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When studying the quantization of the electromagnetic field, one seems to always derive everything for free space (no charges/currents). This involves solving Maxwell's equations to find modes (in this case plane waves) that are occupied by photons.

How does this translate to situations where one also has a medium (e.g. waveguide, cavity,...)?

In practice, I see people calculating EM modes by solving Maxwell's equations as if they were classical, and then stating that this is the mode a photon can occupy. I see this is the case for free space, but I wonder what the theoretical basis is to get to the case of non-free space.

Qmechanic
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dumkar
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1 Answers1

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This seems to be what you are looking for: Canonical quantization of macroscopic electromagnetism

Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic quantum electrodynamics where no canonical formulation is attempted. In this paper macroscopic electromagnetism is canonically quantized. The results apply to any linear, inhomogeneous, magnetodielectric medium with dielectric functions that obey the Kramers-Kronig relations. The prescriptions of the phenomenological approach are derived from the canonical theory.

Rexcirus
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