Characterization of FDTD artifacts and modes in photonic crystals

FDTD algorithms are being used as a numeric tool for the analysis of photonic crystals. The definition of the modes associated with them is of interest for the study of the capabilities of photonic crystal devices. The Principal Component Analysis (PCA) has been applied here to a sequence of images corresponding to the electromagnetic fields obtained from the FDTD simulations. PCA has revealed and quantified the importance of the modes appearing in the photonic crystals. The capability of PCA to produce spatial structures, or maps, associated with temporal evolutions has made possible the calculation of the modulus and phase of the modes existing in the photonic crystal. Some other modes, contributing with an almost negligible amount to the total variance of the original data, are also revealed by the method. Besides, PCA has been used to quantify the contribution of the numerical noise of the algorithm and to identify the effect of artifacts related with the matching of the computational grid and the inner geometry of the photonic crystal