus, while generation of high harmonics from long trajectory can be obtained off-axis when the generating gas is located before the focus.^[20]

Furthermore, the implementation of loose focusing geometry for the driving field enables a higher number of emitters and photons to contribute to the generation process and thus, enhance the harmonic yield.^[21] When using a gas jet geometry, focusing the laser into the Mach disk can increase the efficiency of harmonic generation.^[22]

More generally, in the X-ray spectral region, materials have a refractive index that is very close to 1. To balance the phase mismatch, $\Delta k=k_{q}-qk_{L}$ , we need to find such parameters in the high dimensional space that will effectively make the combined refractive index at the driving laser wavelength nearly 1.

In order to achieve intensity levels that can distort an atom's binding potential, it is necessary to focus the driving laser beam. This introduces dispersion terms affecting the phase mismatch, depending on the specific geometry (such as plane wave propagation, free focusing, hollow core waveguide, etc.). Additionally, during the high harmonic generation process, electrons are accelerated, and some of them return to their parent ion, resulting in X-ray bursts. However, the majority of these electrons do not return and instead contribute to dispersion for the co-propagating waves. The returning electrons carry phase due to processes like ionization, recombination, and propagation. Furthermore, the ionized atoms can influence the refractive index of the medium, providing another source of dispersion.

The phase mismatch (> 0 phase velocity of the laser is faster than that of the X-rays) can be represented as:

\Delta k=k_{q}-qk_{L}=\underbrace {\Delta k_{\mathrm {neutrals} }} _{<0}+\underbrace {\Delta k_{\mathrm {ions} }} _{<0}+\underbrace {\Delta k_{\mathrm {electrons} }} _{>0}+\underbrace {\Delta k_{\mathrm {geometry} }} _{>0}+\underbrace {\Delta k_{\mathrm {intrinsic} }} _{>\;\!0}+\cdots

where $\Delta k_{\mathrm {neutrals} }$ is the neutral atoms contribution, $\Delta k_{\mathrm {ions} }$ is the contribution from ions (when neutrals are ionized, this term can be still sufficiently large in the UV^[23]), $\Delta k_{\mathrm {electrons} }$ is the plasma contribution, $\Delta k_{\mathrm {geometry} }$ is the free focusing geometry, plane-wave of waveguiding geometry, $\Delta k_{\mathrm {intrinsic} }$ is the phase accumulated by the electron during the time it spends away from the atom, etc. Each term has a specific sign which allows balancing the mismatch at a particular time and frequency.

The contribution from the electrons scales quadratically with the wavelength: $\Delta n_{\mathrm {electrons} }\sim -\lambda ^{2}$ , while the contribution from atoms scales inversely with wavelength: $\Delta n_{\mathrm {atoms} }\sim 1/\lambda ^{2}$ . Thus at long IR wavelengths, the term $\left|\Delta n_{\mathrm {electrons} }\right|$ is quite large per electron, while the term $\Delta n_{\mathrm {atoms} }$ is quite small and close to one. To phase-match the process of HHG, very high pressures and low ionization levels are required, thus giving a large number of emitters.^[24] In the opposite UV spectral range, the term $\Delta n_{\mathrm {atoms} }$ is large because of the closely located UV resonances, and in addition, the term $\left|\Delta n_{\mathrm {electrons} }\right|$ is small. To phase-match the process, low pressures are needed. Moreover, in the UV, very high ionization levels can be tolerated (much larger than 100%). This gives HHG photon energy scalability with the intensity of the driving UV laser.^[23] Plain-wave geometry or loose focusing geometry allows highly collinear phase matching and maximum flux extraction at the driving wavelengths where the ${\vec {v}}\times {\vec {B}}$ term is small. The generation of High-order harmonics in waveguide allows propagation with characteristics close to those of plane wave propagation.^[25] Such geometries benefit, especially X-ray spectra generated by IR beams, where long interaction volumes are needed for optimal power extraction. In such geometries, spectra extending to 1.6 keV, have been generated.^[24] For UV-VIS driven high harmonics, the waveguide term is small, and the phase-matching picture resembles the plane-wave geometry. In such geometries, narrow bandwidth harmonics extending to the carbon edge (300 eV) have been generated.^[23]

Related Research Articles

<span class="mw-page-title-main">Nonlinear optics</span> Branch of physics

Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typically observed only at very high light intensities (when the electric field of the light is >10⁸ V/m and thus comparable to the atomic electric field of ~10¹¹ V/m) such as those provided by lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear. In nonlinear optics, the superposition principle no longer holds.

