High-harmonics generation in Krypton. This technology is one of the most used techniques to generate attosecond burst of light.

Attosecond physics, also known as attophysics, or more generally attosecond science, is a branch of Atomic, molecular, and optical physics and light-matter interaction wherein attosecond (10−18 s) photon pulses are used to unravel dynamical processes in matter with unprecedented time resolution.

Attosecond science mainly employs pump–probe spectroscopic methods to investigate the physical process of interest. Due to the complexity of this field of study, it generally requires a synergistic interplay between state-of-the-art experimental setup and advanced theoretical tools to interpret the data collected from attosecond experiments[1].

The main interests of attosecond physics are:

  1. Atomic physics: investigation of electron correlation effects, photo-emission delay and ionization tunneling[2] .
  2. Molecular physics and molecular chemistry: role of electronic motion in molecular excited states (e.g. charge-transfer processes), light-induced photo-fragmentation, and light-induced electron transfer processes[3].
  3. Solid-state physics: investigation of exciton dynamics in advanced 2D materials, petahertz charge carrier motion in solids, spin dynamics in ferromagnetic materials[4].

One of the primary goals of attosecond science is to provide advanced insights into the quantum dynamics of electrons in atoms, molecules and solids with the long-term challenge of achieving real-time control of the electron motion in matter [5].

The current world record for the shortest light-pulse generated by human technology is 43 as[6].

Introduction

edit

The advent of broadband solid-state titanium-doped sapphire based (Ti:Sa) lasers (1986)[7], chirped pulse amplification (CPA)[8] (1988), spectral broadening of high-energy pulse [9] (e.g. gas-filled hollow-core fiber via self-phase modulation) (1996), mirror-dispersion-controlled technology (chirped mirrors)[10] (1994), and carrier envelop offset stabilization[11] (2003) enable the creation of isolated-attosecond light pulse (generated by the non-linear process high-harmonics generation in noble gas)[12][13] (2004,2006),

which gave birth to the field of attosecond science[14].

"Electron motion" in a hydrogen atom. The period of this states superposition (1s-2p) is around 400 as.

Motivation to attosecond physics

edit

The natural time scale of electrons motion in atoms, molecules and solids is the attosecond (1 as= 10−18 s). This fact is a direct consequence of quantum mechanics laws.

Indeed, for simplicity, consider a quantum particle in superposition between ground-level, of energy  , and the first excited level, of energy  :

 

with   and   chosen as simply the square roots of the quantum probability of observing the particle in the corresponding state and,

 

are the time-dependent ground   and excited state   respectively, with   the reduced Planck constant.

The expectation value of a generic hermitian and symmetric operator[15],  , can be written as  , as a consequence the time evolution of this observable is:

 

While the first two terms do not depend on time, the third, instead, does. This creates a dynamic for the observable   with a characteristic time,  , given by  .

 
Evolution of the radial probability density of the superposition between 1s and 2p state in hydrogen atoms. The color bar indicates the probability density as a function of the radius (x-axis), at which one can find the particle, and time (y-axis).

As a consequence, for energy levels in the range of   10 eV, which is the typical electronic energy range in matter[5],

the characteristic time of the dynamic of any associated physical observable is approximately 400 as.

To measure the time evolution of  , one needs to use a controlled tool, or a process, with an even shorter time-duration that can interact with that dynamic.

This is the reason why attosecond light pulses are used to disclose the physics of ultra-fast phenomena in the few-femtosecond and attosecond time-domain[16] .

Generation of attosecond pulse

edit

To generate a traveling pulse with an ultrashort time duration, two key elements are needed: bandwidth and central wavelength of the electromagnetic wave[17].

From Fourier analysis, the more the available spectral bandwidth of a light pulse, the shorter, potentially, is its time duration.

There is however, a lower-limit in the minimum duration exploitable for a given pulse central wavelength. This limit is the optical cycle[18].

