Abstract
The manufacture of a photonic crystal always produce deviations from the ideal case. In this paper we present a detailed analysis of the influence of the manufacture errors in the resulting electric field distribution of a photonic crystal microcavity. The electromagnetic field has been obtained from a FDTD algorithm. The results are studied by using the Principal Component Analysis method. This approach quantifies the influence of the error in the preservation of the spatialtemporal structure of electromagnetic modes of the ideal microcavity. The results show that the spatial structure of the excited mode is well preserved within the range of imperfection analyzed in the paper. The deviation from the ideal case has been described and quantitatively estimated.
© 2005 Optical Society of America
Full Article  PDF ArticleOSA Recommended Articles
José M. LópezAlonso, José M. RicoGarcía, and Javier Alda
Opt. Express 12(10) 21762186 (2004)
José Manuel LópezAlonso, Brian Monacelli, Javier Alda, and Glenn Boreman
Appl. Opt. 44(21) 45574568 (2005)
Alejandro Ferrero, Javier Alda, Joaquín Campos, Jose Manuel LópezAlonso, and Alicia Pons
Appl. Opt. 46(1) 917 (2007)
References
 View by:
 Article Order
 
 Year
 
 Author
 
 Publication
 G. Guida, T. Brillat, A. Amouche, F. Gadot, A. De Lustrac, and A. Priou “Dissociating the effect of different disturbances on the band gap of a two dimensional photonic crystal,” J. App. Phys. 88, 4491–4497 (2000).
[Crossref]  N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, K. P. Hansen, and J. Lgsgaard “Smallcore photonic crystal fibers with weakly disordered airhole claddings,” J. Opt. A Pure Appl. Opt. 6, 221–223 (2004).
[Crossref]  M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. Soukoulis. “Photonic band gaps, defect characteristics, and waveguiding in twodimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B, 64, 195113–7 (2001).
[Crossref]  G. Guida, “Numerical studies of disordered photonic crystals,” Progress in Electromagnetic Research (PIER), 41, 107–131, (2003).
[Crossref]  W. R. Frei and H. T. Johnson “Finiteelement analysis of disorder effects in photonic crystals,” Phys. Rev. B, 70, 165116–11 (2004).
[Crossref]  D. F. Morrison, Multivariate Statistical Methods, 3rd ed. (McGrawHill, Singapore, 1990) Chap. 8.

J. M. LópezAlonso, J. Alda, and E. Bernabéu, “Principal component characterization of noise for infrared images,” Appl. Opt. 41, 320–331 (2002).
[Crossref] [PubMed] 
J. M. LópezAlonso, J. M. RicoGarcía, and J. Alda, “Photonic crystal characterization by FDTD and principal component analysis,” Opt. Express, 12, 2176–2186 (2004).
[Crossref] [PubMed] 
S. Guo and S. Albin “Numerical Techniques for excitation and analysis of defect modes in photonic crystals,” Opt. Express, 11, 1080–1089 (2003).
[Crossref] [PubMed]  J. M. LópezAlonso, J. M. RicoGarcía, and J. Alda, “Numerical artifacts in finitedifference timedomain algorithms analyzed by means of Principal Components,” IEEE Trans. Antennas and Propagation (in press) (2005).

M. Skorobogatiy, G. Bégin, and A. Talneau, “Statistical analysis of geometrical imperfections from the images of 2D photonic crystals,” Opt. Express, 13, 2487–2502 (2005).
[Crossref] [PubMed]  P. R. Villeneuve, S. Fan, and J. D. Joannopoulos “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B, 54, 7837–7842 (1996).
[Crossref]  M. Qiu and S. He “Numerical method for computing defect modes in twodimensional photonic crystals with dielectric or metallic inclusions,” Phys. Rev. B, 61, 12871–12876 (2000).
[Crossref]  A. Taflove and S. Hagness, Computacional Electrodynamics: The FiniteDifference Time Domain Method, 2nd edition, Artech House (2000).
