Light–Matter Interaction

Preface
Light–Matter Interaction
Contents
Main Abbreviations and Symbols
Survey of Constants
Part ISelected Facets of the Light–Matter Interaction in Classical Physics
1 Introduction
1.1 Some Characteristic Dimensions
1.2 The Organization of This Book
1.3 A Remark on Calculations
1.4 Two Useful Integrals
1.5 Tasks for Self-check
References
2 Simplest Model Treatment of the Classical Interaction of Light with Matter
2.1 Starting Point
2.2 Physical Idea
2.3 Theoretical Considerations
2.3.1 On the Two-Body System
2.3.2 The Classical Picture of Light Absorption
2.3.3 The Classical Picture of Light Emission
2.4 Consistency Considerations
2.5 Application to Practical Problems
2.5.1 Simple Classical Estimation of the Frequency of Nuclei Vibration in a Diatomic Molecule
2.5.2 Classical Estimation of the Vibration Frequency of a Valence Electron in an Atom or Molecule
2.5.3 Classical Estimation of the Characteristic Angular Frequency of the Rotation of a Diatomic Molecule
2.6 Advanced Material: Doppler Broadening in Gases
2.7 Tasks for Self-check
References
Part IIA Pedestrian’s Guide to Quantum Mechanics
3 Waves as Particles and Particles as Waves
3.1 Starting Point
3.2 Physical Idea
3.2.1 Energy and Momentum of „Light Particles“
3.2.2 Phase and Group Velocities
3.3 Theoretical Considerations
3.3.1 Waves as Particles
3.3.2 Particles as Waves
3.4 Consistency Considerations
3.5 Application to Practical Problems
3.5.1 The Compton Effect
3.5.2 Absorption of a Photon by an Initially Resting Atom
3.5.3 Emission of a Photon by an Initially Resting Atom
3.5.4 Radiation Pressure
3.6 Advanced Material: Wave Packet Distortion
3.7 Tasks for Self-check
References
4 The Schrödinger Equation and Model System I
4.1 Starting Point
4.2 Physical Idea
4.3 Theoretical Considerations
4.3.1 The Time-Independent Schrödinger Equation
4.3.2 The Free Particle
4.3.3 Model System I: Particle in a Box
4.4 Consistency Considerations
4.5 Application to Practical Problems
4.5.1 Size Effects
4.5.2 Color Centers in Ionic Crystals
4.5.3 Organic Chain Molecules with Conjugated Double Bonds
4.6 Advanced Material
4.6.1 Densities of States
4.6.2 Quantum Tunneling
4.6.3 Model Potential for Describing the α-decay in Nuclear Physics
4.7 Tasks for Self-check
References
5 Operators in Quantum Mechanics and Model System II
5.1 Starting Point
5.2 Physical Idea
5.3 Theoretical Considerations
5.3.1 General Properties of the Wavefunction
5.3.2 Continuity Equation and Probability Current Density
5.3.3 Relevant Properties of Linear Operators
5.3.4 Operators with Joint Eigenfunctions
5.3.5 Quantum Mechanical Expectation Values
5.3.6 Ehrenfests Theorems
5.3.7 Matrix Representation
5.3.8 Time-Independent First-Order Perturbation Theory (Without Degeneration)
5.4 Consistency Considerations
5.5 Application to Practical Problems
5.5.1 Model System II: Harmonic Oscillator (1D)
5.5.2 Anharmonic Oscillator
5.6 Advanced Material
5.6.1 Derivation of Heisenbergs Uncertainty Relation (1D-Version)
5.6.2 Harmonic Oscillator and Ladder Operators
5.6.3 Remarks on the Quantization of the Free Electromagnetic Field
5.7 Tasks for Self-check
References
6 Einstein Coefficients and Quantum Transitions
6.1 Starting Point
6.2 Physical Idea
6.3 Theoretical Considerations
6.3.1 The Rate Equation
6.3.2 Perturbation Theory of Quantum Transitions
6.4 Consistency Considerations
6.5 Application to Practical Problems
6.5.1 Light Absorption and Light Amplification
6.5.2 Feedback
6.6 Advanced Material
6.6.1 The Parity Selection Rule
6.7 Fermi’s Golden Rule
6.8 Tasks for Self-check
