Theory for Broadband Large-Area Purcell Enhancement

Using coupled-mode theory, we present a general analysis of the bandwidth-averaged large-area Purcell factor, defined as the ratio between power radiated to free space by an active structure and that emitted in bulk, and confirm the results with exact simulations. We show the possibility of a large broadband enhancement using a slot waveguide design with large-period patterning. Enhancement increases with the index contrast and decreases with parasitic absorption and slot thickness with specific scalings. Larger enhancement and total power can be achieved by stacking multiple thin slots. The physics discussed here opens the door to further improved design for broadband spontaneous emission enhancement and is relevant for many applications.