Abstract

Photonic crystal fibers (PCF) containing coated holes have recently been demonstrated experimentally, but haven’t been studied theoretically and numerically thus far. We extend the multipole formalism to take into account coated cylinders, and demonstrate its accuracy even with metallic coatings. We provide numerical tables for calibration of other numerical methods. Further, we study the guidance properties of several PCF with coated holes: we demonstrate that the confinement mechanisms of PCFs with high index coated holes depend on wavelength, and exhibit plasmonic resonances in metal coated PCFs.

© 2006 Optical Society of America

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2006 (5)

V. Dangui, M. J. F. Digonnet, and G. S. Kino, "A fast and accurate numerical tool to model the modal properties of photonic-bandgap fibers," Opt. Express 14, 2979-2993 (2006).
[CrossRef] [PubMed]

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

P. Boyer, G. Renversez, E. Popov, and M. Neviere, "A new differential method applied to the study of arbitrary cross section microstructured optical fibers," Opt. Quantum Electron. 38, 217-230 (2006).
[CrossRef]

J. M. Stone, G. J. Pearce, F. Luan, T. A. Birks, J. C. Knight, A. K. George, and D. M. Bird, "An improved photonic bandgap fiber based on an array of rings," Opt. Express 14, 6291-6296 (2006).
[CrossRef] [PubMed]

G. Renversez, P. Boyer, and A. Sagrini, "Antiresonant reflecting optical waveguide microstructured fibers revisited: a new analysis based on leaky mode coupling," Opt. Express 14, 5682-5687 (2006).
[CrossRef] [PubMed]

2005 (6)

2004 (11)

C. P. Yu and H. C. Chang, "Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers," Opt. Express 12, 6165-6177 (2004).
[CrossRef] [PubMed]

H. Cheng, W. Y. Crutchfield, M. Doery, and L. Greengard, "Fast, accurate integral equation methods for the analysis of photonic crystal fibers - I: Theory," Opt. Express 12, 3791-3805 (2004).
[CrossRef] [PubMed]

S. P. Guo, F. Wu, S. Albin, H. Tai, and R. S. Rogowski, "Loss and dispersion analysis of microstructured fibers by finite-difference method," Opt. Express 12, 3341-3352 (2004).
[CrossRef] [PubMed]

H. P. Uranus and H. Hoekstra, "Modelling of microstructured waveguides using a finite-element-based vectorial mode solver with transparent boundary conditions," Opt. Express 12, 2795-2809 (2004).
[CrossRef] [PubMed]

V. P. Minkovich, A. V. Kir’yanov, A. B. Sotsky, and L. I. Sotskaya, "Large-mode-area holey fibers with a few air channels in cladding: modeling and experimental investigation of the modal properties," J. Opt. Soc. Am. B 21, 1161-1169 (2004).
[CrossRef]

A. B. Sotsky and L. I. Sotskaya, "Modes of capillary optical fibers," Opt. Commun. 230, 67-79 (2004).
[CrossRef]

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
[CrossRef] [PubMed]

J. Laegsgaard, "Gap formation and guided modes in photonic bandgap fibres with high-index rods," J. Opt. A 6, 798-804 (2004).
[CrossRef]

S. Campbell, R. C. McPhedran, C.M. de Sterke, and L. C. Botten, "Differential multipole method for microstructured optical fibers," J. Opt. Soc. Am. B 21, 1919-1928 (2004).
[CrossRef]

P. Steinvurzel, B. T. Kuhlmey, T. P. White, M. J. Steel, C. M. de Sterke, and B. J. Eggleton, "Long wavelength anti-resonant guidance in high index inclusion microstructured fibers," Opt. Express 12, 5424-5433 (2004).
[CrossRef] [PubMed]

J.-L. A. F. Gérôme and J.-M. Blondy, "Design of dispersion-compensating fibers based on a dual-concentric-core photonic crystal fiber," Opt. Lett. 29, 2725-2727 (2004).
[CrossRef] [PubMed]

2003 (4)

