Optical Pulse Generation

Our study of THz wave generation in the pulsed laser induced air plasma with individually controlled phase, polarization, and amplitude of the optical fundamental wave (!) and its second harmonic (2!) indicates that the third-order nonlinear optical process mixing the ! and 2! beams in the ionized plasma is the main mechanism of the efficient THz wave generation. The polarity and the strength of the emitted THz field are completely controlled by the relative phase between the ! and 2! waves. The measured THz field amplitude is proportional to the pulse energy of the fundamental beam and to the square root of the pulse energy of the second-harmonic beam once the total optical pulse energy exceeds the plasma formation threshold. The optimal THz field is achieved when all waves (!, 2!, and THz waves) are at the same polarization in the four-wave-mixing process.

Ultrafast fiber lasers with short pulses and broad bandwidth are in great demand for a variety of applications, such as spectroscopy, biomedical diagnosis and optical communications. In particular sub-200fs pulses are required for ultrafast spectroscopy with high temporal resolution. Graphene is an ideal ultra-wide-band saturable absorber. We report the generation of 174fs pulses from a graphene-based fiber laser.

We demonstrate the generation of optical vortices with radial or azimuthal polarization using a space variant polarization converter, fabricated by femtosecond laser writing of self-assembled nanostructures in silica glass. Manipulation of the induced form birefringence is achieved by controlling writing parameters, in particular, the polarization azimuth of the writing beam. The fabricated converter allows switching from radial to azimuthal polarization by controlling the handedness of incident circular polarization.

We demonstrated a novel optical switch to control the high-order harmonic generation process so that single attosecond pulses can be generated with multiple-cycle pulses. The technique combines two powerful optical gating methods: polarization gating and two-color gating. An extreme ultraviolet supercontinuum supporting 130 as was generated with neon gas using 9 fs laser pulses. We discovered a unique dependence of the harmonic spectra on the carrier-envelope phase of the laser fields, which repeats every 2 radians.

We take advantage of nonlinear properties associated with ͑3͒ tensor elements in BaF 2 cubic crystal to improve the temporal contrast of femtosecond laser pulses. The technique presented is based on cross-polarized wave (XPW) generation. We have obtained a transmission efficiency of 10% and 10 −10 contrast with an input pulse in the millijoule range. This filter does not affect the spectral shape or the phase of the cleaned pulse. It also acts as an efficient spatial filter. In this method the contrast enhancement is limited only by the extinction ratio of the polarization discrimination device.

A simple optical interference method to fabricate microperiodic structures was demonstrated. Femtosecond laser pulse was split by a diffractive beam splitter and overlapped with two lenses. Temporal overlap of the split femtosecond pulses, which requires 10 m order accuracy in optical path lengths, was automatically achieved by this optical setup. One-, two-, and three-dimensional periodic microstructures with micrometer-order periods were fabricated using this method.

We demonstrate that rogue waves provide a powerful tool to actively control a nonlinear system with minimal effort. Specifically, optical rogue waves-rare, bright flashes of broadband light arising in subthreshold supercontinuum generation-are initiated by an exceedingly weak stimulus. Using this effect, we produce an optically switchable, ultrastable, and bright supercontinuum with greatly enhanced coherence.

Event horizons of astrophysical black holes and gravitational analogues have been predicted to excite the quantum vacuum and give rise to the emission of quanta, known as Hawking radiation. We experimentally create such a gravitational analogue using ultrashort laser pulse filaments and our measurements demonstrate a spontaneous emission of photons that confirms theoretical predictions.

A passively mode-locked fiber laser is theoretically investigated. The mode locking is achieved using the nonlinear polarization technique. We consider the practical case of the ytterbium-doped fiber laser operating in the normal dispersion regime. The effect of the phase plates is explicitly taken into account. The resulting model reduces to one iterative equation for the optical Kerr nonlinearity, the phase plates and the polarizer, and one partial differential equation for the gain and the dispersion. Numerical simulations allow us to describe several features observed in passively mode-locked fiber lasers such as bistability between the mode lock and the continuous regime, multiple pulse behavior, hysteresis phenomena. The dynamics of the number of pulses as a function of the pumping power is also reported. Pump power hysteresis is demonstrated.

