Introduction to Quantum Electronics and Nonlinear Optics

✍ Scribed by Vitaliy V. Shtykov, Sergey M. Smolskiy

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 341
• Edition: 1
• Category: Library

✦ Synopsis

This textbook, based on the authors’ class-tested material, is accessible to students at the advanced undergraduate and graduate level in physics and engineering. While its primary function is didactic, this book’s comprehensive choice of topics and its clear and authoritative synthesis of ideas make it a useful reference for researchers, device engineers, and course instructors who wish to consolidate their knowledge of this field. 

The book takes the semi-classical approach where light is treated as a wave in accordance with the classical Maxwell equations, while matter is governed by quantum theory. It begins by introducing the postulates and mathematical framework of quantum theory, followed by the formalism of the density matrix which allows the transition from microscopic (quantum) quantities to macroscopic (classical) ones. Consequently, the equations describing the reaction of matter to the electromagnetic field in the form of polarization, magnetization, and current are derived. These equations (together with the Maxwell equations) form the complete system of equations sufficient to model a wide class of problems surrounding linear and nonlinear interactions of electromagnetic fields with matter. The nonlinear character of the governing equations determines parameters of the steady-state mode of the quantum generator and is also demonstrated in harmonic generation via propagation of laser radiation in various media. The touchstone description of magnetic phenomena will be of interest to scientists who deal with applications of magneto-resonance phenomena in biology and medicine. 

Other advanced topics covered include electric dipole transitions, magnetic dipole transitions, plasma transitions, and the devices that can be based on these and other electro-optical and nonlinear-optical systems. This textbook features numerous exercises, some of which are investigatory and some of which require computational solutions.