 R. Schuhmann and T. Weiland, “The Nonorthogonal Finite IntegrationTechnique Applied to 2D and 3DEigenvalue Problems,” IEEE Trans. on Magnetics, 36, 897–901 (2000).
[Crossref]  J. M. LópezAlonso and J. Alda, “Bad pixel identification by means of the principal component analysis,” Opt. Eng. 41, 2152–2157 (2002).
[Crossref]  J. M. LópezAlonso and J. Alda, “Characterization of artifacts in fullydigital imageacquisition systems. Application to web cameras,” Opt. Eng. 43, 257–265 (2004).
[Crossref]
2005 (1)
M. Skorobogatiy, G. Bégin, and A. Talneau, “Statistical analysis of geometrical imperfections from the images of 2D photonic crystals,” Opt. Express, 13, 2487–2502 (2005).
[Crossref]
[PubMed]
2004 (4)
J. M. LópezAlonso and J. Alda, “Characterization of artifacts in fullydigital imageacquisition systems. Application to web cameras,” Opt. Eng. 43, 257–265 (2004).
[Crossref]
N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, K. P. Hansen, and J. Lgsgaard “Smallcore photonic crystal fibers with weakly disordered airhole claddings,” J. Opt. A Pure Appl. Opt. 6, 221–223 (2004).
[Crossref]
W. R. Frei and H. T. Johnson “Finiteelement analysis of disorder effects in photonic crystals,” Phys. Rev. B, 70, 165116–11 (2004).
[Crossref]
J. M. LópezAlonso, J. M. RicoGarcía, and J. Alda, “Photonic crystal characterization by FDTD and principal component analysis,” Opt. Express, 12, 2176–2186 (2004).
[Crossref]
[PubMed]
2003 (2)
S. Guo and S. Albin “Numerical Techniques for excitation and analysis of defect modes in photonic crystals,” Opt. Express, 11, 1080–1089 (2003).
[Crossref]
[PubMed]
G. Guida, “Numerical studies of disordered photonic crystals,” Progress in Electromagnetic Research (PIER), 41, 107–131, (2003).
[Crossref]
2002 (2)
J. M. LópezAlonso, J. Alda, and E. Bernabéu, “Principal component characterization of noise for infrared images,” Appl. Opt. 41, 320–331 (2002).
[Crossref]
[PubMed]
J. M. LópezAlonso and J. Alda, “Bad pixel identification by means of the principal component analysis,” Opt. Eng. 41, 2152–2157 (2002).
[Crossref]
2001 (1)
M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. Soukoulis. “Photonic band gaps, defect characteristics, and waveguiding in twodimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B, 64, 195113–7 (2001).
[Crossref]
2000 (3)
G. Guida, T. Brillat, A. Amouche, F. Gadot, A. De Lustrac, and A. Priou “Dissociating the effect of different disturbances on the band gap of a two dimensional photonic crystal,” J. App. Phys. 88, 4491–4497 (2000).
[Crossref]
M. Qiu and S. He “Numerical method for computing defect modes in twodimensional photonic crystals with dielectric or metallic inclusions,” Phys. Rev. B, 61, 12871–12876 (2000).
[Crossref]
R. Schuhmann and T. Weiland, “The Nonorthogonal Finite IntegrationTechnique Applied to 2D and 3DEigenvalue Problems,” IEEE Trans. on Magnetics, 36, 897–901 (2000).
[Crossref]
1996 (1)
P. R. Villeneuve, S. Fan, and J. D. Joannopoulos “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B, 54, 7837–7842 (1996).
[Crossref]
Albin, S.
S. Guo and S. Albin “Numerical Techniques for excitation and analysis of defect modes in photonic crystals,” Opt. Express, 11, 1080–1089 (2003).
[Crossref]
[PubMed]
Alda, J.
J. M. LópezAlonso, J. M. RicoGarcía, and J. Alda, “Photonic crystal characterization by FDTD and principal component analysis,” Opt. Express, 12, 2176–2186 (2004).
[Crossref]
[PubMed]
J. M. LópezAlonso and J. Alda, “Characterization of artifacts in fullydigital imageacquisition systems. Application to web cameras,” Opt. Eng. 43, 257–265 (2004).