N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Resonances in microstructured optical waveguides," Opt. Express 11, 1243-1251 (2003).
[CrossRef] [PubMed]

S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. J. Wen, "Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders," J. Appl. Phys. 93, 9401-9403 (2003).
[CrossRef]

V. Poborchii, T. Tada, T. Kanayama, and A. Moroz, "Silver-coated silicon pillar photonic crystals: Enhancement of a photonic band gap," Appl. Phys. Lett. 82, 508-510 (2003).
[CrossRef]

P. Russell, "Photonic Crystal Fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

2002 (3)

2001 (1)

2000 (1)

A. Moroz, "Photonic crystals of coated metallic spheres," Europhysics Letters 50, 466-472 (2000).
[CrossRef]

1999 (1)

J. Homola, S. S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

1998 (1)

J. C. Knight, T. A. Birks, and S. J. Russell, "Properties of photonic crystal fiber and the effective index model," J. Opt. Soc. Am. A 15, 746-750 (1998).
[CrossRef]

1996 (2)

1994 (1)

Albin, S.

Amezcua-Correa, A.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Atkin, D. M.

Badding, J. V.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Baril, N. F.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Berghmans, F.

Bird, D. M.

Birks, T. A.

Blondy, J.-M.

Bottacini, M.

Botten, L. C.

Boyer, P.

G. Renversez, P. Boyer, and A. Sagrini, "Antiresonant reflecting optical waveguide microstructured fibers revisited: a new analysis based on leaky mode coupling," Opt. Express 14, 5682-5687 (2006).
[CrossRef] [PubMed]

P. Boyer, G. Renversez, E. Popov, and M. Neviere, "A new differential method applied to the study of arbitrary cross section microstructured optical fibers," Opt. Quantum Electron. 38, 217-230 (2006).
[CrossRef]

Burani, N.

Campbell, S.

Chang, H. C.

Chen, X. S.

S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. J. Wen, "Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders," J. Appl. Phys. 93, 9401-9403 (2003).
[CrossRef]

Cheng, H.

Citrin, D. S.

H. Kurt and D. S. Citrin, "Annular photonic crystals," Opt. Express 13, 10,316-10,326 (2005).
[CrossRef]

Crespi, V. H.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Crutchfield, W. Y.

Cucinotta, A.

Dangui, V.

de Sterke, C.

de Sterke, C. M.

de Sterke, C.M.

Digonnet, M. J. F.

Doery, M.

Dunn, S. C.

Eggleton, B. J.

Finlayson, C. E.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Foroni, M.

Fuochi, M.

Gauglitz, G.

J. Homola, S. S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

George, A. K.

Gérôme, J.-L. A. F.

Gopalan, V.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Greengard, L.

Guo, S. P.

Hayes, J. R.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Hedley, T. D.

Hochman, A.

Hoekstra, H.

Homola, J.

J. Homola, S. S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

Huttunen, A.

Jackson, B. R.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Kanayama, T.

V. Poborchii, T. Tada, T. Kanayama, and A. Moroz, "Silver-coated silicon pillar photonic crystals: Enhancement of a photonic band gap," Appl. Phys. Lett. 82, 508-510 (2003).
[CrossRef]

Kino, G. S.

Kir’yanov, A. V.

Klimek, J.

Knight, J. C.

Kowalczyk, P.

P. Kowalczyk, M. Wiktor, and M. Mrozowski, "Efficient finite difference analysis of microstructured optical fibers," Opt. Express 13, 10,349-10,359 (2005).
[CrossRef]

Kozminski, K.

Kuhlmey, B.

Kuhlmey, B. T.

Kurt, H.

H. Kurt and D. S. Citrin, "Annular photonic crystals," Opt. Express 13, 10,316-10,326 (2005).
[CrossRef]

Laegsgaard, J.

J. Laegsgaard, "Gap formation and guided modes in photonic bandgap fibres with high-index rods," J. Opt. A 6, 798-804 (2004).
[CrossRef]

Leviatan, Y.

Li, L.

Li, Z. F.

S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. J. Wen, "Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders," J. Appl. Phys. 93, 9401-9403 (2003).
[CrossRef]

Litchinitser, N. M.

