Light and Matter
Electromagnetism, Optics, Spectroscopy and Lasers

Yehuda B. Band

Table of Contents

1.  Electromagnetic Radiation
	1.1.  Brief History of the Interaction of Light and Matter
	1.2.  Light in Vacuum
		1.2.1.  The Electromagnetic Spectrum
		  	1.2.1.1.  Radio waves
		  	1.2.1.2.  Microwaves
		  	1.2.1.3.  Infra-red
		  	1.2.1.4.  Visible
		  	1.2.1.5.  Ultraviolet
		  	1.2.1.6.  X-rays
		  	1.2.1.7.  -rays
		  	1.2.1.8.  Blackbody Radiation
		  	1.2.1.9.  The Sun and Stars as Light Sources
		1.2.2.  The Wave Equation in Vacuum
		1.2.3.  Propagation of One Component in One Dimension
			1.2.3.1.  The Slowly Varying Envelope
		1.2.4.  Phase and Group Velocity of a Light Pulse
		1.2.5.  Amplitude Modulation
		1.2.6.  Frequency and Phase Modulation
			1.2.6.1.  Pulse Shaping and Characterization
		1.2.7.  Energy, Momentum and Angular Momentum of Electromagnetic Waves
			1.2.7.1.  Modes of the Radiation Field and Cavity Modes
			1.2.7.2.  Gaussian beams in a Homogeneous Medium
		1.2.8.  Polarized Light
			1.2.8.1.  Linear and Circular Polarization
			1.2.8.2.  Elliptical Polarization
			1.2.8.3.  Unpolarized Light
			1.2.8.4.  Jones Matrices
			1.2.8.5.  Stokes Parameters
			1.2.8.6.  Mueller Matrices
		1.2.9.  Diffraction
			1.2.9.1.  Kirchhoff Diffraction Theory
			1.2.9.2.  Fresnel and Fraunhofer Diffraction
			1.2.9.3.  Near-Field Diffraction
		1.2.10.  Interference
			1.2.10.1.  Interferometers
			1.2.10.2.  Fabry-Perot Interferometer
		1.2.11.  Temporal and Spatial Coherence
		1.2.12.  Photons: Quantization of The Electromagnetic Field
	1.3.  Matter - Source of Light
		1.3.1.  Classical and Quantum Expressions for the Charge Density and Current
		1.3.2.  The Wave Equation with Source Terms: Lienard-Wiechert potentials

2.  Phenomenology of Light Propagation in Matter
	2.1.  Absorption of Light
		2.1.1.  Color of Materials
	2.2.  Nonlinear Absorption
		2.2.1.  Saturable Absorption
		2.2.2.  Reverse Saturable Absorption
		2.2.3.  Two-Photon Absorption
		2.2.4.  An Aside on Einstein Absorption and Emission Coefficients
	2.3.  Index of Refraction
		2.3.1.  Reflection and Refraction at a Boundary Interface
		2.3.2.  Relationship between Refractive Index and Absorption: Kramers-Kronig Relation
		2.3.3.  Dispersion
			2.3.3.1.  Propagation Equation for Light in a Dispersive Medium
		2.3.4.  Refractive Index Temperature Dependence: Thermal lensing
	2.4.  Optical Phenomena in Non-isotropic Media
		2.4.1.  Introduction to Crystallography and Optics in Crystals
		2.4.2.  Dichroism
		2.4.3.  Birefringence
			2.4.3.1.  Fresnel's Equation of Wave Normals
			2.4.3.2.  Uniaxial Crystals
			2.4.3.3.  Biaxial Crystals
			2.4.3.4.  Double Refraction
			2.4.3.5.  Wavepacket Propagation in a Birefringent Medium
			2.4.3.6.  Frequency Filters: Application of Birefringence
		2.4.4.  Optical Activity, Optical Rotatory Dispersion and Circular Dichroism
	2.5.  Electric Field Effects
		2.5.1.  Kerr Effect
		2.5.2.  Pockels Effect
		2.5.3.  Piezoelectricity
		2.5.4.  Pyroelectric Effect
		2.5.5.  Ferroelectric Effect
		2.5.6.  Electrostriction
		2.5.7.  Photorefractive Effect
	2.6.  Photoacoustic Effects
		2.6.1.  Diffraction by Acoustic Waves: Brillouin Scattering
		2.6.2.  Photoelastic Effect (Stress-Birefringence)
		2.6.3.  Acousto-Optic Detection of Light
	2.7.  Magnetic Field Effects
		2.7.1.  Faraday Effect
		2.7.2.  Voigt and Cotton-Mouton Effects
		2.8.3.  Magnetic Circular Birefringence and Dichoism
		2.7.4.  Magnetostriction and Magnetoelasticity

