Photonic crystal characterization by FDTD and principal component analysis

Abstract

Abstract:We demonstrate the capabilities of principal component analysis (PCA) for studying the results of finite-difference time-domain (FDTD) algorithms in simulating photonic crystal microcavities. The spatial-temporal structures provided by PCA are related to the actual electric field vibrating inside the photonic microcavity. A detailed analysis of the results has made it possible to compute the phase maps for each mode of the arrangement at their respective resonant frequencies. The existence of standing wave behavior is revealed by this analysis. In spite of this, some numerical artifacts induced by FDTD algorithms have been clearly detailed through PCA analysis. The data we have analyzed are a given set of maps of the electric field recorded during the simulation.

Characterization of photonic crystal microcavities with manufacture imperfections

“…They can be added to form a complex electromagnetic distribution. The first and second principal component have been identified with the real and imaginary part of a complex electromagnetic distribution corresponding with the monopolar mode (see [9] and [8]). The third and fourth principal components configure the second quasi-monochromatic process.…”

“…The filtered data resembles very much the shape of the monopolar mode. The evolution of the difference should be compared with the plot of Figure 4 of reference [8] where the same kind of filtering was applied to the results obtained for the unperturbed crystal. Fig.…”

“…When the temporal evolution is quasi-harmonic, the identification of those eigenimages having a similar temporal evolution makes possible the definition of quasi-harmonic processes. All these facts where used in a previous contribution to characterize the presence of numerical noise, and some other artifacts, in the FDTD simulation of microcavities [8] [10]. The PCA method proved its validity to extract hidden spatial-temporal structures embedded in the original data and having interesting physical meanings.…”

“…This is the case of the characterization of noise in imaging devices, identification of bad pixels, extraction of spatial-temporal features in web cameras, both in the visible and the infrared [7,15,16]. We have also applied it to the analysis numeric artifacts appearing in FDTD results [8], in the characterization of a photonic crystal microcavity [10]. Although the basis of the method have been well established and fully developed in the referenced papers, we include a very short description of the characteristics of the method when applied to the analysis of FDTD frames.…”

“…in a similar manner. In a previous paper [8], PCA has successfully characterized the modes of a well-known photonic structure [9]. Also, the numerical noise embedded in FDTD simulations has been quantified and filtered using PCA [10].…”