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Lasers are the basic building block of the technologies for the generation of short light pulses. Only two decades after the laser had been invented, the duration of the shortest produced pulse had shrunk down six orders of magnitude, going from the nanosecond regime to the femtosecond regime. “Light amplification by stimulated emission of radiation” is the misleading meaning of the word “laser”.The real instrument is not only an amplifier but also a resonant optical cavity implementing a positive feedback between the emitted light and the amplifying medium. A laser also needs to be fed with energy of some sort.

Optics is the field of physics which comprises knowledge on the interaction between light and matter. When the superposition principle can be applied to electromagnetic waves or when the properties of matter do not depend on the intensity of light, one speaks of linear optics. This situation occurs with regular light sources such as light bulbs, low-intensity light-emitting diodes and the sun. With such low-intensity sources the reaction of matter to light can be characterized by a set of parameters such as the index of refraction, the absorption and reflection coefficients and the orientation of the medium with respect to the polarization of the light. These parameters depend only on the nature of the medium. The situation changed dramatically after the development of lasers in the early sixties, which allowed the generation of light intensities larger than a kilowatt per square centimeter. Actual large-scale short-pulse lasers can generate peak powers in the petawatt regime. In that large-intensity regime the optical parameters of a material become functions of the intensity of the impinging light. In 1818 Fresnel wrote a letter to the French Academy of Sciences in which he noted that the proportionality between the vibration of the light and the subsequent vibration of matter was only true because no high intensities were available. The intensity dependence of the material response is what usually defines nonlinear optics.

After the considerations developed in the preceding chapter, it seems contradictory, a priori, to generate ultrashort pulses with a laser source, because of the frequency selection imposed by the laser cavity. Indeed, the Fourier transform of an extremely short light pulse is spectrally very broad. Yet, a laser cavity will allow oscillation in only a few very narrow frequency domains around the discrete resonance frequencies ν _q = qc/2 L (where q is an integer, c the speed of light and L the optical length of the laser cavity). Therefore a laser cannot deliver ultrashort pulses while functioning in its usual regime, in which the cavity plays the part of a frequency selector. However, it has been shown in Chap.1 that when a laser operates in its most usual regime, it oscillates simultaneously over all the resonance frequencies of the cavity for which the unsaturated gain is greater than the cavity losses. These frequencies make up the set of longitudinal modes of the laser. While operating in the multimode regime, the output intensity of the laser is no longer necessarily constant with time. Its time distribution depends essentially on the phase relations existing between the different modes, as illustrated by the simulation in Fig.3.1. Figure 3.1a shows the intensity of oscillation of a single mode, Fig.3.1b that of the resultant intensity of two modes in phase, and Figs.3.1c and d that of eight modes. In the case of Fig.3.1c, where the phase differences between the modes were chosen randomly, the time distribution of the intensity shows a random distribution of maxima. In the case of Fig.3.1d, the eight modes oscillate with the same initial phase, and the time distribution shows a periodic repetition of a wave packet resulting from the constructive interference of the eight modes.

Up to the beginning of the sixties, the shortest measurable time duration was of the order of one nanosecond (10^−9 s). Short pulses were produced through the generation of short electrical discharges. After the laser was invented in 1960, the situation quite rapidly changed. In 1965, the picosecond (10^−12 s) regime was reached by placing a saturable absorber inside a laser cavity. Twenty years of continuous progress led to the production of light pulses of less than 10 femtoseconds. In the race towards ever shorter pulses, recent developments in the generation of tabletop X-ray lasers have opened the way to dynamical studies in the attosecond (10^−18 s)regime [4.1-2]. In the meantime, progress was made on the tunability of the pulsed-laser sources. Today’s tunability extends from the near ultraviolet to the near infrared [4.2-6].

Semiconductor (SC) lasers are widely used as coherent light sources in many applications. Their pulsed operation is particularly attractive in the fields of optical sampling, optical spectroscopy and telecommunications. SC lasers have very different characteristics compared to conventional atomic or molecular laser sources [5.1,2 ]. We recall here briefly the main features of SC lasers [5.3]: very small size (300 × 300 × 100 μm^3 typically); high efficiency (up to 50 %in commercial devices); for instance, an optical output power P_opt. of 100 mW for an electric input power of 2 V ×100 mA; low prices thanks to the performance of semiconductor fabrication technology.

Up to this point in this book, we have dealt successively with the basics of producing ultrashort laser pulses and the main types of laser sources that make it possible to generate these pulses. However, for a given laser system the pulse duration, wavelength and energy are, in practice, fixed. But specific applications may require one to change the pulse duration, or to get more energy or even generate pulse replicas at different wavelengths. This chapter will present various ways to compress or stretch femtosecond optical pulses, amplify them or change their wavelength. This description is not aimed at an exhaustive description of all the various techniques or technologies used in these fields, but more as an introduction to these techniques based on particular examples.

In the previous chapter we showed how to produce and how to manipulate ultrashort laser pulses.But before such pulses are used for experiments, it is necessary to characterize these pulses properly to determine the experimental conditions. This chapter deals with such characterization.

In the previous chapters of this book, we dealt with ultrashort laser pulses by themselves, without paying attention to their possible uses. Since you are now familiar with the methods of generation of ultrashort laser pulses, with their manipulation and with the associated difficulties, it is now time to consider an important topic: what can we do with these ultrashort laser pulses?.

Femtosecond spectroscopy aims at characterizing the dynamics of elementary excitations in material systems. One of the most common experimental techniques, spectrally resolved pump-probe spectroscopy, may in some cases present artifacts, the so-called coherent effects , which make data interpretation less straightforward than the incoherent picture would lead one to believe. It is therefore desirable to be able to rely on a theoretical model in order to assess the importance of coherent effects in these experiments. In this chapter, we will introduce such a formalism, which will also help in the discussion of other experimental techniques, such as photon echo, wave-packet excitation, and multidimensional spectroscopy.

As was shown in previous chapters, the large peak intensities associated with femtosecond laser pulses make them well suited to nonlinear wave-mixing processes, allowing the generation of new colors. Such processes include second-harmonic generation, sum-frequency generation, parametric oscillation and amplification, and continuum generation. However, there is yet another route for generating new frequencies, which relies on a quite different approach. It is actually based on a very old technique, first developed by Hertz in the last century: a transient polarization or current surge, occurring for example in a spark, will act as a source term in the Maxwell equations and radiate a pulsed electromagnetic wave. If the polarization transient does not exhibit any well-defined oscillatory feature but is, rather, a rapid change such as a step or a pulse, then the radiated wave has no well-defined frequency. Its spectrum will therefore be extremely broad and will peak at a frequency inversely proportional to the timescale of the transient. Because all these frequency components are emitted in phase, this technique is very well suited to the generation of broadband coherent radiation at the lower end of the electromagnetic spectrum.