References
7 Planck’s Formula and Einstein Coefficients
7.1 Starting Point
7.2 Physical Idea
7.3 Theoretical Considerations
7.3.1 Planck’s Formula
7.3.2 Final Expressions for Einstein Coefficients in the Dipole Approximation
7.4 Consistency Considerations
7.5 Application to Practical Problems
7.5.1 Number of Photons in a Cavity Held at Temperature T
7.5.2 Black and Gray Bodies: Selective Absorbers
7.6 Advanced Material
7.6.1 Spectrally Selective Absorbers in Solar Energy Conversion
7.6.2 Spontaneous Emission Revisited
7.7 Tasks for Self-check
References
Part IIIEnergy Levels and Spectroscopic Properties of Simple Atoms
8 The Hydrogen Atom
8.1 Starting Point
8.2 Physical Idea
8.3 Theoretical Considerations
8.3.1 Bohr’s Theory
8.3.2 Emission Spectrum of the Hydrogen Atom in the Bohr Theory
8.3.3 Relativistic Corrections to the Rydberg Energy Levels
8.3.4 Quantum Mechanical Treatment of the Hydrogen-Like Atom
8.4 Consistency Considerations
8.4.1 Characteristic Spatial Dimensions of the Hydrogen Ground State
8.4.2 Important Expectation Values
8.4.3 Highly Excited Hydrogen-Like Atoms
8.5 Application to Practical Problems
8.5.1 Rigid Spherical Rotor
8.5.2 Particle in a Spherical Box Potential
8.5.3 The Hydrogen Atom in a Magnetic Field: Bohr Theory and Gyromagnetic Factor
8.6 Advanced Material
8.6.1 Electron Spin and Spin–orbit Interaction
8.6.2 Spinors and Pauli Matrices
8.6.3 Remarks on Selection Rules for Optical Transitions (Electric Dipole Interaction)
8.7 Tasks for Self-Check
References
9 The Helium Atom
9.1 Starting Point
9.2 Physical Ideas
9.3 Theoretical Considerations
9.3.1 The Pauli Exclusion Principle
9.3.2 The Helium Atom Ground State Without Spin Contributions
9.4 Consistency Considerations
9.4.1 Screening
9.4.2 Comparison of the Presented Approaches
9.4.3 Symmetry Requirements
9.4.4 Selection Rules
9.5 Application to Practical Problems
9.6 Advanced Material
9.6.1 Structure of the Wavefunction of Two Electrons in a Helium Atom (LS-Coupling)
9.6.2 Hund’s Rules
9.7 Tasks for Self-check
References
Part IVIntroduction to Molecular Physics and Spectroscopy
10 The Hydrogen Molecule
10.1 Starting Point
10.2 Physical Idea
10.3 Theoretical Considerations
10.3.1 The Adiabatic Approximation
10.3.2 Simplest Example of Covalent Bonding: The H2+- Molecule Ion
10.4 Consistency Considerations
10.5 Application to Practical Problems
10.5.1 Interatomic Interaction Potentials
10.5.2 A Simple Model Potential
10.5.3 Model Potentials for Ionic Bonding
10.5.4 The Lennard-Jones Potential
10.5.5 The Morse Potential
10.6 Advanced Material: The Hydrogen Molecule
10.7 Tasks for Self-check
References
11 Optical Spectra of Molecules
11.1 Starting Point
11.2 Physical Idea
11.3 Theoretical Material
11.3.1 Vibration and Rotation of the Diatomic Molecule
11.3.2 Rotation Spectra of a Gas of Diatomic Molecules
11.3.3 Molecule Vibration (Diatomic Molecules)
11.3.4 Rotational-Vibrational Spectra (Diatomic Molecules)
11.3.5 Electronic Transitions
11.4 Consistency Considerations
11.5 Application to Practical Problems
11.5.1 Example 1: Estimation of Interatomic Distance
11.5.2 Example 2: Estimation of the Temperature
11.5.3 Example 3: Estimation of the Dissociation Energy
11.6 Advanced Material: Polyatomic Molecules
11.6.1 Rotation
11.6.2 Molecule Vibration
11.6.3 Rotational-Vibrational Spectra
11.7 Tasks for Self-check
References
12 From Atoms and Molecules to Continuous Media
12.1 Starting Point
12.2 Physical Idea
12.3 Theoretical Material
12.3.1 Microscopic Dipoles and Microscopic Polarizability
12.3.2 The Oscillator Model