We report a comprehensive investigation of femtosecond continuum generation in single crystals of several common laser host materials. The absolute spectral energy density, pulse-to-pulse stability, pump threshold, and beam profile are studied in dependence on the focusing conditions, crystal thickness, pump pulse energy, and pump wavelength (775-1600 nm). Continuum generation is shown at repetition rates of up to 80 MHz and for pump pulse durations of up to 350 fs. In yttrium aluminum garnet (YAG), yttrium vanadate (YVO 4), gadolinium vanadate (GdVO 4), and potassium-gadolinium tungstate (KGW) thresholds below 50 nJ, plateau-like visible and infrared spectra, and higher infrared photon flux as compared to conventional materials like sapphire are found. We discuss the particular advantages of these materials for application in parametric amplification, femtosecond spectroscopy, and carrier-envelope phase stabilization.

Ultrashort, high-power laser pulses propagating vertically in the atmosphere have been observed over more than 20 km using an imaging 2-m astronomical telescope. This direct observation in several wavelength bands shows indications for filament formation at distances as far as 2 km in the atmosphere. Moreover, the beam divergence at 5 km altitude is smaller than expected, bearing evidence for whole-beam parallelization about the nonlinear focus. We discuss implications for white-light Lidar applications.

Linear-accelerator-based sources will revolutionize ultrafast x-ray science due to their unprecedented brightness and short pulse duration. However, time-resolved studies at the resolution of the x-ray pulse duration are hampered by the inability to precisely synchronize an external laser to the accelerator. At the Sub-Picosecond Pulse Source at the Stanford Linear-Accelerator Center we solved this problem by measuring the arrival time of each high energy electron bunch with electro-optic sampling. This measurement indirectly determined the arrival time of each x-ray pulse relative to an external pump laser pulse with a time resolution of better than 60 fs rms.

This letter presents a method aimed at quantifying the dimensions of the heat-affected zone ͑HAZ͒, produced during nanosecond and femtosecond laser-matter interactions. According to this method, 0.1 m thick Al samples were microdrilled and observed by a transmission electronic microscopy technique. The holes were produced at laser fluences above the ablation threshold in both nanosecond and femtosecond regimes ͑i.e., 5 and 2 J/cm 2 , respectively͒. The grain size in the samples was observed near the microholes. The main conclusion is that a 40 m wide HAZ is induced by the nanosecond pulses, whereas the femtosecond regime does not produce any observable HAZ. It turns out that the width of the femtosecond HAZ is less than 2 m, which is our observation limit.

A high-speed camera that combines a customized rotating mirror camera frame with charge coupled device ͑CCD͒ image detectors and is practically fully operated by computer control was constructed. High sensitivity CCDs are used so that image intensifiers, which would degrade image quality, are not necessary. Customized electronics and instruments were used to improve the flexibility and control precisely the image acquisition process. A full sequence of 128 consecutive image frames with 500ϫ292 pixels each can be acquired at a maximum frame rate of 25 million frames/s. Full sequences can be repeated every 20 ms, and six full sequences can be stored on the in-camera memory buffer. A high-speed communication link to a computer allows each full sequence of about 20 Mbytes to be stored on a hard disk in less than 1 s. The sensitivity of the camera has an equivalent International Standards Organization number of 2500. Resolution was measured to be 36 lp/mm on the detector plane of the camera, while under a microscope a bar pattern of 400 nm spacing line pairs could be resolved. Some high-speed events recorded with this camera, dubbed Brandaris 128, are presented.

By moving silica glass in a preprogrammed structure, we directly produced three-dimensional holes with femtosecond laser pulses in single step. When distilled water was introduced into a hole drilled from the rear surface of the glass, the effects of blocking and redeposition of ablated material were greatly reduced and the aspect ratio of the depth of the hole was increased. Straight holes of 4-mm diameter were more than 200 mm deep. Three-dimensional channels can be micromachined inside transparent materials by use of this method, as we have demonstrated by drilling a square-wave-shaped hole inside silica glass.

We demonstrate generation of 3.8-fs pulses with energies of up to 15 mJ from a supercontinuum produced in two cascaded hollow fibers. Ultrabroadband dispersion compensation was achieved through a closed-loop combination of a spatial light modulator for adaptive pulse compression and spectral-phase interferometry for direct electric-field reconstruction (SPIDER) measurements as feedback signal.

