Abstract

We give a geometrical theory of resonances in Maxwell’s equations that generalizes the Mie formulae for spheres to all scattering channels of any dielectric or metallic particle without sharp edges. We show that the electromagnetic response of a particle is given by a set of modes of internal and scattered fields that are coupled pairwise on the surface of the particle and reveal that resonances in nanoparticles and excess noise in macroscopic cavities have the same origin. We give examples of two types of optical resonances: those in which a single pair of internal and scattered modes become strongly aligned in the sense defined in this paper, and those resulting from constructive interference of many pairs of weakly aligned modes, an effect relevant for sensing. This approach calculates resonances for every significant mode of particles, demonstrating that modes can be either bright or dark depending on the incident field. Using this extra mode information we then outline how excitation can be optimized. Finally, we apply this theory to gold particles with shapes often used in experiments, demonstrating effects including a Fano-like resonance.

© 2011 OSA

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  1. D. Graham and R. Goodacre, “Chemical and bioanalytical applications of surface enhanced Raman scattering spectroscopy,” Chem. Soc. Rev. 37, 883–884 (2008).
    [CrossRef] [PubMed]
  2. T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
    [CrossRef] [PubMed]
  3. B. Lukyanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Tow Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
    [CrossRef]
  4. N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetic induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
    [CrossRef] [PubMed]
  5. J. Schuller, E. Barnard, W. Cai, Y. C. Jun, J. White, and M. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
    [CrossRef] [PubMed]
  6. Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12, 60–69 (2009).
    [CrossRef]
  7. J. Pendry, D. Schuring, and D. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [CrossRef] [PubMed]
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  13. A. Knyazev, A. Jujusnashvili, and M. Argentati, “Angles between Infinite Dimensional Subspaces with Applications to the Rayleigh-Ritz and Alternating Projectors Methods,” J. Func. Anal. 259, 1323–1345 (2010).
    [CrossRef]
  14. K. Holms, B. Hourahine, and F. Papoff, “Calculation of internal and scattered fields of axisymmetric nanoparticles at any point in space,” J. Opt. A, Pure Appl. Opt. 11, 054009 (2009).
    [CrossRef]
  15. A. Aydin and A. Hizal, “On the completeness of the spherical vector wave functions,” J. Math. Anal. Appl. 117, 428–440 (1986).
    [CrossRef]
  16. A. Doicu, T. Wriedt, and Y. Eremin, Light Scattering by Systems of Particles (Springer, 2006).
  17. Complete sets of functions exist on surfaces (Lyapunov surfaces) that are mathematically characterized by three conditions: the normal is well defined at every point; the angle between the normals at any two points on the surface is bounded from above by a function of the distance between these points; all the lines parallel to a normal at an arbitrary point on the surface intercept only once the patches of surface contained in balls centered at the point and smaller than a critical value [18].
  18. V. S. Vladimirov, Equations of mathematical physics (MIR, Moscow, 1984).
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    [CrossRef]
  20. A. Doicu and T. Wriedt, “Extended boundary condition method with multipole sources located in the complex plane,” Opt. Commun. 139, 85–91 (1997).
    [CrossRef]
  21. T. Rother, M. Kahnert, A. Doicu, and J. Wauer, “Surface Green’s Function of the Helmholtz Equation in Spherical Coordinates,” Prog. Electromagn. Res. 38, 47–95 (2002).
    [CrossRef]
  22. A. Knyazev and M. Argentati, “Principal angles between subspaces in an A-based scalar product: algorithms and perturbation estimates,” SIAM J. Sci. Comput. 23, 2008–2040 (2002).
    [CrossRef]
  23. E. Hannan, “The general theory of canonical correlation and its relation to functional analysis,” J. Aust. Math. Soc. 2, 229–242 (1961/1962).
    [CrossRef]
  24. B. Hourahine, K. Holms, and F. Papoff, “Accurate near and far field determination for non spherical particles from Mie-type theory,” submitted (2011).
  25. The angles relevant to this work are the point angles 0 < ξ < π/2 of the infinite dimensional theory [13], together with the corresponding subspaces (principal modes) and their orthogonal complements (bi-orthogonal modes).
  26. G. New, “The origin of excess noise,” J. Mod. Opt. 42, 799–810 (1995).
    [CrossRef]
  27. W. J. Firth and A. Yao, “Giant excess noise and transient gain in misaligned laser cavities,” Phys. Rev. Lett. 95, 073903 (2005).
    [CrossRef] [PubMed]
  28. F. Papoff, G. D’Alessandro, and G.-L. Oppo, “State dependent pseudoresonances and excess noise,” Phys. Rev. Lett. 100, 123905 (2008).
    [CrossRef] [PubMed]
  29. M. I. Tribelsky and B. S. Lukyanchuk, “Anomalous light scattering by small particles,” Phys Rev. Lett. 97, 263902 (2006).
    [CrossRef]
  30. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).
    [CrossRef] [PubMed]
  31. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, Erratum: “An analytic model for the optical properties of gold”. J. Chem. Phys. 127, 189901 (2007).
    [CrossRef]
  32. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
  33. Evaluation of the data for the disc at 81 wavelengths required 418 seconds using the same machine as described in the caption of Table 1.
  34. J. Aizpurua, P. Hanarp, D. Sutherland, M. Kall, G. Bryant, and F. J. G. de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
    [CrossRef] [PubMed]
  35. H. Okamoto and K. Imura, “Near field optical imaging of enhanced electric fields and plasmon waves in metal nanostructures,” Prog. Surf. Sci. 84, 199–229 (2009).
    [CrossRef]