Indeed, for a pulse centered in the low-frequency region, e.g. infrared (IR)  800 nm, its minimum time duration is around  2.67 fs, where   is the speed of light; whereas, for a light field with central wavelength in the extreme ultraviolet (XUV) at  30 nm the minimum duration is around  100 as [18].

Thus, smaller time duration requires the use of shorter, and more energetic wavelength, even down to the soft-X-ray (SXR) region.

For this reason, standard techniques to create attosecond light pulses are based on radiation sources with broad spectral bandwidths and central wavelength located in the XUV-SXR range[19].

The most common sources that fit these requirements are free-electron lasers (FEL) and high-harmonics generation (HHG) setups.

Physical observables and attosecond experiments

edit

Once an attosecond light source is available, one has to drive the pulse towards the sample of interest and, then, measures its dynamics.

The most suitable experimental observables to analyze the electron dynamics in matter are:

Pump-probe techniques are used to image ultra-fast processes occurring in matter.

The general strategy is to use a pump-probe scheme to "image" through one of the aforementioned observables the ultra-fast dynamics occurring in the material under investigation[1].

Few-femtosecond IR-XUV/SXR attosecond pulse pump-probe experiments

edit

As an example, in a typical pump-probe experimental apparatus, an attosecond (XUV-SXR) pulse and an intense (  W/cm2) low-frequency infrared (IR) pulse with a time duration of few to tens femtoseconds are collinearly focused on the studied sample.

At this point, by varying the delay of the attosecond pulse, which depending on the experiment could be pump/probe, with respect the IR pulse (probe/pump), the desired physical observable is recorded [24].

The subsequent challenge is to interpret the collected data and retrieve fundamental information on the hidden dynamics and quantum processes occurring in the sample. This can be achieved with advanced theoretical tools and numerical calculations[25][26].

By exploiting this experimental scheme, several kinds of dynamics can be explored in atoms, molecules and solids; typically light-induced dynamics and out-of-equilibrium excited state within attosecond time-resolution [20][21][23].

Quantum mechanics foundations

edit

Attosecond physics typically deals with non-relativistic bounded particles and employs electromagnetic fields with a moderately high intensity (  W/cm2) [27].

This fact allows to set up a discussion in a non-relativistic-semi-classical quantum mechanics environment for light-matter interaction.

Atoms

edit

Resolution of time dependent Schrödinger equation in an electromagnetic field

edit

The time evolution of a single electronic wave function in an atom,   is described by the Schrödinger equation (in atomic units):

 

where the light-matter interaction Hamiltonian,  , can be expressed in the length gauge, within the dipole approximation, as[28][29]:

 

where   is the Coulomb potential of the atomic species considered;   are the momentum and position operator, respectively; and   is the total electric field evaluated in the neighbor of the atom.

The formal solution of the Schrödinger equation is given by the propagator formalism:

 

where  , is the electron wave function at time  .

This exact solution cannot be used for almost any practical purpose.

However, it can be proved, using Dyson's equations[30][31] that the previous solution can also be written as:

 

where,

  is the bounded Hamiltonian and   is the interaction Hamiltonian.

The formal solution of Eq.  , which previously was simply written as Eq.  , can now be regarded in Eq.   as a superposition of different quantum paths (or quantum trajectory), each one of them with a peculiar interaction time   with the electric field.

In other words, each quantum path is characterized by three steps:

  1. An initial evolution without the electromagnetic field. This is described by the left-hand side   term in the integral.
  2. Then, a "kick" from the electromagnetic field,   that "excite" the electron. This event occurs at an arbitrary time that uni-vocally characterizes the quantum path  .
  3. A final evolution driven by both the field and the Coulomb potential, given by  .

In parallel, you also have a quantum path that do not perceive the field at all, this trajectory is indicated by the right-hand side term in Eq.  .

This process is entirely time-reversible, i.e. can also occur in the opposite order[32].