We demonstrate a passively mode-locked diode-pumped thin-disk Yb:YAG laser generating 810-fs pulses at 1030 nm with as much as 60 W of average output power (without using an amplifier). At a pulse repetition rate of 34.3 MHz, the pulse energy is 1.75 mJ and the peak power is as high as 1.9 MW. The beam quality is close to the diffraction limit, with M 2 , 1.1.

A remarkable phenomenon in ultrafast laser processing of transparent materials, in particular, silica glass, manifested as a change in material modification by reversing the writing direction is observed. The effect resembles writing with a quill pen and is interpreted in terms of anisotropic trapping of electron plasma by a tilted front of the ultrashort laser pulse along the writing direction.

The multiphoton multichannel photodynamics of NO 2 has been studied using femtosecond time-resolved coincidence imaging. A novel photoelectron-photoion coincidence imaging machine was developed at the laboratory in Amsterdam employing velocity map imaging and "slow" charged particle extraction using additional electron and ion optics. The NO 2 photodynamics was studied using a two color pump-probe scheme with femtosecond pulses at 400 and 266 nm. The multiphoton excitation produces both NO 2 + parent ions and NO + fragment ions. Here we mainly present the time dependent photoelectron images in coincidence with NO 2 + or NO + and the ͑NO + , e͒ photoelectron versus fragment ion kinetic energy correlations. The coincidence photoelectron spectra and the correlated energy distributions make it possible to assign the different dissociation pathways involved. Nonadiabatic dynamics between the ground state and the A 2 B 2 state after absorption of a 400 nm photon is reflected in the transient photoelectron spectrum of the NO 2 + parent ion. Furthermore, Rydberg states are believed to be used as "stepping" states responsible for the rather narrow and well-separated photoelectron spectra in the NO 2 + parent ion. Slow statistical and fast direct fragmentation of NO 2 + after prompt photoelectron ejection is observed leading to formation of NO + + O. Fragmentation from both the ground state and the electronically excited a 3 B 2 and b 3 A 2 states of NO 2 + is observed. At short pump probe delay times, the dominant multiphoton pathway for NO + formation is a 3 ϫ 400 nm+ 1 ϫ 266 nm excitation. At long delay times ͑Ͼ500 fs͒ two multiphoton pathways are observed. The dominant pathway is a 1 ϫ 400 nm+ 2 ϫ 266 nm photon excitation giving rise to very slow electrons and ions. A second pathway is a 3 ϫ 400 nm photon absorption to NO 2 Rydberg states followed by dissociation toward neutral electronically and vibrationally excited NO͑A 2 ⌺ , v =1͒ fragments, ionized by one 266 nm photon absorption. As is shown in the present study, even though the pump-probe transients are rather featureless the photoelectron-photoion coincidence images show a complex time varying dynamics in NO 2 . We present the potential of our novel coincidence imaging machine to unravel in unprecedented detail the various competing pathways in femtosecond time-resolved multichannel multiphoton dynamics of molecules.

The nonlinear absorption mechanisms of neon atoms to intense, femtosecond kilovolt x rays are investigated. The production of Ne 9þ is observed at x-ray frequencies below the Ne 8þ , 1s 2 absorption edge and demonstrates a clear quadratic dependence on fluence. Theoretical analysis shows that the production is a combination of the two-photon ionization of Ne 8þ ground state and a high-order sequential process involving single-photon production and ionization of transient excited states on a time scale faster than the Auger decay. We find that the nonlinear direct two-photon ionization cross section is orders of magnitude higher than expected from previous calculations.

Amplified dispersive Fourier transformation ͑ADFT͒ is a powerful technique that maps the spectrum of an optical pulse into a time-domain waveform using group-velocity dispersion ͑GVD͒ and simultaneously amplifies it in the optical domain. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector, greatly simplifying the system and, more importantly, enabling ultrafast real-time spectroscopic measurements. Here we present a theory of ADFT by deriving the general equation and spectral resolution for ADFT and studying the evolution of the pulse spectrum into time, the effect of GVD coefficients on ADFT, and the requirement for dispersion. This theory is expected to lend valuable insights into the process and implementation of ADFT.

