Abstract

The Drude model for metal is extended to include complex relaxation rates. As a test for what happens to the surface plasmon resonances with such metals, the lifetime is examined for propagating waves across a single planar metal-dielectric interface. By analytically solving the dispersion relation being fourth-order in the complex frequency, group-velocity dispersion and quality factors are explicitly found. Due to the symmetry breaking between the forward and backward waves, standing waves are not allowed in general.

© 2011 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2011

N. Nakai, N. Hayashi, and M. Machida, “Direct numerical confirmation of pinning-induced sign change in the superconducting Hall effect in type-II superconductors,” Phys. Rev. B 83(2), 024507 (2011).
[CrossRef]

F. Hébert, M. Schram, R. T. Scalettar, W. B. Chen, and Z. Bai, “Hatano-Nelson model with a periodic potential,” Eur. Phys. J. B 79(4), 465–471 (2011).
[CrossRef]

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

A. Z. Abbasi, F. Amin, T. Niebling, S. Friede, M. Ochs, S. Carregal-Romero, J.-M. Montenegro, P. Rivera Gil, W. Heimbrodt, and W. J. Parak, “How colloidal nanoparticles could facilitate multiplexed measurements of different analytes with analyte-sensitive organic fluorophores,” ACS Nano 5(1), 21–25 (2011).
[CrossRef] [PubMed]

2010

A. Haddadpour and Y. Yi, “Metallic nanoparticle on micro ring resonator for bio optical detection and sensing,” Biomed. Opt. Express 1(2), 378–384 (2010).
[CrossRef]

V. A. Fedotov, A. Tsiatmas, J. H. Shi, R. Buckingham, P. de Groot, Y. Chen, S. Wang, and N. I. Zheludev, “Temperature control of Fano resonances and transmission in superconducting metamaterials,” Opt. Express 18(9), 9015–9019 (2010).
[CrossRef] [PubMed]

J. S. Yang, J.-H. Sung, and B.-H. O, “Novel elastic scattering model for the understanding of the Anomalous transmittance for Au nanoparticle layer,” Opt. Express 18(13), 13418–13424 (2010).
[CrossRef] [PubMed]

H.-I. Lee and J. Mok, “On the cubic zero-order solution of electromagnetic waves. I. Periodic slabs with lossy plasmas,” Phys. Plasmas 17(7), 072108 (2010).
[CrossRef]

H.-I. Lee and J. Mok, “On the cubic zero-order solution of electromagnetic waves. II. Isolated particles with lossy plasmas,” Phys. Plasmas 17(7), 072109 (2010).
[CrossRef]

H.-I. Lee, “Wave classification and resonant excitations in lossy metal-dielectric multilayers,” Photonics Nanostruct. Fundam. Appl. 8(3), 183–197 (2010).
[CrossRef]

2008

A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: dispersive properties of surface plasmon polaritions in linear chains of metallic nanospheroids,” Phys. Rev. B 78(3), 035403 (2008).
[CrossRef]

S. John and R. Wang, “Metallic photonic-band-gap filament architectures for optimized incandescent lighting,” Phys. Rev. A 78(4), 043809 (2008).
[CrossRef]

N. Nakai, N. Hayashi, and M. Machida, “Simulation studies for the vortex-depinning dynamics around a columnar defect in superconductors,” Physica C 468(15–20), 1270–1273 (2008).
[CrossRef]

S. Zou, “Electromagnetic wave propagation in a multilayer silver particle,” Chem. Phys. Lett. 454(4–6), 289–293 (2008).
[CrossRef]

2007

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99(17), 173603 (2007).
[CrossRef] [PubMed]

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[CrossRef]

A. Kaso and S. John, “Nonlinear Bloch waves in metallic photonic band-gap filaments,” Phys. Rev. A 76(5), 053838 (2007).
[CrossRef]

2006

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes-part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006).
[CrossRef]

2005

T. Savin and P. S. Doyle, “Role of a finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(4), 041106 (2005).
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94(12), 123901 (2005).
[CrossRef] [PubMed]

