  Based on the reciprocity theorem, we present a formalism to calculate the
power emitted by a dipole source into a particular propagating mode leaving an
open optical system. The open system is completely arbitrary and the approach
can be used in analytical calculations but may also be combined with numerical
electromagnetic solvers to describe the emission of light sources into complex
systems. We exemplify the use of the formalism in numerical simulations by
analyzing the emission of a dipole that is placed inside a cavity with
connected single mode exit waveguide. Additionally, we show at the example of a
practical ring resonator system how the approach can be applied to systems that
offer multiple electromagnetic energy decay channels. As a consequence of its
inherent simplicity and broad applicability, the approach may serve as a
powerful and practical tool for engineering light-matter-interaction in a
variety of active optical systems.