12.3.3 Electrostatics of Dielectric Media: Macroscopic Polarization of the Medium
12.3.4 Clausius–Mossotti Equation
12.3.5 Electrical Conductors
12.4 Consistency Considerations
12.5 Application to Practical Problems
12.5.1 The Static Polarizability of a Dielectric Sphere in Vacuum
12.5.2 The Static Dielectric Constant of an Ensemble of Permanent Dipole
12.5.3 Idea on Light Scattering
12.6 Advanced Material: A Quantum Mechanical Expression for the Polarizability
12.7 Tasks for Self-check
References
Part VOptical Properties of Continuous Media
13 Linear Optical Constants I
13.1 Starting Point
13.2 Physical Idea
13.3 Theoretical Material
13.3.1 The Linear Dielectric Susceptibility
13.3.2 Linear Optical Constants
13.4 Consistency Considerations
13.5 Application to Practical Problems
13.5.1 Energy Dissipation
13.5.2 Interface Reflection
13.6 Advanced Material
13.6.1 Orientation Polarization
13.6.2 Material Mixtures
13.7 Tasks for Self-check
References
14 Linear Optical Constants II: Classical Dispersion Models
14.1 Starting Point
14.2 Physical Idea
14.3 Theoretical Material
14.3.1 Free Charge Carriers and Drude Function
14.3.2 Specifics of Ultrathin Metal Films
14.3.3 Bound Charge Carriers and Lorentzian Oscillator Model
14.4 Consistency Considerations
14.5 Application to Practical Problems
14.5.1 Sellmeier and Cauchy Formulas
14.5.2 Inhomogeneous Broadening
14.6 Advanced Material
14.6.1 Oscillator Model and Dispersion Law
14.6.2 The Dielectric Function of a Gas of Diatomic Molecules in the FIR
14.7 Tasks for Self-check
References
15 Linear Optical Constants III: The Kramers–Kronig Relations
15.1 Starting Point
15.2 Physical Idea
15.3 Theoretical Material: Kramers–Kronig Relations for Dielectrics
15.4 Consistency Considerations
15.5 Application to Practical Problems
15.6 Advanced Material
15.6.1 Kramers–Kronig Relations for Conductors
15.6.2 Once More: The f-sum Rule
15.7 Taks for Self-check
References
Part VIOptical Properties of Solids
16 Introduction to Solid-State Physics
16.1 Starting Point
16.2 Physical Idea
16.3 Theoretical Considerations: Basics of Crystalline Solids
16.3.1 Translation and Rotational Invariance
16.3.2 Single-Electron Approximation
16.3.3 Reciprocal Lattice
16.4 Consistency Considerations
16.5 Application to Practical Problems
16.5.1 Model Calculation: Energy Bands in a Tight Binding Approach
16.5.2 Effective Masses
16.6 Advanced Material
16.6.1 The Kronig–Penney Model
16.6.2 Once More About Consistency: Delocalized and Localized Electron States
16.7 Tasks for Self-check
References
17 Introduction to Solid-State Optics
17.1 Starting Point
17.2 Physical Idea
17.3 Theoretical Material
17.3.1 Crystals: Direct Electronic Transitions
17.3.2 Crystals: Phonons
17.3.3 Crystals: Indirect Transitions
17.3.4 Amorphous Solids
17.3.5 Dielectric Function of a Crystal: Contributions of Direct Electronic Transitions
17.4 Consistency Considerations
17.5 Application to Concrete Problems
17.5.1 Optical Properties of Amorphous Semiconductors: Parameters for a Practical Description
17.5.2 The Tauc–Lorentz Model
17.6 Advanced Material: Spatial Dispersion of the Dielectric Function
17.7 Tasks for Self-check
References
18 Basic Effects of Nonlinear Optics
18.1 Starting Point
18.2 Physical Idea
18.3 Theoretical Material
18.3.1 Nonlinear Material Equation
18.3.2 Frequency Conversion Processes
18.4 Consistency Considerations
18.5 Application to Concrete Problems
18.5.1 The Pockels Effect
18.5.2 Nonlinear Refraction
18.6 Advanced Material: Nonlinear Wave Equations
18.7 Tasks for Self-check
References
19 Solutions to Tasks
Index