Equation   is not straightforward to handle. However, physicists use it as the starting point for numerical calculation, more advanced discussion or several approximations[31] [33].

For strong-field interaction problems, where ionization may occurs, one can imagine to project Eq.   in a certain continuum state (unbounded state or free state)  , of momentum  , so that:

 

 is the probability amplitude to find at a certain time  , the electron in the continuum states  .

If this probability amplitude is greater than zero than the electron is photo-ionized.

For the majority of application, the second term in   is not considered, and only the first one is used in discussions[31], hence:

 

Equation   is also known as time reversed S-matrix amplitude[31] and it gives the probability of photo-ionization by a generic time-varying electric field.

Strong field approximation (SFA)

edit

Strong field approximation (SFA), or Keldysh-Faisal-Reiss theory is a physical model, started in 1964 by the Russian physicist Keldysh [34], is currently used to describe the behavior of atoms (and molecules) in intense laser fields.

SFA is the starting theory for discussing both high-harmonic generation and attosecond pump-probe interaction with atoms.

The main assumption made in SFA is that the free-electron dynamics is dominated by the laser field, while the Coulomb potential is regarded as a negligible perturbation[35].

This fact re-shape equation   into:

 

where,   is the Volkov Hamiltonian, here expressed for simplicity in the velocity gauge[36], with  ,  , the electromagnetic vector potential [37].

At this point, to keep the discussion at its basic level, lets consider an atom with a single energy level  , ionization energy   and populated by a single electron (single active electron approximation).

We can consider the initial time of the wave function dynamics as  , and we can assume that initially the electron is in the atomic ground state  .

So that,

  and  

Moreover, we can regard the continuum states as plane wave functions state,  .

This is a rather simplified assumption, a more reasonable choice would have be to use as continuum state the exact atom scattering states[38].

The time evolution of simple plane wave states with the Volkov Hamiltonian is given by:

 

here for consistency with Eq.   the evolution has already been properly converted into the length gauge[39].

As a consequence, the final momentum distribution of a single electron in a single-level atom, with ionization potential  , is expressed as:

 

where,

 

is the dipole expectation value (or transition dipole moment), and

 

is the semiclassical action.

The result of Eq.   is the basic tool to understand phenomena like:

Weak Attosecond pulse-strong-IR-fields-atoms interactions
edit

Attosecond pump-probe experiments with simple atoms is a fundamental tool to measure the time duration of an attosecond pulse[44] and to explore several quantum proprieties of matter[41].

 
Scheme of a strong IR field and a delayed attosecond XUV pulse interacting with a single electron in a single level atom. The XUV can ionize the electron, which "jumps" in the continuum by direct ionization (blue path in the figure). The IR pulse, later, "streaks" up and down in energy the photo-electron. After the interaction, the electron has final energy which can be subsequently detected and measured (e.g. time-of-flight apparatus). The multi-photon ionization process (red path in the figure) is also possible, but, since it is relevant in different energetic region, it can be disregarded.

This kind of experiments can be easily described within strong field approximation by exploiting the results of Eq.  , as discussed below.

As a simple model, consider the interaction between a single active electron in a single-level atom and two fields: an intense femtosecond infrared (IR) pulse ( ,

and a weak attosecond pulse (centered in the extreme ultraviolet (XUV) region)  .

Then, by substituting these fields to   it results:

 

with  .

At this point, we can divide Eq.   in two contributions: direct ionization and strong field ionization (multiphoton regime), respectively.

Typically, these two terms are relevant in different energetic regions of the continuum.

Consequently, for typical experimental condition, the latter process is disregarded, and only direct ionization from the attosecond pulse is considered[31].

Then, since the attosecond pulse is weaker than the infrared one, it holds  . Thus,   is typically neglected in Eq.  .

In addition to that, we can re-write the attosecond pulse as a delayed function with respect to the IR field,  .