3.  The Interaction of Light and Matter
	3.1.  Lorentz Force Law, F = q[E + (v/c)B]
	3.2.  Motion of a Charged Particle in Static Electric and Magnetic Fields
		3.2.1.  Motion in a Magnetic Field - Cyclotron Frequency
		3.2.2.  Crossed Electric and Magnetic Fields
		3.2.3.  Conductivity, Magnetoconductivity and Hall Effect
	3.3.  Motion of a Bound Electron in an Electromagnetic Field
		3.3.1.  Linewidth Due to Spontaneous Emission
		3.3.2.  Rayleigh Scattering, Thomson Scattering, and Resonant Line Scattering Limits
			3.3.2.1.  Doppler Shift of Resonant Line Scattering and Doppler Broadening
			3.3.2.2.  Collisional Shifts and Widths of Resonant Line Scattering
		3.3.3.  Polarization of a Medium
			3.3.3.1.  Electromagnetic waves in Dielectric Media, Conductors and Insulators
			3.3.3.2.  Power Broadening
			3.3.3.3.  Raman Scattering
		3.3.5.  Polarization of a Medium in a Static Magnetic Field
			3.3.5.1.  Hanle effect
		3.3.6.  Electromagnetic Field and a Static Electric Field 
		3.3.7.  Nonlinear Polarization of a Medium
	3.4.  Radiation Due to Acceleration of Charges
		3.4.1.  Radiation from Relativistically Moving Charges
		3.4.2.  Synchrotron Emission
		3.4.3.  Radiative Damping Force Revisited
		3.4.4.  Cherenkov Radiation
	3.5.  Multipole Radiation
		3.5.1.  Scattering of Long Wavelength Electromagnetic Radiation from Small Particles
	3.6.  Scattering of a Light Wavepacket
	3.7.  Cooling and Trapping of Atoms
		3.7.1.  Far Off-Resonance Trapping, Atom Mirrors and Optical Tweezers
		3.7.2.  Doppler Cooling
		3.7.3.  Polarization Gradient Cooling (Sisyphus Cooling) of Atoms

4.  Magnetic Phenomena, Constitutive Relations and Plasmas
	4.1.  Magnetic Moments
	4.2.  Magnetization
		4.2.1.  Diamagnetism
		4.2.2.  Paramagnetism
			4.2.2.1.  Pauli Paramagnetism
			4.2.2.2.  Van Vleck Paramagnetism
		4.2.3.  Ferromagnetism
		4.2.4.  Ferrimagnetism
		4.2.5.  Antiferromagnetism
		4.2.6.  Permeability Resonances
	4.3.  Magnetic Resonance
		4.3.1.  Nuclear Magnetic Resonance
	4.4.  Polarization and Magnetization as Source Terms
	4.5.  Atomistic Derivation of Macroscopic Electromagnetism and The Constitutive Relations
	4.6.  Microscopic Polarizability and Macroscopic Polarization
		4.6.1.  Clausius-Mossotti Equation and The Lorentz-Lorenz Correction Factor
		4.6.2.  Microscopic Magnetic Moment and Macroscopic Magnetization
	4.7.  Dielectric Relaxation
		4.7.1.  Molecular Orientation (and Re-orientation) in an Applied Field
		4.7.2.  Dispersion Relations for Light in Dielectric Crystals
	4.8.  Plasmas
		4.8.1.  Plasma Parameters
		4.8.2.  Constitutive Equations in a Plasma
		4.8.3.  Kinetic Theory
		4.8.4.  Hydrodynamic Model of Plasmas
		4.8.5.  Waves in a Plasma

