Mode-selective quantization and multimodal effective models for spherically layered systems

We propose a geometry-specific, mode-selective quantization scheme in coupled field-emitter systems which makes it easy to include material and geometrical properties, and intrinsic losses, as well as the positions of an arbitrary number of quantum emitters. The method is presented through the example of a spherically symmetric, nonmagnetic, arbitrarily layered system. We follow it up by a framework to project the system on simpler, effective cavity QED models. Maintaining a well-defined connection to the original quantization, we derive the emerging effective quantities from the full, mode-selective model in a mathematically consistent way. We discuss the uses and limitations of these effective models.