[Crossref]
J. M. LópezAlonso and J. Alda, “Bad pixel identification by means of the principal component analysis,” Opt. Eng. 41, 2152–2157 (2002).
[Crossref]
J. M. LópezAlonso, J. Alda, and E. Bernabéu, “Principal component characterization of noise for infrared images,” Appl. Opt. 41, 320–331 (2002).
[Crossref]
[PubMed]
J. M. LópezAlonso, J. M. RicoGarcía, and J. Alda, “Numerical artifacts in finitedifference timedomain algorithms analyzed by means of Principal Components,” IEEE Trans. Antennas and Propagation (in press) (2005).
Amouche, A.
G. Guida, T. Brillat, A. Amouche, F. Gadot, A. De Lustrac, and A. Priou “Dissociating the effect of different disturbances on the band gap of a two dimensional photonic crystal,” J. App. Phys. 88, 4491–4497 (2000).
[Crossref]
Bayindir, M.
M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. Soukoulis. “Photonic band gaps, defect characteristics, and waveguiding in twodimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B, 64, 195113–7 (2001).
[Crossref]
Bégin, G.
M. Skorobogatiy, G. Bégin, and A. Talneau, “Statistical analysis of geometrical imperfections from the images of 2D photonic crystals,” Opt. Express, 13, 2487–2502 (2005).
[Crossref]
[PubMed]
Bernabéu, E.
J. M. LópezAlonso, J. Alda, and E. Bernabéu, “Principal component characterization of noise for infrared images,” Appl. Opt. 41, 320–331 (2002).
[Crossref]
[PubMed]
Brillat, T.
G. Guida, T. Brillat, A. Amouche, F. Gadot, A. De Lustrac, and A. Priou “Dissociating the effect of different disturbances on the band gap of a two dimensional photonic crystal,” J. App. Phys. 88, 4491–4497 (2000).
[Crossref]
Bulu, I.
M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. Soukoulis. “Photonic band gaps, defect characteristics, and waveguiding in twodimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B, 64, 195113–7 (2001).
[Crossref]
Cubukcu, E.
M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. Soukoulis. “Photonic band gaps, defect characteristics, and waveguiding in twodimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B, 64, 195113–7 (2001).
[Crossref]
De Lustrac, A.
G. Guida, T. Brillat, A. Amouche, F. Gadot, A. De Lustrac, and A. Priou “Dissociating the effect of different disturbances on the band gap of a two dimensional photonic crystal,” J. App. Phys. 88, 4491–4497 (2000).
[Crossref]
Fan, S.
P. R. Villeneuve, S. Fan, and J. D. Joannopoulos “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B, 54, 7837–7842 (1996).
[Crossref]
Folkenberg, J. R.
N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, K. P. Hansen, and J. Lgsgaard “Smallcore photonic crystal fibers with weakly disordered airhole claddings,” J. Opt. A Pure Appl. Opt. 6, 221–223 (2004).
[Crossref]
Frei, W. R.
W. R. Frei and H. T. Johnson “Finiteelement analysis of disorder effects in photonic crystals,” Phys. Rev. B, 70, 165116–11 (2004).
[Crossref]
Gadot, F.
G. Guida, T. Brillat, A. Amouche, F. Gadot, A. De Lustrac, and A. Priou “Dissociating the effect of different disturbances on the band gap of a two dimensional photonic crystal,” J. App. Phys. 88, 4491–4497 (2000).
[Crossref]
Guida, G.
G. Guida, “Numerical studies of disordered photonic crystals,” Progress in Electromagnetic Research (PIER), 41, 107–131, (2003).
[Crossref]
G. Guida, T. Brillat, A. Amouche, F. Gadot, A. De Lustrac, and A. Priou “Dissociating the effect of different disturbances on the band gap of a two dimensional photonic crystal,” J. App. Phys. 88, 4491–4497 (2000).
[Crossref]
Guo, S.