5.  Quantum Description of Absorption, Emission and Scattering
	5.1.  Charged Particle in an Electromagnetic Field
		5.1.1.  Electron Spin Coupling
		5.1.2.  Landau Levels in a Static Magnetic Field
	5.2.  Absorption and Emission
		5.2.1.  Time Dependent Perturbation Theory
		5.2.2.  Spontaneous Emission
			5.2.2.1.  The Dipole Approximation
			5.2.2.2.  Multipole Expansions
		5.2.3.  Stimulated Emission and Absorption
		5.2.4.  Finite Lifetime Considerations for Stimulated Emission and Absorption
		5.2.5.  Finite Duration Pulses
	5.3.  Rayleigh and Raman Scattering
		5.3.1.  Why is the Sky Blue, the Setting Sun Red and Clouds White?
	5.4.  Thomson Scattering

6.  Spectroscopy
	6.1.  Atoms
		6.1.1.  The Hydrogen Atom
			6.1.1.1.  Fine and Hyperfine Structure
			6.1.1.2.  Zeeman Splitting
			6.1.1.3.  Stark Shift
		6.1.2.  Multi-electron Atomic Systems
			6.1.2.1.  Hartree-Fock Method
			6.1.2.2.  Thomas-Fermi Approximation
			6.1.2.3.  Fine Structure of Multi-electron Atoms
			6.1.2.4.  Hyperfine Structure of Multi-electron Atoms
		6.1.3.  Selection Rules
		6.1.4.  Broadening Due to the Lifetime and Collisions
	6.2.  Molecules
		6.2.1.  Hamiltonian for Molecular Systems
		6.2.2.  Born-Oppenheimer Approximation and Potential Energy Surfaces
		6.2.3.  Molecular Orbitals
	6.3.  Diatomic Molecules
			6.3.1.  Diatomic Rotational and Vibrational States and Transitions
			6.3.2.  Electric Dipole Transitions
			6.3.3.  The Franck-Condon Principle
			6.3.4.  More About Rotational States and Transitions: Microwave Spectroscopy
			6.3.5. H2+ Ion
			6.3.6.  H2 Molecule
	6.4.  Polyatomic Molecules
			6.4.1.  Multidimensional Born-Oppenheimer Potential Surfaces
			6.4.2  The Nuclear Hamiltonian for Molecular Systems
				6.4.2.1.  Normal Modes
			6.4.3.  Rotational Degrees of Freedom
				6.4.3.1.  Spherical Top Molecule
					6.4.3.1.1.  Stark Shift of a Spherical Top
					6.4.3.1.2.  Zeeman Splitting of a Spherical Top Molecule
				6.4.3.2.  Symmetric Top Molecule
					6.4.3.2.1.  Stark Shift of a Symmetric Top
				6.4.3.3.  Asymmetric Top Molecule
				6.4.3.4.  Interaction between Vibrations and Rotations
				6.4.3.5.  CO2 Molecule
			6.4.4.  Large Molecules
				6.4.4.1.  Dye Molecules
	6.5.  Condensed-Phase Materials
		6.5.1.  Crystals Doped with Metal Ions
			6.5.1.1. d-orbitals and configurations
			6.5.1.2.  The Crystal Field Approximation
			6.5.1.3. Transition-Metal Complexes
			6.5.1.4. Tanabe-Sugano diagrams
			6.5.1.5. Octahedral Crystal Field Transitions 
		6.5.2.  Metals
			6.5.2.1.  Fermi-Dirac Distribution Function
		6.5.3.  Semiconductor Materials
			6.5.3.1. Donor and Acceptor Impurities
			6.5.3.2. p-n Junctions
			6.5.3.3. Heterojunctions, Quantum Wells and Superlattices
			6.5.3.4. Absorption and Emission Spectra
				6.5.3.4.1.  Exciton Absorption and Emission

