The objective of this chapter is to highlight that for lossless material platforms formed by arbitrary inhomogeneous bianisotropic and possibly nonreciprocal materials, the natural modes of oscillation form, indeed, a complete set of expansion functions. Based on our recent work, it is proven that the Maxwell equations in dispersive systems can always be reduced to a generalized dynamical problem whose time evolution is described by a Hermitian operator. The effects of material dispersion are taken into account by introducing additional variables that may model the internal degrees of freedom of the material. With such a result, we construct formal expansions of the electromagnetic field in terms of the normal modes, and in particular it is highlighted that the modal expansion coefficients are not unique. The developed theory is used to obtain a modal expansion of the system Green function.

Chapter Contents:

• 24.1 Introduction
• 24.2 Electrodynamics of dispersive media
• 24.3 Hermitian formulation in the time domain
• 24.4 Poynting theorem and stored energy
• 24.5 Canonical momentum
• 24.6 Modal expansions
• 24.7 Green's function
• 24.8 Positive and negative frequency components of the Green function
• 24.9 Application to topological photonics
• 24.10 Application to quantum optics
• 24.11 Summary
• Acknowledgments
• References

Inspec keywords: Green's function methods; optical materials; quantum optics; optical dispersion; electromagnetic fields

Other keywords: topological photonics; lossless material platforms; Hermitian operator; dispersive material systems; arbitrary inhomogeneous bianisotropic materials; electromagnetic field; modal expansion coefficients; normal modes; oscillation form; expansion functions; system Green function; generalized dynamical problem; nonreciprocal materials; quantum optics; Maxwell equations

Subjects: Quantum optics; Optical materials; Optical propagation, transmission and absorption