Principal Component Analysis of Results Obtained from Finite-Difference Time-Domain Algorithms

Finite-Differences Time-Domain (FDTD) algorithms are well
established tools of computational electromagnetism. Because of their practical
implementation as computer codes, they are affected by many numerical
artefact and noise. In order to obtain better results we propose using Principal
Component Analysis (PCA) based on multivariate statistical techniques. The
PCA has been successfully used for the analysis of noise and spatial temporal
structure in a sequence of images. It allows a straightforward discrimination
between the numerical noise and the actual electromagnetic variables, and the
quantitative estimation of their respective contributions. Besides, The GDTD
results can be filtered to clean the effect of the noise. In this contribution we
will show how the method can be applied to several FDTD simulations: the
propagation of a pulse in vacuum, the analysis of two-dimensional photonic
crystals. In this last case, PCA has revealed hidden electromagnetic structures
related to actual modes of the photonic crystal.