Extreme ultraviolet Fourier-transform spectroscopy with high order harmonics

Generalized central slice theorem perspective on Fourier-transform spectral imaging at a sub-Nyquist sampling rate

Fourier-transform spectral imaging captures frequency-resolved images with high spectral resolution, broad spectral range, high photon flux, and low stray light. In this technique, spectral information is resolved by taking Fourier transformation of the interference signals of two copies of the incident light at different time delays. The time delay should be scanned at a high sampling rate beyond the Nyquist limit to avoid aliasing, at the price of low measurement efficiency and stringent requirements on motion control for time delay scan. Here we propose, what we believe to be, a new perspective on Fourier-transform spectral imaging based on a generalized central slice theorem analogous to computerized tomography, using an angularly dispersive optics decouples measurements of the spectral envelope and the central frequency. Thus, as the central frequency is directly determined by the angular dispersion, the smooth spectral-spatial intensity envelope is reconstructed from interferograms measured at a sub-Nyquist time delay sampling rate. This perspective enables high-efficiency hyperspectral imaging and even spatiotemporal optical field characterization of femtosecond laser pulses without a loss of spectral and spatial resolutions.

Phase-locking of time-delayed attosecond XUV pulse pairs

We present a setup for the generation of phase-locked attosecond extreme ultraviolet (XUV) pulse pairs. The attosecond pulse pairs are generated by high harmonic generation (HHG) driven by two phase-locked near-infrared (NIR) pulses that are produced using an actively stabilized Mach-Zehnder interferometer compatible with near-single cycle pulses. The attosecond XUV pulses can be delayed over a range of 400 fs with a sub-10-as delay jitter. We validate the precision and the accuracy of the setup by XUV optical interferometry and by retrieving the energies of Rydberg states of helium in an XUV pump-NIR probe photoelectron spectroscopy experiment.

Table-top interferometry on extreme time and wavelength scales

Short-pulse metrology and dynamic studies in the extreme ultraviolet (XUV) spectral range greatly benefit from interferometric measurements. In this contribution a Michelson-type all-reflective split-and-delay autocorrelator operating in a quasi amplitude splitting mode is presented. The autocorrelator works under a grazing incidence angle in a broad spectral range (10 nm - 1 μm) providing collinear propagation of both pulse replicas and thus a constant phase difference across the beam profile. The compact instrument allows for XUV pulse autocorrelation measurements in the time domain with a single-digit attosecond precision and a useful scan length of about 1 ps enabling a decent resolution of E/ΔE = 2000 at 26.6 eV. Its performance for selected spectroscopic applications requiring moderate resolution at short wavelengths is demonstrated by characterizing a sharp electronic transition at 26.6 eV in Ar gas. The absorption of the 11^th harmonic of a frequency-doubled Yb-fiber laser leads to the well-known 3s3p⁶4p¹P¹ Fano resonance of Ar atoms. We benchmark our time-domain interferometry results with a high-resolution XUV grating spectrometer and find an excellent agreement. The common-path interferometer opens up new opportunities for short-wavelength femtosecond and attosecond pulse metrology and dynamic studies on extreme time scales in various research fields.

All-optical attosecond time domain interferometry

Interferometry, a key technique in modern precision measurements, has been used for length measurement in engineering metrology and astronomy. An analogous time-domain interferometric technique would represent a significant complement to spatial domain applications and require the manipulation of interference on extreme time and energy scales. Here, we report an all-optical interferometer using laser-driven high order harmonics as attosecond temporal slits. By controlling the phase of the temporal slits with an external field, a time domain interferometer that preserves both attosecond temporal resolution and hundreds of meV energy resolution is implemented. We apply this exceptional temporal resolution to reconstruct the waveform of an arbitrarily polarized optical pulse, and utilize the provided energy resolution to interrogate the abnormal character of the transition dipole near the Cooper minimum in argon. This novel attosecond interferometry paves the way for high precision measurements in the time-energy domain using all-optical approaches.