<span class="mw-page-title-main">Bremsstrahlung</span> Electromagnetic radiation due to deceleration of charged particles

In particle physics, bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation, thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases.

Ionization is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules, electrons, positrons, protons, antiprotons and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected.

Coherence expresses the potential for two waves to interfere. Two monochromatic beams from a single source always interfere. Wave sources are not strictly monochromatic: they may be partly coherent. Beams from different sources are mutually incoherent.

In physics, a squeezed coherent state is a quantum state that is usually described by two non-commuting observables having continuous spectra of eigenvalues. Examples are position $and momentum of a particle, and the (dimension-less) electric field in the amplitude and in the mode of a light wave. The product of the standard deviations of two such operators obeys the uncertainty principle:$

In physics, the Lamb shift, named after Willis Lamb, is an anomalous difference in energy between two electron orbitals in a hydrogen atom. The difference was not predicted by theory and it cannot be derived from the Dirac equation, which predicts identical energies. Hence the Lamb shift is a deviation from theory seen in the differing energies contained by the ²S_1/2 and ²P_1/2 orbitals of the hydrogen atom.

Resolved sideband cooling is a laser cooling technique allowing cooling of tightly bound atoms and ions beyond the Doppler cooling limit, potentially to their motional ground state. Aside from the curiosity of having a particle at zero point energy, such preparation of a particle in a definite state with high probability (initialization) is an essential part of state manipulation experiments in quantum optics and quantum computing.

Local-density approximations (LDA) are a class of approximations to the exchange–correlation (XC) energy functional in density functional theory (DFT) that depend solely upon the value of the electronic density at each point in space. Many approaches can yield local approximations to the XC energy. However, overwhelmingly successful local approximations are those that have been derived from the homogeneous electron gas (HEG) model. In this regard, LDA is generally synonymous with functionals based on the HEG approximation, which are then applied to realistic systems.

<span class="mw-page-title-main">Optical lattice</span> Atomic-scale structure formed through the Stark shift by opposing beams of light

An optical lattice is formed by the interference of counter-propagating laser beams, creating a spatially periodic polarization pattern. The resulting periodic potential may trap neutral atoms via the Stark shift. Atoms are cooled and congregate at the potential extrema. The resulting arrangement of trapped atoms resembles a crystal lattice and can be used for quantum simulation.

Second-harmonic generation (SHG), also known as frequency doubling, is the lowest-order wave-wave nonlinear interaction that occurs in various systems, including optical, radio, atmospheric, and magnetohydrodynamic systems. As a prototype behavior of waves, SHG is widely used, for example, in doubling laser frequencies. SHG was initially discovered as a nonlinear optical process in which two photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with twice the energy of the initial photons, that conserves the coherence of the excitation. It is a special case of sum-frequency generation (2 photons), and more generally of harmonic generation.

An X-ray laser can be created by several methods either in hot, dense plasmas or as a free-electron laser in an accelerator. This article describes the x-ray lasers in plasmas, only.

Photoelectrochemical processes are processes in photoelectrochemistry; they usually involve transforming light into other forms of energy. These processes apply to photochemistry, optically pumped lasers, sensitized solar cells, luminescence, and photochromism.

In atomic, molecular, and optical physics, above-threshold ionization (ATI) is a multi-photon effect where an atom is ionized with more than the energetically required number of photons. It was first observed in 1979 by Pierre Agostini and colleagues in xenon gas.

Double ionization is a process of formation of doubly charged ions when laser radiation is exerted on neutral atoms or molecules. Double ionization is usually less probable than single-electron ionization. Two types of double ionization are distinguished: sequential and non-sequential.

