Coupled mode theory for plasmonic couplers

Photonic integrated circuits play an increasingly important role in several emerging technologies. Their functionality arises from a combination of integrated components, e.g., couplers, splitters, polarization rotators, and wavelength selective filters. Efficient and accurate simulation of these components is crucial for circuit design and optimization. In dielectric systems, design procedures typically rely on coupled-mode theory (CMT) methods, which then guide subsequent refined full-wave calculations. Miniaturization to deep sub-wavelength scales requires the inclusion of lossy plasmonic (metal) components, making optimization more complicated by the interplay between coupling and absorption. Even though CMT is well developed, there is no consensus as to how to rigorously and quantitatively implement it for lossy systems. Here we present an intuitive coupled-mode theory framework for quantitative analysis of dielectric-plasmonic directional and adiabatic couplers, whose large-scale implementation in 3D is prohibitively slow with full-wave methods. This framework relies on adapting existing coupled mode theory approaches by including loss as a perturbation. This approach will be useful in designing dielectric-plasmonic circuits, providing a first reference point for anyone using techniques such as inverse design and deep learning optimization methods.