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The experiment involving Ferenc Krausz combined a subfemtosecond soft-X-ray pulse with a few-cycle visible electric field. Its delay-dependent krypton photoelectron spectra tested the field-controlled response. The reported pulse duration was $650\pm 150$ attoseconds. Changing delay compared the emitted electron distributions at different reference phases; the spectral-width trace supplied a further duration-sensitive observable.^[ref]

The distinction from RABBITT is the measurement regime and reconstruction, rather than merely calling one trace a clock. The attosecond streaking momentum map is a limiting model; a finite-duration wave packet requires a quantum transition calculation. Inferring an emission delay also requires separating the illuminating pulse's spectral phase from the target response. The measurement supports time-dependent photoionization in a specified model, with no unique classical electron trajectory inside an atomic orbital implied.

Attosecond physics resolves changes on the scale of $10^{-18}$ seconds, especially electron dynamics. Its central trick is to convert a short optical event into an experimentally accessible energy or phase change. A broad optical spectrum provides the ingredients for a short optical pulse; their spectral phases determine when those ingredients add constructively. High harmonic generation supplies the optical spectrum, while RABBITT and attosecond streaking supply complementary timing measurements. XUV denotes extreme ultraviolet radiation.

There are two separate timing problems: characterize the incident optical pulse, then infer the response of the target. A photoelectron measurement mixes the incident spectral phase, the target's transition response and the probing electric field. Recovering one requires constraints on the others. These methods measure distributions of photoelectron energies over repeated shots, rather than photographing a moving atomic orbital.

Attosecond streaking uses a synchronized reference electric field to change a photoelectron's outgoing momentum. Scanning relative delay produces an energy-versus-delay distribution. A short emission interval samples only a small part of the reference cycle; a longer interval samples a range of kicks and can broaden or reshape the distribution.

For an explicit classical limit, use the electric dipole approximation and choose the magnetic vector potential $A(t)$ along the detection axis with $E(t)=-dA/dt$ and $A(\infty )=0$. Neglect the residual ion's Coulomb force. An electron released at $t_i$ with mechanical momentum $p_0$ obeysIndeed, integrating $\dot{p}=-eE=e\dot{A}$ from release to the end of the field gives the stated minus sign. The useful clock variable here is $A$, rather than the instantaneous $E$ itself. If $A$ is nearly linear across a narrow emission window with temporal standard deviation ${\sigma }_t$, and initial momentum is sharp, thenThis local mapping fails near a zero of $E$, where first-order timing sensitivity vanishes. A real inversion must include the incident bandwidth, initial photoelectron distribution, collection angles and target–field response.

For an original dimensionless example in atomic units, choose $p_0=2$, $m=e=1$ and $A(t_i)=0.10$. Then $p_f=1.9$ and $K_f=1.805$, compared with initial kinetic energy $2$. Reversing $A$ gives $K_f=2.205$: the shifts are asymmetric because of the $A^2/2$ term. A measurement that keeps only the term linear in $A$ would miss $0.005$ in both cases.

BKS theory was a 1924 attempt to describe light interacting with chemical atoms through continuous radiation fields, while allowing energy conservation and momentum conservation to hold statistically rather than in every individual atomic event. Its crucial experimental consequence was the absence of the event-by-event correlations expected from a photon collision picture of Compton scattering.

Walther Bothe and Hans Geiger tested whether a recoil electron and the photoelectron produced by the scattered radiation appeared together. Their coincident detections contradicted the predicted independent event times. In his 1925 response, John C. Slater explicitly discussed this conflict and also the observed correlation of the scattered radiation's direction with that of the recoil electron. BKS theory is therefore a useful example of testing a physical interpretation through individual-event correlations, even when average radiation intensities alone do not decide between pictures.^[ref]

An electron multiplier amplifies a signal by accelerating incoming electrons into surfaces that emit additional secondary electrons. Repeating this process at successive stages produces a measurable charge packet from a small initial signal.

A photomultiplier adds a photosensitive input that converts incident light into a photoelectron; its dynodes then perform multiplication. In a simple equal-stage model with mean secondary yield $\delta$, $m$ stages give mean gain ${\delta }^m$. The output fluctuates because emission is stochastic, and saturation can invalidate constant gain. Multiplication increases the signal scale but cannot recreate input events that were never detected.

