A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

High-harmonic generation (HHG) traditionally combines ~100 near-infrared laser photons to generate bright, phase-matched, extreme ultraviolet beams when the emission from many atoms adds constructively. Here, we show that by guiding a mid-infrared femtosecond laser in a high-pressure gas, ultrahigh harmonics can be generated, up to orders greater than 5000, that emerge as a bright supercontinuum that spans the entire electromagnetic spectrum from the ultraviolet to more than 1.6 kilo-electron volts, allowing, in principle, the generation of pulses as short as 2.5 attoseconds. The multiatmosphere gas pressures required for bright, phase-matched emission also support laser beam self-confinement, further enhancing the x-ray yield. Finally, the x-ray beam exhibits high spatial coherence, even though at high gas density the recolliding electrons responsible for HHG encounter other atoms during the emission process.

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Bright Coherent Ultrahigh Harmonics in the keV X-ray Regime from Mid-Infrared Femtosecond Lasers

The frequency doubling of laser light was one of the first new phenomena observed following the invention of the laser over 50 years ago. Since then, the quest to extend nonlinear optical upconversion to ever-shorter wavelengths has been a grand challenge in laser science. Two decades of research into high-order harmonic generation has recently uncovered several feasible routes for generating bright coherent X-ray beams using small-scale femtosecond lasers. The physics of this technique combines the microscopic attosecond science of atoms driven by intense laser fields with the macroscopic extreme nonlinear optics of phase matching, thus essentially realizing a coherent, tabletop version of the Roentgen X-ray tube.

The attosecond nonlinear optics of bright coherent X-ray generation

High-harmonic generation provides an attractive light source of coherent radiation in the extreme-ultraviolet (XUV) and soft-x-ray regions of the spectrum and allows for the production of single attosecond pulses or pulse trains. This Colloquium covers the control of high-harmonic spectra by temporal and spatial pulse shaping of the driving laser pulses and its implications on time-resolved XUV spectroscopy and attosecond pulse shaping. It summarizes important steps for extending existing pulse shaping techniques and control schemes from the near-infrared or visible part to shorter wavelengths. Using adaptive pulse shaping of the driving laser pulses, several groups have demonstrated control of the high-harmonic spectrum, including the author's work on the complete control over the XUV spectrum of high-order harmonics, generated in a gas-filled hollow fiber. It is possible to achieve both the enhancement and the suppression of single or several selected harmonic orders. These arbitrarily shaped soft-x-ray spectra will allow for important modifications of the resulting harmonic pulses in the temporal domain. This constitutes first steps towards direct attosecond pulse shaping in the soft-x-ray domain. Moreover, high-harmonic generation in a hollow-core fiber can be enhanced by coupling into a single fiber mode using a feedback-controlled adaptive two-dimensional spatial light modulator.

Colloquium : Optimal control of high-harmonic generation

The concerted motion of two or more bound electrons governs atomic and molecular non-equilibrium processes including chemical reactions, and hence there is much interest in developing a detailed understanding of such electron dynamics in the quantum regime. However, there is no exact solution for the quantum three-body problem, and as a result even the minimal system of two active electrons and a nucleus is analytically intractable. This makes experimental measurements of the dynamics of two bound and correlated electrons, as found in the helium atom, an attractive prospect. However, although the motion of single active electrons and holes has been observed with attosecond time resolution, comparable experiments on two-electron motion have so far remained out of reach. Here we show that a correlated two-electron wave packet can be reconstructed from a 1.2-femtosecond quantum beat among low-lying doubly excited states in helium. The beat appears in attosecond transient-absorption spectra measured with unprecedentedly high spectral resolution and in the presence of an intensity-tunable visible laser field. We tune the coupling between the two low-lying quantum states by adjusting the visible laser intensity, and use the Fano resonance as a phase-sensitive quantum interferometer to achieve coherent control of the two correlated electrons. Given the excellent agreement with large-scale quantum-mechanical calculations for the helium atom, we anticipate that multidimensional spectroscopy experiments of the type we report here will provide benchmark data for testing fundamental few-body quantum dynamics theory in more complex systems. They might also provide a route to the site-specific measurement and control of metastable electronic transition states that are at the heart of fundamental chemical reactions.

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Reconstruction and control of a time-dependent two-electron wave packet

We report the wave-front phase measurement of high-order harmonics employing point-diffraction interferometry. The high-order harmonics generated in a gas-filled hollow tube showed excellent spatial coherence over nearly the whole cross section of the harmonic beams. Using this coherent harmonic source in the extreme-ultraviolet-soft-x-ray region, we have demonstrated the operation of a point-diffraction interferometer and measured the wave-front phase of high-order harmonics.

Wave-front phase measurements of high-order harmonic beams by use of point-diffraction interferometry.

Pulse compression in a differentially pumped neon-filled hollow fiber was used to generate high-power few-cycle laser pulses. The pulse compression process was optimized by adjusting gas pressure and laser chirp to produce the shortest laser pulses. Precise dispersion control enabled the generation of laser pulses with duration of 3.7 fs and energy of 1.2 mJ. This corresponds to an output of 1.5 cycle, 0.3 TW pulses at a 1 kHz repetition rate using positively chirped 33 fs laser pulses.

Generation of 1.5 cycle 0.3 TW laser pulses using a hollow-fiber pulse compressor.

Optical pulses with 1.1-mJ energy and 5.5-fs duration have been generated at 1-kHz repetition rate from a chirped pulse amplification Ti:Sapphire laser incorporating a differentially pumped hollow-fiber chirped-mirror compressor. The effects of self-focusing and multi-photon ionization during the beam propagation were minimized by differentially pumping the hollow fiber filled with neon. The spectral broadening at the hollow-fiber compressor was optimized by adjusting gas pressure, laser intensity, and laser chirp, covering from 540 nm to 950 nm.

Generation of 0.2-TW 5.5-fs optical pulses at 1 kHz using a differentially pumped hollow-fiber chirped-mirror compressor

By generating broadband high-harmonic pulses from neon and compensating for attosecond chirp by the material dispersion of argon, the generation of near transform-limited 63 as pulses was achieved. The spectral phase analysis showed that, without proper compensation, the attosecond chirp of the broadband harmonics caused splitting of attosecond high-harmonic pulses in addition to pulse broadening. Although it was attained only within a limited spectral range, the attosecond chirp compensation was successful in bringing out pulse compression over broad harmonics, which signifies the effectiveness of the attosecond chirp compensation by material dispersion.

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Attosecond chirp compensation over broadband high-order harmonics to generate near transform-limited 63 as pulses

The influence of laser chirp on the formation of femtosecond laser filamentation in Ar was investigated for the generation of few-cycle high-power laser pulses The condition for the formation of a single filament has been carefully examined using 28-fs laser pulses with energy over 3 mJ The filament formation and output spectrum changed very sensitively to the initial laser chirp and gas pressure Much larger spectral broadening was obtained with positively chirped pulses, compared to the case of negatively chirped pulses that generated much longer filament, and compressed pulses of 55 fs with energy of 05 mJ were obtained from the filamentation of positively chirped 30-fs laser pulses in a single Ar cell

Juyun Park

Papers

Wave-front phase measurements of high-order harmonic beams by use of point-diffraction interferometry.

Generation of 1.5 cycle 0.3 TW laser pulses using a hollow-fiber pulse compressor.

Generation of 0.2-TW 5.5-fs optical pulses at 1 kHz using a differentially pumped hollow-fiber chirped-mirror compressor

Attosecond chirp compensation over broadband high-order harmonics to generate near transform-limited 63 as pulses

Laser chirp effect on femtosecond laser filamentation generated for pulse compression.