2010

B. Lukyanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Tow Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

J. Schuller, E. Barnard, W. Cai, Y. C. Jun, J. White, and M. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef] [PubMed]

A. Knyazev, A. Jujusnashvili, and M. Argentati, “Angles between Infinite Dimensional Subspaces with Applications to the Rayleigh-Ritz and Alternating Projectors Methods,” J. Func. Anal. 259, 1323–1345 (2010).
[CrossRef]

2009

K. Holms, B. Hourahine, and F. Papoff, “Calculation of internal and scattered fields of axisymmetric nanoparticles at any point in space,” J. Opt. A, Pure Appl. Opt. 11, 054009 (2009).
[CrossRef]

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12, 60–69 (2009).
[CrossRef]

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetic induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef] [PubMed]

H. Okamoto and K. Imura, “Near field optical imaging of enhanced electric fields and plasmon waves in metal nanostructures,” Prog. Surf. Sci. 84, 199–229 (2009).
[CrossRef]

2008

F. Papoff, G. D’Alessandro, and G.-L. Oppo, “State dependent pseudoresonances and excess noise,” Phys. Rev. Lett. 100, 123905 (2008).
[CrossRef] [PubMed]

D. Graham and R. Goodacre, “Chemical and bioanalytical applications of surface enhanced Raman scattering spectroscopy,” Chem. Soc. Rev. 37, 883–884 (2008).
[CrossRef] [PubMed]

2007

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, Erratum: “An analytic model for the optical properties of gold”. J. Chem. Phys. 127, 189901 (2007).
[CrossRef]

2006

M. I. Tribelsky and B. S. Lukyanchuk, “Anomalous light scattering by small particles,” Phys Rev. Lett. 97, 263902 (2006).
[CrossRef]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[CrossRef] [PubMed]

J. Pendry, D. Schuring, and D. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

2005

W. J. Firth and A. Yao, “Giant excess noise and transient gain in misaligned laser cavities,” Phys. Rev. Lett. 95, 073903 (2005).
[CrossRef] [PubMed]

2003

J. Aizpurua, P. Hanarp, D. Sutherland, M. Kall, G. Bryant, and F. J. G. de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef] [PubMed]

2002

T. Rother, M. Kahnert, A. Doicu, and J. Wauer, “Surface Green’s Function of the Helmholtz Equation in Spherical Coordinates,” Prog. Electromagn. Res. 38, 47–95 (2002).
[CrossRef]

A. Knyazev and M. Argentati, “Principal angles between subspaces in an A-based scalar product: algorithms and perturbation estimates,” SIAM J. Sci. Comput. 23, 2008–2040 (2002).
[CrossRef]

2001

2000

1999

1997

A. Doicu and T. Wriedt, “Extended boundary condition method with multipole sources located in the complex plane,” Opt. Commun. 139, 85–91 (1997).
[CrossRef]

1995

G. New, “The origin of excess noise,” J. Mod. Opt. 42, 799–810 (1995).
[CrossRef]

1986

A. Aydin and A. Hizal, “On the completeness of the spherical vector wave functions,” J. Math. Anal. Appl. 117, 428–440 (1986).
[CrossRef]

1908

G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys. 330, 377–445 (1908).
[CrossRef]

1875

C. Jordan, “Essai sur la géométrie à n dimension,” Bul. Soc. Math. France 3, 103–174 (1875).

Aizpurua, J.

