Abstract

We proposed a quantitative theory based on the surface plasmon polariton (SPP) coupled-mode model for SPP-Bragg reflectors composed of N periodic defects of any geometry and any refractive index profile. A SPP coupled-mode model and its recursive form were developed and shown to be equivalent. The SPP absorption loss, as well as high-order modes in each defect and possible radiation loss, is incorporated without effort. The simple recursive equations derived from the recursive model bridge the reflectance and the transmittance of N periodic defects to those of a single one, resulting in that the computational cost of the geometry optimization or the spectra calculation for N periodic defects is reduced into that for a single one. The model predictions show good agreement with fully vectorial computation data on the reflectance and the transmittance. From the recursive model, the generalized Bragg condition is proposed, which is verified by SPP-Bragg reflectors of various structures. The quantitative theory and the generalized Bragg condition proposed will greatly simplify the design of SPP-Bragg reflectors.

© 2010 Optical Society of America

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2010 (1)

2009 (4)

J. S. Q. Liu, J. S. White, S. Fan, and M. L. Brongersma, “Side-coupled cavity model for surface plasmon-polariton transmission across a groove,” Opt. Express 17, 17837–17848 (2009).
[CrossRef] [PubMed]

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-? metallic surfaces,” Surf. Sci. Rep. 64, 453–469 (2009).
[CrossRef]

S. B. Choi, D. J. Park, Y. K. Jeong, Y. C. Yun, M. S. Jeong, C. C. Byeon, J. H. Kang, Q. H. Park, and D. S. Kim, “Directional control of surface plasmon polariton waves propagating through an asymmetric Bragg resonator,” Appl. Phys. Lett. 94, 063115 (2009).
[CrossRef]

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett. 102, 153903 (2009).
[CrossRef] [PubMed]

2008 (5)

H. T. Liu, and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

J.-Q. Liu, L.-L. Wang, M.-D. He, W.-Q. Huang, D. Wang, B. S. Zou, and S. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express 16, 4888–4894 (2008).
[CrossRef] [PubMed]

A. Hosseini, H. Nejati, and Y. Massoud, “Modeling and design methodology for metal-insulator-metal plasmonic Bragg reflectors,” Opt. Express 16, 1475–1480 (2008).
[CrossRef] [PubMed]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

Z. Fu, Q. Gan, K. Gao, Z. Pan, and F. J. Bartoli, “Numerical investigation of a bidirectional wave coupler based on plasmonic Bragg gratings in the near infrared domain,” J. Lightwave Technol. 26, 3699–3703 (2008).
[CrossRef]

2007 (6)

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Normal-incidence scattering of surface plasmon polaritons by one-dimensional nanoindentations: a multimodal description,” Appl. Phys., A Mater. Sci. Process. 89, 251–258 (2007).
[CrossRef]

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

N. C. Lindquist, A. Lesuffleur, and S.-H. Oh, “Periodic modulation of extraordinary optical transmission through subwavelength hole arrays using surrounding Bragg mirrors,” Phys. Rev. B 76, 155109 (2007).
[CrossRef]

R. Gordon, and P. Marthandam, “Plasmonic Bragg reflectors for enhanced extraordinary optical transmission through nano-hole arrays in a gold film,” Opt. Express 15, 12995–13002 (2007).
[CrossRef] [PubMed]

A. Y. Nikitin, F. López-Tejeira, and L. Martín-Moreno, “Scattering of surface plasmon polaritons by one-dimensional inhomogeneities,” Phys. Rev. B 75, 035129 (2007).
[CrossRef]

2006 (4)

A. Hosseini, and Y. Massoud, “A low-loss metal-insulator-metal plasmonic Bragg reflector,” Opt. Express 14, 11318–11323 (2006).
[CrossRef]

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45? surface-plasmon Bragg mirrors,” Phys. Rev. B 73, 155416 (2006).
[CrossRef]

A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightwave Technol. 24, 912–3703 (2006).
[CrossRef]

T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, “Theoretical analysis of ridge gratings for long-range surface plasmon polaritons,” Phys. Rev. B 73, 045320 (2006).
[CrossRef]

2005 (3)

B. Wang, and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107 (2005).
[CrossRef]

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B 72, 161405 (2005).
[CrossRef]

J. A. Sánchez-Gil, and A. A. Maradudin, “Surface-plasmon polariton scattering from a finite array of nanogrooves/ridges: Efficient mirrors,” Appl. Phys. Lett. 86, 251106 (2005).
[CrossRef]

2004 (1)

J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. W. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, “Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides,” Phys. Rev. B 70, 235406 (2004).
[CrossRef]

2001 (1)

1999 (1)

J. A. Sánchez-Gil, and A. A. Maradudin, “Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B 60, 8359–8367 (1999).
[CrossRef]

1996 (1)

Bartoli, F. J.

