  The interaction between localized emitters and quantum fields, both in
relativistic settings and in the case of ultra-strong couplings, requires
non-perturbative methods beyond the rotating-wave approximation. In this work
we employ chain-mapping methods to achieve a numerically exact treatment of the
interaction between a localized emitter and a scalar quantum field. We extend
the application range of these methods beyond emitter observables and apply
them to study field observables. We first provide an overview of chain-mapping
methods and their physical interpretation, and discuss the thermal double
construction for systems coupled to thermal field states. Modelling the emitter
as an Unruh-DeWitt particle detector, we then calculate the energy density
emitted by a detector coupling strongly to the field. As a stimulating
demonstration of the approach's potential, we calculate the radiation emitted
from an accelerated detector in the Unruh effect, which is closely related to
the thermal double construction as we discuss. We comment on prospects and
challenges of the method.
