Multi-Scale Multi-Domain Hybrid Finite Element Modeling of Light Propagation

We revisit finite element method of modeling multi-scale photonic/electromagnetic devices via the proposed beam basis function, in combination with domain decompositions. Our approach ensures mathematical and physical consistency, can also handle multi-scale computational tasks efficiently with the assistance of the damping block-Jacobi iterative solver. By implementing the first-order Robin transmission condition at the interfaces between neighboring subdomains and introducing the dual “current” variables, we can significantly reduce the computational burden and communication data volume during the iterative solving process. The theoretical foundation and detailed implementation procedures are presented, accompanied with two representative examples. The first example is a refractive-diffractive hybrid optical system with feature size contrast up to 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup>, while the second example is the free surface optical system wherein the geometric ray tracing algorithm is inadequate. The obtained results for the two examples show excellent agreement with the standard finite element method (standard FEM) with significantly reducing the number of meshes required for computation and memory usages to nearly one-fifth. Since the computational time is inversely proportional to the number of decomposed subdomains <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(N)$</tex> under the parallel computing configuration, the computational time in our work is approximately reduced to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1/3N$</tex> of that using standard FEM for the two examples.