FEM (Finite Element Method) in optics

FEM (Finite Element Method) is a numerical method that divides an optical structure into a mesh of small elements (usually triangles or tetrahedra), within which the wave equations are solved.

How does FEM work in a photonics context?

Unlike the regular grids used in FDTD, an FEM mesh can be locally refined where the field changes rapidly — e.g. at waveguide edges — giving high accuracy with fewer elements. FEM is especially effective for determining the modes of waveguides with complex, irregular cross-sections.

Applications

FEM is used mainly as the computational engine of mode solvers for waveguides with complicated geometry — rib waveguides, polymer waveguides, or waveguides with a non-standard refractive-index profile, where a regular difference grid would be inefficient.

Related terms

Mode solver

Optical waveguide

FDTD