  The properties that quantify photonic topological insulators (PTIs), Berry
phase, Berry connection, and Chern number, are typically obtained by making
analogies between classical Maxwell's equations and the quantum mechanical
Schr\"{o}dinger equation, writing both in Hamiltonian form. However, the
aforementioned quantities are not necessarily quantum in nature, and for
photonic systems they can be explained using only classical concepts. Here we
provide a derivation and description of PTI quantities using classical
Maxwell's equations, we demonstrate how an electromagnetic mode can acquire
Berry phase, and we discuss the ramifications of this effect. We consider
several examples, including wave propagation in a biased plasma, and radiation
by a rotating isotropic emitter. These concepts are discussed without invoking
quantum mechanics, and can be easily understood from an engineering
electromagnetics perspective.
