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Variational Effective Index Method for 3D Vectorial Scattering Problems in Photonics: TE Polarization
 

Summary: 1
Variational Effective Index Method for 3D Vectorial Scattering
Problems in Photonics: TE Polarization
O. V. Ivanova1
, R. Stoffer2
, L. Kauppinen1
, and M. Hammer1
1
MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands
2
Phoenix Software, Enschede, The Netherlands
Abstract-- Fully vectorial 3D simulations of photonic components are often almost pro-
hibitively CPU-time and memory-intensive, so one would opt for reduced models that capture the
essence of the full 3D structure, while being computationally much more efficient. Traditionally,
integrated optics designers use a technique called the Effective Index Method (EIM) to reduce a
simulation of a 3D structure to two spatial dimensions. However, frequently, as is the case for the
photonic crystal slabs (Figure 1), the effective parameters for the 2D simulation are only rather
ambiguously defined, i.e., rely more or less on guesswork. Here we have developed a mathemati-
cal formulation that allows to a priori derive these parameters when going from 3D to 2D based
on a sound variational reasoning (Variational EIM, VEIM). This is achieved by approximating

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente
Hammer, Manfred - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering; Mathematics