Optical Resonance and Two-Level Atoms

L. Allen, J. H. Eberly, J. H. Eberly

• Publisher: Dover Publications
• Year: 2012
• Print ISBN: 9780486655338
• eBook ISBN: 9780486136172
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

"Coherent and lucid…a valuable summary of a subject to which [the authors] have made significant contributions by their own research." — Contemporary Physics
Offering an admirably clear account of the basic principles behind all quantum optical resonance phenomena, and hailed as a valuable contribution to the literature of nonlinear optics, this distinguished work provides graduate students and research physicists probing fields such as laser physics, quantum optics, nonlinear optics, quantum electronics, and resonance optics an ideal introduction to the study of the interaction of electromagnetic radiation with matter.
The book first examines the applicability of the two-level model for atoms to real atoms, then explores semiclassical radiation theory, and derives the optical Bloch equations. It then examines Rabi inversion, optical nutation, free-induction decay, coherent optical transient effects, light amplification, superradiance, and photon echoes in solids and gases.
Before the publication of this book, much of the material discussed was widely scattered in other books and research journals. This comprehensive treatment brings it together in one convenient resource. The style of writing is clear and informal and the emphasis throughout is always on the physics of the processes taking place. There are numerous helpful illustrations, excellent introductions to each chapter, and lists of references for further reading.
"The authors have endeavored to create a primer for the field of optical resonance…they have succeeded admirably. Their coverage of the subject is remarkably complete." — IEEE Journal of Quantum Electronics

CHAPTER 1

Classical Theory of Resonance Optics

1.1 Introduction

1.2 The Linear Dipole Oscillator

13 The Classical Rabi Problem

1.4 Emission Lineshape and Linewidth

1.5 Free Induction Decay

1.6 Electromagnetic Wave Propagation

1.7 The Classical Area Theorem

1.8 Anomalous Classical Absorption

References

1.1 INTRODUCTION

The classical theory of the linear interaction of light with matter was largely the creation of H. A. Lorentz. It was Lorentz who systematically explored the idea that optical phenomena in general arise from the motion of elementary charges and dipoles that are more or less free to respond to the electric and magnetic fields associated with light waves. This view is now regarded as so obviously the correct one that it serves as the starting point of every modern study of optical properties of dielectrics.

From a practical point of view, the classical Lorentzian theory requires modifications only in the most extreme circumstances. The classical Rayleigh and Thomson optical scattering formulas do not need to be supplanted by the quantum mechanical Compton formula until the scattered light has its wavelength well into the X-ray region. Furthermore, classical Lorentzian dispersion and absorption formulas reappear in quantum mechanical treatments, and were first derived quantum mechanically by Kramers and Heisenberg simply by applying correspondence principle arguments to the classical expressions. Only for fields which are so intense as to excite intrinsic atomic nonlinearities will there be appreciable departures from the predictions of the Lorentz-Kramers-Heisenberg dispersion theory.

With the assumption that the Lorentzian oscillating-electron approach and its standard results are familiar, we devote the following sections in this chapter to a review of Lorentzian theory in unconventional notation. This is done for two reasons. First, it will be useful to have the classical formulas at hand for comparison with the quantum mechanical expressions derived in later chapters. In this way it will be clear just how much of any given result is, in fact, quantum mechanical. Second, by introducing in an entirely classical context the notation, the near-resonance approximations, and a number of the physical phenomena to be dealt with later, we hope they will not appear puzzling or strange when encountered again. Thus, in this first chapter, the so-called Rabi problem, free induction decay, an “area” theorem, and ultrashort pulses are all discussed in addition to the standard formulas for index of refraction and attenuation coefficient.

1.2 THE LINEAR DIPOLE OSCILLATOR

According to Lorentz, the majority of optical phenomena can be accounted for by the interaction of electric charges with the electromagnetic field [1]. We begin by assuming that these charges are bound into neutral atoms, and that they oscillate about their equilibrium positions with very small amplitudes. That is, each electron-ion pair behaves as a simple harmonic oscillator, which cou...

Table of contents

• DOVER BOOKS ON PHYSICS
• Title Page
• Copyright Page
• Dedication
• Preface
• Related Books and Reviews
• Table of Contents
• CHAPTER 1 - Classical Theory of Resonance Optics
• CHAPTER 2 - The Optical Bloch Equation
• CHAPTER 3 - Two-Level Atoms in Steady Fields
• CHAPTER 4 - Pulse Propagation
• CHAPTER 5 - Pulse Propagation Experiments
• CHAPTER 6 - Saturation Phenomena
• CHAPTER 7 - Quantum Electrodynamics and Spontaneous Emission
• CHAPTER 8 - N-Atom Spontaneous Emission and Superradiant Decay
• CHAPTER 9 - Photon Echoes
• Index