Oscillatory absorption above a core-ionization edge caused by interference between outgoing and neighbor-scattered photoelectron waves. It probes local coordination, distances and disorder. The high-energy shell expansion is distinct from the more complicated near-edge regime; phase corrections are required before interpreting Fourier-transform peaks as bond lengths.

Ferenc Krausz coauthored a 2001 demonstration of attosecond timing using photoionization. A synchronized visible electric field changes the energy distribution of photoelectrons released by a soft-X-ray optical pulse. Scanning their relative delay converts an otherwise inaccessible time interval into a measured electron spectrum. The report inferred a soft-X-ray duration of $650\pm 150$ attoseconds and demonstrated an instrument for probing electron dynamics on that scale.^[ref]

A physicist who leads research in attosecond physics.^[ref]

An experimental optical physicist who coauthored attosecond pulse measurements. Combining a short extreme-ultraviolet excitation with a synchronized optical field lets emitted photoelectrons carry information about the pulse's timing. This makes a subfemtosecond optical event measurable through an electron-energy distribution rather than by an electronic stopwatch.^[ref]

The binding energies are referred to the common Fermi level. Immediately outside the copper surface, conservation of energy givesThis is the emitted photoelectron energy at the sample. On reaching the electrically connected, unbiased analyser, its energy is instead $K_a=h\nu -E_B-{\varphi }_a=\boxed{111.4\mathrm{eV}}$. The 0.4 eV difference is the contact-potential correction, not an additional binding-energy shift. Distinguishing these two reference positions is essential for the retarding-voltage calculation.

Define the retard ratio using the kinetic energy at the analyser entrance before the deliberate retardation: $R=K_a/E_p$. Initially $R=111.4/100.0=1.114$. With the original excitation, a carbon photoelectron arrives with $K_{a,C}=515.0-284.8-4.4=225.8\mathrm{eV}$. ThusThe new deliberate retardation is $225.8-202.69=23.11\mathrm{eV}$. For fixed slits, angular acceptance and hemisphere radii, the geometrical fractional energy width is approximately constant, so the absolute analyser width grows in proportion to pass energy: about 2.03 times poorer absolute energy resolution. Counts may improve, but closely separated chemical shifts become harder to resolve. An alternative definition $(K_a-E_p)/E_p$ gives 0.114 rather than 1.114 for the same physical setting and leads to the same final pass energy when used consistently.

Only the photon energy above the hydrogen ionization threshold initially becomes photoelectron kinetic energy. The stated mean therefore suppliesLet $\mathcal{R}$ be the local number of ionizations per volume per time. Photoionization equilibrium makes this equal to the recombination rate. If $⟨E_{\mathrm{rec}}(T)⟩$ is the mean kinetic energy removed per recombination, thermal balance reduces toNeither the ionization threshold nor the density remains in this event-by-event balance. The threshold energy is stored as atomic ionization energy and returned in recombination radiation; it is not a net thermal input. This separation between photoelectron heating and kinetic energy lost by recombining electrons is the relevant cooling balance.^[ref]

In the elementary mean-thermal-energy approximation, a captured electron removes $\frac{3}{2}{k}_{B}T$. This gives the concise estimateThat coefficient is a stated approximation, not a universal recombination identity. Real recombination weights the electron distribution by its velocity-dependent capture rate. If the chosen cooling model instead writes $⟨E_{\mathrm{rec}}⟩={\eta }_{\mathrm{rec}}(T)k_{B}T$, the precise answer is ${\eta }_{\mathrm{rec}}(T_{\mathrm{eq}})T_{\mathrm{eq}}=T_{\ast }$. The source supplies no recombination cooling coefficient or capture kernel from which a unique more accurate coefficient can be computed. Its emitted-photon average is also being used as the average of the absorbed ionizing photons; spectral filtering would require a different weighted average.

In photoemission electron microscopy, illuminate a surface with ultraviolet light or X-rays and form an electron-optical image of the emitted electrons. An extraction field accelerates them away from the sample; an immersion objective and projection lenses magnify their spatial distribution onto an electron detector. Unlike a scanned probe, this is a full-field image. Surface preparation and vacuum matter because the emitted low-energy electrons are strongly affected by contamination and local electric fields.

