Abstract

We investigate the characteristics of higher-lying band gaps for two-dimensional photonic crystals with large dielectric contrast. An optimal common band gap is attained on a hexagonal lattice of circular dielectric cylinders at relatively higher bands. The corresponding TM and TE modes exhibit simultaneous band edges, around which the frequency branches tend to be dispersionless. Unlike the fundamental band gap which usually appears between the dielectric and air bands, the optimal higher-lying gap in the present study occurs between two consecutive dielectric-like bands with high energy fill factors. The underlying mechanism is illustrated with the apparent change of eigenmode patterns inside the dielectric regions for both polarizations. In particular, the common gap region is bounded by two successive orders of Mie resonance frequencies on a single dielectric cylinder with the same geometry and material, where the Mie resonance modes show similar internal fields with the respective eigenmodes for the photonic crystal.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2006

2005

2004

R. L. Chern, C. C. Chang, C. C. Chang, and R. R. Hwang, "Two Classes of Photonic Crystals with Simultaneous Band Gaps," Jpn. J. Appl. Phys. 43, 3484-3490 (2004).
[CrossRef]

J. Y. Ye, S. Matsuo, V. Mizeikis, and H. Misawa, "Silicon-based honeycomb photonic crystal structures with complete photonic band gap at 1.5 μm wavelength," J. Appl. Phys. 96, 6934 (2004).
[CrossRef]

R. L. Chern, C. C. Chang, C. C. Chang, and R. R. Hwang, "Numerical Study of Three-Dimensional Photonic Crystals with Large Band Gaps," J. Phys. Soc. Jpn. 73, 727-737 (2004).
[CrossRef]

C. C. Chang, J. Y. Chi, R. L. Chern, C. C. Chang, C. H. Lin, and C. O. Chang, "Effect of the inclusion of small metallic components in a two-dimensional dielectric photonic crystal with large full band gap," Phys. Rev. B 70, 75,108 (2004).
[CrossRef]

2003

R. L. Chern, C. C. Chang, C. C. Chang, and R. Hwang, "Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration," Phys. Rev. E 68, 26,704 (2003).
[CrossRef]

M. Straub, M. Ventura, and M. Gu, "Multiple Higher-Order Stop Gaps in Infrared Polymer Photonic Crystals," Phys. Rev. Lett. 91, 43,901 (2003).
[CrossRef]

L. Shen, Z. Ye, and S. He, "Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm," Phys. Rev. B 68, 35,109 (2003).
[CrossRef]

2002

J. Y. Ye, V. Mizeikis, Y. Xu, S. Matsuo, and H. Misawa, "Fabrication and optical characteristics of silicon-based two-dimensional photonic crystals with honeycomb lattice," Opt. Commun. 211, 205-213 (2002).
[CrossRef]

L. Shen, S. He, and S. Xiao, "Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels," Phys. Rev. B 66, 165,315 (2002).
[CrossRef]

2000

M. G. Salt and W. L. Barnes, "Flat photonic bands in guided modes of textured metallic microcavities," Phys. Rev. B 61, 11,125-11,135 (2000).

1999

A. Moroz and A. Tip, "Resonance-induced effects in photonic crystals," J. Phys. Condens Matter 11, 2503-2512 (1999).
[CrossRef]

1997

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature 386, 143-149 (1997).
[CrossRef]

C. S. Kee, J. E. Kim, and H. Y. Park, "Absolute photonic band gap in a two-dimensional square lattice of square dielectric rods in air," Phys. Rev. E 56, 6291-6293 (1997).
[CrossRef]

1996

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and D. Turner, "Localization of electromagnetic waves in twodimensional disordered systems," Phys. Rev. B 53, 8340-8348 (1996).
[CrossRef]

K. Ohtaka and Y. Tanabe, "Photonic Band using Vector Spherical Waves. I. Various Properties of Bloch Electric Fields and Heavy Photons," J. Phys. Soc. Jpn. 65, 2265-2275 (1996).
[CrossRef]

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

1993

1992

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Existence of a photonic band gap in two dimensions," Appl. Phys. Lett. 61, 495-497 (1992).
[CrossRef]

P. R. Villeneuve and M. Piche´, "Photonic band gaps in two-dimensional square and hexagonal lattices," Phys. Rev. B 46, 4969-4972 (1992).
[CrossRef]

1987

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

1973

R. C. Kell, A. C. Greenham, and G. C. E. Olds, "High-Permittivity Temperature-Stable Ceramic Dielectrics with Low Microwave Loss," J. Am. Ceram. Soc. 56, 352-354 (1973).
[CrossRef]

Barnes, W. L.