S. Guo and S. Albin “Numerical Techniques for excitation and analysis of defect modes in photonic crystals,” Opt. Express, 11, 1080–1089 (2003).
[Crossref]
[PubMed]
Hagness, S.
A. Taflove and S. Hagness, Computacional Electrodynamics: The FiniteDifference Time Domain Method, 2nd edition, Artech House (2000).
Hansen, K. P.
N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, K. P. Hansen, and J. Lgsgaard “Smallcore photonic crystal fibers with weakly disordered airhole claddings,” J. Opt. A Pure Appl. Opt. 6, 221–223 (2004).
[Crossref]
He, S.
M. Qiu and S. He “Numerical method for computing defect modes in twodimensional photonic crystals with dielectric or metallic inclusions,” Phys. Rev. B, 61, 12871–12876 (2000).
[Crossref]
Joannopoulos, J. D.
P. R. Villeneuve, S. Fan, and J. D. Joannopoulos “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B, 54, 7837–7842 (1996).
[Crossref]
Johnson, H. T.
W. R. Frei and H. T. Johnson “Finiteelement analysis of disorder effects in photonic crystals,” Phys. Rev. B, 70, 165116–11 (2004).
[Crossref]
Lgsgaard, J.
N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, K. P. Hansen, and J. Lgsgaard “Smallcore photonic crystal fibers with weakly disordered airhole claddings,” J. Opt. A Pure Appl. Opt. 6, 221–223 (2004).
[Crossref]
LópezAlonso, J. M.
J. M. LópezAlonso and J. Alda, “Characterization of artifacts in fullydigital imageacquisition systems. Application to web cameras,” Opt. Eng. 43, 257–265 (2004).
[Crossref]
J. M. LópezAlonso, J. M. RicoGarcía, and J. Alda, “Photonic crystal characterization by FDTD and principal component analysis,” Opt. Express, 12, 2176–2186 (2004).
[Crossref]
[PubMed]
J. M. LópezAlonso, J. Alda, and E. Bernabéu, “Principal component characterization of noise for infrared images,” Appl. Opt. 41, 320–331 (2002).
[Crossref]
[PubMed]
J. M. LópezAlonso and J. Alda, “Bad pixel identification by means of the principal component analysis,” Opt. Eng. 41, 2152–2157 (2002).
[Crossref]
J. M. LópezAlonso, J. M. RicoGarcía, and J. Alda, “Numerical artifacts in finitedifference timedomain algorithms analyzed by means of Principal Components,” IEEE Trans. Antennas and Propagation (in press) (2005).
Morrison, D. F.
D. F. Morrison, Multivariate Statistical Methods, 3rd ed. (McGrawHill, Singapore, 1990) Chap. 8.
Mortensen, N. A.
N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, K. P. Hansen, and J. Lgsgaard “Smallcore photonic crystal fibers with weakly disordered airhole claddings,” J. Opt. A Pure Appl. Opt. 6, 221–223 (2004).
[Crossref]
Nielsen, M. D.
N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, K. P. Hansen, and J. Lgsgaard “Smallcore photonic crystal fibers with weakly disordered airhole claddings,” J. Opt. A Pure Appl. Opt. 6, 221–223 (2004).
[Crossref]
Ozbay, E.
M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. Soukoulis. “Photonic band gaps, defect characteristics, and waveguiding in twodimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B, 64, 195113–7 (2001).
[Crossref]
Priou, A.
G. Guida, T. Brillat, A. Amouche, F. Gadot, A. De Lustrac, and A. Priou “Dissociating the effect of different disturbances on the band gap of a two dimensional photonic crystal,” J. App. Phys. 88, 4491–4497 (2000).
[Crossref]
Qiu, M.
M. Qiu and S. He “Numerical method for computing defect modes in twodimensional photonic crystals with dielectric or metallic inclusions,” Phys. Rev. B, 61, 12871–12876 (2000).
[Crossref]
RicoGarcía, J. M.
J. M. LópezAlonso, J. M. RicoGarcía, and J. Alda, “Photonic crystal characterization by FDTD and principal component analysis,” Opt. Express, 12, 2176–2186 (2004).