7.  Lasers
	7.1.  Laser Dynamics
		7.1.1.  Three and Four Level Lasers
		7.1.2.  Laser Rate Equations
	7.2.  Threshold
	7.3.  Steady State
		7.3.1.  Small Signal Gain and Gain Saturation
		7.3.2.  Circulating Intracavity Intensity
		7.3.3.  CW Output Versus Input
	7.4.  Pulsed Laser Operation
		7.4.1.  Relaxation Oscillations
		7.4.2.  Q-Switching
		7.4.3.  Mode-Locking
			7.4.3.1.  Active Mode-Locking
				7.4.3.1.1.  AM Mode-Locking
				7.4.3.1.2.  FM Mode-Locking
			7.4.3.2.  Passive Mode-Locking
		7.4.4.  Extra-Cavity Pulse Compressor
		7.4.5.  Chirped Pulse Amplifiers
	7.5.  Cavity Modes
		7.5.1.  Longitudinal Modes
			7.5.1.1.  Fabry-Perot Resonator
		7.5.2.  Transverse Modes
			7.5.2.1.  Higher Order Gaussian Modes
			7.5.2.2.  Spherical Mirror Resonators
	7.6.  Amplified Spontaneous Emission
	7.7.  Laser Linewidth
	7.8.  Laser Coherence
	7.9.  Specific Laser Systems
		7.9.1.  He-Ne Laser
		7.9.2.  Ar Ion and Kr Ion Lasers
		7.9.3.  C02 Laser
		7.9.4.  Nitrogen Laser
		7.9.5.  Excimer and Exciplex Lasers
		7.9.6.  Dye lasers
		7.9.7.  Solid-State Lasers
			7.9.7.1.  Nd:YAG
			7.9.7.2.  Nd Glass
			7.9.7.3.  Ruby
			7.9.7.4.  Vibronic Lasers
				7.9.7.4.1.  Alexandrite
				7.9.7.4.1.  Ti:Sapphire
		7.9.8.  Semiconductor Diode Lasers: GaAs, AlGaAs Heterostructures

8.  Nonlinear Optics
	8.1.  Expansion of the Polarization in the Electric Field
		8.1.1.  Symmetry Relations of the Nonlinear Susceptibilities
		8.1.2.  Electromagnetic energy density in a nonlinear medium
		8.1.3.  Local Field Corrections to Nonlinear Susceptibilities
		8.1.4.  The Nonlinear Wave Equation for the Slowly Varying Envelope
			8.1.4.1.  Split-Step Fast-Fourier Transform Propagation Method
		8.1.5.  Manley-Rowe Relations
	8.2.  Phase Matching
		8.2.1.  Collinear Phase Matching
		8.2.2.  Non-Collinear Phase Matching
	8.3.  Second Harmonic Generation
		8.3.1.  Second Harmonic Generation with Multimode Light
		8.3.2.  Short-Pulse Second Harmonic Generation
	8.4.  Three-Wave Mixing
		8.4.1.  Sum Frequency Generation
			8.4.1.1.  Short Pulse Sum Frequency Generation
				8.4.1.1.  Sum Frequency Generation for Frequency Modulated Input Fields
				8.4.1.2.  Short Pulse Sum Frequency Generation
		8.4.2.  Difference Frequency Generation
	8.5.  Third Harmonic Generation
		8.5.1.  Third Harmonic Generation in Rare Gas Mixtures
		8.5.2.  Effects of Self Phase Modulation on Third Harmonic Generation
	8.6.  Self-Focusing and Self Phase Modulation
		8.6.1.  The Nonlinear Schrödinger Equation
		8.6.2.  Optical Solitons
	8.7.  Four-Wave Mixing
		8.7.1.  Coherent Anti-Stokes Raman Spectroscopy
	8.8.  Stimulated Raman Processes
	8.9.  Stimulated Brillouin Processes
	8.10.  Nonlinear Matter-Wave Optics