Baudrion, A.-L.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45? surface-plasmon Bragg mirrors,” Phys. Rev. B 73, 155416 (2006).
[CrossRef]

J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. W. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, “Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides,” Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Boltasseva, A.

A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightwave Technol. 24, 912–3703 (2006).
[CrossRef]

T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, “Theoretical analysis of ridge gratings for long-range surface plasmon polaritons,” Phys. Rev. B 73, 045320 (2006).
[CrossRef]

Bozhevolnyi, S. I.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, “Theoretical analysis of ridge gratings for long-range surface plasmon polaritons,” Phys. Rev. B 73, 045320 (2006).
[CrossRef]

A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightwave Technol. 24, 912–3703 (2006).
[CrossRef]

Brongersma, M. L.

Byeon, C. C.

S. B. Choi, D. J. Park, Y. K. Jeong, Y. C. Yun, M. S. Jeong, C. C. Byeon, J. H. Kang, Q. H. Park, and D. S. Kim, “Directional control of surface plasmon polariton waves propagating through an asymmetric Bragg resonator,” Appl. Phys. Lett. 94, 063115 (2009).
[CrossRef]

Cai, L.

Cao, Q.

Choi, S. B.

S. B. Choi, D. J. Park, Y. K. Jeong, Y. C. Yun, M. S. Jeong, C. C. Byeon, J. H. Kang, Q. H. Park, and D. S. Kim, “Directional control of surface plasmon polariton waves propagating through an asymmetric Bragg resonator,” Appl. Phys. Lett. 94, 063115 (2009).
[CrossRef]

Dereux, A.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45? surface-plasmon Bragg mirrors,” Phys. Rev. B 73, 155416 (2006).
[CrossRef]

J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. W. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, “Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides,” Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Devaux, E.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45? surface-plasmon Bragg mirrors,” Phys. Rev. B 73, 155416 (2006).
[CrossRef]

J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. W. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, “Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides,” Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Dintinger, J.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

Ebbesen, T. W.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45? surface-plasmon Bragg mirrors,” Phys. Rev. B 73, 155416 (2006).
[CrossRef]

J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. W. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, “Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides,” Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Fan, S.

Forsberg, E.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

Fu, Z.

Gan, Q.

Gao, K.

García-Vidal, F. J.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Normal-incidence scattering of surface plasmon polaritons by one-dimensional nanoindentations: a multimodal description,” Appl. Phys., A Mater. Sci. Process. 89, 251–258 (2007).
[CrossRef]

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B 72, 161405 (2005).
[CrossRef]

Girard, C.

J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. W. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, “Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides,” Phys. Rev. B 70, 235406 (2004).
[CrossRef]

González, M. U.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45? surface-plasmon Bragg mirrors,” Phys. Rev. B 73, 155416 (2006).
[CrossRef]

J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. W. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, “Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides,” Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Gordon, R.

Greffet, J.-J.

Han, Z.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

He, M.-D.

He, S.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

Hosseini, A.

Huang, W.-Q.

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-? metallic surfaces,” Surf. Sci. Rep. 64, 453–469 (2009).
[CrossRef]

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18, 2865–2875 (2001).
[CrossRef]

Jeong, M. S.

S. B. Choi, D. J. Park, Y. K. Jeong, Y. C. Yun, M. S. Jeong, C. C. Byeon, J. H. Kang, Q. H. Park, and D. S. Kim, “Directional control of surface plasmon polariton waves propagating through an asymmetric Bragg resonator,” Appl. Phys. Lett. 94, 063115 (2009).
[CrossRef]

Jeong, Y. K.