High complexity femtosecond pulse duplicator

This paper presents a theoretical and numerical study of a 0-π fan-out phase grating placed in the Fourier plane of a spatio-spectral pulse shaper followed by a spherical focusing lens. It is shown that this device acts as a high complexity femtosecond pulse duplicator designed for two source interferometry. At the focus of the lens, the electric field displays two spatially separated intense spots in which relative delay can be continuously tuned over 4 orders of magnitude, typically from a few attoseconds to a few tens of femtoseconds. Because the two pulses do not spatially overlap, their intensity remains unchanged when the relative delay is smaller than the pulse duration. Detailed simulations of the shaped electric field are presented.

Attosecond chirp effect on the transient absorption spectrum of laser-dressed helium atom

We theoretically investigate the attosecond transient absorption spectrum of helium atom in the presence of an infrared-dressed laser pulse upon scanning their relative delay, with the particular emphasis on the chirp effect of the attosecond pulse. By numerically solving the fully three-dimensional time-dependent Schrödinger equation, we identify the attoscecond chirp can induce the temporal shift of the absorption spectrogram along the delay axis. Additionally, it is found that the extent of the temporal shift is dependent on both the position of the absorption line and the infrared pulse wavelength, which is well confirmed and reproduced by a three-level model. Moreover, we demonstrate that the observed features can be quantitatively explained in terms of the indirect two-photon absorption processes through some virtual states. This effect might provide a way to measure the chirp of attosecond pulse in an all-optical way.

Phase-modulated harmonic light spectroscopy

By combining phase-modulated nonlinear spectroscopy with second harmonic generation, the concept of phase-modulated harmonic light spectroscopy is introduced. Simultaneous spectroscopy with different harmonics of the light is demonstrated and linear and nonlinear excitation of the spectroscopic sample is investigated. Sum frequency generation and stray light effects during temporal pulse overlap have been evaluated in detail, accompanied by simulations. The presented work provides a promising concept to facilitate coherent nonlinear time-domain spectroscopy in the extreme ultraviolet wavelength regime and contributes valuable insights for future studies in this direction.

Generation of Phase-Locked Pulses from a Seeded Free-Electron Laser

In a coherent control experiment, light pulses are used to guide the real-time evolution of a quantum system. This requires the coherence and the control of the pulses' electric-field carrier waves. In this work, we use frequency-domain interferometry to demonstrate the mutual coherence of time-delayed pulses generated by an extreme ultraviolet seeded free-electron laser. Furthermore, we use the driving seed laser to lock and precisely control the relative phase between the two free-electron laser pulses. This new capability opens the way to a multitude of coherent control experiments, which will take advantage of the high intensity, short wavelength, and short duration of the pulses generated by seeded free-electron lasers.

Octave-spanning hyperspectral coherent diffractive imaging in the extreme ultraviolet range

Soft x-ray microscopy is a powerful imaging technique that provides sub-micron spatial resolution, as well as chemical specificity using core-level near-edge x-ray absorption fine structure (NEXAFS). Near the carbon K-edge (280-300 eV) biological samples exhibit high contrast, and the detailed spectrum contains information about the local chemical environment of the atoms. Most soft x-ray imaging takes place on dedicated beamlines at synchrotron facilities or at x-ray free electron laser facilities. Tabletop femtosecond laser systems are now able to produce coherent radiation at the carbon K-edge and beyond through the process of high harmonic generation (HHG). The broad bandwidth of HHG is seemingly a limitation to imaging, since x-ray optical elements such as Fresnel zone plates require monochromatic sources. Counter-intuitively, the broad bandwidth of HHG sources can be beneficial as it permits chemically-specific hyperspectral imaging. We apply two separate techniques - Fourier transform spectroscopy, and lensless holographic imaging - to obtain images of an object simultaneously at multiple wavelengths using an octave-spanning high harmonic source with photon energies up to 30 eV. We use an interferometric delay reference to correct for nanometer-scale fluctuations between the two HHG sources.

Wave packet interferometry with attosecond precision and picometric structure

Wave packet (WP) interferometry is applied to the vibrational WPs of the iodine molecule. Interference fringes of quantum waves weave highly regular space-time images called "quantum carpets." The structure of the carpet has picometre and femtosecond resolutions, and changes drastically depending on the amplitudes and phases of the vibrational eigenstates composing the WP. In this review, we focus on the situation where quantum carpets are created by two counter-propagating nuclear vibrational WPs. Such WPs can be prepared with either a single or double femtosecond (fs) laser pulse. In the single pulse scheme, the relevant situation appears around the half revival time. Similar situations can be generated with a pair of fs laser pulses whose relative phase is stabilized on the attosecond time scale. In the latter case we can design the quantum carpet by controlling the timing between the phase-locked pulses. We demonstrate this carpet design and visualize the designed carpets by the fs pump-probe measurements, tuning the probe wavelength to resolve the WP density-distribution along the internuclear axis with ~3 pm spatial resolution and ~100 fs temporal resolution.

