Optimization of a Photonic Crystal Waveguide Termination using the Geometry Projection Method and COMSOL

W. R. Frei
COMSOL, Inc., Burlington, MA, USA

Using nonlinear programming, the shape of a set of dielectric rods surrounding the termination of a photonic crystal waveguide is optimized to increase the directional emission.

The Geometry Projection Method (GPM) is used to define the shape of the dielectric rods around the termination of a waveguide in a square lattice rods-in-air photonic crystal. GPM uses a set of control points in a higher dimensional space to define the shape and topology of the interfaces between the different material regions.

The performance of the device is quantified via a 2D finite element model. The sensitivities of the performance to the material distribution are computed via the Adjoint method. GPM is used to project the sensitivity of the performance function onto the control points. A gradient-based optimizer is then used to adjust the control points, which changes the shape of the dielectric rods.