Heat transfer physics describes the kinetics of energy storage, transport, and energy transformation by principal energy carriers: phonons, electrons, fluid particles, and photons. Heat is thermal energy stored in temperature-dependent motion of particles including electrons, atomic nuclei, individual atoms, and molecules. Heat is transferred to and from matter by the principal energy carriers. The state of energy stored within matter, or transported by the carriers, is described by a combination of classical and quantum statistical mechanics. The energy is different made (converted) among various carriers. The heat transfer processes are governed by the rates at which various related physical phenomena occur, such as the rate of particle collisions in classical mechanics. These various states and kinetics determine the heat transfer, i.e., the net rate of energy storage or transport. Governing these process from the atomic level to macroscale are the laws of thermodynamics, including conservation of energy.

The interaction of matter with light, i.e., electromagnetic fields, is able to generate a coherent superposition of excited quantum states in the material. Coherent denotes the fact that the material excitations have a well defined phase relation which originates from the phase of the incident electromagnetic wave. Macroscopically, the superposition state of the material results in an optical polarization, i.e., a rapidly oscillating dipole density. The optical polarization is a genuine non-equilibrium quantity that decays to zero when the excited system relaxes to its equilibrium state after the electromagnetic pulse is switched off. Due to this decay which is called dephasing, coherent effects are observable only for a certain temporal duration after pulsed photoexcitation. Various materials such as atoms, molecules, metals, insulators, semiconductors are studied using coherent optical spectroscopy and such experiments and their theoretical analysis has revealed a wealth of insights on the involved matter states and their dynamical evolution.

In quantum optics, a superradiant phase transition is a phase transition that occurs in a collection of fluorescent emitters, between a state containing few electromagnetic excitations and a superradiant state with many electromagnetic excitations trapped inside the emitters. The superradiant state is made thermodynamically favorable by having strong, coherent interactions between the emitters.

A phonovoltaic (pV) cell converts vibrational (phonons) energy into a direct current much like the photovoltaic effect in a photovoltaic (PV) cell converts light (photon) into power. That is, it uses a p-n junction to separate the electrons and holes generated as valence electrons absorb optical phonons more energetic than the band gap, and then collects them in the metallic contacts for use in a circuit. The pV cell is an application of heat transfer physics and competes with other thermal energy harvesting devices like the thermoelectric generator.

High Harmonic Generation (HHG) is a non-perturbative and extremely nonlinear optical process taking place when a highly intense ultrashort laser pulse undergoes an interaction with a nonlinear media. A typical high order harmonic spectra contains frequency combs separated by twice the laser frequency. HHG is an excellent table top source of highly coherent extreme ultraviolet and soft X-ray laser pulses.

In physics and chemistry, photoemission orbital tomography is a combined experimental / theoretical approach which was initially developed to reveal information about the spatial distribution of individual one-electron surface-state wave functions and later extended to study molecular orbitals. Experimentally, it uses angle-resolved photoemission spectroscopy (ARPES) to obtain constant binding energy photoemission angular distribution maps. In their pioneering work, Mugarza et al. in 2003 used a phase-retrieval method to obtain the wave function of electron surface states based on ARPES data acquired from stepped gold crystalline surfaces; they obtained the respective wave functions and, upon insertion into the Schrödinger equation, also the binding potential. More recently, photoemission maps, also known as tomograms, have been shown to reveal information about the electron probability distribution in molecular orbitals. Theoretically, one rationalizes these tomograms as hemispherical cuts through the molecular orbital in momentum space. This interpretation relies on the assumption of a plane wave final state, i.e., the idea that the outgoing electron can be treated as a free electron, which can be further exploited to reconstruct real-space images of molecular orbitals on a sub-Ångström length scale in two or three dimensions. Presently, POT has been applied to various organic molecules forming well-oriented monolayers on single crystal surfaces or to two-dimensional materials.

