The rise time of intense radiation determines the maximum field strength atoms can be exposed to before their polarizability dramatically drops due to the detachment of an outer electron. Recent progress in ultrafast optics has allowed the generation of ultraintense light pulses comprising merely a few field oscillation cycles. The arising intensity gradient allows electrons to survive in their bound atomic state up to external field strengths many times higher than the binding Coulomb field and gives rise to ionization rates comparable to the light frequency, resulting in a significant extension of the frontiers of nonlinear optics and (nonrelativistic) high-field physics. Implications include the generation of coherent harmonic radiation up to kiloelectronvolt photon energies and control of the atomic dipole moment on a subfemtosecond $(1{\mathrm{f}\mathrm{s}=10}^{\mathrm{\ensuremath{-}}15}\mathrm{}\mathrm{s})$ time scale. This review presents the landmarks of the 30-odd-year evolution of ultrashort-pulse laser physics and technology culminating in the generation of intense few-cycle light pulses and discusses the impact of these pulses on high-field physics. Particular emphasis is placed on high-order harmonic emission and single subfemtosecond extreme ultraviolet/x-ray pulse generation. These as well as other strong-field processes are governed directly by the electric-field evolution, and hence their full control requires access to the (absolute) phase of the light carrier. We shall discuss routes to its determination and control, which will, for the first time, allow access to the electromagnetic fields in light waves and control of high-field interactions with never-before-achieved precision.

Intense few-cycle laser fields: Frontiers of nonlinear optics

Mathematical Handbook for Scientists and Engineers

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

A theoretical analysis of third-order nonlinear interactions of focused laser beams is performed for the processes \omega_{1} + \omega_{2} + \omega_{3} \rightarrow \omega_{4}, \omega_{1} + \omega_{2} - \omega_{3} \rightarrow \omega_{4} , and \omega_{1} - \omega_{2} - \omega_{3} \rightarrow \omega_{4} . The total power and far-field beam profile of the generated radiation is related to the total powers of the fundamental beams, to the tightness and location of the focus, and to the value of the difference between the wave vectors of the generated radiation and driving polarization. The optimum degree of wave-vector mismatch as a function of tightness and location of focus is determined for each of the three processes. The process \omega_{1} + \omega_{2} - \omega_{3} \rightarrow \omega_{4} is found to be unique in that it is always optimized by focusing as tightly as possible. Experimental results, which verify the theory for the processes \omega_{1} + \omega_{2} + \omega_{3} \rightarrow \omega_{4} and \omega_{1} + \omega_{2} - \omega_{3} \rightarrow \omega_{4} , are presented.

Effects of focusing on third-order nonlinear processes in isotropic media. [laser beam interactions

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

We theoretically demonstrate the feasibility of optimal quasi-phase-matching (QPM) of high-order harmonic generation in gases and plasma with modulated density. QPM optimization, being possible for both tight and loose focusing of the fundamental beam, may increase the conversion efficiency of high-order harmonic generation by several orders of magnitude as compared to the efficiency attainable now.

Optimal quasi-phase-matching for high-order harmonic generation in gases and plasma.

We consider phase matching in the generation of very short-wavelength coherent radiation by nonlinear frequency upconversion in plasma and suggest some ways to improve phase matching in high-order harmonic generation. We obtain what are to our knowledge the first simple analytical expressions for a phase-matching factor in multiphoton mixing of an arbitrary order and demonstrate theoretically that high-order difference-frequency mixing in plasma could be, owing to its potential for phase-matching optimization, a more promising method of large-scale frequency upconversion than high-order harmonic generation.

Phase Matching For Large-scale Frequency Upconversion in Plasma.

Optical fibers were used to induce fluorescence by means of two-photon absorption in fluorophores. The effect, studied in a solution of 4′,6-diamidino-2-phenylindole, demonstrated that a single-mode fiber is a more efficient two-photon excitation source than a multimode fiber. This was shown with three different fibers.

http://striky.ece.jhu.edu/~sasha/AEK.pubs/94.pdf

Two-photon-induced fluorescence of biological markers based on optical fibers.

We suggest and discuss two techniques that could radically improve the efficiency of large-scale nonlinear frequency upconversion: quasi-phase matching of high-order harmonic generation in density-modulated media and high-order difference-frequency mixing in plasma. We demonstrate theoretically that both techniques permit optimal phase matching with tight focusing of pump beams, which is detrimental to current approaches to frequency upconversion, with a potentially drastic increase in conversion efficiency. Optimal phase-matching conditions that we obtained in the perturbation limit are shown to be likely to hold for strong pumping fields as well.

A. Lago

Papers

Optimal quasi-phase-matching for high-order harmonic generation in gases and plasma.

Phase Matching For Large-scale Frequency Upconversion in Plasma.

Two-photon-induced fluorescence of biological markers based on optical fibers.

Phase-matching optimization of large-scale nonlinear frequency upconversion in neutral and ionized gases

Phase-matching optima for high-order multiwave mixing and harmonic generation beyond perturbation limit