[Crossref]
[PubMed]
J. M. LópezAlonso, J. M. RicoGarcía, and J. Alda, “Numerical artifacts in finitedifference timedomain algorithms analyzed by means of Principal Components,” IEEE Trans. Antennas and Propagation (in press) (2005).
Schuhmann, R.
R. Schuhmann and T. Weiland, “The Nonorthogonal Finite IntegrationTechnique Applied to 2D and 3DEigenvalue Problems,” IEEE Trans. on Magnetics, 36, 897–901 (2000).
[Crossref]
Skorobogatiy, M.
M. Skorobogatiy, G. Bégin, and A. Talneau, “Statistical analysis of geometrical imperfections from the images of 2D photonic crystals,” Opt. Express, 13, 2487–2502 (2005).
[Crossref]
[PubMed]
Soukoulis, C.
M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. Soukoulis. “Photonic band gaps, defect characteristics, and waveguiding in twodimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B, 64, 195113–7 (2001).
[Crossref]
Taflove, A.
A. Taflove and S. Hagness, Computacional Electrodynamics: The FiniteDifference Time Domain Method, 2nd edition, Artech House (2000).
Talneau, A.
M. Skorobogatiy, G. Bégin, and A. Talneau, “Statistical analysis of geometrical imperfections from the images of 2D photonic crystals,” Opt. Express, 13, 2487–2502 (2005).
[Crossref]
[PubMed]
Tut, T.
M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. Soukoulis. “Photonic band gaps, defect characteristics, and waveguiding in twodimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B, 64, 195113–7 (2001).
[Crossref]
Villeneuve, P. R.
P. R. Villeneuve, S. Fan, and J. D. Joannopoulos “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B, 54, 7837–7842 (1996).
[Crossref]
Weiland, T.
R. Schuhmann and T. Weiland, “The Nonorthogonal Finite IntegrationTechnique Applied to 2D and 3DEigenvalue Problems,” IEEE Trans. on Magnetics, 36, 897–901 (2000).
[Crossref]
Appl. Opt. (1)
J. M. LópezAlonso, J. Alda, and E. Bernabéu, “Principal component characterization of noise for infrared images,” Appl. Opt. 41, 320–331 (2002).
[Crossref]
[PubMed]
IEEE Trans. on Magnetics (1)
R. Schuhmann and T. Weiland, “The Nonorthogonal Finite IntegrationTechnique Applied to 2D and 3DEigenvalue Problems,” IEEE Trans. on Magnetics, 36, 897–901 (2000).
[Crossref]
J. App. Phys. (1)
G. Guida, T. Brillat, A. Amouche, F. Gadot, A. De Lustrac, and A. Priou “Dissociating the effect of different disturbances on the band gap of a two dimensional photonic crystal,” J. App. Phys. 88, 4491–4497 (2000).
[Crossref]
J. Opt. A Pure Appl. Opt. (1)
N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, K. P. Hansen, and J. Lgsgaard “Smallcore photonic crystal fibers with weakly disordered airhole claddings,” J. Opt. A Pure Appl. Opt. 6, 221–223 (2004).
[Crossref]
Opt. Eng. (2)
J. M. LópezAlonso and J. Alda, “Bad pixel identification by means of the principal component analysis,” Opt. Eng. 41, 2152–2157 (2002).
[Crossref]
J. M. LópezAlonso and J. Alda, “Characterization of artifacts in fullydigital imageacquisition systems. Application to web cameras,” Opt. Eng. 43, 257–265 (2004).
[Crossref]
Opt. Express (3)
M. Skorobogatiy, G. Bégin, and A. Talneau, “Statistical analysis of geometrical imperfections from the images of 2D photonic crystals,” Opt. Express, 13, 2487–2502 (2005).
[Crossref]
[PubMed]
J. M. LópezAlonso, J. M. RicoGarcía, and J. Alda, “Photonic crystal characterization by FDTD and principal component analysis,” Opt. Express, 12, 2176–2186 (2004).
