The simplest two-dimensional (2D) spectra show how excitation with one (variable) frequency affects the spectrum at all other frequencies, thus revealing the molecular connections between transitions. Femtosecond 2D Fourier transform (2D FT) spectra are more flexible and share some of the remarkable properties of their conceptual parent, 2D FT nuclear magnetic resonance. When 2D FT spectra are experimentally separated into real absorptive and imaginary refractive parts, the time resolution and frequency resolution can both reach the uncertainty limit set for each resonance by the sample itself. Coherent four-level contributions to the signal provide new molecular phase information, such as relative signs of transition dipoles. The nonlinear response can be picked apart by selecting a single coherence pathway (e.g., specifying the relative signs of energy level difference frequencies during different time intervals as in the photon echo). Because molecules are frozen on the femtosecond timescale, femtosecond 2D FT experiments can separate a distribution of instantaneous molecular environments and intramolecular geometries as inhomogeneous broadening. This review provides an introduction to two-dimensional Fourier transform experiments exploiting second- and third-order vibrational and electronic nonlinearities.

Two-dimensional femtosecond spectroscopy

Modern laser sources nowadays deliver ultrashort light pulses reaching few cycles in duration and peak powers exceeding several terawatt (TW). When such pulses propagate through optically transparent media, they first self-focus in space and grow in intensity, until they generate a tenuous plasma by photo-ionization. For free electron densities and beam intensities below their breakdown limits, these pulses evolve as self-guided objects, resulting from successive equilibria between the Kerr focusing process, the chromatic dispersion of the medium and the defocusing action of the electron plasma. Discovered one decade ago, this self-channeling mechanism reveals a new physics, widely extending the frontiers of nonlinear optics. Implications include long-distance propagation of TW beams in the atmosphere, supercontinuum emission, pulse shortening as well as high-order harmonic generation. This review presents the landmarks of the 10-odd-year progress in this field. Particular emphasis is laid on the theoretical modeling of the propagation equations, whose physical ingredients are discussed from numerical simulations. The dynamics of single filaments created over laboratory scales in various materials such as noble gases, liquids and dielectrics reveal new perspectives in pulse shortening techniques. Far-field spectra provide promising diagnostics. Attention is also paid to the multifilamentation instability of broad beams, breaking up the energy distribution into small-scale cells along the optical path. The robustness of the resulting filaments in adverse weathers, their large conical emission exploited for multipollutant remote sensing, nonlinear spectroscopy and the possibility of guiding electric discharges in air are finally addressed on the basis of experimental results.

https://iopscience.iop.org/article/10.1088/0034-4885/70/10/R03/pdf

Ultrashort filaments of light in weakly ionized, optically transparent media

In this article, we review progress in the development of high peak-power ultrafast lasers, and discuss in detail the design issues which determine the performance of these systems. Presently, lasers capable of generating terawatt peak powers with unprecedented short pulse duration can now be built on a single optical table in a small-scale laboratory, while large-scale lasers can generate peak power of over a petawatt. This progress is made possible by the use of the chirped-pulse amplification technique, combined with the use of broad-bandwidth laser materials such as Ti:sapphire, and the development of techniques for generating and propagating very short (10–30 fs) duration light pulses. We also briefly summarize some of the new scientific advances made possible by this technology, such as the generation of coherent femtosecond x-ray pulses, and the generation of MeV-energy electron beams and high-energy ions.

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High power ultrafast lasers

Femtosecond time-resolved two-photon photoemission studies of electron dynamics in metals

Pulses of sub-6-fs duration have been obtained from a Kerr-lens mode-locked Ti:sapphire laser at a repetition rate of 100 MHz and an average power of 300 mW. Fitting an ideal sech(2) to the autocorrelation data yields a 4.8-fs pulse duration, whereas reconstruction of the pulse amplitude profile gives 5.8 fs. The pulse spectrum covers wavelengths from above 950 nm to below 630 nm, extending into the yellow beyond the gain bandwidth of Ti:sapphire. This improvement in bandwidth has been made possible by three key ingredients: carefully designed spectral shaping of the output coupling, better suppression of the dispersion oscillation of the double-chirped mirrors, and a novel broadband semiconductor saturable-absorber mirror.

Semiconductor saturable-absorber mirror assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime.

We describe a simple method for generating sub-20-fs ultraviolet light pulses with useful average powers, using a kilohertz Ti:sapphire laser system. By focusing a 22-fs, 1-mJ laser pulse in air, we obtain ultraviolet pulses with an energy of 1 microJ and at a wavelength of 266 nm and with an average power of 1 mW. The pulse duration of the ultraviolet pulses was measured to be 16 fs with frequency-resolved optical gating.

16-fs, 1-microJ ultraviolet pulses generated by third-harmonic conversion in air.