Lu, W.

S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. J. Wen, "Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders," J. Appl. Phys. 93, 9401-9403 (2003).
[CrossRef]

Luan, F.

Makara, M.

Margine, E. R.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Martynkien, T.

Mattis, R. E.

Maystre, D.

McPhedran, R.

McPhedran, R. C.

Minkovich, V. P.

Moroz, A.

V. Poborchii, T. Tada, T. Kanayama, and A. Moroz, "Silver-coated silicon pillar photonic crystals: Enhancement of a photonic band gap," Appl. Phys. Lett. 82, 508-510 (2003).
[CrossRef]

A. Moroz, "Photonic crystals of coated metallic spheres," Europhysics Letters 50, 466-472 (2000).
[CrossRef]

Mrozowski, M.

P. Kowalczyk, M. Wiktor, and M. Mrozowski, "Efficient finite difference analysis of microstructured optical fibers," Opt. Express 13, 10,349-10,359 (2005).
[CrossRef]

Nasilowski, T.

Neviere, M.

P. Boyer, G. Renversez, E. Popov, and M. Neviere, "A new differential method applied to the study of arbitrary cross section microstructured optical fibers," Opt. Quantum Electron. 38, 217-230 (2006).
[CrossRef]

Olszewski, J.

Pearce, G. J.

Poborchii, V.

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P. Russell, "Photonic Crystal Fibers," Science 299, 358-362 (2003).
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Russell, P. St. J.

Russell, S. J.

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Sagrini, A.

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P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Scheidemantel, T. J.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Selleri, S.

Shen, X. C.

S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. J. Wen, "Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders," J. Appl. Phys. 93, 9401-9403 (2003).
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V. Poborchii, T. Tada, T. Kanayama, and A. Moroz, "Silver-coated silicon pillar photonic crystals: Enhancement of a photonic band gap," Appl. Phys. Lett. 82, 508-510 (2003).
[CrossRef]

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S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. J. Wen, "Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders," J. Appl. Phys. 93, 9401-9403 (2003).
[CrossRef]

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S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. J. Wen, "Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders," J. Appl. Phys. 93, 9401-9403 (2003).
[CrossRef]

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White, T. P.

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P. Kowalczyk, M. Wiktor, and M. Mrozowski, "Efficient finite difference analysis of microstructured optical fibers," Opt. Express 13, 10,349-10,359 (2005).
[CrossRef]

Wojcik, J.

Won, D.-J.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
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J. Homola, S. S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

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P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

V. Poborchii, T. Tada, T. Kanayama, and A. Moroz, "Silver-coated silicon pillar photonic crystals: Enhancement of a photonic band gap," Appl. Phys. Lett. 82, 508-510 (2003).
[CrossRef]

Europhysics Letters (1)

A. Moroz, "Photonic crystals of coated metallic spheres," Europhysics Letters 50, 466-472 (2000).
[CrossRef]

J. Appl. Phys. (1)

S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. J. Wen, "Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders," J. Appl. Phys. 93, 9401-9403 (2003).
[CrossRef]

J. Opt. A (1)

J. Laegsgaard, "Gap formation and guided modes in photonic bandgap fibres with high-index rods," J. Opt. A 6, 798-804 (2004).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (5)

Opt. Commun. (1)

A. B. Sotsky and L. I. Sotskaya, "Modes of capillary optical fibers," Opt. Commun. 230, 67-79 (2004).
[CrossRef]

Opt. Express (12)

P. Kowalczyk, M. Wiktor, and M. Mrozowski, "Efficient finite difference analysis of microstructured optical fibers," Opt. Express 13, 10,349-10,359 (2005).
[CrossRef]

P. Steinvurzel, B. T. Kuhlmey, T. P. White, M. J. Steel, C. M. de Sterke, and B. J. Eggleton, "Long wavelength anti-resonant guidance in high index inclusion microstructured fibers," Opt. Express 12, 5424-5433 (2004).
[CrossRef] [PubMed]