Therefore, the probability distribution of finding an electron ionized in the continuum with momentum  , after the interaction has occurred (at  ), in a pump-probe experiments,

with an intense IR pulse and a delayed-attosecond XUV pulse, is given by:

 

with  

Equation   describes the photo-ionization phenomenon of two-color interaction (XUV-IR) with a single level atom and single active electron.

This peculiar result can be regarded as a quantum interference process between all the possible ionization paths, started by a delayed XUV attosecond pulse, with a following motion in the continuum states driven by a strong IR field[31].

The resulting 2D photo-electron (momentum, or equivalently energy, vs delay) distribution is called streaking trace[45].

Attosecond techniques

edit

Here are listed and discussed some of the most common technique and approach pursued in attosecond research centers.

Attosecond metrology with photo-electron spectroscopy (FROG-CRAB)

edit
 
Simulation of a streaking trace in Neon. The attosecond pulse duration is 350 as,with central wavelength at the 33 harmonics of an 800 nm laser. The 800 nm pulse, which has the role of streaking up and down the photoelectron trace, has a duration of 7 fs with a peak intensity of 5 TW/cm2.

A daily-challenge in attosecond science is to characterize the temporal proprieties of the attosecond pulses used in any pump-probe experiments with atoms, molecules or solids.

The most used technique is based on the frequency-resolved optical gating for complete reconstruction of attosecond bursts (FROG-CRAB) [46].

The main advantage of this technique is that it allows to exploit the corroborated FROG technique[47], developed in 1991 for picosecond-femtosecond pulse characterization, to the attosecond field.

CRAB is an extension of FROG and it is based on the same idea for the field reconstruction.

In other words, FROG-CRAB is based on the conversion of an attosecond pulse into an electron wave-packet that is freed in the continuum by atomic photo-ionization, as already described with Eq. .

The role of the low-frequency driving laser pulse( e.g. infra-red pulse) is to behave as gate for the temporal measurement.

Then, by exploring different delays between the low-frequency and the attosecond pulse a streaking trace (or streaking spectrogram) can be obtained[45] .

This 2D-spectrogram is later analyzed by a reconstruction algorithm with the goal of retrieving both the attosecond pulse and the IR pulse, with no need of a prior knowledge on any of them.

However, as Eq.   pinpoints, the intrinsic limits of this technique is the knowledge on atomic dipole proprieties, in particular on the atomic dipole quantum phase[41][48].

The reconstruction of both the low-frequency field and the attosecond pulse from a streaking trace is typically achieved through iterative algorithms, such as:

  • Principal component generalized projections algorithm (PCGPA)[49].
  • Volkov transform generalized projection algorithm (VTGPA)[50].
  • extended ptychographic iterative engine (ePIE)[51].

