The shortest light pulses produced to date are of the order of a few tens of attoseconds, with central frequencies in the extreme UV range and bandwidths exceeding tens of electronvolts. They are often produced as a train of pulses separated by half the driving laser period, leading in the frequency domain to a spectrum of high, odd-order harmonics. As light pulses become shorter and more spectrally wide, the widely used approximation consisting of writing the optical waveform as a product of temporal and spatial amplitudes does not apply anymore. Here, we investigate the interplay of temporal and spatial properties of attosecond pulses. We show that the divergence and focus position of the generated harmonics often strongly depend on their frequency, leading to strong chromatic aberrations of the broadband attosecond pulses. Our argument uses a simple analytical model based on Gaussian optics, numerical propagation calculations, and experimental harmonic divergence measurements. This effect needs to be considered for future applications requiring high-quality focusing while retaining the broadband/ultrashort characteristics of the radiation.
We measure spectrally and spatially resolved high-order harmonics generated in argon using chirped multi-cycle laser pulses. Using a stable, high-repetition rate laser we observe detailed interference structures in the far-field. The structures are of two kinds; off-axis interference from the long trajectory only and on-axis interference including the short and long trajectories. The former is readily visible in the far-field spectrum, modulating both the spectral and spatial profile. To access the latter, we vary the chirp of the fundamental, imparting different phases on the different trajectories, thereby changing their relative phase. Using this method together with an analytical model, we are able to explain the on-axis behaviour and access the dipole phase parameters for the short (a s ) and long (a l ) trajectories. The extracted results compare very well with phase parameters calculated by solving the time-dependent Schrödinger equation. Going beyond the analytical model, we are also able to successfully reproduce the off-axis interference structure.
Ultrafast processes in matter can be captured and even controlled by using sequences of fewcycle optical pulses, which need to be well characterized, both in amplitude and phase. The same degree of control has not yet been achieved for few-cycle extreme ultraviolet pulses generated by high-order harmonic generation (HHG) in gases, with duration in the attosecond range. Here, we show that by varying the spectral phase and carrier-envelope phase (CEP) of a high-repetition rate laser, using dispersion in glass, we achieve a high degree of control of the relative phase and CEP between consecutive attosecond pulses. The experimental results are supported by a detailed theoretical analysis based upon the semi-classical three-step model for HHG.
We generate high-order harmonics at high pulse repetition rates using a turnkey laser. High-order harmonics at 400 kHz are observed when argon is used as target gas. In neon, we achieve generation of photons with energies exceeding 90 eV (∼13 nm) at 20 kHz. We measure a photon flux of up to 4.4 × 10(10) photons per second per harmonic in argon at 100 kHz. Many experiments employing high-order harmonics would benefit from higher repetition rates, and the user-friendly operation opens up for applications of coherent extreme ultra-violet pulses in new research areas.
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