S. B. Choi, D. J. Park, Y. K. Jeong, Y. C. Yun, M. S. Jeong, C. C. Byeon, J. H. Kang, Q. H. Park, and D. S. Kim, “Directional control of surface plasmon polariton waves propagating through an asymmetric Bragg resonator,” Appl. Phys. Lett. 94, 063115 (2009).
[CrossRef]

Kang, J. H.

S. B. Choi, D. J. Park, Y. K. Jeong, Y. C. Yun, M. S. Jeong, C. C. Byeon, J. H. Kang, Q. H. Park, and D. S. Kim, “Directional control of surface plasmon polariton waves propagating through an asymmetric Bragg resonator,” Appl. Phys. Lett. 94, 063115 (2009).
[CrossRef]

Kim, D. S.

S. B. Choi, D. J. Park, Y. K. Jeong, Y. C. Yun, M. S. Jeong, C. C. Byeon, J. H. Kang, Q. H. Park, and D. S. Kim, “Directional control of surface plasmon polariton waves propagating through an asymmetric Bragg resonator,” Appl. Phys. Lett. 94, 063115 (2009).
[CrossRef]

Krenn, J. R.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45? surface-plasmon Bragg mirrors,” Phys. Rev. B 73, 155416 (2006).
[CrossRef]

Lacroute, Y.

J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. W. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, “Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides,” Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Lalanne, P.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-? metallic surfaces,” Surf. Sci. Rep. 64, 453–469 (2009).
[CrossRef]

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett. 102, 153903 (2009).
[CrossRef] [PubMed]

H. T. Liu, and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18, 2865–2875 (2001).
[CrossRef]

Leosson, K.

Lesuffleur, A.

N. C. Lindquist, A. Lesuffleur, and S.-H. Oh, “Periodic modulation of extraordinary optical transmission through subwavelength hole arrays using surrounding Bragg mirrors,” Phys. Rev. B 76, 155109 (2007).
[CrossRef]

Li, G.

Lindquist, N. C.

N. C. Lindquist, A. Lesuffleur, and S.-H. Oh, “Periodic modulation of extraordinary optical transmission through subwavelength hole arrays using surrounding Bragg mirrors,” Phys. Rev. B 76, 155109 (2007).
[CrossRef]

Liu, H. T.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-? metallic surfaces,” Surf. Sci. Rep. 64, 453–469 (2009).
[CrossRef]

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett. 102, 153903 (2009).
[CrossRef] [PubMed]

H. T. Liu, and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

Liu, J. S. Q.

Liu, J.-Q.

López-Tejeira, F.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Normal-incidence scattering of surface plasmon polaritons by one-dimensional nanoindentations: a multimodal description,” Appl. Phys., A Mater. Sci. Process. 89, 251–258 (2007).
[CrossRef]

A. Y. Nikitin, F. López-Tejeira, and L. Martín-Moreno, “Scattering of surface plasmon polaritons by one-dimensional inhomogeneities,” Phys. Rev. B 75, 035129 (2007).
[CrossRef]

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B 72, 161405 (2005).
[CrossRef]

Maradudin, A. A.

J. A. Sánchez-Gil, and A. A. Maradudin, “Surface-plasmon polariton scattering from a finite array of nanogrooves/ridges: Efficient mirrors,” Appl. Phys. Lett. 86, 251106 (2005).
[CrossRef]

J. A. Sánchez-Gil, and A. A. Maradudin, “Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B 60, 8359–8367 (1999).
[CrossRef]

Marthandam, P.

Martín-Moreno, L.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Normal-incidence scattering of surface plasmon polaritons by one-dimensional nanoindentations: a multimodal description,” Appl. Phys., A Mater. Sci. Process. 89, 251–258 (2007).
[CrossRef]

A. Y. Nikitin, F. López-Tejeira, and L. Martín-Moreno, “Scattering of surface plasmon polaritons by one-dimensional inhomogeneities,” Phys. Rev. B 75, 035129 (2007).
[CrossRef]

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B 72, 161405 (2005).
[CrossRef]

Massoud, Y.

Nejati, H.

Nikitin, A. Y.

A. Y. Nikitin, F. López-Tejeira, and L. Martín-Moreno, “Scattering of surface plasmon polaritons by one-dimensional inhomogeneities,” Phys. Rev. B 75, 035129 (2007).
[CrossRef]

Nikolajsen, T.

