The topological properties of electronic systems are often linked to the quantization of electric conductivity observed in the integer quantum Hall effect. A precise analogue of such a quantization in optics remains elusive. Here, I bridge this gap between electronics and optics by demonstrating that the response of the Poynting vector to the mechanical acceleration of a medium provides a photonic analogue of the electric conductivity. In particular, I prove that the photonic conductivity determines the energy irreversibly transferred from a periodic mechanical driving of the medium to the electromagnetic field. Furthermore, I demonstrate that for nonreciprocal systems enclosed in a cavity, the constant acceleration of the system induces a flow of photons along a direction perpendicular to the acceleration, analogous to the Hall effect but for light. The spectral density of the photonic conductivity is quantized in the band gaps of the bulk region with the conductivity quantum determined by the gap Chern number.
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