J. Aizpurua, P. Hanarp, D. Sutherland, M. Kall, G. Bryant, and F. J. G. de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef] [PubMed]

Aoki, T.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[CrossRef] [PubMed]

Argentati, M.

A. Knyazev, A. Jujusnashvili, and M. Argentati, “Angles between Infinite Dimensional Subspaces with Applications to the Rayleigh-Ritz and Alternating Projectors Methods,” J. Func. Anal. 259, 1323–1345 (2010).
[CrossRef]

A. Knyazev and M. Argentati, “Principal angles between subspaces in an A-based scalar product: algorithms and perturbation estimates,” SIAM J. Sci. Comput. 23, 2008–2040 (2002).
[CrossRef]

Aydin, A.

A. Aydin and A. Hizal, “On the completeness of the spherical vector wave functions,” J. Math. Anal. Appl. 117, 428–440 (1986).
[CrossRef]

Barnard, E.

J. Schuller, E. Barnard, W. Cai, Y. C. Jun, J. White, and M. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Bowen, W. P.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[CrossRef] [PubMed]

Brongersma, M.

J. Schuller, E. Barnard, W. Cai, Y. C. Jun, J. White, and M. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef] [PubMed]

Bryant, G.

J. Aizpurua, P. Hanarp, D. Sutherland, M. Kall, G. Bryant, and F. J. G. de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef] [PubMed]

Cai, W.

J. Schuller, E. Barnard, W. Cai, Y. C. Jun, J. White, and M. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef] [PubMed]

D’Alessandro, G.

F. Papoff, G. D’Alessandro, and G.-L. Oppo, “State dependent pseudoresonances and excess noise,” Phys. Rev. Lett. 100, 123905 (2008).
[CrossRef] [PubMed]

Dayan, B.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[CrossRef] [PubMed]

de Abajo, F. J. G.

J. Aizpurua, P. Hanarp, D. Sutherland, M. Kall, G. Bryant, and F. J. G. de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef] [PubMed]

Doicu, A.

T. Rother, M. Kahnert, A. Doicu, and J. Wauer, “Surface Green’s Function of the Helmholtz Equation in Spherical Coordinates,” Prog. Electromagn. Res. 38, 47–95 (2002).
[CrossRef]

A. Doicu and T. Wriedt, “Calculation of the T matrix in the null-field method with discrete sources,” J. Opt. Soc. Am. A 16, 2539–2544 (1999).
[CrossRef]

A. Doicu and T. Wriedt, “Extended boundary condition method with multipole sources located in the complex plane,” Opt. Commun. 139, 85–91 (1997).
[CrossRef]

A. Doicu, T. Wriedt, and Y. Eremin, Light Scattering by Systems of Particles (Springer, 2006).

Eremin, Y.

A. Doicu, T. Wriedt, and Y. Eremin, Light Scattering by Systems of Particles (Springer, 2006).

Etchegoin, P. G.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, Erratum: “An analytic model for the optical properties of gold”. J. Chem. Phys. 127, 189901 (2007).
[CrossRef]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

Firth, W. J.

W. J. Firth and A. Yao, “Giant excess noise and transient gain in misaligned laser cavities,” Phys. Rev. Lett. 95, 073903 (2005).
[CrossRef] [PubMed]

Fleischhauer, M.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetic induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef] [PubMed]

Giessen, H.

B. Lukyanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Tow Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetic induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef] [PubMed]

Goodacre, R.

D. Graham and R. Goodacre, “Chemical and bioanalytical applications of surface enhanced Raman scattering spectroscopy,” Chem. Soc. Rev. 37, 883–884 (2008).
[CrossRef] [PubMed]

Graham, D.