Oh, S.-H.

N. C. Lindquist, A. Lesuffleur, and S.-H. Oh, “Periodic modulation of extraordinary optical transmission through subwavelength hole arrays using surrounding Bragg mirrors,” Phys. Rev. B 76, 155109 (2007).
[CrossRef]

Pan, Z.

Park, D. J.

S. B. Choi, D. J. Park, Y. K. Jeong, Y. C. Yun, M. S. Jeong, C. C. Byeon, J. H. Kang, Q. H. Park, and D. S. Kim, “Directional control of surface plasmon polariton waves propagating through an asymmetric Bragg resonator,” Appl. Phys. Lett. 94, 063115 (2009).
[CrossRef]

Park, Q. H.

S. B. Choi, D. J. Park, Y. K. Jeong, Y. C. Yun, M. S. Jeong, C. C. Byeon, J. H. Kang, Q. H. Park, and D. S. Kim, “Directional control of surface plasmon polariton waves propagating through an asymmetric Bragg resonator,” Appl. Phys. Lett. 94, 063115 (2009).
[CrossRef]

Pincemin, F.

Radko, I. P.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

Rodrigo, S. G.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

Sánchez-Gil, J. A.

J. A. Sánchez-Gil, and A. A. Maradudin, “Surface-plasmon polariton scattering from a finite array of nanogrooves/ridges: Efficient mirrors,” Appl. Phys. Lett. 86, 251106 (2005).
[CrossRef]

J. A. Sánchez-Gil, and A. A. Maradudin, “Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B 60, 8359–8367 (1999).
[CrossRef]

Silberstein, E.

Søndergaard, T.

T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, “Theoretical analysis of ridge gratings for long-range surface plasmon polaritons,” Phys. Rev. B 73, 045320 (2006).
[CrossRef]

Stepanov, A. L.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45? surface-plasmon Bragg mirrors,” Phys. Rev. B 73, 155416 (2006).
[CrossRef]

Wang, B.

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-? metallic surfaces,” Surf. Sci. Rep. 64, 453–469 (2009).
[CrossRef]

B. Wang, and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107 (2005).
[CrossRef]

Wang, D.

Wang, G. P.

B. Wang, and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107 (2005).
[CrossRef]

Wang, L.-L.

Wang, Z.

Weeber, J. C.

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

Weeber, J.-C.

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45? surface-plasmon Bragg mirrors,” Phys. Rev. B 73, 155416 (2006).
[CrossRef]

J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. W. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, “Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides,” Phys. Rev. B 70, 235406 (2004).
[CrossRef]

Wen, S.

White, J. S.

Xu, A.

Yang, X. Y.

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett. 102, 153903 (2009).
[CrossRef] [PubMed]

Yun, Y. C.

S. B. Choi, D. J. Park, Y. K. Jeong, Y. C. Yun, M. S. Jeong, C. C. Byeon, J. H. Kang, Q. H. Park, and D. S. Kim, “Directional control of surface plasmon polariton waves propagating through an asymmetric Bragg resonator,” Appl. Phys. Lett. 94, 063115 (2009).
[CrossRef]

Zou, B. S.

Appl. Phys. Lett. (3)

J. A. Sánchez-Gil, and A. A. Maradudin, “Surface-plasmon polariton scattering from a finite array of nanogrooves/ridges: Efficient mirrors,” Appl. Phys. Lett. 86, 251106 (2005).
[CrossRef]

B. Wang, and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107 (2005).
[CrossRef]

S. B. Choi, D. J. Park, Y. K. Jeong, Y. C. Yun, M. S. Jeong, C. C. Byeon, J. H. Kang, Q. H. Park, and D. S. Kim, “Directional control of surface plasmon polariton waves propagating through an asymmetric Bragg resonator,” Appl. Phys. Lett. 94, 063115 (2009).
[CrossRef]

Appl. Phys., A Mater. Sci. Process. (1)

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Normal-incidence scattering of surface plasmon polaritons by one-dimensional nanoindentations: a multimodal description,” Appl. Phys., A Mater. Sci. Process. 89, 251–258 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

N. J. Phys. (1)

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, J. Dintinger, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Modulation of surface plasmon coupling-in by one-dimensional surface corrugation,” N. J. Phys. 10, 033035 (2008).
[CrossRef]