See also

edit

References

edit
  1. ^ a b Krausz, Ferenc; Ivanov, Misha (2009-02-02). "Attosecond physics". Reviews of Modern Physics. 81 (1): 163–234.
  2. ^ a b Schultze, M.; Fiess, M.; Karpowicz, N.; Gagnon, J.; Korbman, M.; Hofstetter, M.; Neppl, S.; Cavalieri, A. L.; Komninos, Y.; Mercouris, T.; Nicolaides, C. A. (2010-06-25). "Delay in Photoemission". Science. 328 (5986): 1658–1662. doi:10.1126/science.1189401. ISSN 0036-8075.
  3. ^ Nisoli, Mauro; Decleva, Piero; Calegari, Francesca; Palacios, Alicia; Martín, Fernando (2017-08-23). "Attosecond Electron Dynamics in Molecules". Chemical Reviews. 117 (16): 10760–10825. doi:10.1021/acs.chemrev.6b00453. ISSN 0009-2665.
  4. ^ Ghimire, Shambhu; Ndabashimiye, Georges; DiChiara, Anthony D; Sistrunk, Emily; Stockman, Mark I; Agostini, Pierre; DiMauro, Louis F; Reis, David A (2014-10-08). "Strong-field and attosecond physics in solids". Journal of Physics B: Atomic, Molecular and Optical Physics. 47 (20): 204030. doi:10.1088/0953-4075/47/20/204030. ISSN 0953-4075.
  5. ^ a b P. Agostini, L.F. DiMauro (2004). "The physics of attosecond light pulses". Reports on Progress in Physics. 67 (6): 813–855. Bibcode:2004RPPh...67..813A. doi:10.1088/0034-4885/67/6/R01. S2CID 53399642.
  6. ^ Gaumnitz, Thomas; Jain, Arohi; Pertot, Yoann; Huppert, Martin; Jordan, Inga; Ardana-Lamas, Fernando; Wörner, Hans Jakob (2017-10-30). "Streaking of 43-attosecond soft-X-ray pulses generated by a passively CEP-stable mid-infrared driver". Optics Express. 25 (22): 27506–27518. doi:10.1364/OE.25.027506. ISSN 1094-4087.
  7. ^ Moulton, P. F. (1986-01-01). "Spectroscopic and laser characteristics of Ti:Al_2O_3". Journal of the Optical Society of America B. 3 (1): 125. doi:10.1364/josab.3.000125. ISSN 0740-3224.
  8. ^ Maine, P.; Strickland, D.; Pessot, M.; Squier, J.; Bado, P.; Mourou, G.; Harter, D. (1988), "Chirped Pulse Amplification: Present and Future", Ultrafast Phenomena VI, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 2–7, ISBN 978-3-642-83646-6, retrieved 2021-06-17
  9. ^ Nisoli, M.; De Silvestri, S.; Svelto, O. (1996-05-13). "Generation of high energy 10 fs pulses by a new pulse compression technique". Applied Physics Letters. 68 (20): 2793–2795. doi:10.1063/1.116609. ISSN 0003-6951.
  10. ^ Szipöcs, Robert; Spielmann, Christian; Krausz, Ferenc; Ferencz, Kárpát (1994-02-01). "Chirped multilayer coatings for broadband dispersion control in femtosecond lasers". Optics Letters. 19 (3): 201. doi:10.1364/ol.19.000201. ISSN 0146-9592.
  11. ^ Baltuška, A.; Udem, Th.; Uiberacker, M.; Hentschel, M.; Goulielmakis, E.; Gohle, Ch.; Holzwarth, R.; Yakovlev, V. S.; Scrinzi, A.; Hänsch, T. W.; Krausz, F. (2003-02-06). "Attosecond control of electronic processes by intense light fields". Nature. 421 (6923): 611–615. doi:10.1038/nature01414. ISSN 0028-0836.
  12. ^ Kienberger, R.; Goulielmakis, E.; Uiberacker, M.; Baltuska, A.; Yakovlev, V.; Bammer, F.; Scrinzi, A.; Westerwalbesloh, Th.; Kleineberg, U.; Heinzmann, U.; Drescher, M. (2004). "Atomic transient recorder". Nature. 427 (6977): 817–821. doi:10.1038/nature02277. ISSN 0028-0836.
