1 CHAPTER 1 EFFICIENT AND ACCURATE BOUNDARY METHODS FOR COMPUTATIONAL OPTICS

The Multiple Multipole Program (MMP) is an advanced boundary method for computational electromagnetics and optics. Its closeness to analytical methods allows one to obtain highly accurate and reliable results. After a short introduction of the fundamentals of MMP, additional techniques are introduced that allow one to drastically improve the performance for various applications. This includes 1) a special consideration of ill-conditioned matrices, 2) the so-called connection concept, 3) an advanced eigenvalue solver with a special eigenvalue tracing procedure, and 4) the Parameter Estimation Technique (PET). Special attention is paid to the error estimation and validation of the results. In a second section, the most recent MMP version of the MaX-1 software with its advanced modeling, visualization, and animation features is presented and it is demonstrated how this software is used for handling complicated projects. Thereafter, some typical applications of computational optics with a focus on photonic bandgap computations and photonic crystal structures are presented. 1. The Multiple Multipole Program (MMP) concept for electrodynamics The Multiple Multipole Program (MMP) concept was developed since 1980 [1] at ETH Zurich as an extension of the traditional multipole Ch. Hafner and J. Smajic 2 approximation that was used by Mie in 1900 for the computation of electromagnetic waves along circular wires [2] and in 1908 [3] for the scattering at a spherical particle. MMP is therefore very close to analytical solutions and is sometimes called a semi-analytical approach. In fact, MMP approximates the field in any domain by a series expansio