D. Graham and R. Goodacre, “Chemical and bioanalytical applications of surface enhanced Raman scattering spectroscopy,” Chem. Soc. Rev. 37, 883–884 (2008).
[CrossRef] [PubMed]

Halas, N.

B. Lukyanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Tow Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Han, Y.

Hanarp, P.

J. Aizpurua, P. Hanarp, D. Sutherland, M. Kall, G. Bryant, and F. J. G. de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef] [PubMed]

Hannan, E.

E. Hannan, “The general theory of canonical correlation and its relation to functional analysis,” J. Aust. Math. Soc. 2, 229–242 (1961/1962).
[CrossRef]

Hizal, A.

A. Aydin and A. Hizal, “On the completeness of the spherical vector wave functions,” J. Math. Anal. Appl. 117, 428–440 (1986).
[CrossRef]

Holms, K.

K. Holms, B. Hourahine, and F. Papoff, “Calculation of internal and scattered fields of axisymmetric nanoparticles at any point in space,” J. Opt. A, Pure Appl. Opt. 11, 054009 (2009).
[CrossRef]

B. Hourahine, K. Holms, and F. Papoff, “Accurate near and far field determination for non spherical particles from Mie-type theory,” submitted (2011).

Hourahine, B.

K. Holms, B. Hourahine, and F. Papoff, “Calculation of internal and scattered fields of axisymmetric nanoparticles at any point in space,” J. Opt. A, Pure Appl. Opt. 11, 054009 (2009).
[CrossRef]

B. Hourahine, K. Holms, and F. Papoff, “Accurate near and far field determination for non spherical particles from Mie-type theory,” submitted (2011).

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Imura, K.

H. Okamoto and K. Imura, “Near field optical imaging of enhanced electric fields and plasmon waves in metal nanostructures,” Prog. Surf. Sci. 84, 199–229 (2009).
[CrossRef]

Jordan, C.

C. Jordan, “Essai sur la géométrie à n dimension,” Bul. Soc. Math. France 3, 103–174 (1875).

Jujusnashvili, A.

A. Knyazev, A. Jujusnashvili, and M. Argentati, “Angles between Infinite Dimensional Subspaces with Applications to the Rayleigh-Ritz and Alternating Projectors Methods,” J. Func. Anal. 259, 1323–1345 (2010).
[CrossRef]

Jun, Y. C.

J. Schuller, E. Barnard, W. Cai, Y. C. Jun, J. White, and M. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef] [PubMed]

Kahnert, M.

T. Rother, M. Kahnert, A. Doicu, and J. Wauer, “Surface Green’s Function of the Helmholtz Equation in Spherical Coordinates,” Prog. Electromagn. Res. 38, 47–95 (2002).
[CrossRef]

Kall, M.

J. Aizpurua, P. Hanarp, D. Sutherland, M. Kall, G. Bryant, and F. J. G. de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef] [PubMed]

Kästel, J.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetic induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef] [PubMed]

Kimble, H. J.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[CrossRef] [PubMed]

Kippenberg, T. J.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[CrossRef] [PubMed]

Knyazev, A.

A. Knyazev, A. Jujusnashvili, and M. Argentati, “Angles between Infinite Dimensional Subspaces with Applications to the Rayleigh-Ritz and Alternating Projectors Methods,” J. Func. Anal. 259, 1323–1345 (2010).
[CrossRef]

A. Knyazev and M. Argentati, “Principal angles between subspaces in an A-based scalar product: algorithms and perturbation estimates,” SIAM J. Sci. Comput. 23, 2008–2040 (2002).
[CrossRef]

Langguth, L.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetic induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef] [PubMed]

Le Ru, E. C.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, Erratum: “An analytic model for the optical properties of gold”. J. Chem. Phys. 127, 189901 (2007).
[CrossRef]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

Lippens, D.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12, 60–69 (2009).
[CrossRef]

Liu, N.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetic induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[CrossRef] [PubMed]

Lukyanchuk, B.

B. Lukyanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Tow Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Lukyanchuk, B. S.

M. I. Tribelsky and B. S. Lukyanchuk, “Anomalous light scattering by small particles,” Phys Rev. Lett. 97, 263902 (2006).
[CrossRef]

Maier, S.

B. Lukyanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Tow Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Meyer, M.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, Erratum: “An analytic model for the optical properties of gold”. J. Chem. Phys. 127, 189901 (2007).
[CrossRef]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125, 164705 (2006).
[CrossRef] [PubMed]

Mie, G.

G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys. 330, 377–445 (1908).
[CrossRef]

New, G.

G. New, “The origin of excess noise,” J. Mod. Opt. 42, 799–810 (1995).
[CrossRef]

Nordlander, P.

B. Lukyanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Tow Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Okamoto, H.

H. Okamoto and K. Imura, “Near field optical imaging of enhanced electric fields and plasmon waves in metal nanostructures,” Prog. Surf. Sci. 84, 199–229 (2009).
[CrossRef]

Oppo, G.-L.

F. Papoff, G. D’Alessandro, and G.-L. Oppo, “State dependent pseudoresonances and excess noise,” Phys. Rev. Lett. 100, 123905 (2008).
[CrossRef] [PubMed]

Papoff, F.

K. Holms, B. Hourahine, and F. Papoff, “Calculation of internal and scattered fields of axisymmetric nanoparticles at any point in space,” J. Opt. A, Pure Appl. Opt. 11, 054009 (2009).
[CrossRef]

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T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
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N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetic induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
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J. Schuller, E. Barnard, W. Cai, Y. C. Jun, J. White, and M. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
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T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
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B. Lukyanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Tow Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
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Mater. Today

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12, 60–69 (2009).
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Nat. Mater.

B. Lukyanchuk, N. Zheludev, S. Maier, N. Halas, P. Nordlander, H. Giessen, and C. Tow Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetic induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009).
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J. Schuller, E. Barnard, W. Cai, Y. C. Jun, J. White, and M. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[CrossRef] [PubMed]

Nature

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[CrossRef] [PubMed]

Opt. Commun.

A. Doicu and T. Wriedt, “Extended boundary condition method with multipole sources located in the complex plane,” Opt. Commun. 139, 85–91 (1997).
[CrossRef]

Phys Rev. Lett.

M. I. Tribelsky and B. S. Lukyanchuk, “Anomalous light scattering by small particles,” Phys Rev. Lett. 97, 263902 (2006).
[CrossRef]

Phys. Rev. Lett.

W. J. Firth and A. Yao, “Giant excess noise and transient gain in misaligned laser cavities,” Phys. Rev. Lett. 95, 073903 (2005).
[CrossRef] [PubMed]

F. Papoff, G. D’Alessandro, and G.-L. Oppo, “State dependent pseudoresonances and excess noise,” Phys. Rev. Lett. 100, 123905 (2008).
[CrossRef] [PubMed]

J. Aizpurua, P. Hanarp, D. Sutherland, M. Kall, G. Bryant, and F. J. G. de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef] [PubMed]

Prog. Electromagn. Res.

T. Rother, M. Kahnert, A. Doicu, and J. Wauer, “Surface Green’s Function of the Helmholtz Equation in Spherical Coordinates,” Prog. Electromagn. Res. 38, 47–95 (2002).
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Other

B. Hourahine, K. Holms, and F. Papoff, “Accurate near and far field determination for non spherical particles from Mie-type theory,” submitted (2011).

The angles relevant to this work are the point angles 0 < ξ < π/2 of the infinite dimensional theory [13], together with the corresponding subspaces (principal modes) and their orthogonal complements (bi-orthogonal modes).

A. Doicu, T. Wriedt, and Y. Eremin, Light Scattering by Systems of Particles (Springer, 2006).

Complete sets of functions exist on surfaces (Lyapunov surfaces) that are mathematically characterized by three conditions: the normal is well defined at every point; the angle between the normals at any two points on the surface is bounded from above by a function of the distance between these points; all the lines parallel to a normal at an arbitrary point on the surface intercept only once the patches of surface contained in balls centered at the point and smaller than a critical value [18].

V. S. Vladimirov, Equations of mathematical physics (MIR, Moscow, 1984).

M. I. Mishchenko, J. H. Hovernier, and L. D. Travis, eds., Light scattering by nonspherical particles: Theory, Measurements and Applications (Academic Press, 2000).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Evaluation of the data for the disc at 81 wavelengths required 418 seconds using the same machine as described in the caption of Table 1.

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