Inverse Design Problems in Electromagnetics and Nano-Photonics

Eli Yablonovitch
University of California, Los Angeles

Photonic crystals, are 2 and 3 dimensional structures, that are the analog for electromagnetics of the semiconductor crystals that play such an important role in electronics. Thus Maxwell’s equations are to photonic crystals, what Schrodinger’s equation is to conventional crystals. Since photonic crystals are purely products of our imagination, the question has always been what is the exact structure that should be fabricated?

Engineering design is formally a type of mathematical Inverse Problem. The design goal is a certain electromagnetic specification or desired electromagnetic performance. It is necessary to work backward from that goal to the exact design of the dielectric boundary that achieves the objective. For example, in mathematics, the Level Set Method has emerged as an excellent tool that can contribute to algorithms for the optimization of boundaries and edges.

In the Photonic Crystal field, the era of purely intuitive design may be obsolete. We must now concentrate more on design software, rational design, and the numerical solution of inverse problems. There are a number of inverse algorithms, including genetic algorithms, the error-propagation method, and simulated annealing that can contribute to future progress in photonic crystal design. It is expected that the study of photonic crystals will more and more be study and development of rational inverse design algorithms and software.