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Oxford University Press eBooks

Basic Classical Concepts

Stephen Colby Rand

Published May 26, 2010• 0 citations
Publisher

Abstract

Chapter 1 is an extremely brief review of the elementary aspects of light as a classical electromagnetic wave. Maxwell's equations are outlined and the scalar wave equation is derived from them. Then the most basic features of the interaction of light with matter are considered, namely absorption and dispersion.
DOI
10.1093/acprof:oso/9780199574872.003.0001

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Thus far, we have developed the properties of the electromagnetic field at optical frequencies, based on Maxwell’s equations. These equations further give a classical macroscopic perspective on the coupling of the propagation media to the field, as presented in Chapter 2. The macroscopic properties of a medium are based on averaged microscopic properties. The microscopic energy structure of matter was presented in Chapter 3, covering gases, solids, and liquids by employing mostly quantum models. We now proceed to the next level of development, the dynamic description of the interaction between the optical field and the propagation medium as a function of the field frequency and propagation media variables (e.g., energy structure, temperature, and pressure). In this chapter, the classical electromagnetic field is coupled to discrete frequency oscillators via Newton’s equation of motion. This approach leads to the popular classical oscillator model, often presented in introductory books on lasers. The classical oscillator model is an incomplete theory and can be only a semiempirical model. In the next chapter, a more detailed and comprehensive approach, which also includes statistical and quantum mechanics, is used leading to robust semiclassical and quantum oscillator models. This chapter and the next are the basis for the applied models presented in Part II of this book. Classical electrodynamics is based on Maxwell’s equations, as given in Chapter 2, and the Lorentz force relation, as given below: . . . F = q[E + (v × B)]. (4.1) . . . These equations cover the classical description of the interaction of light and matter. The first term in Eq. 4.1 represents coupling of the electric field to the medium. As discussed in Chapter 2 (Section 2.2), the leading mechanism for this is the electric dipole moment. To see that this is the coupling mechanism in the first term, consider the potential function driving this force, F = −∇V(r) = −∇(−qr · E). The above expression contains the dipole moment, as defined in Chapter 2. The second term in Eq. 4.1 represents coupling of the magnetic field to the medium.
This chapter provides a brief overview of quantum mechanics and light. It begins with a discussion on the purpose and practice of spectroscopy, which involves the investigation of the interaction of light with matter. It then breaks down the nature of electromagnetic radiation, expounding on the classical theory of light before turning to photons and how they make up light. Next, the chapter elaborates on the properties of lasers and how these same remarkable properties are achieved largely from the process of stimulated emission. Afterward, the chapter presents the wave mechanical description of an atom, and considers the Schrödinger equation and the Hamiltonian operator. Lastly, angular momentum is explored.
The study of light through the centuries has produced a number of theories and experiments. Newton advanced the corpuscular theory, building on the early Greek view of matter composed of atoms. Then Young essentially proved the wave nature of light through the interference experiments. Maxwell provided the firm theoretical basis for the wave nature. During the late 1800s and early 1900s, further experiments showed predictions based on a continuous wave led to the well-known ultraviolet catastrophe. Plank and Einstein originated and developed the notion of the photon as an elementary quantum of propagating electromagnetic (EM) energy. The first half of the 20th century saw the development of the field quantization and the quantum electrodynamics (QED). Feynmann labeled QED as ‘‘the best theory we have’’ to describe the matter-light interaction. The second half of the 20th century witnessed the development of the coherent and squeezed optical states attributable to Glauber and Yuen. The study of light and electromagnetic fields has a long history. This chapter explores the nature of light in terms of quantum optics.
This textbook provides an accessible introduction to laser physics, exploring three key questions: What is special about laser light? What is the physics underlying its generation? And how can laser light be manipulated and used? The material is presented in a manner that helps the reader develop an understanding of the underlying physics principles and processes without getting bogged down in mathematical details, but there is enough mathematics for the understanding to be quantitative. The book begins by describing the special properties of laser light and focuses on the physics of light-matter interaction to understand how it acquires them. It builds upon Maxwells equations for light and the classical electron oscillator model for the atoms, augmented with a quantum mechanical picture of atomic energy levels, to provide an accurate physical understanding of light-matter interaction. This approach bypasses the need for a course in quantum theory. Derivations of key equations are included not only to help readers follow the development of the subject, but also to illustrate that to approximate, simplify, and get analytic results is integral to understanding any complex phenomenon. Subjects such as nonlinear pulse propagation and nonlinear optics are discussed, but only at a level that should help readers to get started in these fields. The choice of topics has been limited to atomic/molecular lasers to allow for their coverage in one semester-long course. Problems, references and illustrations are included throughout the book, making it an ideal textbook for advanced undergraduate and graduate physics and engineering students. Students do not require prior knowledge of physics much beyond an undergraduate-level introduction to electromagnetic theory, including Maxwell’s equations, polarization in atomic media and electromagnetic wave propagation. Key features: · Provides a qualitative and quantitative understanding of, and appreciation for, the special properties of laser light · Explores quantum statistics of laser light · Presents an analytical approach to pulse formation
A detectable nonlinear response between light and matter depends on one of two key ingredients: Either there is a resonance between the light wave and some natural oscillation mode of the material, or the light is sufficiently intense. In this chapter, the authors let the matter variables themselves play active roles and derive coupled nonlinear differential equations for the electric and matter fields. They outline the use of Schrodinger's equation to derive the Bloch equations, which describe the dynamics of the oscillators of matter and help to derive the Maxwell equation for the envelope of an almost monochromatic electromagnetic wave. The authors analyse the case of two distinct co- or counter-propagating waves interacting with a three-level medium where both waves excite separate quantum transitions sharing a common level. They also help to derive an effective two-level atom model that describes two-photon absorption and stimulated Raman scattering.