Coherent phonons are excited in single-crystal tellurium by above-band-gap excitation with femtosecond laser pulses. Coherent infrared-active lattice vibrations give rise to the emission of electromagnetic waves at the phonon frequency. The excitation mechanism is based on the ultrafast buildup of a photo-Dember field and the coupling of a polar lattice mode to this field. The dynamics of the Dember field is obtained from a numerical simulation of the electron-hole plasma dynamics close to the crystals surface. This effect itself gives rise to a broadband emission of THz radiation from highly absorbing semiconductor surfaces. Details of the generation and the outcoupling of the radiation are discussed.

We generate ultrabroadband biphotons via the process of spontaneous parametric down-conversion (SPDC) in quasi-phase-matched nonlinear gratings that have a linearly chirped wave vector. By using these ultrabroadband biphotons (300-nm bandwidth), we measure the narrowest Hong-Ou-Mandel dip to date, having a full width at half maximum of 7.1 fs. This enables the generation of a high flux of nonoverlapping biphotons with ultrabroad bandwidth, thereby promoting the use of SPDC light in many nonclassical applications.

Fabrication of silver nanoparticle colloids using ultrashort pulse laser ablation in water is studied. Ablation in liquid flow improves the reproducibility and increases the nanoparticle productivity by 380% compared to stationary liquid. Femtosecond laser ablation in water is 20% more efficient than picosecond laser ablation, but due to higher picosecond laser power ͑higher repetition rate͒, the nanoparticle productivity at the same pulse fluence is three times higher for picosecond laser ablation. With picosecond laser pulses, the maximum productivity of 8.6 g / s is achieved at a pulse energy of 110 J and repetition rate of 50 kHz.

We report the experimental realization of an ultrafast all-optical temporal differentiator. Differentiation is obtained via all-fiber filtering based on a simple diffraction grating-assisted mode coupler (uniform longperiod fiber grating) that performs full energy conversion at the optical carrier frequency. Due to its high bandwidth, this device allows processing of arbitrary optical signals with sub-picosecond temporal features (down to 180-fs with the specific realizations reported here). Functionality of this device was tested by differentiating a 700-fs Gaussian optical pulse generated from a fiber laser (@ 1535nm). The derivative of this pulse is an odd-symmetry Hermite-Gaussian waveform, consisting of two linked 500-fslong, π-phase-shifted temporal lobes. This waveform is noteworthy for its application in advanced ultrahigh-speed optical communication systems.

We report on the temporal and spatial stability of the first tunable femtosecond undulator hard-x-ray source for ultrafast diffraction and absorption experiments. The 2:5-1 A output radiation is driven by an initial 50 fs laser pulse employing the laser-electron slicing technique. By using x-ray diffraction to probe laser-induced coherent optical phonons in bulk bismuth, we estimate an x-ray pulse duration of 140 30 fs FWHM with timing drifts below 30 fs rms measured over 5 days. Optical control of coherent lattice motion is demonstrated.

We have developed a diode-pumped Yb 31 :Sr 3 Y͑BO 3 ͒ 3 (Yb:BOYS) laser generating 69-fs pulses, at a central wavelength of 1062 nm. This laser is mode locked by use of a semiconductor saturable-absorber mirror and emits 80 mW of average power at 113 MHz. This is, to our knowledge, the first mode-locked Yb:BOYS laser and the shortest duration obtained from an ytterbium laser with a crystalline host. The central wavelength can be tuned from 1051 to 1070 nm, for sub-100-fs pulses. We have also achieved an average power as high as 300 mW with pulse duration of 86 fs at 1068 nm.

We report on what is believed to be the first observation of coherent subterahertz (sub-THz) emission from a 1-m string in the atmosphere. The sub-THz pulse emitted by the filamentary structure from an intense IR femtosecond laser pulse is detected perpendicularly to the laser propagation axis by use of two heterodyne detectors at 94 6 1 and 118 6 1 GHz. We describe the characteristics of this emission and show evidence of constructive interference between two separate strings.

Rational harmonic mode locking takes place in an actively mode-locked fiber laser when the modulation frequency = ( + 1 ) , where and are both integers and is the inverse of the cavity round-trip time. the 22nd order of rational harmonic mode locking has been observed when 1

We demonstrate the use of a fiber-based femtosecond laser locked onto an ultra-stable optical cavity to generate a low-noise microwave reference signal. Comparison with both a liquid Helium cryogenic sapphire oscillator (CSO) and a Ti:Sapphire-based optical frequency comb system exhibit a stability about 3×10 −15 between 1 s and 10 s. The microwave signal from the fiber system is used to perform Ramsey spectroscopy in a state-of-the-art Cesium fountain clock. The resulting clock system is compared to the CSO and exhibits a stability of 3.5 × 10 −14 τ −1/2 . Our continuously operated fiber-based system therefore demonstrates its potential to replace the CSO for atomic clocks with high stability in both the optical and microwave domain, most particularly for operational primary frequency standards.