2004

L. Prkna, J. Čtyroký, and M. Hubálek, “Ring microresonator as a photonic structure with complex eigenfrequency,” Opt. Quantum Electron. 36(1–3), 259–269 (2004).
[CrossRef]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

1998

G. Cuniberti, M. Sassetti, and B. Kramer, “Ac conductance of a quantum wire with electron-electron interactions,” Phys. Rev. B 57(3), 1515–1526 (1998).
[CrossRef]

1997

V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55(12), 7427–7444 (1997).
[CrossRef]

1994

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B Condens. Matter 50(23), 16835–16844 (1994).
[CrossRef] [PubMed]

1993

R. W. D. Nickalls, “A new approach to solving the cubic: Cardan's solution revealed,” The Mathematical Gazette 77(480), 354–359 (1993).
[CrossRef]

Abbasi, A. Z.

A. Z. Abbasi, F. Amin, T. Niebling, S. Friede, M. Ochs, S. Carregal-Romero, J.-M. Montenegro, P. Rivera Gil, W. Heimbrodt, and W. J. Parak, “How colloidal nanoparticles could facilitate multiplexed measurements of different analytes with analyte-sensitive organic fluorophores,” ACS Nano 5(1), 21–25 (2011).
[CrossRef] [PubMed]

Aktsipetrov, O. A.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

Ameloot, M.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

Amin, F.

A. Z. Abbasi, F. Amin, T. Niebling, S. Friede, M. Ochs, S. Carregal-Romero, J.-M. Montenegro, P. Rivera Gil, W. Heimbrodt, and W. J. Parak, “How colloidal nanoparticles could facilitate multiplexed measurements of different analytes with analyte-sensitive organic fluorophores,” ACS Nano 5(1), 21–25 (2011).
[CrossRef] [PubMed]

Bai, Z.

F. Hébert, M. Schram, R. T. Scalettar, W. B. Chen, and Z. Bai, “Hatano-Nelson model with a periodic potential,” Eur. Phys. J. B 79(4), 465–471 (2011).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Benson, O.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99(17), 173603 (2007).
[CrossRef] [PubMed]

Biris, C. G.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

Bogaerts, W.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94(12), 123901 (2005).
[CrossRef] [PubMed]

Buckingham, R.

Carregal-Romero, S.

A. Z. Abbasi, F. Amin, T. Niebling, S. Friede, M. Ochs, S. Carregal-Romero, J.-M. Montenegro, P. Rivera Gil, W. Heimbrodt, and W. J. Parak, “How colloidal nanoparticles could facilitate multiplexed measurements of different analytes with analyte-sensitive organic fluorophores,” ACS Nano 5(1), 21–25 (2011).
[CrossRef] [PubMed]

Chen, W. B.

F. Hébert, M. Schram, R. T. Scalettar, W. B. Chen, and Z. Bai, “Hatano-Nelson model with a periodic potential,” Eur. Phys. J. B 79(4), 465–471 (2011).
[CrossRef]

Chen, Y.

Chulkov, E. V.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[CrossRef]

Ctyroký, J.

L. Prkna, J. Čtyroký, and M. Hubálek, “Ring microresonator as a photonic structure with complex eigenfrequency,” Opt. Quantum Electron. 36(1–3), 259–269 (2004).
[CrossRef]

Cuniberti, G.

G. Cuniberti, M. Sassetti, and B. Kramer, “Ac conductance of a quantum wire with electron-electron interactions,” Phys. Rev. B 57(3), 1515–1526 (1998).
[CrossRef]

De Clercq, B.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

de Groot, P.

de S. Menezes, L.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99(17), 173603 (2007).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Doyle, P. S.

T. Savin and P. S. Doyle, “Role of a finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(4), 041106 (2005).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Echenique, P. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[CrossRef]

Engelen, R. J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94(12), 123901 (2005).
[CrossRef] [PubMed]

Engheta, N.

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

Fedotov, V. A.

Friede, S.