  13. ^ Sansone, G.; Benedetti, E.; Calegari, F.; Vozzi, C.; Avaldi, L.; Flammini, R.; Poletto, L.; Villoresi, P.; Altucci, C.; Stagira, S.; Nisoli, M. (2006-10-20). "Isolated Single-Cycle Attosecond Pulses". Science. 314 (5798): 443–446. doi:10.1126/science.1132838. ISSN 0036-8075.
  14. ^ Krausz, Ferenc (2016-05-25). "The birth of attosecond physics and its coming of age". Physica Scripta. 91 (6): 063011. doi:10.1088/0031-8949/91/6/063011. ISSN 0031-8949.
  15. ^ Sakurai, J. J. (2017). Modern quantum mechanics. Jim Napolitano (2 ed.). Cambridge. ISBN 978-1-108-49999-6. OCLC 1105708539.{{cite book}}: CS1 maint: location missing publisher (link)
  16. ^ Corkum, P. B.; Krausz, Ferenc (2007). "Attosecond science". Nature Physics. 3 (6): 381–387. doi:10.1038/nphys620. ISSN 1745-2481.
  17. ^ Chang, Zenghu (2011). Fundamentals of attosecond optics. Boca Raton, Fla.: CRC Press. ISBN 978-1-4200-8938-7. OCLC 713562984.
  18. ^ a b Zavelani-Rossi, Margherita (2020). High-intensity lasers for nuclear and physical applications. ESCULAPIO. ISBN 88-9385-188-1. OCLC 1142519514.{{cite book}}: CS1 maint: date and year (link)
  19. ^ Johnson, Allan S.; Avni, Timur; Larsen, Esben W.; Austin, Dane R.; Marangos, Jon P. (2019-05-20). "Attosecond soft X-ray high harmonic generation". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 377 (2145): 20170468. doi:10.1098/rsta.2017.0468. PMC 6452054. PMID 30929634.{{cite journal}}: CS1 maint: PMC format (link)
  20. ^ a b Sansone, G.; Kelkensberg, F.; Pérez-Torres, J. F.; Morales, F.; Kling, M. F.; Siu, W.; Ghafur, O.; Johnsson, P.; Swoboda, M.; Ferrari, F.; Nisoli, M. (2010). "Electron localization following attosecond molecular photoionization". Nature. 465 (7299): 763–766. doi:10.1038/nature09084. ISSN 1476-4687.
  21. ^ a b Calegari, F.; Ayuso, D.; Trabattoni, A.; Belshaw, L.; Camillis, S. De; Anumula, S.; Frassetto, F.; Poletto, L.; Palacios, A.; Greenwood, J.B.; Nisoli, M. (2014-10-17). "Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses". Science. 346 (6207): 336–339. doi:10.1126/science.1254061. ISSN 0036-8075. PMID 25324385.
  22. ^ Kobayashi, Yuki; Chang, Kristina F.; Zeng, Tao; Neumark, Daniel M.; Leone, Stephen R. (2019-07-05). "Direct mapping of curve-crossing dynamics in IBr by attosecond transient absorption spectroscopy". Science. 365 (6448): 79–83. doi:10.1126/science.aax0076. ISSN 0036-8075. PMID 31273121.
  23. ^ a b Lucchini, Matteo; Sato, Shunsuke A.; Lucarelli, Giacinto D.; Moio, Bruno; Inzani, Giacomo; Borrego-Varillas, Rocío; Frassetto, Fabio; Poletto, Luca; Hübener, Hannes; De Giovannini, Umberto; Rubio, Angel (2021-02-15). "Unravelling the intertwined atomic and bulk nature of localised excitons by attosecond spectroscopy". Nature Communications. 12 (1): 1021. doi:10.1038/s41467-021-21345-7. ISSN 2041-1723.
  24. ^ Lucarelli, Giacinto D.; Moio, Bruno; Inzani, Giacomo; Fabris, Nicola; Moscardi, Liliana; Frassetto, Fabio; Poletto, Luca; Nisoli, Mauro; Lucchini, Matteo (2020-05-01). "Novel beamline for attosecond transient reflection spectroscopy in a sequential two-foci geometry". Review of Scientific Instruments. 91 (5): 053002. doi:10.1063/5.0005932. ISSN 0034-6748.