G. Renversez, P. Boyer, and A. Sagrini, "Antiresonant reflecting optical waveguide microstructured fibers revisited: a new analysis based on leaky mode coupling," Opt. Express 14, 5682-5687 (2006).
[CrossRef] [PubMed]

N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Resonances in microstructured optical waveguides," Opt. Express 11, 1243-1251 (2003).
[CrossRef] [PubMed]

C. P. Yu and H. C. Chang, "Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers," Opt. Express 12, 6165-6177 (2004).
[CrossRef] [PubMed]

H. Cheng, W. Y. Crutchfield, M. Doery, and L. Greengard, "Fast, accurate integral equation methods for the analysis of photonic crystal fibers - I: Theory," Opt. Express 12, 3791-3805 (2004).
[CrossRef] [PubMed]

S. P. Guo, F. Wu, S. Albin, H. Tai, and R. S. Rogowski, "Loss and dispersion analysis of microstructured fibers by finite-difference method," Opt. Express 12, 3341-3352 (2004).
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H. P. Uranus and H. Hoekstra, "Modelling of microstructured waveguides using a finite-element-based vectorial mode solver with transparent boundary conditions," Opt. Express 12, 2795-2809 (2004).
[CrossRef] [PubMed]

V. Dangui, M. J. F. Digonnet, and G. S. Kino, "A fast and accurate numerical tool to model the modal properties of photonic-bandgap fibers," Opt. Express 14, 2979-2993 (2006).
[CrossRef] [PubMed]

H. Kurt and D. S. Citrin, "Annular photonic crystals," Opt. Express 13, 10,316-10,326 (2005).
[CrossRef]

A. Huttunen and P. Törmä, "Optimization of dual-core and microstructure fiber geometries for dispersion compensation and large mode area," Opt. Express 13, 627-635 (2005).
[CrossRef] [PubMed]

J. M. Stone, G. J. Pearce, F. Luan, T. A. Birks, J. C. Knight, A. K. George, and D. M. Bird, "An improved photonic bandgap fiber based on an array of rings," Opt. Express 14, 6291-6296 (2006).
[CrossRef] [PubMed]

Opt. Lett. (5)

Opt. Quantum Electron. (1)

P. Boyer, G. Renversez, E. Popov, and M. Neviere, "A new differential method applied to the study of arbitrary cross section microstructured optical fibers," Opt. Quantum Electron. 38, 217-230 (2006).
[CrossRef]

Science (2)

P. Russell, "Photonic Crystal Fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Sens. Actuators B (1)

J. Homola, S. S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

Other (6)

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[CrossRef]

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M. Nevière and E. Popov, Light propagation in Periodic Media - Differential theory and design (Marcel Dekker, Inc., New York, Basel, 2003).

A. Snyder and J. Love, Optical waveguide theory (Chapman & Hall, London, 1996).

B. T. Kuhlmey, "Theoretical and Numerical Investigation of the Physics of Microstructured Optical Fibres," Ph.D. thesis, University of Sydney and Université Aix-Marseille III (2003). http://setis.library.usyd.edu.au/adt/public html/adt-NU/public/adt-NU20040715.171105/.

E. D. Palik, ed., Handbook of optical constants of solids (Academic Press, 1985).

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Figures (10)

Fig. 1.
Fig. 1.

Geometry of a PCF with coated cylinders.

Fig. 2.
Fig. 2.

Geometry and field expansion coefficients for a single coated inclusion.

Fig. 3.
Fig. 3.

Selected field distributions of the mode studied in Table 1: (a) ∣Ez ∣, (b) ∣Hz ∣, (c) Re(Sz ). (d) color scale. All fields are computed with M = 8. The color scale for this and all subsequent figures is linear.

Fig. 4.
Fig. 4.

Selected field distributions of the mode studied in Table 2: (a) ∣Ez ∣, (b) ∣Hz ∣, (c) ∣Sz ∣, (d) detail of ∣Sz ∣ around the rightmost cylinder, showing the strong field concentration on the silver surface. All fields computed with M = 9. The color scale is the same as in Fig. 3.