We have investigated the intensity dependence of high-order harmonic generation in argon when the two shortest quantum paths contribute to the harmonic emission. For the first time to our knowledge, experimental conditions were found to clearly observe interference between these two quantum paths that are in excellent agreement with theoretical predictions. This result is a first step towards the direct experimental characterization of the full single-atom dipole moment and demonstrates an unprecedented accuracy of quantum path control on an attosecond time scale.

The effect of asymmetric laser pulses on electron yield from a laser wakefield accelerator has been experimentally studied using > 10 19 cm ÿ3 plasmas and a 10 TW, > 45 fs, Ti:Al 2 O 3 laser. The laser pulse shape was controlled through nonlinear chirp with a grating pair compressor. Pulses (76 fs FWHM) with a steep rise and positive chirp were found to significantly enhance the electron yield compared to pulses with a gentle rise and negative chirp. Theory and simulation show that fast rising pulses can generate larger amplitude wakes that seed the growth of the self-modulation instability, and that frequency chirp is of minimal importance for the experimental parameters.

We present a first-principles calculation for an optical dielectric breakdown in a diamond, which is induced by an intense laser field. We employ the time-dependent density-functional theory by solving the timedependent Kohn-Sham equation in real time and real space. For low intensities, the ionization agrees well with the Keldysh formula. The calculation shows a qualitative change of electron dynamics as the laser intensity increases, from dielectric screening at low intensities to optical breakdown at and above 7 ϫ 10 14 W / cm 2. Following the pulse, the electrons excited into the conduction band exhibit a coherent plasma oscillation that persists for tens of femtoseconds.

We demonstrate a single-shot digitizer with a 10 Tsample/ s sampling rate. This feat is accomplished with a photonic time stretch preprocessor that slows down the electrical waveform by an unprecedented factor of 250 before it is captured by a commercial electronic digitizer. To achieve such a large stretch factor, distributed Raman optical amplification is realized inside the dispersive element that performs the time stretch.

The authors demonstrate an efficient room temperature source of terahertz radiation using femtosecond laser pulses as a pump and GaAs structures with periodically inverted crystalline orientation, such as diffusion-bonded stacked GaAs and epitaxially grown orientation-patterned GaAs, as a nonlinear optical medium. By changing the GaAs orientation-reversal period ͑504-1277 m͒, or the pump wavelength ͑2 -4.4 m͒, we were able to generate narrow-bandwidth ͑ϳ100 GHz͒ terahertz wave packets, tunable between 0.9 and 3 THz, with the optical-to-terahertz photon conversion efficiency of 3.3%.

We present a combined theoretical and experimental study of spatiotemporal propagation effects in terahertz (THz) generation in gases using two-color ionizing laser pulses. The observed strong broadening of the THz spectra with increasing gas pressure reveals the prominent role of spatiotemporal reshaping and of a plasma-induced blueshift of the pump pulses in the generation process. Results obtained from (3 þ 1)-dimensional simulations are in good agreement with experimental findings and clarify the mechanisms responsible for THz emission.

The observation of nonperturbative high-order-harmonic generation in periodic solids has been interpreted in terms of a two step process comprising tunnel ionization and radiation from electrons undergoing frequency modulated Bloch oscillations in a strong laser field [Ghimire et al., Nat. Phys. 7, 138 (2011)]. Here we extend the model to include propagation effects. We show that the predicted efficiency is limited by phase velocity mismatch for emission below the band gap and by absorption above the band gap. The efficiency of harmonics scales with the square of the carrier density, suggesting that direct seeding could lead to higher yield. The emitted harmonics should have a temporal profile consisting of a train of subcycle pulses with duration on the order of 650 as depending on the crystal thickness.

