The study of optical effects in active media is rich with unexpected consequences. For instance, one may imagine that absorption and amplification in a dielectric medium will exhibit some sort of symmetry because both are related to the same imaginary part of the dielectric constant, except for a sign change. It turns out that such a symmetry does not exist [1]. This issue has also been investigated in detail for random or disordered gain media, with varying viewpoints [2]. Traditionally, much of the research on amplifying media has considered the interaction of light within the entire volume of such a medium. Recent interest in metamaterials and other esoteric structures in which plasmons are used to manipulate optical signals has brought attention to the role of surface waves in active dielectrics [3, 4]. From a fundamental perspective, the main difference between active and passive media is that spontaneous emission cannot be avoided in gain media. As a result, a rigorous analysis of gain media demands a quantum-mechanical treatment. Spontaneous emission in a gain medium depends not only on the material properties of that medium but also on the optical modes supported by the structure containing that material [5]. By a clever design of this structure (e.g., photonic crystals or microdisk resonators with a metallic cladding), it is possible to control the local density of optical modes and the spontaneous emission process itself. In Chapter 4, we discuss how to model a gain medium under such conditions by deploying optical Bloch equations.
The study of optical effects in active media is rich with unexpected consequences. For instance, one may imagine that absorption and amplification in a dielectric medium will exhibit some sort of symmetry because both are related to the same imaginary part of the dielectric constant, except for a sign change. It turns out that such a symmetry does not exist [1]. This issue has also been investigated in detail for random or disordered gain media, with varying viewpoints [2]. Traditionally, much of the research on amplifying media has considered the interaction of light within the entire volume of such a medium. Recent interest in metamaterials and other esoteric structures in which plasmons are used to manipulate optical signals has brought attention to the role of surface waves in active dielectrics [3, 4]. From a fundamental perspective, the main difference between active and passive media is that spontaneous emission cannot be avoided in gain media. As a result, a rigorous analysis of gain media demands a quantum-mechanical treatment. Spontaneous emission in a gain medium depends not only on the material properties of that medium but also on the optical modes supported by the structure containing that material [5]. By a clever design of this structure (e.g., photonic crystals or microdisk resonators with a metallic cladding), it is possible to control the local density of optical modes and the spontaneous emission process itself. In Chapter 4, we discuss how to model a gain medium under such conditions by deploying optical Bloch equations.
Over the past two decades, optical amplifiers have become of key importance in modern communications. In addition to this, the technology has applications in cutting-edge research such as biophotonics and lab-on-a-chip devices. This book provides a comprehensive treatment of the fundamental concepts, theory and analytical techniques behind the modern optical amplifier technology. The book covers all major optical amplification schemes in conventional materials, including the Raman and parametric gain processes. The final chapter is devoted to optical gain in metamaterials, a topic that has been attracting considerable attention in recent years. The authors emphasize analytical insights to give a deeper, more intuitive understanding of various amplification schemes. The book assumes background knowledge of electrical engineering or applied physics, including exposure to electrodynamics and wave motion, and is ideal for graduate students and researchers in physics, optics, bio-optics and communications.
A rigorous description of the light–matter interaction requires the use of quantized Maxwell equations to describe the light field and the Schrödinger equation to describe the material medium. This book does not attempt to deal with quantum optical problems that necessitate a field quantization. Instead we focus on properties that are generally grouped under the umbrella of nonlinear optics . Although many definitions of this expression exist, we use it in the sense that the properties we deal with do not depend in a crucial way on the field quantization. For practical purposes, this means in general that the average photon number is large and that we can neglect spontaneous emission as a dynamical process. Rather, we include the consequence of spontaneous emission, that is, the instability of the atomic levels, in a purely phenomenological way. When this is done, we call the material equations the Bloch equations instead of the Schrödinger equation. References [1] through [4] are the classical textbooks that contain a tentative justification for the transition from the Schrödinger to the Bloch equations. None of these attempts is satisfactory from a fundamental viewpoint because the real difficulty is to incorporate the finite lifetime (or natural linewidth) of the atomic energy levels in the Schrödinger equation. This remains an open problem as of now. The Maxwell–Schrödinger equations We consider atoms interacting with an intense electromagnetic field. By intense we mean a field for which the quantization is not necessary.