Contrast can come from work-function differences, composition, occupied electronic states, illumination and topography. Near threshold, a small work-function change can produce a large emission-yield change. Therefore brightness is not simply geometrical height. An energy filter can select an emitted-electron energy interval; scanning the selection yields spatially resolved spectra. Sweeping the photon energy across an absorption edge can add element and chemical-state sensitivity. Appropriate polarization-dependent measurements can probe magnetic domains.^[ref]

Resolution depends on electron-lens aberrations, the accepted angular and energy spread, extraction geometry, sample flatness, space charge, mechanical stability and detector sampling. Rejecting electrons improves some aberrations at a cost in signal. An unfiltered photoelectron image and a chemically selected image therefore answer different questions even when they use the same microscope.

The large rises mark the opening of Ga and As K-shell photoionization channels at their respective thresholds. Above each edge, the outgoing photoelectron interferes with waves backscattered by neighboring atoms; that interference modulates the absorption transition probability. Near-edge resonances and multiple scattering require a different level of treatment from the simple high-energy single-scattering formula. Ga has four As nearest neighbors, while As has four Ga nearest neighbors, so the two edges sample different central atoms and scattering factors even though they probe the same nearest-neighbor bond lengths.

Write $k=\sqrt{2m_e(E-E_0)}/\hslash$ and $\chi =(\mu -{\mu }_0)/{\mu }_0$ relative to a smooth atomic background. The phase $2k{R}_j+{\varphi }_j(k)$ includes the outward-and-return propagation distance and atomic phase shifts. The factor $R_j^{-2}$ describes geometrical spreading; the backscattering amplitude depends on the neighbor species. The exponential $e^{-2R_j/\lambda (k)}$ accounts for loss of coherent photoelectron propagation. Averaging over Gaussian bond-length fluctuations gives $⟨e^{2ik\delta R}⟩=e^{-2k^2{\sigma }_j^2}$.

The printed polarization factor needs a notation correction: for K-shell dipole absorption it is proportional to $({\hat{\mathbf{R}}}_j\cdot \mathbf{ϵ}{)}^2={\cos }^2{\theta }_j$, not literally the cosine of a dimensional vector dot product. Four equivalent tetrahedral bonds have an isotropic sum of these projection weights. If the sum is over shells rather than individual neighbors, it also needs the coordination number. A common conventional amplitude contains $S_0^2{f}_j(k)/(k{R}_j^2)$; omitted normalization and $1/k$ factors must be absorbed in the printed $f_B$ convention rather than silently changing its dimensions.

These are the ingredients of extended X-ray absorption fine structure. A shell fit uses calculated or reference scattering amplitudes and phases, and refines bond distances, coordination and mean-square relative disorder together with an edge-energy correction. Fourier transformation separates approximate distance contributions, but the uncorrected peak position is shifted by the scattering phase and is not an exact bond length.^[ref]

Sample A has the larger Ga–As bond length. Its oscillations advance slightly faster with $k$: at higher $k$ its corresponding maxima lie to the left of B's. Reading several full cycles gives approximate periods $\Delta k_A\simeq 1.47{\mathring{\mathrm{A}}}^{-1}$ and $\Delta k_B\simeq 1.50{\mathring{\mathrm{A}}}^{-1}$. In the constant/common-phase-slope estimate, $R\propto 1/\Delta k$, soThis is a rough percent-level difference, not a precise fitted strain. Nonconstant atomic phase shifts affect the absolute distance inferred from a period and also limit this fractional estimate. The graph does not establish which alloy has which indium concentration or how much its bulk lattice parameter changed. Local Ga–As relaxation need not follow a uniform bulk strain exactly.

Low temperature reduces thermal relative motion, preserving high-$k$ oscillations and separating small phase changes more clearly. It does not remove zero-point motion or static alloy disorder. To obtain an illustrative disorder estimate, take the high-$k$ envelope of the plotted $k\chi (k)$ to fall from about $0.19$ at $k=7.5{\mathring{\mathrm{A}}}^{-1}$ to $0.12$ at $k=10.4{\mathring{\mathrm{A}}}^{-1}$. If other envelope factors vary slowly over this interval,The value is only an order-of-magnitude, model-dependent reading: the backscattering amplitude, mean free path and normalization have not been independently removed. In particular, ${\sigma }^2$ is the bond-projected mean-square relative displacement,including correlations and static disorder. It is not uniquely either atom's mean-square displacement. Equal uncorrelated projected displacements would each contribute ${\sigma }^2/2$, but that extra assumption is not supplied by the figure.