Nat. Phys. (1)

F. López-Tejeira, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. González, J. C. Weeber, and A. Dereux, “Efficient unidirectional nanoslit couplers for surface plasmons,” Nat. Phys. 3, 324–328 (2007).
[CrossRef]

Nature (1)

H. T. Liu, and P. Lalanne, “Microscopic theory of the extraordinary optical transmission,” Nature 452, 728–731 (2008).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. B (7)

A. Y. Nikitin, F. López-Tejeira, and L. Martín-Moreno, “Scattering of surface plasmon polaritons by one-dimensional inhomogeneities,” Phys. Rev. B 75, 035129 (2007).
[CrossRef]

N. C. Lindquist, A. Lesuffleur, and S.-H. Oh, “Periodic modulation of extraordinary optical transmission through subwavelength hole arrays using surrounding Bragg mirrors,” Phys. Rev. B 76, 155109 (2007).
[CrossRef]

J. A. Sánchez-Gil, and A. A. Maradudin, “Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B 60, 8359–8367 (1999).
[CrossRef]

J.-C. Weeber, Y. Lacroute, A. Dereux, E. Devaux, T. W. Ebbesen, C. Girard, M. U. González, and A.-L. Baudrion, “Near-field characterization of Bragg mirrors engraved in surface plasmon waveguides,” Phys. Rev. B 70, 235406 (2004).
[CrossRef]

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B 72, 161405 (2005).
[CrossRef]

T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, “Theoretical analysis of ridge gratings for long-range surface plasmon polaritons,” Phys. Rev. B 73, 045320 (2006).
[CrossRef]

M. U. González, J.-C. Weeber, A.-L. Baudrion, A. Dereux, A. L. Stepanov, J. R. Krenn, E. Devaux, and T. W. Ebbesen, “Design, near-field characterization, and modeling of 45? surface-plasmon Bragg mirrors,” Phys. Rev. B 73, 155416 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

X. Y. Yang, H. T. Liu, and P. Lalanne, “Cross conversion between surface plasmon polaritons and quasicylindrical waves,” Phys. Rev. Lett. 102, 153903 (2009).
[CrossRef] [PubMed]

Surf. Sci. Rep. (1)

P. Lalanne, J. P. Hugonin, H. T. Liu, and B. Wang, “A microscopic view of the electromagnetic properties of sub-? metallic surfaces,” Surf. Sci. Rep. 64, 453–469 (2009).
[CrossRef]

Other (1)

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

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Figures (9)

Fig. 1.
Fig. 1.

(a) Schematic of SPP-Bragg reflectors composed of N periodic defects. (b) Some typical surface defect units on the air-metal interface (from left to right): rectangle groove [4, 5], rectangle dielectric ridge [1, 17], Gaussian-shaped metallic ridge [6], Gaussian-shaped dielectric ridge. (c) and (d) show the rectangle [12,13] and the triangle defect units in the MIM structure, respectively.

Fig. 2.
Fig. 2.

Schematics of the SPP coupled-mode model (a) and the recursive model (b) for the SPP-Bragg reflector composed of N periodic defects. The electromagnetic quantities A 0,⋯,AN ,B 0,⋯,B N-1 are all defined in the text. (c) and (d) show the scattering of the SPP modes by a single defect with reflectance coefficient ρ 1 ± and transmittance coefficient τ 1 ± , where the superscripts “+” and “-” are for the left- and right-incident modes, respectively.

Fig. 3.
Fig. 3.

Comparisons among the SPP coupled-mode model predictions (blue circles), the recursive model predictions (blue-dashed lines), and fully vectorial a-FMM computation data (red-solid lines) on the reflectance of ten defects vs the period. (a) is for rectangle grooves with h = 100 nm, w = 160 nm; (b) is for rectangle dielectric ridges with h = 160 nm, w = 150 nm; (c) is for Gaussian-shaped metallic ridges with h = 60 nm, A = 20 nm; (d) is for Gaussian-shaped dielectric ridges with h = 200 nm, A = 80 nm; (e) is for rectangle defects in the MIM structure with h = 50 nm, w = 230 nm; (f) is for R - of triangle defects in the MIM structure with h = 60 nm, w = 160 nm. The insets show details around the reflectance peaks.