M. G. Salt and W. L. Barnes, "Flat photonic bands in guided modes of textured metallic microcavities," Phys. Rev. B 61, 11,125-11,135 (2000).

Bertho, D.

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

Brommer, K. D.

R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, "Nature of the photonic band gap: some insights from a field analysis," J. Opt. Soc. Am. B 10, 328-332 (1993).

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Existence of a photonic band gap in two dimensions," Appl. Phys. Lett. 61, 495-497 (1992).
[CrossRef]

Carras, M.

Cassagne, D.

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

Chan, C. T.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and D. Turner, "Localization of electromagnetic waves in twodimensional disordered systems," Phys. Rev. B 53, 8340-8348 (1996).
[CrossRef]

Chang, C. C.

R. L. Chern, C. C. Chang, and C. C. Chang, "Analysis of surface plasmon modes and band structures for plasmonic crystals in one and two dimensions," Phys. Rev. E 73, 36,605 (2006).
[CrossRef]

R. L. Chern, C. C. Chang, and C. C. Chang, "Analysis of surface plasmon modes and band structures for plasmonic crystals in one and two dimensions," Phys. Rev. E 73, 36,605 (2006).
[CrossRef]

H. K. Fu, Y. F. Chen, R. L. Chern, and C. C. Chang, "Connected hexagonal photonic crystals with largest full band gap," Opt. Express 13, 7854-7860 (2005).
[CrossRef] [PubMed]

R. L. Chern, C. C. Chang, C. C. Chang, and R. R. Hwang, "Two Classes of Photonic Crystals with Simultaneous Band Gaps," Jpn. J. Appl. Phys. 43, 3484-3490 (2004).
[CrossRef]

R. L. Chern, C. C. Chang, C. C. Chang, and R. R. Hwang, "Two Classes of Photonic Crystals with Simultaneous Band Gaps," Jpn. J. Appl. Phys. 43, 3484-3490 (2004).
[CrossRef]

C. C. Chang, J. Y. Chi, R. L. Chern, C. C. Chang, C. H. Lin, and C. O. Chang, "Effect of the inclusion of small metallic components in a two-dimensional dielectric photonic crystal with large full band gap," Phys. Rev. B 70, 75,108 (2004).
[CrossRef]

R. L. Chern, C. C. Chang, C. C. Chang, and R. R. Hwang, "Numerical Study of Three-Dimensional Photonic Crystals with Large Band Gaps," J. Phys. Soc. Jpn. 73, 727-737 (2004).
[CrossRef]

R. L. Chern, C. C. Chang, C. C. Chang, and R. R. Hwang, "Numerical Study of Three-Dimensional Photonic Crystals with Large Band Gaps," J. Phys. Soc. Jpn. 73, 727-737 (2004).
[CrossRef]

C. C. Chang, J. Y. Chi, R. L. Chern, C. C. Chang, C. H. Lin, and C. O. Chang, "Effect of the inclusion of small metallic components in a two-dimensional dielectric photonic crystal with large full band gap," Phys. Rev. B 70, 75,108 (2004).
[CrossRef]

R. L. Chern, C. C. Chang, C. C. Chang, and R. Hwang, "Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration," Phys. Rev. E 68, 26,704 (2003).
[CrossRef]

R. L. Chern, C. C. Chang, C. C. Chang, and R. Hwang, "Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration," Phys. Rev. E 68, 26,704 (2003).
[CrossRef]

Chang, C. O.

C. C. Chang, J. Y. Chi, R. L. Chern, C. C. Chang, C. H. Lin, and C. O. Chang, "Effect of the inclusion of small metallic components in a two-dimensional dielectric photonic crystal with large full band gap," Phys. Rev. B 70, 75,108 (2004).
[CrossRef]

Chen, Y. F.

Chern, R. L.

