Efficient modeling of tapered photonic structures

Tapered optical structures play a crucial role in modern photonics, enabling efficient coupling, mode conversion, and multiplexing. Modeling such structures is challenging since, as the region of interest shrinks, there is a significant loss of numerical resolution. We present a novel approach to modeling tapered structures by introducing the taper reference frame, which renders the tapered refractive index profile constant. Working in this frame eliminates the need for recalculating or resizing the refractive index distribution, which reduces computational overhead. Most importantly, our approach maintains high resolution in the region of interest, critical for capturing intricate features of the taper. We validate our method by comparing our simulations with analytical solutions. We applied our model to the analysis of photonic lanterns. Our results demonstrate vastly improved accuracy and computational efficiency compared to existing approaches. The proposed taper reference frame technique enables major advancements in the design and optimization of optical devices across various applications.