The analysis in Chapter 3 used a phenomenological form of the permittivity to describe active materials. A proper understanding of optical amplification requires a quantum-mechanical approach for describing the interaction of light with atoms of an active medium [1]. However, even a relatively simple atom such as hydrogen or helium allows so many energy transitions that its full description is intractable even with modern computing machinery [2, 3]. The only solution is to look for idealized models that contain the most essential features of a realistic system. The semiclassical two-level-atom model has proven to be quite successful in this respect [4]. Even though a real atom has infinitely many energy levels, two energy levels whose energy difference nearly matches the photon energy suffice to understand the interaction dynamics when the atom interacts with nearly monochromatic radiation. Moreover, if the optical field contains a sufficiently large number of photons (> 100), it can be treated classically using a set of optical Bloch equations. In this chapter, we learn the underlying physical concepts behind the optical Bloch equations. We apply these equations in subsequent chapters to actual optical amplifiers and show that they can be solved analytically under certain conditions to provide a realistic description of optical amplifiers. It is essential to have a thorough understanding of the concept of a quantum state [5]. To effectively use the modern machinery of quantum mechanics, physical states need to be represented as vectors in so-called Hilbert space [6].
Over the past two decades, optical amplifiers have become of key importance in modern communications. In addition to this, the technology has applications in cutting-edge research such as biophotonics and lab-on-a-chip devices. This book provides a comprehensive treatment of the fundamental concepts, theory and analytical techniques behind the modern optical amplifier technology. The book covers all major optical amplification schemes in conventional materials, including the Raman and parametric gain processes. The final chapter is devoted to optical gain in metamaterials, a topic that has been attracting considerable attention in recent years. The authors emphasize analytical insights to give a deeper, more intuitive understanding of various amplification schemes. The book assumes background knowledge of electrical engineering or applied physics, including exposure to electrodynamics and wave motion, and is ideal for graduate students and researchers in physics, optics, bio-optics and communications.
Nonlinear optics is the study of the response of dielectric media to strong optical fields. The fields are sufficiently strong that the response of the medium is, as its name implies, nonlinear. That is, the polarization, which is the dipole moment per unit volume in the medium, is not a linear function of the applied electric field. In the equation for the polarization, there is a linear term, but, in addition, there are terms containing higher powers of the electric field. This leads to significant new types of behavior, one of the most notable being that frequencies different from that of the incident electromagnetic wave, such as harmonics or subharmonics, can be generated. Linear media do not change the frequency of light incident upon them. The first observation of a nonlinear optical effect was, in fact, second-harmonic generation – a laser beam entering a nonlinear medium produced a second beam at twice the frequency of the original. Another type of behavior that becomes possible in nonlinear media is that the index of refraction, rather than being a constant, is a function of the intensity of the light. For a light beam with a nonuniform intensity profile, this can lead to self-focusing of the beam. Most nonlinear optical effects can be described using classical electromagnetic fields, and, in fact, the initial theory of nonlinear optics was formulated assuming the fields were classical. When the fields are quantized, however, a number of new effects emerge. Quantized fields are necessary if we want to describe fields that originate from spontaneous emission. For example, in a process known as spontaneous parametric down-conversion, a beam of light at one frequency, the pump, produces a beam at half the original frequency, the signal. This second beam is a result of spontaneous emission.
Light propagation in matter is described by vibration eigenstates, called modes, which characterize the light-matter interaction. In the specific case of random media, according to the strength of the disorder, the modes can be either extended over the whole system or spatially localized. This disorder-based confinement is called Anderson’s localization.In the first part, we introduce basic notions used along this manuscript. In particular the light-matter interaction requires a semiclassical approach: The electromagnetic field is described by Maxwell’s equations while the quantum nature of matter must be considered. In this thesis open media are studied. In such systems the modal description requires a specific analytic treatment different from closed problems. In the second part, we focus on Anderson-localized modes in open passive random media. Any change of the disorder induces modifications of modes. Therefore, it enables the control over the light properties. Moreover, when inserting an emitter inside an Anderson-localized mode, strong light-matter interaction regimes can be reached. In the third part, active random media, commonly called random lasers, are introduced. Using our experimental achievements, characteristics of random lasers are presented. The notion of mode enables us to describe complex mechanisms involved in the lasing emission. Last, we demonstrate both experimentally and numerically that a non-uniform excitation of random lasers can lead to a control of the properties of the emission. In particular a multimode spectrum for a uniform pumping can be turned into single-mode using an adapted pumping.