References

↑ P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
↑ New, G. H. C.; Ward, J. F. (1967). "Optical Third-Harmonic Generation in Gases". Phys. Rev. Lett. 19 (10): 556–559. Bibcode:1967PhRvL..19..556N. doi:10.1103/physrevlett.19.556.
↑ J. Wildenauer, Journal of Applied Physics 62, 41 (1987).
↑ Burnett, N. H.; et al. (1977). "Harmonic generation in CO2 laser target interaction". Appl. Phys. Lett. 31 (3): 172–174. Bibcode:1977ApPhL..31..172B. doi:10.1063/1.89628.
↑ McPherson, A.; et al. (1987). "Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases". JOSA B. 4 (4): 595. Bibcode:1987JOSAB...4..595M. doi:10.1364/JOSAB.4.000595.
↑ Ferray, M.; et al. (1988). "Multiple-harmonic conversion of 1064 nm radiation in rare gases". Journal of Physics B: Atomic, Molecular and Optical Physics. 21 (3): L31. Bibcode:1988JPhB...21L..31F. doi:10.1088/0953-4075/21/3/001. S2CID 250827054.
↑ Li, X. F.; L'Huillier, A.; Ferray, M.; Lompre, L. A.; Mainfray, G. (1989). "Multiple-harmonic generation in rare gases at high laser intensity". Physical Review A. 39 (11): 5751–5761. Bibcode:1989PhRvA..39.5751L. doi:10.1103/physreva.39.5751. PMID 9901157.
↑ Seres, J.; et al. (2005). "Laser technology: Source of coherent kiloelectronvolt X-rays". Nature. 433 (7026): 596. Bibcode:2005Natur.433..596S. doi: 10.1038/433596a . PMID 15703738. S2CID 4425428.
↑ Brabec, T.; Krausz, F. (2000). "Intense few-cycle laser fields: Frontiers of nonlinear optics". Reviews of Modern Physics . 72 (2): 545–591. Bibcode:2000RvMP...72..545B. doi:10.1103/revmodphys.72.545.
↑ L'Huillier, A.; Schafer, K. J.; Kulander, K. C. (1991). "Theoretical aspects of intense field harmonic generation". Journal of Physics B: Atomic, Molecular and Optical Physics . 24 (15): 3315–3341. Bibcode:1991JPhB...24.3315L. doi:10.1088/0953-4075/24/15/004. S2CID 250751106.
↑ Streaking of 43-attosecond soft-X-ray pulses generated by a passively CEP-stable mid-infrared, https://doi.org/10.1364/OE.25.027506
↑ Schafer, K. J.; Kulander, K. C. (1997). "High Harmonic Generation from Ultrafast Pump Lasers". Physical Review Letters . 78 (4): 638–641. Bibcode:1997PhRvL..78..638S. doi:10.1103/physrevlett.78.638.
↑ Tisch, J. W. G.; et al. (1994). "Angularly resolved high-order harmonic generation in helium". Physical Review A. 49 (1): R28–R31. Bibcode:1994PhRvA..49...28T. doi:10.1103/physreva.49.r28. PMID 9910285.
↑ Krause, Jeffrey L.; Schafer, Kenneth J.; Kulander, Kenneth C. (1992). "High-order harmonic generation from atoms and ions in the high intensity regime". Physical Review Letters. 68 (24): 3535–3538. Bibcode:1992PhRvL..68.3535K. doi:10.1103/PhysRevLett.68.3535. PMID 10045729.
↑ Corkum, P. B. (1993). "Plasma perspective on strong field multiphoton ionization". Physical Review Letters. 71 (13): 1994–1997. Bibcode:1993PhRvL..71.1994C. doi:10.1103/physrevlett.71.1994. PMID 10054556. S2CID 29947935.
↑ Dietrich, P.; Burnett, N. H.; Ivanov, M.; Corkum, P. B. (1994). "High-harmonic generation and correlated two-electron multiphoton ionization with elliptically polarized light". Physical Review A. 50 (5): R3585–R3588. Bibcode:1994PhRvA..50.3585D. doi:10.1103/physreva.50.r3585. PMID 9911439.