R. L. Chern, C. C. Chang, and C. C. Chang, "Analysis of surface plasmon modes and band structures for plasmonic crystals in one and two dimensions," Phys. Rev. E 73, 36,605 (2006).
[CrossRef]

H. K. Fu, Y. F. Chen, R. L. Chern, and C. C. Chang, "Connected hexagonal photonic crystals with largest full band gap," Opt. Express 13, 7854-7860 (2005).
[CrossRef] [PubMed]

R. L. Chern, C. C. Chang, C. C. Chang, and R. R. Hwang, "Two Classes of Photonic Crystals with Simultaneous Band Gaps," Jpn. J. Appl. Phys. 43, 3484-3490 (2004).
[CrossRef]

C. C. Chang, J. Y. Chi, R. L. Chern, C. C. Chang, C. H. Lin, and C. O. Chang, "Effect of the inclusion of small metallic components in a two-dimensional dielectric photonic crystal with large full band gap," Phys. Rev. B 70, 75,108 (2004).
[CrossRef]

R. L. Chern, C. C. Chang, C. C. Chang, and R. R. Hwang, "Numerical Study of Three-Dimensional Photonic Crystals with Large Band Gaps," J. Phys. Soc. Jpn. 73, 727-737 (2004).
[CrossRef]

R. L. Chern, C. C. Chang, C. C. Chang, and R. Hwang, "Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration," Phys. Rev. E 68, 26,704 (2003).
[CrossRef]

Chi, J. Y.

C. C. Chang, J. Y. Chi, R. L. Chern, C. C. Chang, C. H. Lin, and C. O. Chang, "Effect of the inclusion of small metallic components in a two-dimensional dielectric photonic crystal with large full band gap," Phys. Rev. B 70, 75,108 (2004).
[CrossRef]

de Rossi, A.

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature 386, 143-149 (1997).
[CrossRef]

Fu, H. K.

Greenham, A. C.

R. C. Kell, A. C. Greenham, and G. C. E. Olds, "High-Permittivity Temperature-Stable Ceramic Dielectrics with Low Microwave Loss," J. Am. Ceram. Soc. 56, 352-354 (1973).
[CrossRef]

Gu, M.

M. Straub, M. Ventura, and M. Gu, "Multiple Higher-Order Stop Gaps in Infrared Polymer Photonic Crystals," Phys. Rev. Lett. 91, 43,901 (2003).
[CrossRef]

He, S.

L. Shen, Z. Ye, and S. He, "Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm," Phys. Rev. B 68, 35,109 (2003).
[CrossRef]

L. Shen, S. He, and S. Xiao, "Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels," Phys. Rev. B 66, 165,315 (2002).
[CrossRef]

Hwang, R.

R. L. Chern, C. C. Chang, C. C. Chang, and R. Hwang, "Large full band gaps for photonic crystals in two dimensions computed by an inverse method with multigrid acceleration," Phys. Rev. E 68, 26,704 (2003).
[CrossRef]

Hwang, R. R.

R. L. Chern, C. C. Chang, C. C. Chang, and R. R. Hwang, "Two Classes of Photonic Crystals with Simultaneous Band Gaps," Jpn. J. Appl. Phys. 43, 3484-3490 (2004).
[CrossRef]

R. L. Chern, C. C. Chang, C. C. Chang, and R. R. Hwang, "Numerical Study of Three-Dimensional Photonic Crystals with Large Band Gaps," J. Phys. Soc. Jpn. 73, 727-737 (2004).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature 386, 143-149 (1997).
[CrossRef]

R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, "Nature of the photonic band gap: some insights from a field analysis," J. Opt. Soc. Am. B 10, 328-332 (1993).

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Existence of a photonic band gap in two dimensions," Appl. Phys. Lett. 61, 495-497 (1992).
[CrossRef]

John, S.

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Jouanin, C.

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134-7142 (1996).
[CrossRef]

Kee, C. S.

C. S. Kee, J. E. Kim, and H. Y. Park, "Absolute photonic band gap in a two-dimensional square lattice of square dielectric rods in air," Phys. Rev. E 56, 6291-6293 (1997).
[CrossRef]

Kell, R. C.

R. C. Kell, A. C. Greenham, and G. C. E. Olds, "High-Permittivity Temperature-Stable Ceramic Dielectrics with Low Microwave Loss," J. Am. Ceram. Soc. 56, 352-354 (1973).
[CrossRef]

Kim, J. E.

C. S. Kee, J. E. Kim, and H. Y. Park, "Absolute photonic band gap in a two-dimensional square lattice of square dielectric rods in air," Phys. Rev. E 56, 6291-6293 (1997).
[CrossRef]

Lederer, F.

Lin, C. H.

