Thermal Models for Optical Circuit Simulation Using a Finite Cloud Method and Model Reduction Techniques

This paper presents a procedure for the creation of versatile and powerful thermal compact models of integrated optical devices and demonstrates their use in an optical circuit level simulator. A detailed 3-D model of the device is first built using a meshless finite cloud method, producing a large linear sparse set of equations. This model is then reduced to a compact representation using a Krylov subspace model reduction (MR) technique. Such a reduced model is described by small dense matrices, but can reproduce the original temperature distribution within acceptable error. Three devices are used as demonstration models for the technique: a microdisc laser and two microring-based devices, a modulator, and an optical switch. All three devices are built in a silicon on oxide platform. Using MR the linear systems describing these models are reduced from thousands of unknowns to systems with less than 100 reduced variables. It is then demonstrated how the reduced compact models can be linked together to describe a complete optical system with solution errors of lower than 1%. Finally, it is shown how this reduced thermal model can be utilized in a circuit level opto-electronic circuit simulator and simulations are presented, demonstrating the effectiveness of the reduced models in speeding up simulation times or enabling otherwise intractable problems.