This chapter provides the essential concepts of compressive sensing (CS), also called compressed sensing, compressive sampling, or sparse sampling. A basic knowledge of signal processing is assumed. The treatment is rigorous but limited: more details can be found on the recommended textbooks given at the end of the chapter.

Supercontinuum generation is a nonlinear optical process that produces a broad continuous spectrum, often spanning over an octave, when an intense laser beam of an initially narrow bandwidth propagates through a nonlinear medium. Given a sufficiently high laser power, supercontinuum generation can be observed in any material. In general, many nonlinear processes are involved, including self-phase modulation, cross-phase modulation, four-wave mixing, modulation instability, self-focusing, stimulated Raman scattering, soliton dynamics, and dispersive wave generation. The specific nonlinear optical processes that are involved depend on the optical properties of the material and on the wavelength and the temporal characteristics of the laser beam. The usage of optical fibers greatly facilitated the development of supercontinuum generation because an optical fiber provides the favorable combination of both high intensity and long interaction length for efficient supercontinuum generation.

Optical nonlinearity manifests nonlinear interaction of an optical field with a material. The origin of optical nonlinearity is the nonlinear response of electrons in a material to an optical field. Macroscopically, the nonlinear optical response of a material is described by an optical polarization that is a nonlinear function of the optical field. This optical polarization is obtained through density matrix analysis by using the interaction Hamiltonian, which can be approximated with electric dipole interaction in most cases. When the interaction Hamiltonian is small compared to the Hamiltonian of the system, it can be treated as a perturbation to the system by expanding the density matrix in a perturbation series and the total optical polarization in terms of a series of polarizations. In most nonlinear optical processes of interest, the perturbation expansion of the polarization is valid and only the three terms of linear, second-order, and third-order polarizations are significant. The perturbation expansion is not valid in the cases of high-order harmonic generation and optical saturation. Then, a full analysis is required.

There are basically two types of nonlinear optical frequency converters. The majority are based on parametric processes, which require phase matching. Devices that use the nonparametric third-order processes of stimulated Raman or Brillouin scattering to shift the optical frequency are the other type. In this chapter, only those based on parametric processes are considered. The first six sections cover practical optical frequency converters that are based on second-order parametric processes, including second-harmonic generation, sum-frequency generation, difference-frequency generation, optical parametric up-conversion, optical parametric down-conversion, optical parametric amplification, optical parametric generation, and optical parametric oscillation. Frequency conversion based on the third-order parametric four-wave mixing of small frequency shifts is discussed in Section 10.7. The generation of high-order harmonics is discussed in Section 10.8.

This chapter collects a series of problems and solutions spanning all the sections of this book.

The noise performance and the main characteristics of electronics devices and elementary building blocks have been discussed in earlier chapters. Here, more complex techniques for sensing interfaces are presented. Architectures tailored for specific cases such as resistive and capacitive sensing are analyzed. Furthermore, modulation, feedback, and time-to-digital techniques for signal detection are shown.

The purpose of this chapter is to set up the framework on which the book will be shaped up and it is intentionally based on informal descriptions of concepts. This is obviously a nonrigorous approach but is a fundamental step toward an abstraction process about artificial sensing: what are the ideas behind the general definition of sensors, their main performance limiting processes and essential tradeoffs. Using this inductive approach, we will first define concepts, leaving the formalization to the next chapters of the book. However, if the reader is facing this field for the first time, the argumentation could appear vague and fuzzy; therefore this first chapter should be read again after the rest of the book as the last one.

This chapter starts by first describing techniques to reduce errors. As far as the random ones are concerned, reduction approaches oriented to increase the signal-to-noise ratio on the spectrum domain and their strict relationship with sample averaging are discussed. Following, strategies for limitation of systematic errors are presented, especially based on the feedback concept. However, since the error reduction techniques allow several degrees of freedom, this chapter discusses the tradeoffs in optimizing sensing systems from the resolution, bandwidth, and power consumption point of view. More specifically, the resolution optimization of the sensing process is treated under the information theory point of view and the approach is extended to acquisition chains to understand the role of single building blocks.

Ionic–electronic transduction is at the base of biosensing. We start by addressing some basic principles emphasizing the common background between the electronic and ionic behavior on the base of some classical statistical mechanics concepts. Then, we focus on more specific examples of application in this framework. Of course, the covered examples are only a very small part of the subject and are intended as proof of application to consider the transduction process in the electronic design of biosensor interfaces.

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.