↑ Altucci, C.; Starczewski, T.; Mevel, E.; Wahlström, C.-G.; Carré, B.; L'Huillier, A. (1996). "Influence of atomic density in high-order harmonic generation". J. Opt. Soc. Am. B. 13 (1): 148–156. Bibcode:1996JOSAB..13..148A. doi:10.1364/JOSAB.13.000148.
↑ Pascal, Salieres; L'Huillier, Anne; Lewenstein, Maciej (1995). "Coherence control of high-order harmonics" (PDF). Physical Review Letters. 74 (19): 3776–3779. Bibcode:1995PhRvL..74.3776S. doi:10.1103/physrevlett.74.3776. PMID 10058294. S2CID 35091499.
↑ Lewenstein, Maciej; Salieres, Pascal; L'huillier, Anne (1995). "Phase of the atomic polarization in high-order harmonic generation". Physical Review A. 52 (6): 4747–4754. Bibcode:1995PhRvA..52.4747L. doi:10.1103/physreva.52.4747. PMID 9912816.
↑ Balcou, Philippe; Salieres, Pascal; L'Huillier, Anne; Lewenstein, Maciej (1997). "Generalized phase-matching conditions for high harmonics: The role of field-gradient forces". Physical Review A. 55 (4): 3204–3210. Bibcode:1997PhRvA..55.3204B. doi:10.1103/PhysRevA.55.3204.
↑ Takahashi, E.; Nabekawa, Y.; Midorikawa, K. (2002). "Generation of 10-uj coherent extreme-ultraviolet light by use of high-order harmonics". Optics Letters. 27 (21): 1920–1922. Bibcode:2002OptL...27.1920T. doi:10.1364/OL.27.001920. PMID 18033402.
↑ Grant-Jacob, James; Mills, Ben; Butcher, Tom; Chapman, Richard; Brocklesby, William; Frey, Jeremy (2011). "Gas jet structure influence on high harmonic generation" (PDF). Optics Express. 19 (10): 9801–9806. Bibcode:2011OExpr..19.9801G. doi: 10.1364/OE.19.009801 . PMID 21643236.
1 2 3 Popmintchev, D.; Hernández-García, C.; Dollar, F.; Mancuso, C. A.; Peng, P.-C.; Barwick, B.; Gorman, T. T.; Alonso-Mori, R.; Ališauskas, S.; Andriukaitis, G.; Baltuška, A.; Bostedt, C.; Chen, M.-C.; Dakovski, G. L.; Durfee, C. G.; Eckert, S.; Fan, T.-M.; Ferguson, W. R.; Frischkorn, C. G.; et al. (2015). "Ultraviolet surprise: Efficient soft x-ray high-harmonic generation in multiply ionized plasmas". Science . 350 (6265): 1225–1231. Bibcode:2015Sci...350.1225P. doi:10.1126/science.aac9755. hdl: 10366/147088 . PMID 26785483. S2CID 2342988.
1 2 Popmintchev, T.; Chen, M.-C.; Popmintchev, D.; Arpin, P.; Brown, S.; Alisauskas, S.; Andriukaitis, G.; Balciunas, T.; Mücke, O. D.; Pugzlys, A.; Baltuska, A.; Shim, B.; Schrauth, S. E.; Gaeta, A.; Hernández-García, C.; Plaja, L.; Becker, A.; Jaron-Becker, A.; Murnane, M. M.; et al. (2012). "Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers". Science . 336 (6086): 1287–1291. arXiv: 2403.19535 . Bibcode:2012Sci...336.1287P. doi:10.1126/science.1218497. hdl: 10366/147089 . PMID 22679093. S2CID 24628513.
↑ Rundquist, A.; Durfee, C. G.; Chang, Z.; Herne, C.; Backus, S.; Murnane, M. M.; Kapteyn, H. C. (1998). "Phase-matched generation of coherent soft X-rays". Science . 280 (5368): 1412–1415. arXiv: 2403.19636 . Bibcode:1998Sci...280.1412R. doi:10.1126/science.280.5368.1412. PMID 9603725.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[1] P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).