A. Z. Abbasi, F. Amin, T. Niebling, S. Friede, M. Ochs, S. Carregal-Romero, J.-M. Montenegro, P. Rivera Gil, W. Heimbrodt, and W. J. Parak, “How colloidal nanoparticles could facilitate multiplexed measurements of different analytes with analyte-sensitive organic fluorophores,” ACS Nano 5(1), 21–25 (2011).
[CrossRef] [PubMed]

Gersen, H.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94(12), 123901 (2005).
[CrossRef] [PubMed]

Gillijns, W.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

Götzinger, S.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99(17), 173603 (2007).
[CrossRef] [PubMed]

Govyadinov, A. A.

A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: dispersive properties of surface plasmon polaritions in linear chains of metallic nanospheroids,” Phys. Rev. B 78(3), 035403 (2008).
[CrossRef]

Haddadpour, A.

Hayashi, N.

N. Nakai, N. Hayashi, and M. Machida, “Direct numerical confirmation of pinning-induced sign change in the superconducting Hall effect in type-II superconductors,” Phys. Rev. B 83(2), 024507 (2011).
[CrossRef]

N. Nakai, N. Hayashi, and M. Machida, “Simulation studies for the vortex-depinning dynamics around a columnar defect in superconductors,” Physica C 468(15–20), 1270–1273 (2008).
[CrossRef]

Hébert, F.

F. Hébert, M. Schram, R. T. Scalettar, W. B. Chen, and Z. Bai, “Hatano-Nelson model with a periodic potential,” Eur. Phys. J. B 79(4), 465–471 (2011).
[CrossRef]

Heimbrodt, W.

A. Z. Abbasi, F. Amin, T. Niebling, S. Friede, M. Ochs, S. Carregal-Romero, J.-M. Montenegro, P. Rivera Gil, W. Heimbrodt, and W. J. Parak, “How colloidal nanoparticles could facilitate multiplexed measurements of different analytes with analyte-sensitive organic fluorophores,” ACS Nano 5(1), 21–25 (2011).
[CrossRef] [PubMed]

Hubálek, M.

L. Prkna, J. Čtyroký, and M. Hubálek, “Ring microresonator as a photonic structure with complex eigenfrequency,” Opt. Quantum Electron. 36(1–3), 259–269 (2004).
[CrossRef]

Ilchenko, V. S.

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes-part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006).
[CrossRef]

Jeyaram, Y.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

John, S.

S. John and R. Wang, “Metallic photonic-band-gap filament architectures for optimized incandescent lighting,” Phys. Rev. A 78(4), 043809 (2008).
[CrossRef]

A. Kaso and S. John, “Nonlinear Bloch waves in metallic photonic band-gap filaments,” Phys. Rev. A 76(5), 053838 (2007).
[CrossRef]

Karle, T. J.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94(12), 123901 (2005).
[CrossRef] [PubMed]

Kaso, A.

A. Kaso and S. John, “Nonlinear Bloch waves in metallic photonic band-gap filaments,” Phys. Rev. A 76(5), 053838 (2007).
[CrossRef]

Korterik, J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94(12), 123901 (2005).
[CrossRef] [PubMed]

Kramer, B.

G. Cuniberti, M. Sassetti, and B. Kramer, “Ac conductance of a quantum wire with electron-electron interactions,” Phys. Rev. B 57(3), 1515–1526 (1998).
[CrossRef]

Krauss, T. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94(12), 123901 (2005).
[CrossRef] [PubMed]

Kuipers, L.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94(12), 123901 (2005).
[CrossRef] [PubMed]

Kuzmiak, V.

V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55(12), 7427–7444 (1997).
[CrossRef]

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B Condens. Matter 50(23), 16835–16844 (1994).
[CrossRef] [PubMed]

Lee, H.-I.

H.-I. Lee, “Wave classification and resonant excitations in lossy metal-dielectric multilayers,” Photonics Nanostruct. Fundam. Appl. 8(3), 183–197 (2010).
[CrossRef]

H.-I. Lee and J. Mok, “On the cubic zero-order solution of electromagnetic waves. I. Periodic slabs with lossy plasmas,” Phys. Plasmas 17(7), 072108 (2010).
[CrossRef]

H.-I. Lee and J. Mok, “On the cubic zero-order solution of electromagnetic waves. II. Isolated particles with lossy plasmas,” Phys. Plasmas 17(7), 072109 (2010).
[CrossRef]

Machida, M.