  25. ^ Palacios, Alicia; Martín, Fernando (2020). "The quantum chemistry of attosecond molecular science". WIREs Computational Molecular Science. 10 (1): e1430. doi:10.1002/wcms.1430. ISSN 1759-0884.
  26. ^ Sato, Shunsuke A. (2021). "First-principles calculations for attosecond electron dynamics in solids". Computational Materials Science. 194: 110274. doi:10.1016/j.commatsci.2020.110274. ISSN 0927-0256.
  27. ^ Mourou, Gérard. "ICAN: The Next Laser Powerhouse".{{cite web}}: CS1 maint: url-status (link)
  28. ^ Reiss, Howard R. (2008), Yamanouchi, Kaoru; Chin, See Leang; Agostini, Pierre; Ferrante, Gaetano (eds.), "Foundations of the Strong-Field Approximation", Progress in Ultrafast Intense Laser Science III, Springer Series in Chemical Physics, Berlin, Heidelberg: Springer, pp. 1–31, doi:10.1007/978-3-540-73794-0_1, ISBN 978-3-540-73794-0, retrieved 2021-06-15
  29. ^ Maurer, J; Keller, U (2021-05-05). "Ionization in intense laser fields beyond the electric dipole approximation: concepts, methods, achievements and future directions". Journal of Physics B: Atomic, Molecular and Optical Physics. 54 (9): 094001. doi:10.1088/1361-6455/abf731. ISSN 0953-4075.
  30. ^ Ivanov, Misha Yu; Spanner, Michael; Smirnova, Olga (2005-01-20). "Anatomy of strong field ionization". Journal of Modern Optics. 52 (2–3): 165–184. doi:10.1080/0950034042000275360. ISSN 0950-0340.
  31. ^ a b c d e f Mulser, Peter; Bauer, Dieter (2010). High Power Laser-Matter Interaction. Springer Tracts in Modern Physics. Berlin Heidelberg: Springer-Verlag. ISBN 978-3-540-50669-0.
  32. ^ Ivanov, Misha Yu; Spanner, Michael; Smirnova, Olga (2005-01-20). "Anatomy of strong field ionization". Journal of Modern Optics. 52 (2–3): 165–184. doi:10.1080/0950034042000275360. ISSN 0950-0340.
  33. ^ Faisal, F H M (2007-03-15). "Gauge-invariant intense-field approximations to all orders". Journal of Physics B: Atomic, Molecular and Optical Physics. 40 (7): F145–F155. doi:10.1088/0953-4075/40/7/f02. ISSN 0953-4075.
  34. ^ ДОКУЧАЕВ, В.И.; НАЗАРОВА, Н.О. (2019). "ИЗОБРАЖЕНИЕ ГОРИЗОНТА СОБЫТИЙ ВНУТРИ ТЕНИ ЧЕРНОЙ ДЫРЫ". ЖУРНАЛ ЭКСПЕРИМЕНТАЛЬНОЙ И ТЕОРЕТИЧЕСКОЙ ФИЗИКИ. 155 (4): 677–685. doi:10.1134/s0044451019040102. ISSN 0044-4510.
  35. ^ Amini, Kasra; Biegert, Jens; Calegari, Francesca; Chacón, Alexis; Ciappina, Marcelo F; Dauphin, Alexandre; Efimov, Dmitry K; Figueira de Morisson Faria, Carla; Giergiel, Krzysztof; Gniewek, Piotr; Landsman, Alexandra S (2019-11-01). "Symphony on strong field approximation". Reports on Progress in Physics. 82 (11): 116001. doi:10.1088/1361-6633/ab2bb1. ISSN 0034-4885.
  36. ^ University of Kassel. "Physical phenomena in laser-matter interaction" (PDF).{{cite web}}: CS1 maint: url-status (link)
  37. ^ Jackson, John David (1999). Classical electrodynamics (3 ed.). New York: Wiley. ISBN 0-471-30932-X. OCLC 38073290.