[2] New, G. H. C.; Ward, J. F. (1967). "Optical Third-Harmonic Generation in Gases". Phys. Rev. Lett. 19 (10): 556–559. Bibcode:1967PhRvL..19..556N. doi:10.1103/physrevlett.19.556.

[3] J. Wildenauer, Journal of Applied Physics 62, 41 (1987).

[4] Burnett, N. H.; et al. (1977). "Harmonic generation in CO2 laser target interaction". Appl. Phys. Lett. 31 (3): 172–174. Bibcode:1977ApPhL..31..172B. doi:10.1063/1.89628.

[5] McPherson, A.; et al. (1987). "Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases". JOSA B. 4 (4): 595. Bibcode:1987JOSAB...4..595M. doi:10.1364/JOSAB.4.000595.

[6] Ferray, M.; et al. (1988). "Multiple-harmonic conversion of 1064 nm radiation in rare gases". Journal of Physics B: Atomic, Molecular and Optical Physics. 21 (3): L31. Bibcode:1988JPhB...21L..31F. doi:10.1088/0953-4075/21/3/001. S2CID 250827054.

[7] Li, X. F.; L'Huillier, A.; Ferray, M.; Lompre, L. A.; Mainfray, G. (1989). "Multiple-harmonic generation in rare gases at high laser intensity". Physical Review A. 39 (11): 5751–5761. Bibcode:1989PhRvA..39.5751L. doi:10.1103/physreva.39.5751. PMID 9901157.

[8] Seres, J.; et al. (2005). "Laser technology: Source of coherent kiloelectronvolt X-rays". Nature. 433 (7026): 596. Bibcode:2005Natur.433..596S. doi: 10.1038/433596a . PMID 15703738. S2CID 4425428.

[9] Brabec, T.; Krausz, F. (2000). "Intense few-cycle laser fields: Frontiers of nonlinear optics". Reviews of Modern Physics . 72 (2): 545–591. Bibcode:2000RvMP...72..545B. doi:10.1103/revmodphys.72.545.

[10] L'Huillier, A.; Schafer, K. J.; Kulander, K. C. (1991). "Theoretical aspects of intense field harmonic generation". Journal of Physics B: Atomic, Molecular and Optical Physics . 24 (15): 3315–3341. Bibcode:1991JPhB...24.3315L. doi:10.1088/0953-4075/24/15/004. S2CID 250751106.

[11] Streaking of 43-attosecond soft-X-ray pulses generated by a passively CEP-stable mid-infrared, https://doi.org/10.1364/OE.25.027506

[12] Schafer, K. J.; Kulander, K. C. (1997). "High Harmonic Generation from Ultrafast Pump Lasers". Physical Review Letters . 78 (4): 638–641. Bibcode:1997PhRvL..78..638S. doi:10.1103/physrevlett.78.638.

[13] Tisch, J. W. G.; et al. (1994). "Angularly resolved high-order harmonic generation in helium". Physical Review A. 49 (1): R28–R31. Bibcode:1994PhRvA..49...28T. doi:10.1103/physreva.49.r28. PMID 9910285.

[14] Krause, Jeffrey L.; Schafer, Kenneth J.; Kulander, Kenneth C. (1992). "High-order harmonic generation from atoms and ions in the high intensity regime". Physical Review Letters. 68 (24): 3535–3538. Bibcode:1992PhRvL..68.3535K. doi:10.1103/PhysRevLett.68.3535. PMID 10045729.

[15] Corkum, P. B. (1993). "Plasma perspective on strong field multiphoton ionization". Physical Review Letters. 71 (13): 1994–1997. Bibcode:1993PhRvL..71.1994C. doi:10.1103/physrevlett.71.1994. PMID 10054556. S2CID 29947935.

[16] Dietrich, P.; Burnett, N. H.; Ivanov, M.; Corkum, P. B. (1994). "High-harmonic generation and correlated two-electron multiphoton ionization with elliptically polarized light". Physical Review A. 50 (5): R3585–R3588. Bibcode:1994PhRvA..50.3585D. doi:10.1103/physreva.50.r3585. PMID 9911439.