C. C. Chang, J. Y. Chi, R. L. Chern, C. C. Chang, C. H. Lin, and C. O. Chang, "Effect of the inclusion of small metallic components in a two-dimensional dielectric photonic crystal with large full band gap," Phys. Rev. B 70, 75,108 (2004).
[CrossRef]

Matsuo, S.

J. Y. Ye, S. Matsuo, V. Mizeikis, and H. Misawa, "Silicon-based honeycomb photonic crystal structures with complete photonic band gap at 1.5 μm wavelength," J. Appl. Phys. 96, 6934 (2004).
[CrossRef]

J. Y. Ye, V. Mizeikis, Y. Xu, S. Matsuo, and H. Misawa, "Fabrication and optical characteristics of silicon-based two-dimensional photonic crystals with honeycomb lattice," Opt. Commun. 211, 205-213 (2002).
[CrossRef]

Meade, R. D.

R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, "Nature of the photonic band gap: some insights from a field analysis," J. Opt. Soc. Am. B 10, 328-332 (1993).

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Existence of a photonic band gap in two dimensions," Appl. Phys. Lett. 61, 495-497 (1992).
[CrossRef]

Misawa, H.

J. Y. Ye, S. Matsuo, V. Mizeikis, and H. Misawa, "Silicon-based honeycomb photonic crystal structures with complete photonic band gap at 1.5 μm wavelength," J. Appl. Phys. 96, 6934 (2004).
[CrossRef]

J. Y. Ye, V. Mizeikis, Y. Xu, S. Matsuo, and H. Misawa, "Fabrication and optical characteristics of silicon-based two-dimensional photonic crystals with honeycomb lattice," Opt. Commun. 211, 205-213 (2002).
[CrossRef]

Mizeikis, V.

J. Y. Ye, S. Matsuo, V. Mizeikis, and H. Misawa, "Silicon-based honeycomb photonic crystal structures with complete photonic band gap at 1.5 μm wavelength," J. Appl. Phys. 96, 6934 (2004).
[CrossRef]

J. Y. Ye, V. Mizeikis, Y. Xu, S. Matsuo, and H. Misawa, "Fabrication and optical characteristics of silicon-based two-dimensional photonic crystals with honeycomb lattice," Opt. Commun. 211, 205-213 (2002).
[CrossRef]

Moroz, A.

A. Moroz and A. Tip, "Resonance-induced effects in photonic crystals," J. Phys. Condens Matter 11, 2503-2512 (1999).
[CrossRef]

Ohtaka, K.

K. Ohtaka and Y. Tanabe, "Photonic Band using Vector Spherical Waves. I. Various Properties of Bloch Electric Fields and Heavy Photons," J. Phys. Soc. Jpn. 65, 2265-2275 (1996).
[CrossRef]

Olds, G. C. E.

R. C. Kell, A. C. Greenham, and G. C. E. Olds, "High-Permittivity Temperature-Stable Ceramic Dielectrics with Low Microwave Loss," J. Am. Ceram. Soc. 56, 352-354 (1973).
[CrossRef]

Park, H. Y.

C. S. Kee, J. E. Kim, and H. Y. Park, "Absolute photonic band gap in a two-dimensional square lattice of square dielectric rods in air," Phys. Rev. E 56, 6291-6293 (1997).
[CrossRef]

Peschel, U.

Piche´, M.

P. R. Villeneuve and M. Piche´, "Photonic band gaps in two-dimensional square and hexagonal lattices," Phys. Rev. B 46, 4969-4972 (1992).
[CrossRef]

Picon, O.

Plouin, J.

Rappe, A. M.

R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, "Nature of the photonic band gap: some insights from a field analysis," J. Opt. Soc. Am. B 10, 328-332 (1993).

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Existence of a photonic band gap in two dimensions," Appl. Phys. Lett. 61, 495-497 (1992).
[CrossRef]

Richalot, E.

Rockstuhl, C.

Salt, M. G.

M. G. Salt and W. L. Barnes, "Flat photonic bands in guided modes of textured metallic microcavities," Phys. Rev. B 61, 11,125-11,135 (2000).

Shen, L.

