Highly coherent light at 13 nm generated by use of quasi-phase-matched high-harmonic generation

By measuring the fringe visibility in a Young's double pinhole experiment, we demonstrate that quasi-phase-matched high-harmonic generation produces beams with very high spatial coherence at wavelengths around 13 nm. To our knowledge these are the highest spatial coherence values ever measured at such short wavelengths from any source without spatial filtering. This results in a practical, small-scale, coherent, extreme-ultraviolet source that is useful for applications in metrology, imaging, and microscopy.

Quasi-phase-matched generation of coherent extreme-ultraviolet light

High-harmonic generation is a well-known method of producing coherent extreme-ultraviolet (EUV) light, with photon energies up to about 0.5 keV (refs 1, 2). This is achieved by focusing a femtosecond laser into a gas, and high harmonics of the fundamental laser frequency are radiated in the forward direction. However, although this process can generate high-energy photons, efficient high-harmonic generation has been demonstrated only for photon energies of the order 50-100 eV (ref. 5). Ionization of the gas prevents the laser and the EUV light from propagating at the same speed, which severely limits the conversion efficiency. Here we report a technique to overcome this problem, and demonstrate quasi-phase-matched frequency conversion of laser light into EUV. Using a modulated hollow-core waveguide to periodically vary the intensity of the laser light driving the conversion, we efficiently generate EUV light even in the presence of substantial ionization. The use of a modulated fibre shifts the energy spectrum of the high-harmonic light to significantly higher photon energies than would otherwise be possible. We expect that this technique could form the basis of coherent EUV sources for advanced lithography and high-resolution imaging applications. In future work, it might also be possible to generate isolated attosecond pulses.

Attosecond time-scale intra-atomic phase matching of high harmonic generation

Using a model of high-harmonic generation that couples a fully quantum calculation with a semiclassical electron trajectory picture, we show that a new type of phase matching is possible when an atom is driven by an optimal optical waveform. For an optimized laser pulse shape, strong constructive interference is obtained in the frequency domain between emissions from different electron trajectories, thereby selectively enhancing a particular harmonic order. This work demonstrates that coherent control in the strong-field regime is possible by adjusting the peaks of a laser field on an attosecond time scale.

Phase-dependent loss due to nonadiabatic ionization by sub-10-fs pulses

For the first time to the author's knowledge, the effect of phase-dependent loss that can be used to stabilize the phase of a sub-10-fs laser pulse with respect to the envelope is shown. This loss is caused by the nonadiabatic response of an atom illuminated by a short pulse, which leads to the dependence of the tunneling ionization on the absolute phase of the pulse. The phase selectivity can be employed as a phase-dependent filter within the laser cavity with important applications in nonlinear optics in the single-cycle regime.

Sub-10-fs operation of Kerr-lens mode-locked lasers

We present results of a three-dimensional model of a Kerr-lens mode-locked titanium-doped sapphire laser in the sub-10-fs regime of operation. We find that space-time focusing of the pulse within the laser crystal imposes a limitation on the pulse duration as a function of the crystal length. Thus good compensation of the net group-velocity dispersion of the cavity is not sufficient for successful sub-10-fs operation of the laser. The dependence of the pulse duration on the intracavity dispersion is also presented, which demonstrates that pulses as short as 6 fs can be generated directly from the laser.

Mode locking with a compensated space-time astigmatism

We present what is to our knowledge the first full spatial plus temporal model of a self-mode-locked titaniumdoped sapphire laser. The self-consistent evolution of the pulse toward steady state imposes strong space-time focusing in the crystal, where both the space and time foci are located. This combined focusing significantly improves the discrimination properties of the nonlinear resonator for shorter pulses and reduces the transient stage of pulse formation. Our theoretical results are in very good agreement with experiment.

Ultrashort optical waveform measurements using frequency-resolved optical gating

We measure the intensity and phase of ultrashort pulses from a self-mode-locked Ti:sapphire laser using the recently developed technique of frequency-resolved optical gating. These results represent to our knowledge the shortest complete optical waveform characterization measurements performed to date. We also verify recent theoretical calculations that predict that the main limitation on the pulse duration from these lasers is the presence of uncompensated higher-order dispersion.

Space-time focusing of femtosecond pulses in a Ti:sapphire laser

We present what is to our knowledge the first three-dimensional model of a femtosecond pulse propagating in a Ti:sapphire laser crystal, which includes dispersion, self-focusing, and finite response time of the medium and does not assume the slowly varying envelope approximation. The combined action of material dispersion and phase modulation leads to a dramatic space-time focusing on the pulse. Dispersion prevents catastrophic selffocusing and self-steepening of the pulse, even though the peak power of the pulse is much greater than the critical power for self-focusing filamentation. Extrapolation of these results to shorter-pulse durations shows that this space-time focusing mechanism can operate even for pulses with durations close to the response time of the Kerr nonlinearity.

Fourth-order dispersion-limited solitary pulses

We analyze the performance of a Ti:sapphire self-mode-locked laser with near-zero second- and third-order dispersion. Our simulations show that, in the presence of fourth-order dispersion, solitary laser pulses can be supported within a wide parameter range, close to the experimental values of these parameters. We also conclude that it is possible to generate pulses much shorter than 10 fs if fourth-order dispersion is further reduced.

Pulse evolution in a broad-bandwidth Ti:sapphire laser

We demonstrate that by operating near the zero second- and third-order dispersion point in a self-mode-locked Ti:sapphire laser we can generate sub-10-fs pulses. Our numerical simulations show that the pulse duration is limited by fourth-order dispersion and that shorter pulses will be possible if this can be reduced. Also, by inserting a pellicle in various positions in a Ti:sapphire cavity, we have measured the intracavity pulse duration and chirp of the circulating pulse in the laser. Our results demonstrate that the pulse is shortest near the middle of the laser crystal, in one direction of propagation. In the other direction of propagation, the pulse is positively chirped and several times longer.

Amplification of femtosecond pulses in a spatially dispersive scheme

The amplification of 20-fs-duration pulses in an amplifier with spatial dispersion in the gain medium (dye) is theoretically analyzed. Pulse self-shaping was observed during amplification, and further shaping was achieved by spatially modulating the pump. This spatial modulation of the pump permits the elimination of pulse broadening in the amplifier, even in the saturation regime. The possibility of using a compound medium with an ultrabroadband gain profile is also discussed.