[17] Altucci, C.; Starczewski, T.; Mevel, E.; Wahlström, C.-G.; Carré, B.; L'Huillier, A. (1996). "Influence of atomic density in high-order harmonic generation". J. Opt. Soc. Am. B. 13 (1): 148–156. Bibcode:1996JOSAB..13..148A. doi:10.1364/JOSAB.13.000148.

[18] Pascal, Salieres; L'Huillier, Anne; Lewenstein, Maciej (1995). "Coherence control of high-order harmonics" (PDF). Physical Review Letters. 74 (19): 3776–3779. Bibcode:1995PhRvL..74.3776S. doi:10.1103/physrevlett.74.3776. PMID 10058294. S2CID 35091499.

[19] Lewenstein, Maciej; Salieres, Pascal; L'huillier, Anne (1995). "Phase of the atomic polarization in high-order harmonic generation". Physical Review A. 52 (6): 4747–4754. Bibcode:1995PhRvA..52.4747L. doi:10.1103/physreva.52.4747. PMID 9912816.

[20] Balcou, Philippe; Salieres, Pascal; L'Huillier, Anne; Lewenstein, Maciej (1997). "Generalized phase-matching conditions for high harmonics: The role of field-gradient forces". Physical Review A. 55 (4): 3204–3210. Bibcode:1997PhRvA..55.3204B. doi:10.1103/PhysRevA.55.3204.

[21] Takahashi, E.; Nabekawa, Y.; Midorikawa, K. (2002). "Generation of 10-uj coherent extreme-ultraviolet light by use of high-order harmonics". Optics Letters. 27 (21): 1920–1922. Bibcode:2002OptL...27.1920T. doi:10.1364/OL.27.001920. PMID 18033402.

[22] Grant-Jacob, James; Mills, Ben; Butcher, Tom; Chapman, Richard; Brocklesby, William; Frey, Jeremy (2011). "Gas jet structure influence on high harmonic generation" (PDF). Optics Express. 19 (10): 9801–9806. Bibcode:2011OExpr..19.9801G. doi: 10.1364/OE.19.009801 . PMID 21643236.

[Popmintchev2015-23] 1 2 3 Popmintchev, D.; Hernández-García, C.; Dollar, F.; Mancuso, C. A.; Peng, P.-C.; Barwick, B.; Gorman, T. T.; Alonso-Mori, R.; Ališauskas, S.; Andriukaitis, G.; Baltuška, A.; Bostedt, C.; Chen, M.-C.; Dakovski, G. L.; Durfee, C. G.; Eckert, S.; Fan, T.-M.; Ferguson, W. R.; Frischkorn, C. G.; et al. (2015). "Ultraviolet surprise: Efficient soft x-ray high-harmonic generation in multiply ionized plasmas". Science . 350 (6265): 1225–1231. Bibcode:2015Sci...350.1225P. doi:10.1126/science.aac9755. hdl: 10366/147088 . PMID 26785483. S2CID 2342988.

[Popmintchev2012-24] 1 2 Popmintchev, T.; Chen, M.-C.; Popmintchev, D.; Arpin, P.; Brown, S.; Alisauskas, S.; Andriukaitis, G.; Balciunas, T.; Mücke, O. D.; Pugzlys, A.; Baltuska, A.; Shim, B.; Schrauth, S. E.; Gaeta, A.; Hernández-García, C.; Plaja, L.; Becker, A.; Jaron-Becker, A.; Murnane, M. M.; et al. (2012). "Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers". Science . 336 (6086): 1287–1291. arXiv: 2403.19535 . Bibcode:2012Sci...336.1287P. doi:10.1126/science.1218497. hdl: 10366/147089 . PMID 22679093. S2CID 24628513.

[Rundquist1998-25] Rundquist, A.; Durfee, C. G.; Chang, Z.; Herne, C.; Backus, S.; Murnane, M. M.; Kapteyn, H. C. (1998). "Phase-matched generation of coherent soft X-rays". Science . 280 (5368): 1412–1415. arXiv: 2403.19636 . Bibcode:1998Sci...280.1412R. doi:10.1126/science.280.5368.1412. PMID 9603725.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]