[Crossref]
[PubMed]
S. Guo and S. Albin “Numerical Techniques for excitation and analysis of defect modes in photonic crystals,” Opt. Express, 11, 1080–1089 (2003).
[Crossref]
[PubMed]
Phys. Rev. B (4)
M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. Soukoulis. “Photonic band gaps, defect characteristics, and waveguiding in twodimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B, 64, 195113–7 (2001).
[Crossref]
P. R. Villeneuve, S. Fan, and J. D. Joannopoulos “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B, 54, 7837–7842 (1996).
[Crossref]
M. Qiu and S. He “Numerical method for computing defect modes in twodimensional photonic crystals with dielectric or metallic inclusions,” Phys. Rev. B, 61, 12871–12876 (2000).
[Crossref]
W. R. Frei and H. T. Johnson “Finiteelement analysis of disorder effects in photonic crystals,” Phys. Rev. B, 70, 165116–11 (2004).
[Crossref]
Progress in Electromagnetic Research (PIER) (1)
G. Guida, “Numerical studies of disordered photonic crystals,” Progress in Electromagnetic Research (PIER), 41, 107–131, (2003).
[Crossref]
Other (3)
J. M. LópezAlonso, J. M. RicoGarcía, and J. Alda, “Numerical artifacts in finitedifference timedomain algorithms analyzed by means of Principal Components,” IEEE Trans. Antennas and Propagation (in press) (2005).
D. F. Morrison, Multivariate Statistical Methods, 3rd ed. (McGrawHill, Singapore, 1990) Chap. 8.
A. Taflove and S. Hagness, Computacional Electrodynamics: The FiniteDifference Time Domain Method, 2nd edition, Artech House (2000).
Supplementary Material (5)
» Media 1: AVI (1829 KB) 
» Media 2: AVI (1885 KB) 
» Media 3: AVI (1829 KB) 
» Media 4: AVI (1125 KB) 
» Media 5: AVI (1351 KB) 
Cited By
OSA participates in Crossref's CitedBy Linking service. Citing articles from OSA journals and other participating publishers are listed here.
Alert me when this article is cited.
Figures (8)
Permittivity maps for three realizations of the photonic crystal microcavity. The error increases from left to right (1%, 3%, and 5%). The white portion around the rods represent the possible locations of the rods for the statistical realizations analyzed in this paper. This portion grows as the manufacture imperfection increases.
Temporal evolution of the electric field component,
Plot of the basic electric field distributions obtained from the PCA method for several excitations and for the unperturbed photonic crystal microcavity. The columns [MP] and [SW] are for the excitation of the monopolar mode. Only the column [MP] is describing the monopolar mode. These four plots are the first four eigenimages obtained from PCA (see Fig. 6). The columns [Q1] and [Q2] are the first two eigenimages for the two possible quadrupolar excitations. The columns [H1] and [H2] are for the hexapolar excitations. The eigenimages located in the same column correspond with eigenvalues having the same frequency but shifted
Plot of the logarithm of the first ten eigenvalues obtained from the PCA decomposition. The unperturbed case (green) can be compared with the those cases showing a 1% (black), 3% (red), and 5% (blue) of error. The dots are for the ensemble average, 〈
Spatial distribution of the averaged principal components 〈PC_{1}〉, 〈PC_{2}〉, 〈PC_{3}〉, and 〈PC_{4}〉, for the three level of imperfection analyzed in this paper.
On the left of this Fig. we present the spatial temporal evolution of the filtered version of the original data set at 5% level of imperfection (video file
Plots of the average and standard deviation (error bars) of the coefficients (left column) and cosines (right column) obtained when projecting the first three principal components on the basis of electromagnetic distributions obtained from the PCA method applied to the unperturbed photonic crystal. The labels on the horizontal axis denote the modes presented in Fig. 3. The three manufacture imperfections are presented with different colors 1% (black), 3% (red), and 5% (blue).
Tables (2)
Table 1. Relative contribution of
Table 2. Ensemble average of the percentage of energy explained by
Equations (7)
Equations on this page are rendered with MathJax. Learn more.