Ch. Hafner

Model-based parameter estimation (MBPE) for metallic photonic crystal filters

An efficient method for the accurate computation of the response of photonic crystal filters is obtained when model-based parameter estimation (MBPE) is combined with accurate field solvers. In this paper, MBPE is combined with MMP and MAS and the results are compared with results obtained from a commercial field solver. When metals are present in photonic crystal filters, strong material dispersion at optical frequencies causes nonlinearity of the filter response. It is demonstrated that MBPE is still useful although it is originally designed for linear systems.

The Multiple Multipole Program (MMP) and the Generalized Multipole Technique (GMT)

Publisher Summary The Multiple Multipole Program (MMP) was developed in the late 1970s and early 1980s starting from the Point Matching (PM) technique in conjunction with the Circular Harmonic Analysis (CHA). To obtain efficient and reliable codes, the numerical problems of both the CHA and the PM had to be removed. This goal was achieved by a careful analysis and a generalization of both methods. The resulting code was called Multiple Multipole Program (MMP) and the corresponding method was called Multiple Multipole (MMP) method. In 1989, the SPEX code was presented, which was very similar to the 3D MMP code for EM scattering. Moreover, it was recognized that several groups were working on techniques that could be considered as special cases of the MMP method. Therefore, Generalized Multipole Technique (GMT) was proposed as a new generic name. This chapter begins by discussing the expansion from CHA to MMP. All of the MMP expansions are analytic solutions of the Maxwell equations. These equations are linear and only linear material properties are admitted in the MMP code. Therefore, any linear combination of MMP expansions is again an analytic solution of the Maxwell equations. The chapter further discusses special MMP features such as weighting, fictitious boundaries, periodic problems, eigenvalue computation, and ill-conditioned matrix methods.

Shape optimization of microlenses

Microlenses are highly attractive for optical applications such as super resolution and photonic nanojets, but their design is more demanding than the one of larger lenses because resonance effects play an important role, which forces one to perform a full wave analysis. Although mostly spherical microlenses were studied in the past, they may have various shapes and their optimization is highly demanding, especially, when the shape is described with many parameters. We first outline a very powerful mathematical tool: shape optimization based on shape gradient computations. This procedure may be applied with much less numerical cost than traditional optimizers, especially when the number of parameters describing the shape goes to infinity. In order to demonstrate the concept, we optimize microlenses using shape optimization starting from more or less reasonable elliptical and semi-circular shapes. We show that strong increases of the performance of the lenses may be obtained for any reasonable value of the refraction index.

PBG devices based on periodic structures with defects

Most high-density integrated optics components contain optical waveguides, scatterers, resonators, etc. Photonic crystals, as periodical structures with some defects, have attracted much interest in this context as well. In every such device, the optical beam propagates crossing the boundaries of these parts several times. For example, realistic photonic crystals are illuminated by a waveguide mode and, therefore, modeling the coupling of a waveguide in the crystal taking into account the interaction with the walls will be of importance. In this paper we make an attempt to consider the geometry of the crystal and the shape of the boundary as well, especially those parts of the surface, where the optical beams are traveling. In other words, this is an attempt to simulate a more realistic structure in order to optimize the properties of the PBG circuit using the appropriate numerical experiments.

HOFMOPF — A general framework to design and optimize plasmonic structures

Optical nano antennas are currently promising key elements for sensing and optical communication [1, 2]. They may resonate even when they are much smaller than the wavelength. However, this extraordinary behaviour makes the design and simulation very difficult. Traditional RF antennas are essentially scalable, which implies relatively simple design rules [3]. In contrast to this, plasmonic nano antennas are not scalable, thus it is very hard or even impossible to obtain simple design rules.

Parallel computations of electromagnetic fields on PCs using transputers

The MMP (multiple multipole) programs are based on the generalized multipole technique which has been shown to be very efficient, especially for computations of electrodynamic fields. Since this method is relatively simple, there are no problems in implementing it on PCs. A major increase of the power of PCs may be obtained with INMOS T800 transputers, which allow parallel processing. The parallel versions of the MMP programs are presented as well as a comparison of the speed of different configurations for different applications. Three test examples are considered.<<ETX>>