  38. ^ Milošević, D. B.; Becker, W. (2019-04-10). "Atom-Volkov strong-field approximation for above-threshold ionization". Physical Review A. 99 (4). doi:10.1103/physreva.99.043411. ISSN 2469-9926.
  39. ^ Bechler, A.; Ślȩczka, M. (2009-12-25). "Gauge invariance of the strong field approximation". arXiv:0912.4966 [physics].
  40. ^ Brabec, Thomas; Krausz, Ferenc (2000-04-01). "Intense few-cycle laser fields: Frontiers of nonlinear optics". Reviews of Modern Physics. 72 (2): 545–591. doi:10.1103/RevModPhys.72.545. ISSN 0034-6861.
  41. ^ a b c Yakovlev, V. S.; Gagnon, J.; Karpowicz, N.; Krausz, F. (2010-08-10). "Attosecond Streaking Enables the Measurement of Quantum Phase". Physical Review Letters. 105 (7): 073001. doi:10.1103/PhysRevLett.105.073001.
  42. ^ Keller, Ursula (2015-05-10). "Attosecond Ionization Dynamics and Time Delays". CLEO: 2015 (2015), paper FTh3C.1. Optical Society of America: FTh3C.1. doi:10.1364/CLEO_QELS.2015.FTh3C.1.
  43. ^ Kheifets, Anatoli S (2020-03-06). "The attoclock and the tunneling time debate". Journal of Physics B: Atomic, Molecular and Optical Physics. 53 (7): 072001. doi:10.1088/1361-6455/ab6b3b. ISSN 0953-4075.
  44. ^ Mairesse, Y.; Quéré, F. (2005-01-27). "Frequency-resolved optical gating for complete reconstruction of attosecond bursts". Physical Review A. 71 (1): 011401. doi:10.1103/PhysRevA.71.011401.
  45. ^ a b Itatani, J.; Quéré, F.; Yudin, G. L.; Ivanov, M. Yu.; Krausz, F.; Corkum, P. B. (2002-04-16). "Attosecond Streak Camera". Physical Review Letters. 88 (17): 173903. doi:10.1103/PhysRevLett.88.173903.
  46. ^ Mairesse, Y.; Quéré, F. (2005-01-27). "Frequency-resolved optical gating for complete reconstruction of attosecond bursts". Physical Review A. 71 (1). doi:10.1103/physreva.71.011401. ISSN 1050-2947.
  47. ^ Trebino, Rick (2003), "FROG", Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses, Boston, MA: Springer US, pp. 101–115, ISBN 978-1-4613-5432-1, retrieved 2021-06-17
  48. ^ Zhao, Xi; Wei, Hui; Wei, Changli; Lin, C D (2017-10-23). "A new method for accurate retrieval of atomic dipole phase or photoionization group delay in attosecond photoelectron streaking experiments". Journal of Optics. 19 (11): 114009. doi:10.1088/2040-8986/aa8fb6. ISSN 2040-8978.
  49. ^ Kane, Daniel J. (2008-06-01). "Principal components generalized projections: a review [Invited]". JOSA B. 25 (6): A120–A132. doi:10.1364/JOSAB.25.00A120. ISSN 1520-8540.
  50. ^ Keathley, P D; Bhardwaj, S; Moses, J; Laurent, G; Kärtner, F X (2016-07-06). "Volkov transform generalized projection algorithm for attosecond pulse characterization". New Journal of Physics. 18 (7): 073009. doi:10.1088/1367-2630/18/7/073009. ISSN 1367-2630.
  51. ^ Lucchini, M.; Brügmann, M. H.; Ludwig, A.; Gallmann, L.; Keller, U.; Feurer, T. (2015-11-16). "Ptychographic reconstruction of attosecond pulses". Optics Express. 23 (23): 29502–29513. doi:10.1364/OE.23.029502. ISSN 1094-4087.

Further readings

edit
  • Krausz, Ferenc; Ivanov, Misha (2009-02-02). "Attosecond physics". Reviews of Modern Physics. 81 (1): 163–234.
edit

Attosecond groups in the world

edit

Category:Quantum mechanics Category:Optics Category:Physics