Fig. 5.
Fig. 5.

Imaginary part of n eff as a function of wavelength for a PCF with high index coated holes, for an equivalent PCF with homogenized inclusions and for a PCF with inclusions having the refractive index of the coating (ARROW fiber). The three structures are detailed in the text. Green vertical lines denotes cutoffs of the modes of a single coated inclusion. The imaginary part of n eff for the ARROW fiber for V > 5 are too small to be computed with the multipole method.

Fig. 6.
Fig. 6.

Real part of n eff as a function of wavelength for the fundamental mode of a PCF with high index coated holes (red) and of an equivalent PCF with homogenized inclusions (blue). The real part of n eff of modes of a single coated inclusion are also shown; the latter are leaky for Re(n eff) < n e = 1.45 and guided when Re(n eff) > n e = 1.45. The structures are detailed in the text.

Fig. 7.
Fig. 7.

Avoided crossing of the fundamental core mode and a plasmonic resonance in a PCF containing silver coated holes. The figure shows the real (upper curves) and imaginary (lower curves) of the two modes involved in the avoided crossing, as a function of wavelength. The structure is that of Fig. 1, with the second ring of holes coated with 20nm of silver. Λ = 1.5μm, ρ e = 262.5nm, ρ i = 242.5nm, n e = 1.45, n i = 1.0 and n s is wavelength dependent, with values resulting from interpolation of published data for silver [32]. Letters (a-d) indicate the location of field plots in Fig 8.

Fig. 8.
Fig. 8.

Field distribution ∣E∣ of the mode on the upper and lower branch of Fig. 7 just before and just after the avoided crossing of the core mode with a plasmonic resonance: (a) lower branch, l = 1.7mm; (b) upper branch, λ = 1.7μm; (c) lower branch, ρ = 1.74μm; (d) upper branch, ρ = 1.74μm. The color scale is the same as in Fig. 3. The green segment in (c) represents the coordinates along which the field is plotted in Fig. 9.

Fig. 9.
Fig. 9.

Norm of the electric field across the upper central coated cylinder in Fig. 8(c).

Fig. 10.
Fig. 10.

Group velocity dispersion parameter D as a function of wavelength for the structure used in Fig. 7, with silver coatings in the second ring of thickness 20 nm and 30 nm.

Tables (2)

Tables Icon

Table 1. Real and imaginary parts of n eff and Wijngaard parameters W E and W H as a function of truncation parameter M of the Fourier Bessel series. Single hexagon with pitch Λ = 6.75 μm of inclusions having ρ e = 2.5 μm, ρ i = 1.5 μm, n i = 1, n s = 1.7, n e = 1.45, λ = 1.45 μm.

Tables Icon

Table 2. Real and imaginary parts of n eff and Wijngaard parameters W E and W H as a function of truncation parameter M of the Fourier Bessel series. Single hexagon with pitch Λ = 1.5 μm of inclusions having ρ e = 0.4 mm, ρ i = 0.35 mm, n i = 1, n s = 4.33480043837×10-1+i8.70529497278,λ= 1.45μm and n e = 1.45. Note that the value used for n s results from an interpolation of measured data for silver [32]. The value given is the one used in our simulation, however it should be noted that the number of significant digits given here bears no relation to the accuracy with which the refractive index of silver is known at that wavelength.

Equations (7)

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V r θ z t = V t ( r , θ ) exp ( i ( βz ωt ) ) ,
V t r θ z = ν [ A ν V , l J ν ( k l r ) + B ν V , l H ν ( 1 ) ( k l r ) ] exp ( iνθ )
A ˜ l = [ A E z , l A H z , l ]
A ˜ = S ˜ + A ˜ + + S ˜ B ˜
B ˜ + = S ˜ + + A ˜ + + S ˜ + B ˜ ,
S ˜ e e = S ˜ e s + + + S ˜ e s + ( I S ˜ s i + + S ˜ e s ) 1 S ˜ s i + + S ˜ e s + ,
V = 2 π λ ρ e ( n e 2 n s 2 ) 1 2 .

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