A photodetector converts incident light into a measurable signal, often an electric current or stored electric charge. A photodiode collects carriers produced by absorbed photons; a photomultiplier first releases photoelectrons and then amplifies their number.

A basic characterization measures the output with the beam blocked and with several known incident radiant powers. The slope gives spectral responsivity at the chosen wavelength; the blocked signal reveals offsets and dark current. Quantum efficiency, response speed and noise-equivalent power describe different limitations. Detecting a weak signal requires separating its contribution from both background photons and the detector's own fluctuations.

Electron optics forms a magnified spatial image of photoelectrons emitted from an illuminated surface. Emission yield and electron-energy selection can supply work-function, electronic or chemical contrast; brightness is not necessarily geometrical height.

For emission angle $\theta$ measured from the surface normal, a free outgoing photoelectron has parallel wavevector $k_{\parallel }=\sqrt{2m_e{E}_{\mathrm{kin}}}\sin \theta /\hslash$. Translation symmetry parallel to a clean periodic surface conserves this component modulo a surface reciprocal lattice vector, after accounting for photon momentum when needed. With initial binding energy $E_B$ below the Fermi level, its kinetic energy immediately outside the sample is $E_{\mathrm{kin}}=h\nu -{\varphi }_s-E_B$, where ${\varphi }_s$ is the sample work function. This sample-vacuum energy is distinct from the analyzer-referenced energy when contact potentials are present. Perpendicular crystal momentum generally needs a final-state model, whereas a strictly two-dimensional band has no perpendicular dispersion to reconstruct.

Photoelectron spectroscopy measures the kinetic energies of photoelectrons produced by illuminating matter with photons of known energy. The photoelectric effect supplies the emission mechanism; spectroscopy turns the distribution of emitted electron energies into information about occupied energy levels and chemical bonds. A broad survey helps identify chemical elements, while small shifts within one element's lines can distinguish different chemical surroundings. These are different questions: finding carbon does not establish which chemical bonds its chemical atoms form.

The useful inversion is an energy balance. A known incoming photon energy pays for removal of an electron and for its outgoing kinetic energy. To apply that balance to a solid, specify the zero of energy and the work function of the instrument. Photoelectron binding energy reference derives the conversion for a conducting sample in electrical contact with its analyzer. A free molecule instead has an ionization energy referenced to an electron at rest in vacuum; it need not share a Fermi level with the analyzer.

A photomultiplier detects weak light by converting a photon into a photoelectron at a photosensitive cathode, then multiplying electrons through successive dynodes. Each impact can release several secondary electrons, and an anode collects the amplified packet as an electrical pulse.

If each of $m$ stages has mean multiplication $\delta$, the mean gain is approximately ${\delta }^m$. This amplification makes small signals measurable but does not eliminate photon shot noise or fluctuations in multiplication. Quantum efficiency controls the probability of producing an initial useful photoelectron, while dark current and background produce additional signals. Optical shielding, stable applied voltages and a blocked-light measurement are therefore essential to interpreting a weak-light count.^[ref]

In an optically thin plasma, radiative recombination removes the kinetic energy of captured electrons. A radiative recombination photon can also carry the binding energy released when a free electron becomes bound; that part is stored ionization energy, rather than newly removed thermal energy. The kinetic contribution per event is the recombination-weighted electron energy, which need not be $3k_{B}T/2$.

Equality with mean photoelectron heating requires two balances. If photoionization is the only ionization and heating process, and radiative recombination the only recombination and cooling process, photoionization equilibrium equates their event rates. Separately imposing thermal equilibrium then equates the mean heating energy per ionization to the mean kinetic cooling energy per recombination. Photoionization equilibrium alone does not do this: at the same balanced event rate, unequal energies can still heat or cool the gas. Additional atomic line cooling, collisional ionization or trapping of emitted photons changes the energy accounting.

RABBITT measures adjacent harmonic spectral phases through two-photon photoionization. A weak delayed infrared reference opens two interfering paths to a shared photoelectron energy; the two-path attosecond phase reconstruction spells out the inference.