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

Reciprocity approach for calculating the Purcell effect for emission into an open optical system