We have studied terahertz (THz) emission from InAs and GaAs in a magnetic field, and find that the emitted radiation is produced by coupled cyclotron-plasma charge oscillations. Ultrashort pulses of THz radiation were produced at semiconductor surfaces by photoexcitation with a femtosecond Ti-sapphire laser. We recorded the integrated THz power and the THz emission spectrum as a function of magnetic

The authors report a GaAs/ Al 0.1 Ga 0.9 As quantum cascade laser based on a bound-to-continuum transition optimized for low frequency operation. High tunability of the gain curve is achieved by the Stark effect and laser emission is measured between 1.6 and 1.8 THz. Pulsed mode operation up to 95 K and continuous wave operation up to 80 K are reported. The dynamical range in current is as high as 43%.

Pulses as short as 460 fs and a tuning range as wide as 200 nm around 1 m have been achieved from a photonic-crystal-fiber-based parametric oscillator. The ring cavity with only 65 cm of photonic crystal fiber is synchronously pumped with a tunable passively mode-locked Yb-doped fiber laser. Widely extended tunability is achieved by using the modulation instability gain in normal dispersion as the result of high-order dispersion in the photonic crystal fiber.

We demonstrate a 13-fold increase in hard x-ray bremsstrahlung yield (10 -200 keV) emitted by a copper plasma created by 100 fs, 806 nm pulses at 10 14 − 10 15 Wcm −2 . This enhancement is achieved by depositing a thin film of copper nanoparticles of size 15 nm, on the target surface.

We study theoretically and experimentally the so-called self-induced modulational instability laser and show that the passive mode-locking mechanism that is at play in this laser relies on a dissipative four-wave mixing process that leads to generation of a dark-pulse train in the normal-dispersion regime.

We present short cavity erbium/ytterbium fiber lasers that are passively mode-locked with a saturable Bragg reflector. The lasers produce sub-500-fs pulses at fundamental cavity repetition rates as high as 300 MHz. Stable passive harmonic operation increases the repetition rate to 2.0 GHz. The mode-locking mechanism in both the normal and anomalous group velocity dispersion regimes is investigated using complete analytical and numerical models and direct comparison with the experimental results. A simple technique for accurately measuring the total cavity dispersion is presented.

We have employed femtosecond laser writing in order to induce refractive-index changes and waveguides in Ti 3+ -doped sapphire. Doping the sapphire crystal with an appropriate ion significantly reduces the threshold for creating structural changes, thus enabling the writing of waveguide structures. Passive and active buried channel waveguiding is demonstrated and images of the guided modes, propagation-loss values, fluorescence spectra, and output efficiencies are presented. The guiding area is located around the laser-damaged region, indicating that the guiding effect is stress induced. Refractive-index changes are measured by digital holography. Proper active doping should enable femtosecond processing and waveguide writing in various crystalline materials.

With 780-nm, 250-fs laser pulses, ultrafast optical nonlinearity has been observed in a series of thin films containing poly(methyl methacrylate) (PMMA)-TiO2 nanocomposites, which are synthesized by a simple technique of in-situ sol-gel/polymerization. The best figures of merit are found in one of the films prepared with a 60 wt % of titanium isopropoxide. Transmission electron microscopy shows the presence of 5-nm-diameter particles in the film. The observed optical nonlinearity has a recovery time of ~1.5 ps. These findings suggest the strong potential of PMMA-TiO2 nanocomposites for all-optical switching.

By simultaneously controlling repetition and carrier frequencies, one can achieve the phase coherent superposition of a collection of successive pulses from a mode-locked laser. An optical cavity can be used for coherent delay and constructive interference of sequential pulses until a cavity dump is enabled to switch out the amplified pulse. This approach will lead to an effective amplification process through decimation of the original pulse rate while the overall coherence from the oscillator is preserved. Detailed calculations show the limiting effects of intracavity dispersion and indicate that enhancement of sub-100-fs pulses to microjoule energies is experimentally feasible.

The pulse duration of soft x-ray free-electron laser ͑FEL͒ radiation is directly measured by time-resolved observation of doubly charged helium ions at 51.8 eV. A wave front splitting autocorrelator produces two correlated FEL pulses with a resolution of better than a femtosecond. In the interesting intensity range from 10 13 to 10 16 W / cm 2 direct and sequential double ionization contribute to the ion yield which has significant influence on the correlation width, being a general feature at high photon energies. Here, a duration of L = ͑29Ϯ 5͒ fs is derived for the soft x-ray pulses at FLASH.