A generalized form of the Lindstedt-Poincaré frequency-renormalization technique is applied to systems of multilevel atoms coupled to the quantized radiation fields. In the Heisenberg picture, the relevant operator equations are solved and the second-order shift in the frequency of the photon is found. A direct connection is made here between the renormalized photon frequency and the susceptibility of the medium. An example of a spatially dispersive medium, namely, a crystal with exciton-photon interaction, is also discussed.
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