N. Nakai, N. Hayashi, and M. Machida, “Direct numerical confirmation of pinning-induced sign change in the superconducting Hall effect in type-II superconductors,” Phys. Rev. B 83(2), 024507 (2011).
[CrossRef]

N. Nakai, N. Hayashi, and M. Machida, “Simulation studies for the vortex-depinning dynamics around a columnar defect in superconductors,” Physica C 468(15–20), 1270–1273 (2008).
[CrossRef]

Maradudin, A. A.

V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55(12), 7427–7444 (1997).
[CrossRef]

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B Condens. Matter 50(23), 16835–16844 (1994).
[CrossRef] [PubMed]

Markel, V. A.

A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: dispersive properties of surface plasmon polaritions in linear chains of metallic nanospheroids,” Phys. Rev. B 78(3), 035403 (2008).
[CrossRef]

Matsko, A. B.

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes-part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006).
[CrossRef]

Mazzei, A.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99(17), 173603 (2007).
[CrossRef] [PubMed]

Mok, J.

H.-I. Lee and J. Mok, “On the cubic zero-order solution of electromagnetic waves. II. Isolated particles with lossy plasmas,” Phys. Plasmas 17(7), 072109 (2010).
[CrossRef]

H.-I. Lee and J. Mok, “On the cubic zero-order solution of electromagnetic waves. I. Periodic slabs with lossy plasmas,” Phys. Plasmas 17(7), 072108 (2010).
[CrossRef]

Montenegro, J.-M.

A. Z. Abbasi, F. Amin, T. Niebling, S. Friede, M. Ochs, S. Carregal-Romero, J.-M. Montenegro, P. Rivera Gil, W. Heimbrodt, and W. J. Parak, “How colloidal nanoparticles could facilitate multiplexed measurements of different analytes with analyte-sensitive organic fluorophores,” ACS Nano 5(1), 21–25 (2011).
[CrossRef] [PubMed]

Moshchalkov, V. V.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

Nakai, N.

N. Nakai, N. Hayashi, and M. Machida, “Direct numerical confirmation of pinning-induced sign change in the superconducting Hall effect in type-II superconductors,” Phys. Rev. B 83(2), 024507 (2011).
[CrossRef]

N. Nakai, N. Hayashi, and M. Machida, “Simulation studies for the vortex-depinning dynamics around a columnar defect in superconductors,” Physica C 468(15–20), 1270–1273 (2008).
[CrossRef]

Nickalls, R. W. D.

R. W. D. Nickalls, “A new approach to solving the cubic: Cardan's solution revealed,” The Mathematical Gazette 77(480), 354–359 (1993).
[CrossRef]

Niebling, T.

A. Z. Abbasi, F. Amin, T. Niebling, S. Friede, M. Ochs, S. Carregal-Romero, J.-M. Montenegro, P. Rivera Gil, W. Heimbrodt, and W. J. Parak, “How colloidal nanoparticles could facilitate multiplexed measurements of different analytes with analyte-sensitive organic fluorophores,” ACS Nano 5(1), 21–25 (2011).
[CrossRef] [PubMed]

O, B.-H.

Ochs, M.

A. Z. Abbasi, F. Amin, T. Niebling, S. Friede, M. Ochs, S. Carregal-Romero, J.-M. Montenegro, P. Rivera Gil, W. Heimbrodt, and W. J. Parak, “How colloidal nanoparticles could facilitate multiplexed measurements of different analytes with analyte-sensitive organic fluorophores,” ACS Nano 5(1), 21–25 (2011).
[CrossRef] [PubMed]

Paddubrouskaya, H.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

Panoiu, N. C.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

Parak, W. J.

