Electromagnetic Field Equations

This chapter focuses on the Maxwell’s equations driving all large-scale electromagnetic phenomena. We analyze the constitutive relations and properties that the electric and magnetic fields satisfy in the frequency domain for isotropic and anisotropic media. Special emphasis is put on the derivation and examination of the Lorentz and Drude models for the electric permittivity of common dielectrics and metals, respectively. Further, we derive the boundary conditions satisfied by the electromagnetic fields at the interface of two media and revise their conservation of energy (Poynting theorem) for a uniform isotropic–linear medium. We end this chapter by deriving explicit expressions for the six components of the electric and magnetic fields in Cartesian and Cylindrical coordinates. These fundamental equations are the basis for finding the dispersion relation and describing the propagation of surface polaritons in planar and cylindrical structures.