We report full characterization of the intensity and phase of /spl sim/10-fs optical pulses using second-harmonic-generation frequency-resolved-optical-gating (SHG FROG). We summarize the subtleties in such measurements, compare these measurements with predicted pulse shapes, and describe the implications of these measurements for the creation of even shorter pulses. We also discuss the problem of validating these measurements. Previous measurements of such short pulses using techniques such as autocorrelation have been difficult to validate because at best incomplete information is obtained and internal self-consistency checks are lacking. FROG measurements of these pulses, in contrast, can be validated, for several reasons. First, the complete pulse-shape information provided by FROG allows significantly better comparison of experimental data with theoretical models than do measurements of the autocorrelation trace of a pulse. Second, there exist internal self-consistency checks in FROG that are not present in other pulse-measurement techniques. Indeed, we show how to correct a FROG trace with systematic error using one of these checks.

https://frog.gatech.edu/Pubs/Taft-10fsFROGreview-JSTQE-1996.pdf

Measurement of 10-fs laser pulses

There has been remarkable progress in the development of high peak-power ultrafast lasers in recent years. Lasers capable of generating terawatt peak powers with unprecedented short pulse durations can now be built on a single optical table in a small laboratory. The rapid technological progress has made possible a host of new scientific advances in high-field science, such as the generation of coherent femtosecond X-ray pulses, and the generation of MeV-energy electron beams and high-energy ions. In this paper, we review progress in the development and design of ultrafast highpower lasers based on Ti:sapphire, including the ultrafast laser oscillators that are a very important enabling technology for high-power ultrafast systems, and ultrafast amplified laser systems that generate 20 fs duration pulses with several watts average power at kilohertz repetition-rates. Ultrafast waveform measurements of these pulses demonstrate that such short pulses can be generated with high fidelity. Finally, we discuss applications of ultrafast high-power pulses, including the generation of femtosecond to attosecond X-ray pulses. The 1990s have seen rapid progress in ultrafast laser technology [1, 2]. Ultrafast light sources today are “turn-key” devices, producing peak output powers on the order of a megawatt with pulse durations under 10 fs, directly from a simple laser [3–8]. Since an optical cycle period in the visible and near-infrared is 2–3 fs, this pulse duration approaches fundamental limits for devices operating in this wavelength range. Important new measurement techniques [9] have also been developed, which can extract the complete waveform of an optical pulse of only a few cycles in duration [10, 11]. Such precise measurement tools are essential to properly characterize and utilize extremely short optical pulses. A major application of ultrafast lasers is to study the interaction of atoms, molecules, and plasmas with intense light. These high-field science applications require peak power in the range of 1010–1015 W. Such high-power short pulses are generated using laser amplifier systems. The technology for generating high-power amplified ultrafast pulses has progressed very rapidly over the past decade [12–22]. Amplification of the energy in an ultrashort pulse by factors of 107 or more is now routinely achieved, resulting in a peak power of in the terawatt range from small-scale lasers, and of up to a petawatt from larger systems. By focusing these high-power optical pulses, light intensities of greater than 1020 W cm−2 can be generated, which correspond to an intensity greater than that which would be obtained by focusing the entire solar flux incident on the earth onto a pin-head. Because the size of a laser depends primarily on its pulse energy, by reducing the duration of the pulse being amplified, we can achieve extremely-high power densities using lasers of a realistic and compact scale. As a result, by reducing the pulse duration to 10–20 fs, even very small-scale laboratory lasers operating at kilohertz repetition rates [23, 24] are now easily capable of generating light intensities corresponding to an electric field in excess of that binding a valence electron to an atom. Remarkable progress in high-field optical science has followed as a direct result of this technological progress. It is now possible to experimentally investigate highly-nonlinear processes in atomic, molecular, plasma, and solid-state physics, and to access previously-unexplored states of matter. Ultrashort-pulses at ultraviolet and soft X-ray wavelengths can be generated through harmonic upconversion [25–28] and also at hard and soft X-ray wavelengths through the creation of an ultrafast laser-produced plasma [29] or by scattering off electron beams [30–32]. Such ultrafast softand hard-X-ray pulses can be used to directly probe both longand short-range atomic dynamics and to monitor the evolution of highly-excited systems [33]. In other work, the use of extremely short-pulse high-intensity lasers may make it possible to generate coherent X-rays with pulse duration as short as 10−16 seconds (or 100 attoseconds) [34–36]. 1 Ultrashort-pulse sources The technology of femtosecond lasers changed dramatically with the demonstration in 1990 of the self-modelocked Ti:sapphire laser by Sibbett and his group [1]. Titaniumdoped sapphire is a solid-state laser material with extreme-

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Ultrafast laser and amplifier sources

Using second-harmonic frequency-resolved optical gating and a tricyanovinylaniline polymer thin film, we have measured the amplitude and the phase of mode-locked Ti:sapphire laser pulses as short as 13 fs. These thin films are ideally suited for ultrashort-pulse diagnostics because they eliminate the angle tuning associated with birefringent phase-matched crystals, minimize pulse distortions introduced by group-velocity dispersion, and exhibit excellent photochemical stability.

Molecular engineering of polymer films for amplitude and phase measurements of ti:sapphire femtosecond pulses

We describe a Ti:sapphire laser pumped directly with 445nm laser diodes. With 70 mW average power at 800 nm and bandwidth for <13 fs pulses, Kerr-lens-modelocked pulses are available with dramatically decreased pump cost.

G. Taft

Papers

16-fs, 1-microJ ultraviolet pulses generated by third-harmonic conversion in air.

Measurement of 10-fs laser pulses

Ultrafast laser and amplifier sources

Molecular engineering of polymer films for amplitude and phase measurements of ti:sapphire femtosecond pulses

Kerr-Lens Modelocked Ti:Sapphire Laser Oscillator Directly Pumped with Blue Diodes