  We present a perturbative approach to derive the semiclassical equations of
motion for the two-dimensional electron dynamics under the simultaneous
presence of static electric and magnetic fields, where the quantized Hall
conductance is known to be directly related to the topological properties of
translationally invariant magnetic Bloch bands. In close analogy to this
approach, we develop a perturbative theory of two-dimensional photonic
transport in gyrotropic photonic crystals to mimic the physics of quantum Hall
systems. We show that a suitable permittivity grading of a gyrotropic photonic
crystal is able to simulate the simultaneous presence of analog electric and
magnetic field forces for photons, and we rigorously derive the
topology-related term in the equation for the electromagnetic energy velocity
that is formally equivalent to the electronic case. A possible experimental
configuration is proposed to observe a bulk photonic analog to the quantum Hall
physics in graded gyromagnetic photonic crystals.
