Eigencurrent expansion and linear embedding via Green's operators applied to design optimization of devices in electromagnetic band-gap structures

We present an efficient formulation based on the linear embedding via Green's operators (LEGO) and the eigencurrent expansion method to optimize composite wave interaction structures, e.g., photonic-crystal based devices. In LEGO, a composite structure is broken up into "bricks" that are characterized through scattering operators and the interaction among them is captured using transfer operators. By exploiting this diakoptic nature of LEGO, we show how the optimization is accomplished using an effective operator defined over the bricks (usually few) enclosing the space where the fields are sampled. This operator encompasses the effect of the surrounding and separates the domain to be optimized from the fixed one, enabling us to carry out the optimization with little computational effort.