✦ Table of Contents

Preface
Acknowledgements
Introduction
Eq. 1. Historical Information
Eq. 2. Methodical Conception of this Book
Contents
About the Authors
Chapter 1: Excursus on the Atomic-Molecular Theory of Substance
1.1 Introduction: Corpuscular-Wave Dualism
1.2 Postulates of Quantum Mechanics
1.2.1 The First Postulate
1.2.2 The Second Postulate
1.2.3 The Third Postulate
1.2.4 The Fourth Postulate
1.2.5 The Fifth Postulate
1.3 Operator Properties of Observable Variables
1.3.1 The Form of Operators of Some Observable Variables
1.3.2 Properties of Operator Eigenfunctions of Observable Variables
1.3.3 The Condition of Joint Accurate Measurability of Two Variables
1.4 Electron States of Atoms
1.4.1 The Time-Independent Schrödinger Equation
1.4.2 Stationary States of the Single-Electron Atom
1.4.3 Spin of Electrons and Other Particles
1.5 Molecules
1.6 Vibrational and Rotational States of Molecules
1.6.1 The Vibrational Spectrum
1.6.2 The Rotational Spectrum
1.6.3 Total Energy Diagram of the Molecule
1.7 Internal Structure of the Solid Body
1.8 Band Theory of the Solid Body
1.9 Motion of the Electron in an Applied Field: The Effective Mass
1.10 Matrix Formulation of Quantum Mechanics
1.10.1 Wave Functions in the Matrix Representation
1.10.2 Representation of Operators as Matrices
1.11 Description of Particle Ensembles by the Density Matrix
1.11.1 The Density Matrix
1.11.2 The Density Matrix in the Case of a Continuous Spectrum of Eigenvalues
1.12 The Fermi-Dirac and Bose-Einstein Statistics
1.12.1 The Density Matrix in the State of Thermodynamic Equilibrium
1.12.2 Invisibility of Identical Particles and the Pauli Principle
1.12.3 Equilibrium Distribution of the State Population
1.12.4 The Equilibrium Distribution Function for Translational Motion of Fermions
1.13 Problems for Chapter 1
Chapter 2: Interaction of Electric Dipoles
2.1 Introduction: Multipole Expansion of Radiation Energy and Medium Interaction
2.2 Equation for the Density Matrix of a Two-Level System
2.3 Electric Dipole Transitions
2.4 Polarization and Population Difference for Electric Dipole Interactions
2.5 Linear Interaction of an Electromagnetic Field with a Substance
2.6 The Spectral Absorption Line Shape
2.7 Kramers-Kronig Relations
2.8 Anisotropy of the Medium
2.9 Influence of Crystal Symmetry on the View of Material Tensors
2.10 Crystal Symmetry
2.11 The Form of the Linear Dielectric Susceptibility Tensor
2.12 The Saturation Effect
2.13 Problems for Chapter 2
Chapter 3: Magnetic Dipole Interaction
3.1 Introduction: The Magnetic Dipole Moments of Particles
3.2 Magnetic Dipole Transitions
3.3 Pauli Matrices
3.4 Bloch Equations
3.5 Paramagnetism
3.6 Ferromagnetism
3.7 Domains and the Hysteresis Curve
3.8 Magnetic Resonance
3.9 Electron Paramagnetic Resonance
3.10 Nuclear Magnetic Resonance
3.11 Ferromagnetic Resonance
3.12 The Faraday Effect
3.13 Problems for Chapter 3
Chapter 4: Field Interaction with ``Free Charges´´
4.1 Introduction: The Interzone and Fundamental Absorption
4.2 The Kinetic Equation
4.2.1 Statistics of Nonequilibrium States
4.2.2 The Classical Approach to Derivation of the Kinetic Equation
4.2.3 The Collision Integral
4.3 Current Density and Average Energy of Charge Carriers in Plasma
4.3.1 Equation for Current Density
4.3.2 Equation for Electron Energy in Plasma
4.4 Linear Interaction of an Electric Field with Plasma
4.5 Cyclotron Resonance
4.6 Fundamental Absorption
4.7 Other Mechanisms of Absorption
4.8 The Nonequilibrium State of Semiconductors
4.9 Problems for Chapter 4
Chapter 5: Quantum Amplifiers and Generators
5.1 Introduction: Population Inversion
5.2 Linear Amplification of Electromagnetic Waves
5.3 Regenerative Amplification
5.4 Influence of the Saturation Effect on Quantum Amplifier Features
5.5 Self-Excitation Conditions and the Power of Continuous Oscillations
5.6 Steady-State Mode Equations for a Quantum Generator
5.7 Equations for Oscillations in the Resonator
5.8 The Small-Oscillation Mode
5.9 Abbreviated Equations for a Quantum Generator
5.10 Dynamics of a Single-Mode Quantum Generator
5.11 The Multimode Regime: Mode Synchronization
5.12 Problems for Chapter 5
Chapter 6: Nonlinear Interaction of Electromagnetic Waves with a Substance
6.1 Introduction: Methods for Analysis of Nonlinear Interaction of Electromagnetic Waves with a Medium
6.2 Phenomenological Description of Nonlinear Effects
6.3 Classification of Nonlinear Effects
6.4 Cubic Nonlinear Effects
6.5 Nonlinear Absorption
6.6 The Kerr Optical Effect
6.7 The Self-Focusing Phenomenon
6.8 Optical Bistability
6.9 Generation of the Third Harmonic: Multiphoton Processes
6.10 Phase Conjugation
6.11 Quadratic Nonlinear Effects: Generation of the Second Harmonic
6.12 The Linear Electro-optical Effect
6.13 The Electro-optical Amplitude Modulator
6.14 Coupling Mode Equations
6.15 Parametric Amplification: The Parametric Generator
6.16 Problems for Chapter 6
Chapter 7: Some Types of Quantum Generators and Amplifiers
7.1 Introduction: Classification of Quantum Devices
7.2 Gas Quantum Generators and Amplifiers
7.2.1 Quantum Generators Based on Molecular Beams
7.2.2 Gas Lasers
7.3 Solid-State Quantum Devices
7.3.1 Quantum Paramagnetic Amplifiers
7.3.2 Solid-State Lasers
7.4 Semiconductor Lasers
7.5 Liquid Lasers
7.6 Quantum Generators Based on Free Electrons
7.7 Atomic Standards of Frequency and Time
Appendixes
Appendix 1: Fundamental Constants
Appendix 2: Relations Between Physical Quantities´ Values in Different Unit Systems
Appendix 3: Designation of Planes and Directions in a Crystal
Appendix 4: Point Groups of Symmetry
Appendix 5: Tensors of Magnetic Susceptibility
Appendix 6: Properties of Some Semiconductor Crystals
Appendix 7: Tensors of Quadratic Susceptibility
Appendix 8: Cubic Nonlinearity in an Isotropic Medium
Index