Book contents
- Frontmatter
- Dedication
- Contents
- Preface to the First Edition
- Preface to the Second Edition
- Preface to the Third Edition
- 1 Introduction
- 2 Theoretical Foundations
- 3 Propagation and Focusing
- 4 Superresolution
- 5 Near-Field Optics
- 6 Light-Matter Interactions
- 7 Quantum Emitters
- 8 Dipole Emission Near Planar Interfaces
- 9 Photonic Crystals and Metamaterials
- 10 Random Media
- 11 Optical Resonators and Optomechanics
- 12 Coupled-Mode Theory
- 13 Plasmonics
- 14 Optical Antennas
- 15 Optical Forces
- 16 Stochastic Fields and Sources
- 17 Theoretical Methods
- Appendix A Semianalytical Derivation of the Atomic Polarizability
- Appendix B Spontaneous Emission in the Weak-Coupling Regime
- Appendix C Fields of a Dipole Near a Layered Substrate
- Appendix D Far-Field Green Functions
- Appendix E Power Spectral Densities
- Index
17 - Theoretical Methods
Published online by Cambridge University Press: 31 October 2025
Book contents
- Frontmatter
- Dedication
- Contents
- Preface to the First Edition
- Preface to the Second Edition
- Preface to the Third Edition
- 1 Introduction
- 2 Theoretical Foundations
- 3 Propagation and Focusing
- 4 Superresolution
- 5 Near-Field Optics
- 6 Light-Matter Interactions
- 7 Quantum Emitters
- 8 Dipole Emission Near Planar Interfaces
- 9 Photonic Crystals and Metamaterials
- 10 Random Media
- 11 Optical Resonators and Optomechanics
- 12 Coupled-Mode Theory
- 13 Plasmonics
- 14 Optical Antennas
- 15 Optical Forces
- 16 Stochastic Fields and Sources
- 17 Theoretical Methods
- Appendix A Semianalytical Derivation of the Atomic Polarizability
- Appendix B Spontaneous Emission in the Weak-Coupling Regime
- Appendix C Fields of a Dipole Near a Layered Substrate
- Appendix D Far-Field Green Functions
- Appendix E Power Spectral Densities
- Index
Summary
In this chapter we discuss semianalytical methods for calculating optical fields in arbitrary geometries. Semianalytical methods rely on numerical procedures to derive analytical solutions for the problem at hand. Examples are the multiple-multipole method (MMP), the coupled-dipole method (CDM), or the method of moments (MoM). Based on the volume integral equation we show the equivalence of the CDM and the MoM. The comparison allows us to derive the most general form of the polarizability $\alpha$ of a small scatterer. We show that it reproduces the dynamic and quasi-static polarizabilities derived in previous chapters. We derive an equation for calculating the Green function of an arbitrary system, known as the Dyson equation, and discuss how it can be used to iteratively determine the electromagnetic field in an arbitrary geometry.
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- Principles of Nano-Optics , pp. 573 - 596Publisher: Cambridge University PressPrint publication year: 2025
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