9.  Quantum-Optical Processes
	9.1.  Interaction of a Two-Level System with an Electromagnetic Field
		9.1.1.  Rotating Wave Approximation
		9.1.2.  Rabi Oscillations
		9.1.3.  Dressed States
		9.1.4.  Adiabatic Passage and the Adiabatic Theorem
			9.1.4.1.  Chirped Pulse Adiabatic Passage
	9.2.  Liouville von Neumann Equation for the Density Matrix
		9.2.1.  The Density Matrix Description of Matter
			9.2.1.1.  The Decay Matrix
			9.2.1.2.  Optical Bloch Equations for the Two-Level System
			9.2.1.3.  Adiabatic Limit
		9.2.2.  The Steady State Density Matrix Solution
		9.2.3.  Rate Equation Limit
		9.2.4.  Atom Cooling and Trapping Revisited
		9.2.5.  The Adiabatic Theorem for Density Matrix Dynamics
		9.2.6.  Inhomogeneous Broadening
		9.2.7.  Optical Coherent Transient Processes
			9.2.7.1.  Pulse Area and π-pulses
			9.2.7.2.  Pulse Area Theorem
			9.2.7.3.  Self Induced Transparency
			9.2.7.4.  Optical Nutation
			9.2.7.5.  Free Induction Decay
			9.2.7.6.  Photon Echo
	9.3.  Three-Level System
		9.3.1.  Wavefunction Treatment of a Three-Level System
		9.3.2.  Population Transfer using Stimulated Raman Adiabatic Passage
		9.3.3.  Coherent Trapping: Dark States
		9.3.4.  Density Matrix Treatment of a Three-Level System
	9.4.  Coherent States and Squeezed States
		9.4.1.  Position-Momentum Squeezing
		9.4.2.  Number and Phase Squeezing and the Phase Operator
		9.4.3.  Experimental Generation of Squeezed States: Parametric Down Conversion
		9.4.4.  Homodyne Detection of Squeezed States
		9.4.5.  Application of Squeezed States: Sub-Shot-Noise Phase Measurements
	9.5.  The Jaynes-Cummings Model
	9.6.  Interaction between Modes of a Quantum Field
		9.6.1.  Interaction Representation
		9.6.2.  Quantum-Field Two-Mode Rabi Problem
		9.6.3.  Parametric Oscillation

10.  Propagation in Optical Fibers and Introduction to Optical Communication Systems
	10.1.  Fiber Characteristics
		10.1.1.  Attenuation in Fibers
		10.1.2.  Dispersion in Fibers
		10.1.3.  Polarization-Maintaining and Single-Polarization Fibers
		10.1.3.  Gain in Doped Fibers
	10.2.  Transverse Modes of an Optical Fiber 
		10.2.1.  Single-mode Fiber
		10.2.2.  Imperfections in the Fiber
		10.2.3.  Coupling between Fiber Modes
		10.2.4.  Fiber-Bragg Gratings
	10.3.  Nonlinear Processes in Fibers
		10.3.1.  Optical Solitons in Fibers
		10.3.2.  Stimulated Raman Amplification in Fibers
		10.3.3.  Higher order nonlinear effects
			10.3.3.1.  Self-steepening and Self-Frequency shifting
		10.3.4.  Parametric Processes
	10.4.  Fiber Optic Communication Systems
		10.4.1.  Digital Communication
		10.4.2.  Analog Communication
		10.4.3.  Coherent Optical Communication
		10.4.4.  Multiplexing techniques

Appendices
	Appendix A.  Vector Analysis
		A.1.  Scalar and Vector Products
		A.2.  Differential Operators
		A.3.  Divergence and Stokes Theorems
		A.4.  Curvilinear Coordinates
	Appendix B.  Electromagnetism and Maxwell's Equations
		B.1.  The Laws of Electromagnetism
		B.2.  Units
		B.3.  Maxwell's equations
	Appendix C.  Quantum Mechanics and Schrödinger Equation
		C.1.  Time Dependent and Time Independent Eqautions
		C.2.  Spherical Harmonics
		C.3.  The Radial Schrödinger Equation
		C.4.  The Free Particle
		C.5.  The Spherical Top and the Distorted Spherical Top
		C.6.  The Coulomb Potential
		C.7.  Atomic Units
		C.8.  The Morse Potential
		C.9.  The Harmonic Oscillator Potential
	Appendix D.  Perturbation Theory
		D.1.  Non-degenerate Time-Independent Perturbation Theory
		D.2.  Degenerate Perturbation theory
		D.3.  Time Dependent Perturbation Theory

Fundamental Constants

References

Index