Ramsey spectroscopy of bound atomic states with extreme-ultraviolet laser harmonics

We report the experimental measurement of Ramsey interference fringes in the single-photon excitation to a high-lying bound state of atomic argon by pairs of phase-locked, time-delayed, extreme UV high-order-harmonic pulses at 87 nm. High-visibility Ramsey fringes are observed for delays larger than 100 ps, thus demonstrating a potential resolving power >10(5) at this wavelength.

Interferometry of attosecond pulse trains in the extreme ultraviolet wavelength region

The temporal coherence of an attosecond optical field in the extreme ultraviolet wavelength region can be defined in terms of the extent of interference in time domain. We successfully measured this phenomenon both with and without spectral decomposition. We also report the results of using this approach to directly observe both symmetry and symmetry breaking of interference fringes in an attosecond pulse train.

A Fourier transform spectrometer without a beam splitter for the vacuum ultraviolet range: From the optical design to the first UV spectrum

We describe a Fourier transform (FT) spectrometer designed to operate down to 60 nm (20 eV) on a synchrotron radiation beamline for high resolution absorption spectrometry. As far as we know, such an instrument is not available below 140 nm mainly because manufacturing accurate and efficient beam splitters remains a major problem at these wavelengths, especially if a wide bandwidth operation is desired. In order to overcome this difficulty, we developed an interferometer based on wave front division instead of amplitude division. It relies on a modified Fresnel bimirror configuration that requires only flat mirrors. The instrument provides path difference scanning through the translation of one reflector. During the scanning, the moving reflector is controlled by an optical system that keeps its direction constant within a tolerable value and provides an accurate interferometric measurement of the path difference variation. Therefore, a regular interferogram sampling is obtained, producing a nominal spectral impulse response and an accurate spectral calibration. The first results presented in this paper show a measured spectral resolution of delta(sigma)=0.33 cm-1 (interval between spectral samples). This was obtained with a sampling interval of 29 nm (path difference) and 512 K samples from a one-sided interferogram using a cosine FT. Such a sampling interval should allow the recording of large bandwidth spectra down to lambda=58 nm with an ultimate resolving power of 500,000 at this wavelength. In order to check the instrument performances, we first recorded an interferogram from a He-Ne stabilized laser. This provided the actual spectral impulse function, which was found to be fully satisfactory. The determination of the impulse response distortion and of the noise on the vacuum ultraviolet (VUV) spectral range provided accurate information in the sampling error profile over a typical scan. Finally, the instrument has been moved to the SU5 undulator-based synchrotron radiation beamline (Super-ACO facility, LURE, Orsay, France). A high resolution spectrum of O2 (the Schumann-Runge absorption bands, 185-200 nm) was computed from recorded interferograms using the beamline monochromator at the zeroth order to feed the instrument with an 11% relative bandwidth "white" beam (2003). These UV measurements are very close to those found in the literature, showing nominal performances of the FT spectrometer that should translate into an unprecedented resolving power at shortest VUV wavelengths. A recent upgrade (2007) and future developments will be discussed in light of the current installation of the upgraded FT spectrometer as a permanent endstation for ultrahigh resolution absorption spectrometry on the VUV beamline DESIRS at SOLEIL, the new French third generation synchrotron facility.

Spectral phase distribution retrieval through coherent control of harmonic generation

The temporal intensity distribution of the third harmonic of a Ti:sapphire laser generated in Xe gas is fully reconstructed from its spectral phase and amplitude distributions. The spectral phases are retrieved by cross correlating the fundamental laser frequency field with that of the third harmonic, in a three laser versus one harmonic photon coupling scheme. The third harmonic spectral amplitude distribution is extracted from its field autocorrelation. The measured pulse duration is found to be in agreement with that expected from lowest order perturbation theory both for unstretched and chirped pulses.