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We present a perturbative approach to derive the semiclassical equations ofmotion for the two-dimensional electron dynamics under the simultaneouspresence of static electric and magnetic fields, where the quantized Hallconductance is known to be directly related to the topological properties oftranslationally invariant magnetic Bloch bands. In close analogy to thisapproach, we develop a perturbative theory of two-dimensional photonictransport in gyrotropic photonic crystals to mimic the physics of quantum Hallsystems. We show that a suitable permittivity grading of a gyrotropic photoniccrystal is able to simulate the simultaneous presence of analog electric andmagnetic field forces for photons, and we rigorously derive thetopology-related term in the equation for the electromagnetic energy velocitythat is formally equivalent to the electronic case. A possible experimentalconfiguration is proposed to observe a bulk photonic analog to the quantum Hallphysics in graded gyromagnetic photonic crystals.

Topological aspects in the photonic crystal analog of single-particle transport in quantum Hall systems