A. Z. Abbasi, F. Amin, T. Niebling, S. Friede, M. Ochs, S. Carregal-Romero, J.-M. Montenegro, P. Rivera Gil, W. Heimbrodt, and W. J. Parak, “How colloidal nanoparticles could facilitate multiplexed measurements of different analytes with analyte-sensitive organic fluorophores,” ACS Nano 5(1), 21–25 (2011).
[CrossRef] [PubMed]

Pincemin, F.

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B Condens. Matter 50(23), 16835–16844 (1994).
[CrossRef] [PubMed]

Pitarke, J. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[CrossRef]

Prkna, L.

L. Prkna, J. Čtyroký, and M. Hubálek, “Ring microresonator as a photonic structure with complex eigenfrequency,” Opt. Quantum Electron. 36(1–3), 259–269 (2004).
[CrossRef]

Rivera Gil, P.

A. Z. Abbasi, F. Amin, T. Niebling, S. Friede, M. Ochs, S. Carregal-Romero, J.-M. Montenegro, P. Rivera Gil, W. Heimbrodt, and W. J. Parak, “How colloidal nanoparticles could facilitate multiplexed measurements of different analytes with analyte-sensitive organic fluorophores,” ACS Nano 5(1), 21–25 (2011).
[CrossRef] [PubMed]

Sandoghdar, V.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99(17), 173603 (2007).
[CrossRef] [PubMed]

Sassetti, M.

G. Cuniberti, M. Sassetti, and B. Kramer, “Ac conductance of a quantum wire with electron-electron interactions,” Phys. Rev. B 57(3), 1515–1526 (1998).
[CrossRef]

Savin, T.

T. Savin and P. S. Doyle, “Role of a finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(4), 041106 (2005).
[CrossRef] [PubMed]

Scalettar, R. T.

F. Hébert, M. Schram, R. T. Scalettar, W. B. Chen, and Z. Bai, “Hatano-Nelson model with a periodic potential,” Eur. Phys. J. B 79(4), 465–471 (2011).
[CrossRef]

Schram, M.

F. Hébert, M. Schram, R. T. Scalettar, W. B. Chen, and Z. Bai, “Hatano-Nelson model with a periodic potential,” Eur. Phys. J. B 79(4), 465–471 (2011).
[CrossRef]

Shi, J. H.

Silhanek, A. V.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

Silkin, V. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[CrossRef]

Sung, J.-H.

Tsiatmas, A.

Valev, V. K.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

van Hulst, N. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94(12), 123901 (2005).
[CrossRef] [PubMed]

Verbiest, T.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

Volodin, A.

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

Wang, R.

S. John and R. Wang, “Metallic photonic-band-gap filament architectures for optimized incandescent lighting,” Phys. Rev. A 78(4), 043809 (2008).
[CrossRef]

Wang, S.

Yang, J. S.

Yi, Y.

Zheludev, N. I.

Zou, S.

S. Zou, “Electromagnetic wave propagation in a multilayer silver particle,” Chem. Phys. Lett. 454(4–6), 289–293 (2008).
[CrossRef]

Zumofen, G.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99(17), 173603 (2007).
[CrossRef] [PubMed]

ACS Nano

V. K. Valev, A. V. Silhanek, W. Gillijns, Y. Jeyaram, H. Paddubrouskaya, A. Volodin, C. G. Biris, N. C. Panoiu, B. De Clercq, M. Ameloot, O. A. Aktsipetrov, V. V. Moshchalkov, and T. Verbiest, “Plasmons reveal the direction of magnetization in nickel nanostructures,” ACS Nano 5(1), 91–96 (2011).
[CrossRef]

A. Z. Abbasi, F. Amin, T. Niebling, S. Friede, M. Ochs, S. Carregal-Romero, J.-M. Montenegro, P. Rivera Gil, W. Heimbrodt, and W. J. Parak, “How colloidal nanoparticles could facilitate multiplexed measurements of different analytes with analyte-sensitive organic fluorophores,” ACS Nano 5(1), 21–25 (2011).
[CrossRef] [PubMed]

Biomed. Opt. Express

Chem. Phys. Lett.

