We present an analytical model for the dynamical self-heating effect in air-cladded optical microring resonators (ORRs). The spatially and time resolved temperature field is calculated by integrating the corresponding boundary value problem of the heat equation. It turns out that the self-heating amplitude is approximately proportional to the total absorbed power and anti-proportional to the thermal conductivity of the cladding material. Further, two-photon absorption plays a major role in the heating process, even for moderate input powers, due to the strong light confinement. Heating times are determined to be in the microsecond range and may limit the response time of ORR devices. The explicit formulas for the temperature fields allow a much faster determination of heating properties compared to elaborate finite element simulations. Thus, our model is predestinated for scanning large parameter spaces.

This work is funded through the project 17FUN05 “PhotOQuant” within the Programme EMPIR. The EMPIR initiative is co-founded by the European Union’s Horizon 2020 research and innovation program and the EMPIR Participating Countries.

Peer reviewed