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[CrossRef]

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[CrossRef]

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J. Y. Ye, S. Matsuo, V. Mizeikis, and H. Misawa, "Silicon-based honeycomb photonic crystal structures with complete photonic band gap at 1.5 μm wavelength," J. Appl. Phys. 96, 6934 (2004).
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R. L. Chern, C. C. Chang, C. C. Chang, and R. R. Hwang, "Numerical Study of Three-Dimensional Photonic Crystals with Large Band Gaps," J. Phys. Soc. Jpn. 73, 727-737 (2004).
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M. G. Salt and W. L. Barnes, "Flat photonic bands in guided modes of textured metallic microcavities," Phys. Rev. B 61, 11,125-11,135 (2000).

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[CrossRef]

C. C. Chang, J. Y. Chi, R. L. Chern, C. C. Chang, C. H. Lin, and C. O. Chang, "Effect of the inclusion of small metallic components in a two-dimensional dielectric photonic crystal with large full band gap," Phys. Rev. B 70, 75,108 (2004).
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[CrossRef]

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[CrossRef]

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and D. Turner, "Localization of electromagnetic waves in twodimensional disordered systems," Phys. Rev. B 53, 8340-8348 (1996).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef] [PubMed]

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E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, "Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials," Phys. Rev. B 61, 458-13,464 (2000).
[CrossRef]

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (JohnWiley & Sons, New York, 1983).

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D. M. Pozar, Microwave engineering, 3rd ed. (Wiley, New York, 2005).

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Figures (6)

Fig. 1.
Fig. 1.

Contours of the higher-lying common gap ratio for a hexagonal lattice of circular cylinders with varying the dielectric constant ε d and cylinder radius r/a.

Fig. 2.
Fig. 2.

Band structure for a hexagonal lattice of circular cylinders with radius r/a=0.19 and dielectric constant ε d =26. Shaded area is the common band gap for both polarizations; the band gap width is 0.129(2πc/a) and the gap to mid-gap ratio is 25.3%. The unit cell and geometric parameters are shown on the right.

Fig. 3.
Fig. 3.

Magnetic field contours of the TE eigenmodes at the point G for the photonic crystal in Fig. 2. (a) eigenmode near the lower edge with ω=0.429(2πc/a), (b) eigenmode near the upper edge with ω=0.593(2πc/a).

Fig. 4.
Fig. 4.

Electric field contours of the TM eigenmodes at the point G for the photonic crystal in Fig. 2. (a) eigenmode near the lower edge with ω=0.425(2πc/a), (b) eigenmode near the upper edge with ω=0.618(2πc/a).

Fig. 5.
Fig. 5.

Amplitude coefficients of the scattered and internal fields for a dielectric circular cylinder of radius r=0.19a and dielectric constant ε d =26. (a) TE polarization, (b) TM polarization. Shaded areas correspond to the common band gap region for the photonic crystal in Fig. 2. Vertical solid and dashed lines indicate the waveguide mode frequencies related to Mie resonances.

Fig. 6.
Fig. 6.

Internal field patterns of Mie resonances for a dielectric circular cylinder of radius r=0.19a and dielectric constant ε d =26. (a) H int 01 field with ω=0.382(2πc/a), (b) H int 11 field with ω=0.607(2πc/a), (c) E int 11 field with ω=0.382(2πc/a), (d) E int 21 field with ω=0.617(2πc/a).

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

2 E = ε ( ω c ) 2 E ,
· ( 1 ε H ) = ( ω c ) 2 H ,
ϕ ( r + a i ) = e i k · a i ϕ ( r ) ,
Q E = E 2 d τ ε E 2 d τ , Q H = 1 ε H 2 d τ H 2 d τ ,
H scat = n = a n H n ( k ρ ) e i n ϕ , a n = i n J n ( x ) J n ' ( x 1 ) ε d J n ' ( x ) J n ( x 1 ) ε d H n ' ( x ) J n ( x 1 ) H n ( x ) J n ' ( x 1 ) ,
H int = n = b n J n ( ε d k ρ ) e i n ϕ , b n = i n 2 i / π x ε d H n ' ( x ) J n ( x 1 ) H n ( x ) J n ' ( x 1 ) ,
E scat = n = a n H n ( k ρ ) e i n ϕ , a n = i n ε d J n ( x ) J n ' ( x 1 ) J n ' ( x ) J n ( x 1 ) H n ' ( x ) J n ( x 1 ) ε d H n ( x ) J n ' ( x 1 ) ,
E int = n = b n J n ( ε d k ρ ) e i n ϕ , b n = i n 2 i / π x H n ' ( x ) J n ( x 1 ) ε d H n ( x ) J n ' ( x 1 ) ,

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