Publication: Principal Component Analysis of Results Obtained from Finite-Difference Time-Domain Algorithms
Loading...
Official URL
Full text at PDC
Publication Date
2006
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
The Egyptian Society of Solid State Science
Citations
Exportar
Abstract
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.
Description
Accesible a texto completo en la web del editor.
UCM subjects
Unesco subjects
Keywords
Citation
1. Taflove, Computacional Electrodynamics: The Finite-Difference Time Domain Method, 2nd edition, Artech House (2000).
2. L. Gürel and Ugur Ogüz, “Signal-Processing Techniques to Reduce the Sinusoidal Steady-State Error in the FDTD Method”, IEEE Trans. Antennas Propagat., 48, 585-593 (2000).
3. A. Taflove and K. Umashankar, “Radar cross section of general threedimensional scatterers”, IEEE Trans. Electromagn. Compat., EMC- 25, 433-440 (1983).
4. V. Oppenheim and R. W. Schafer, Discrete-Time SignalProcessing, Englewood Cliffs, NJ. Prentice-Hall, 1989.
5. S. Guo and S. Albin, “Numerical Techniques for excitation and analysis of defect modes in photonic crystals”, Opt. Express, 11, 1080-1089 (2003).
6. D. F. Morrison, Multivariate Statistical Methods, 3rd ed. McGraw-Hill, Singapore, 1990, Chap. 8.
7. J. M. López-Alonso, J. Alda, E. Bernabéu, “Principal components characterization of noise for infrared images”, Appl. Opt., 41, 320-331 (2002).
8. J. S. Juntunen, D. Tsiboukis. “Reduction of numerical dispersion in FDTD method through artificial anisotropy”. IEEE Trans. Microwave Theory and Technology 48, 582-588 (2000).
9. U. Ogüz, L. Gürel, and O. Arikan, “An efficient and accurate technique for the incident-wave excitations in the FDTD method”, IEEE Trans. Microwave Theory and Technology, 46, 869-882 (1998).
10. J. M. López-Alonso, J. Alda, “Operational parametrization of the 1/f noise of a sequence of frames by means of the principal components analysis in focal plane arrays”, Optical Engineering, 42, 1915-1922 (2003)
11. R. B. Cattell, “The scree test for the number of factors,” J. Multivar. Behav. Res. 1, 245–276 (1966).
12. J. M. López-Alonso, J. Alda, “Bad pixel identification by means of the principal components analysis” Optical Engineering, 41, 2152-2157 (2002).
13. J. M. López-Alonso, J. Alda, “Characterization of dynamic sea scenarios with infrared imagers”, Infrared Physics and Technology, 46, 355-363 (2005).
14. J. M. López-Alonso, J. Alda, “Characterization of artifacts in fully-digital imageacquisition systems. Application to web cameras”, Optical Engineering, 43, 257-265 (2004).
15. J. M. López-Alonso, J. M. Rico-García, J. Alda, “Numerical artifacts in finitedifference time-domain algorithms analyzed by means of Principal Components”, IEEE Transaction on Antennas and Propagation, 53, 2920-2927 (2005).
16. J. M. López-Alonso, J. M. Rico-García, J. Alda, “Photonic crystal characterization by FDTD and Principal Component Analysis”, Optics Express, 12, 2176-2186 (2004).
17. J. M. Rico-García, J. M. López-Alonso, J. Alda, “Multivariate analysis of photonic crystal microcavities with fabrication defects”, Proceedings SPIE, 5840, 562-571, (2005).
18. J. M. Rico-García, J. M. López-Alonso, J. Alda, “Characterization of Photonic Crystal Microcavities with Manufacture Imperfections”, Optics Express 13, 3802-3815, (2005) .