S. Zou, “Electromagnetic wave propagation in a multilayer silver particle,” Chem. Phys. Lett. 454(4–6), 289–293 (2008).
[CrossRef]

Eur. Phys. J. B

F. Hébert, M. Schram, R. T. Scalettar, W. B. Chen, and Z. Bai, “Hatano-Nelson model with a periodic potential,” Eur. Phys. J. B 79(4), 465–471 (2011).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes-part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006).
[CrossRef]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Quantum Electron.

L. Prkna, J. Čtyroký, and M. Hubálek, “Ring microresonator as a photonic structure with complex eigenfrequency,” Opt. Quantum Electron. 36(1–3), 259–269 (2004).
[CrossRef]

Photonics Nanostruct. Fundam. Appl.

H.-I. Lee, “Wave classification and resonant excitations in lossy metal-dielectric multilayers,” Photonics Nanostruct. Fundam. Appl. 8(3), 183–197 (2010).
[CrossRef]

Phys. Plasmas

H.-I. Lee and J. Mok, “On the cubic zero-order solution of electromagnetic waves. I. Periodic slabs with lossy plasmas,” Phys. Plasmas 17(7), 072108 (2010).
[CrossRef]

H.-I. Lee and J. Mok, “On the cubic zero-order solution of electromagnetic waves. II. Isolated particles with lossy plasmas,” Phys. Plasmas 17(7), 072109 (2010).
[CrossRef]

Phys. Rev. A

A. Kaso and S. John, “Nonlinear Bloch waves in metallic photonic band-gap filaments,” Phys. Rev. A 76(5), 053838 (2007).
[CrossRef]

S. John and R. Wang, “Metallic photonic-band-gap filament architectures for optimized incandescent lighting,” Phys. Rev. A 78(4), 043809 (2008).
[CrossRef]

Phys. Rev. B

N. Nakai, N. Hayashi, and M. Machida, “Direct numerical confirmation of pinning-induced sign change in the superconducting Hall effect in type-II superconductors,” Phys. Rev. B 83(2), 024507 (2011).
[CrossRef]

A. A. Govyadinov and V. A. Markel, “From slow to superluminal propagation: dispersive properties of surface plasmon polaritions in linear chains of metallic nanospheroids,” Phys. Rev. B 78(3), 035403 (2008).
[CrossRef]

V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55(12), 7427–7444 (1997).
[CrossRef]

G. Cuniberti, M. Sassetti, and B. Kramer, “Ac conductance of a quantum wire with electron-electron interactions,” Phys. Rev. B 57(3), 1515–1526 (1998).
[CrossRef]

Phys. Rev. B Condens. Matter

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B Condens. Matter 50(23), 16835–16844 (1994).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

T. Savin and P. S. Doyle, “Role of a finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(4), 041106 (2005).
[CrossRef] [PubMed]

Phys. Rev. Lett.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides,” Phys. Rev. Lett. 94(12), 123901 (2005).
[CrossRef] [PubMed]

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled coupling of counterpropagating whispering-gallery modes by a single Rayleigh scatterer: a classical problem in a quantum optical light,” Phys. Rev. Lett. 99(17), 173603 (2007).
[CrossRef] [PubMed]

Physica C

N. Nakai, N. Hayashi, and M. Machida, “Simulation studies for the vortex-depinning dynamics around a columnar defect in superconductors,” Physica C 468(15–20), 1270–1273 (2008).
[CrossRef]

Rep. Prog. Phys.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[CrossRef]

Science

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

The Mathematical Gazette

R. W. D. Nickalls, “A new approach to solving the cubic: Cardan's solution revealed,” The Mathematical Gazette 77(480), 354–359 (1993).
[CrossRef]

Other

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” arXiv:1006.3126 [physics.optics].

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Figures (5)

Fig. 1
Fig. 1

(a) The real and imaginary parts of complex conductance for the Drude model according to Eq. (3). (b) A single planar interface between the upper dielectric and the lower metal-like medium. The in-plane wave number is denoted by k directed in the x-direction. Non-zero γ r induces cross-interface energy flows, whereas non-zero γ i entails an imbalance between the forward (“F”) and backward (“B”) waves along the interface.

