This volume studies light, electromagnetic fields, and wave propagation.
This volume studies light, electromagnetic fields, and wave propagation. It develops mathematical models for optics and electromagnetism, from Maxwell equations to modern photonics.
Part I. Foundations of Electromagnetism
Chapter 1. Fields and Sources
1.1 Electric charge 1.2 Electric field 1.3 Magnetic field 1.4 Charge density and current density 1.5 Examples
Chapter 2. Vector Calculus for Fields
2.1 Gradient, divergence, curl 2.2 Integral theorems 2.3 Conservative and solenoidal fields 2.4 Boundary surfaces 2.5 Examples
Chapter 3. Maxwell Equations
3.1 Differential form 3.2 Integral form 3.3 Constitutive relations 3.4 Boundary conditions 3.5 Physical interpretation
Part II. Electrostatics and Magnetostatics
Chapter 4. Electrostatics
4.1 Coulomb law 4.2 Electric potential 4.3 Poisson and Laplace equations 4.4 Boundary value problems 4.5 Applications
Chapter 5. Magnetostatics
5.1 Biot-Savart law 5.2 Ampere law 5.3 Magnetic vector potential 5.4 Boundary value problems 5.5 Applications
Chapter 6. Materials
6.1 Dielectrics 6.2 Conductors 6.3 Magnetic materials 6.4 Linear and nonlinear media 6.5 Examples
Part III. Electromagnetic Waves
Chapter 7. Wave Equations
7.1 Derivation from Maxwell equations 7.2 Plane waves 7.3 Polarization 7.4 Energy and momentum 7.5 Examples
Chapter 8. Reflection and Refraction
8.1 Interface conditions 8.2 Fresnel equations 8.3 Snell law 8.4 Total internal reflection 8.5 Applications
Chapter 9. Waveguides and Cavities
9.1 Guided modes 9.2 Boundary conditions 9.3 Resonance 9.4 Applications 9.5 Examples
Part IV. Optics
Chapter 10. Geometrical Optics
10.1 Rays and wavefronts 10.2 Fermat principle 10.3 Lenses and mirrors 10.4 Aberrations 10.5 Applications
Chapter 11. Physical Optics
11.1 Interference 11.2 Diffraction 11.3 Coherence 11.4 Polarization 11.5 Applications
Chapter 12. Fourier Optics
12.1 Optical transfer functions 12.2 Diffraction as transform 12.3 Imaging systems 12.4 Spatial filtering 12.5 Applications
Part V. Advanced Electromagnetic Theory
Chapter 13. Relativistic Electromagnetism
13.1 Four-potentials 13.2 Field tensor 13.3 Lorentz transformations 13.4 Covariant Maxwell equations 13.5 Applications
Chapter 14. Radiation
14.1 Accelerated charges 14.2 Dipole radiation 14.3 Antennas 14.4 Scattering 14.5 Applications
Chapter 15. Electromagnetic Media
15.1 Dispersive media 15.2 Anisotropic media 15.3 Metamaterials 15.4 Nonlinear optics 15.5 Applications
Part VI. Mathematical Methods
Chapter 16. Potential Theory Methods
16.1 Scalar and vector potentials 16.2 Green functions 16.3 Boundary integral methods 16.4 Applications 16.5 Examples
Chapter 17. Spectral and Modal Methods
17.1 Eigenmodes 17.2 Orthogonal expansions 17.3 Resonance problems 17.4 Applications 17.5 Examples
Chapter 18. Numerical Electromagnetics
18.1 Finite difference time domain 18.2 Finite element methods 18.3 Boundary element methods 18.4 Stability and convergence 18.5 Applications
Part VII. Applications
Chapter 19. Communication Systems
19.1 Antennas and propagation 19.2 Transmission lines 19.3 Fiber optics 19.4 Wireless channels 19.5 Applications
Chapter 20. Imaging and Sensing
20.1 Optical imaging 20.2 Radar and lidar 20.3 Tomography 20.4 Remote sensing 20.5 Applications
Chapter 21. Photonics and Devices
21.1 Lasers 21.2 Optical fibers 21.3 Photonic crystals 21.4 Integrated optics 21.5 Applications
Part VIII. Research Directions
Chapter 22. Advanced Topics
22.1 Nanophotonics 22.2 Plasmonics 22.3 Quantum optics overview 22.4 Inverse electromagnetic problems 22.5 Emerging areas
Chapter 23. Open Problems
23.1 Inverse scattering 23.2 Wave control 23.3 Material design 23.4 Computational limits 23.5 Future directions
Chapter 24. Historical and Conceptual Notes
24.1 Development of optics 24.2 Development of electromagnetic theory 24.3 Key contributors 24.4 Evolution of field theory 24.5 Summary
Appendix
A. Maxwell equation reference B. Vector calculus identities C. Boundary condition summary D. Numerical method tables E. Cross-reference to other MSC branches