Optical Waves in Fibers and Components

Electromagnetic Fundamentals

Maxwell’s Equations

Electromagnetic radiations obeys Maxwell’s equations

curl ${\rm {\bf H}} = {{\partial {\bf D}}\over{\partial t}}+{\rm {\bf J}}$ Ampere’s law, (2.1)

curl ${\rm {\bf E}} = -{{\partial {\bf B}}\over{\partial t}}$ Maxwell-Faraday equation, (2.2)

div D = ρ Gauβ’s law, (2.3)

div B = 0 Gauβ’s law for magnetism. (2.4)

We take the divergence of (2.1) and obtain with div curl A = 0 the

div ${\rm {\bf J}} = {{\partial {\rho}}\over{\partial t}}$ continuity equation. (2.5)

It says that the current drained from the surface of a differential volume element equals the reduction of charge per time interval (preservation of charge).