In a nonlinear process of multiphoton absorption, the multiple photons are simultaneously absorbed. These photons can have either the same photon energy or different energies. This chapter begins with a general discussion of multiphoton absorption. The simplest of multiphoton absorption is two-photon absorption. It is a third-order nonparametric nonlinear optical process, in which two photons of the same or different photon energies are simultaneously absorbed. By comparison, three photons of the same or different photon energies are simultaneously absorbed in three-photon absorption, which is a fifth-order nonparametric nonlinear optical process. The detailed characteristics of the typical scenarios of two-photon absorption and three-photon absorption are discussed in this chapter.

Practical electro-optic modulators are based on the Pockels effect. The electro-optic effects are generally discussed in the first section, and the Pockels effect is specifically addressed in the second section. The operational principles and characteristics of basic electro-optic modulators, including phase modulators, polarization modulators, and amplitude modulators, are discussed in the third section. In the fourth section, the structures, principles, characteristics, and advantages of guided-wave electro-optic modulators are discussed and shown through the forms of some well-established device structures, including Mach–Zehnder waveguide interferometers, directional coupler switches, polarization-mode converters, and traveling-wave modulators.

Many techniques have been developed for the generation of laser pulses over a wide range of pulsewidths from the order of milliseconds to femtoseconds. The generation of a laser pulse is inherently a nonlinear optical process because all of the techniques utilize some form of optical nonlinearity that is coupled to the dynamics of a laser. In this chapter, the basic concepts of the primary techniques for the generation of laser pulses are covered, including gain switching, active and passive Q switching, active and passive mode locking, and synchronous pumping.

A brief introductory chapter puts synchrotron radiation in the context of other radiation sources, includes a short historical survey of particle accelerators and then provides an introduction of the origins and basic theory of synchrotron radiation.

Chapter 4 describes the range of methods used to determine the atomic scale structure of crystalline solids based on X-ray diffraction. It includes a brief introduction to the basic theory of X-ray diffraction but focuses on applications that go beyond those achievable using conventional laboratory X-ray sources. Extensions of the methods to study the structure of surfaces are also included

Chapter 3 describes the key components of the beamlines that deliver synchrotron radiation to experimental users. These include the use of mirrors and other focusing optical components to direct the radiation and monochromators for both the X-ray and vacuum ultraviolet spectral ranges.

Chapter 2 provides a detailed description of synchrotron radiation sources including both bending magnets and insertion devices (wigglers and undulators), describing key properties such as the time structure, polarisation, emittance and spectral brightness, and coherence. Key aspects of the constraints that define the source design and the resulting properties are presented. The chapter includes some comparison with free electron lasers and the associated radiation properties.

Chapter 8 introduces the use of synchrotron radiation for imaging and micro- and nano-analysis, a field that is of growing importance at modern synchrotron radiation facilities. The methods include transmission microscopy and tomography (using both hard and soft X-rays) and a range of methods providing spatially-resolved spectroscopic information based on photoemission, photoabsorption and X-rayfluorescence. Finally two very different methods based on X-ray diffraction are described, namely the very well-established method of X-ray diffraction topography, but the much more modern technique of coherent X-ray diffraction imaging for 'lens-less' imagingdown to the nanoscopic scale.

Chapter 7 is a short chapter describing some methods to investigate the vibrational structure of materialsusing infrared radiation and extremely high resolution inelastic X-ray scattering.

Chapter 6 describes a range of methods to determine different aspects of the electronic structure of materials. These include both core level photoemission (and the associated 'chemical' shifts) and valence band photoemission, notably including angle-resolved photoelectron spectroscopy (ARPES). The use of X-ray absorption near-edge structures (XANES) and the related technique of X-ray magnetic circular dicroism (XMCD) using circularly-polarised radiation is also described, as is the use of X-ray emission spectroscopy (XES) and resonant inelastic X-ray scattering (RIXS) and Compton scattering. Finally, the use of photoemission and photoionisation to investigate gas-phase molecular structure is described.