Fig. 4
Fig. 4

The degree of asymmetry e obtained by varying one parameter while fixing the remaining two: e ( k ) based on the data of Fig. 2(a) with γ r as an abscissa; e ( γ r ) based on the data of Fig. 3(a) with k as an abscissa; and e ( γ i ) vs. γ i .

Fig. 2
Fig. 2

(a) Migrations of four roots on the complex ( ω r , ω i ) -plane. (b) The quality factor plotted against ω r . The curves are generated by varying kover the range 0 k 2 , where the arrows mean the direction of increasing k. The filled circles in pink color indicate the starting states at k = 0 , whereas the diamonds indicate the states on the half-way at k = 1 . In the inset of panel (a), we show the symmetric trajectories for the specified data γ r = 0.2 and γ i = 0 (namely, a real-valued γ).

Fig. 3
Fig. 3

(a) Migrations of four roots on the complex ( ω r , ω i ) -plane. The arrows imply the direction of increasing γ r . The filled circles in pink color indicate the starting states at γ r = 0 (where ω i = 0 , thus being neutrally stable), whereas the diamonds indicate the states on the half-way at γ r = 1.5 . In the inset of panel (a), we show the symmetric trajectories for the prescribed data γ i = 0 (a real-valued γ) and k = 0.5 . (b) Migrations of four roots on the complex ( v g r , v g i ) -plane. The thick horizontal arrow in shaded colors indicates the region of the subluminal group velocity, namely, | v g r | < k = 0.5 .

Fig. 5
Fig. 5

The real and imaginary parts of k = ω ( 1 + ε ) 1 ε according to Eq. (13), where both of ( k r , k i ) are positive. Three values of the complex relaxation rate are examined: (a) γ i = 0.2 i 0.2 , (b) γ i = 0.03 i 0.2 , and (c) γ i = 0.2 i .

Equations (14)

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

ε ( ω ) = 1 ω p 2 ω ( ω + i γ ) ,
ε r = 1 ω p 2 ( ω γ i ) ω D ε ,     ε i = ω p 2 γ r ω D ε ,     D ε ( ω γ i ) 2 + γ r 2 .
ε 1 + ω p 2 γ i ω | γ | 2 + i σ ω .
lim ω 0 σ r = ω p 2 γ r | γ | 2 + 2 ω p 2 γ r γ i | γ | 4 ω ,     lim ω 0 σ i = γ r 2 γ i 2 | γ | 4 ω p 2 ω .
ω 4 + i γ ω 3 ( 1 + 2 k 2 ) ω 2 2 i γ k 2 ω + k 2 = 0.
ω L ± ( k ) = ± 1 2 ( 1 + 2 k 2 ) 1 2 1 + 4 k 4 , ω H ± ( k ) = ± 1 2 ( 1 + 2 k 2 ) + 1 2 1 + 4 k 4 .
γ r ω i = I ( k 2 , ω r 2 , ω i 2 ) | D ( k 2 , ω ) | 2 .
I a k 4 + b k 2 + c , a 2 + 4 | ω | 2 > 0 ,     b 3 | ω | 2 + 4 | ω | 4 4 ω r 2 ( 1 + 2 | ω | 2 ) ,     c | ω | 4 + | ω | 6 > 0.
16 ω r 2 ( 2 | ω | 2 + 1 ) 2 ( | ω | 2 ω r 2 ) + ( 5 | ω | 2 + 8 | ω | 4 ) | ω | 2 > 0 ,
( L ) ω = i γ ,       ( H ) ω = 2 k ,       ( L + ) ω = 0 ,       ( H + ) ω = + 2 k .
v g ω k = 2 ω 2 + 2 i γ ω 1 4 ω 3 + 3 i γ ω 2 2 ( 1 + 2 k 2 ) ω 2 i γ k 2 2 k .
e = 1 4 ω / = 1 4 | ω | .
k = ± ω ω 2 + i γ ω 1 2 ω 2 + 2 i γ ω 1 .
exp [ i ( k x ω t ) ] = exp ( k i x ) exp [ i ( k r x ω t ) ] .

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