Fig. 4.
Fig. 4.

Comparisons between the model predictions (top row) and fully vectorial a-FMM computation data (bottom row) on the reflectance of ten periodic defects as a function of the defect size. Four columns from left to right are for R of rectangle grooves (p = 390 nm), Gaussian-shaped metallic ridges (p = 314 nm), and Gaussian-shaped dielectric ridges (p = 780 nm) on the air-metal structure, and R + of triangle defects in the MIM structure (p = 350 nm). The blue circles indicate the optimized defect sizes for the reflectance maxima.

Fig. 5.
Fig. 5.

Comparisons between the model predictions (lines) and fully vectorial a-FMM computation data (circles) on the reflectance (R) and transmittance (T) spectra. (a) is for ten rectangle dielectric surface ridges of h = 160 nm, w = 150 nm, p = 1200 nm; (b) is for ten rectangle defects in the MIM structure of h = 50nm, w = 230 nm, p = 900 nm.

Fig. 6.
Fig. 6.

Comparisons between the model predictions (lines) and fully vectorial a-FMM computation data (symbols) on the reflectance as a function of the number of Gaussian defects in the array (p = λ sp /2 = 314 nm) for metallic ridges (solid lines and filled symbols) and grooves (dashed lines and hollow symbols) of various sizes: A=h = 314 nm (red lines and squares),A =h = 62.8nm (blue lines and diamonds),A = h = 94.2nm (black lines and triangles) [6], and the optimized defect sizes predicted by the model (green lines and circles), i.e., h = 70 nm, A = 5nm for metallic ridges and h = 30nm,A = 75 nm for grooves.

Fig. 7.
Fig. 7.

The reflectance as a function of the number of Gaussian dielectric ridges with comparisons between the model predictions (lines) and the a-FMM computation data (symbols). (a) is for h = 150 nm,A = 45 nm with solid line and dots for p = 770 nm, and dashed lines and circles for p = 785 nm; (b) is for h = 200 nm, A = 80 nm with solid line and dots for p = 745 nm, and dashed lines and circles for p = 785 nm.

Fig. 8.
Fig. 8.

Schematic of the generalized Bragg condition showing the interference between left-going SPPs reflected by two neighboring defects.

Fig. 9.
Fig. 9.

Peak positions on the reflectance spectra predicted by the model (thin-red lines) and by fully vectorial a-FMM calculations (circles), can also be predicted accurately by the generalized Bragg condition (thick-green lines), where m = [arg(τ 1) + k 0Re(nsp )(p - w)]/π are integers. Parameters for (a) and (b) are same as those in Fig. 5.

Tables (1)

Tables Icon

Table 1. Comparisons between the optimal periods for ten periodic defects predicted by the generalized Bragg condition (p ) and those by fully vectorial a-FMM calculations (p), which are performed by scanning in steps of 5 nm and shown as solid lines in Fig. 3. “Type” marked from “(a)” to “(f)” are corresponding to the rectangle groove, the rectangle dielectric ridge, the metallic Gaussian-shaped ridge and the dielectric one on the air-metal interface, the rectangle defect and the triangle one in the MIM structure, respectively. “RErr” means the relative error defined as |p - p |/p × 100%.

Equations (17)

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k0Re(nsp)p=,
k0 [Re(neff)w+Re(nsp)(pw)]=(2m+1)π,
B0=ρ0+ A0+τ1uB1 ,
A1=τ0+ A0+ρ1uB1 ,
Bj=ρ1+uAj+τ1uBj+1 for 1jN2,
Aj+1=τ1+uAj+ρ1uBj+1 for 1jN2,
BN1=ρ1+ u AN1 ,
AN=τ1+ u AN1 ,
B0=ρ1+ A0+τ1uB1 ,
A1=τ1+ A0+ρ1uB1 ,
B1=ρN1+ uA1 ,
AN=τN1+ uA1 .
ρN+=ρ1+ +ρN1+τ12u21ρN1+ρ1u2,
τN=τN+=τN1τ1u1ρN1+ρ1u2 .
ρN=ρ1 +ρN1τ12u21ρN1ρ1+u2.
ρN±ρ1±1τ12u2 ,
arg(τ1)+k0Re(nsp)(pw)=.

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