Abstract

We find exact conditions for the enhancement or suppression of internal and/or scattered fields in any smooth particle and the determination of their spatial distribution or angular momentum through the combination of simple fields. The incident fields can be generated by a single monochromatic or broad band light source, or by several sources, which may also be impurities embedded in the nanoparticle. We can design the lineshape of a particle introducing very narrow features in its spectral response.

© 2013 OSA

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  1. M. Abb, P. Albella, J. Aizpurua, and O. Muskens, “All-optical control of a single plasmonic nanoantenna-ITO hybrid,” Nano Lett.11, 2457–2463 (2011).
    [CrossRef] [PubMed]
  2. A. Kubo, K. Onda, H. Petek, Z. Sun, Y. Jung, and H. Kim, “Femtosecond imaging of surface plasmon dynamics in a nanostructured silver film,” Nano Lett.5, 1123–1127 (2005).
    [CrossRef] [PubMed]
  3. M. Durach, A. Rusina, and M. Stockman, “Full spatiotemporal control on the nanoscale,” Nano Lett.7, 3145–3149 (2007).
    [CrossRef] [PubMed]
  4. M. Martin Aeschlimann, M. Bauer, D. Bayer, T. Tobias Brixner, F. Garcia de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Felix Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature446, 301–304 (2007).
    [CrossRef] [PubMed]
  5. H. Noh, Y. Chomg, A. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett.108, 186805 (2012).
    [CrossRef] [PubMed]
  6. R. Pierrat, C. Vandenbem, M. Fink, and R. Carminati, “Subwavelength focusing inside an open disordered medium by time reversal at a single point antenna,” Phys. Rev. A87, 041801 (2013).
    [CrossRef]
  7. J. Jeffers, “Interference and the lossless lossy beam splitter,” Journ. Mod. Opt.47, 1819–1824 (2000).
  8. J. Zhang, K. MacDonald, and N. Zheludev, “Controlling light-with-light without nonlinearity,” Light: Science & Appl.1, e18 (2012).
    [CrossRef]
  9. M. Mazilu, J. Baumgartl, S. Kosmeier, and K. Dholakia, “Optical eigenmodes; exploiting the quadratic nature of the energy flux and of scattering interactions,” Opt. Express19, 933–945 (2011).
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  10. F. Papoff and B. Hourahine, “Geometrical mie theory for resonances in nanoparticles of any shape,” Opt.Express19, 21432–21444 (2011).
    [CrossRef] [PubMed]
  11. M. Doherty, A. Murphy, R. Pollard, and P. Dawson, “Surface-enhanced raman scattering from metallic nanostructures: Bridging the gap between the near-field and far-field responses,” Phys. Rev. X3, 011001 (2013).
    [CrossRef]
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    [CrossRef]
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  18. J. A. Stratton and L. J. Chu, “Scattering of light from a two-dimensional array of spherical particles on a substrate,” Phys. Rev.56, 99–107 (1939).
    [CrossRef]
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  20. H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and a. J. C. E. Yao, “Simplified measurement of the orbital angular momentum of photons,” Opt. Commun.223, 117–122 (2003).
    [CrossRef]
  21. 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]
  22. T. Rother, M. Kahnert, A. Doicu, and J. Wauer, “Surface Green’s Function of the Helmholtz Equation in Spherical Coordinates,” Prog. Electromag. Res.38, 47–95 (2002).
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  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. A. Knyazev, A. Jujusnashvili, and M. Argentati, “Angles between Infinite Dimensional Subspaces with Applications to the Rayleigh-Ritz and Alternating Projectors Methods,” Journ. of Func. Analys.259, 1323–1345 (2010).
    [CrossRef]
  25. W. J. Firth and A. Yao, “Giant excess noise and transient gain in misaligned laser cavities,” Phys. Rev. Lett.95, 073903 (2005).
    [CrossRef] [PubMed]
  26. F. Papoff, G. D’Alessandro, and G.-L. Oppo, “State dependent pseudoresonances and excess noise,” Phys. Rev. Lett.100, 123905 (2008).
    [CrossRef] [PubMed]
  27. F. Papoff and G. Robb, “Rapid coherent optical modulation of atomic momenta via pseudoresonances,” Phys. Rev. Lett.108, 113902 (2012).
    [CrossRef] [PubMed]
  28. A. Doicu, Y. Eremin, and T. Wreidt, Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources(Accademic Press, 2000).

2013 (2)

R. Pierrat, C. Vandenbem, M. Fink, and R. Carminati, “Subwavelength focusing inside an open disordered medium by time reversal at a single point antenna,” Phys. Rev. A87, 041801 (2013).
[CrossRef]

M. Doherty, A. Murphy, R. Pollard, and P. Dawson, “Surface-enhanced raman scattering from metallic nanostructures: Bridging the gap between the near-field and far-field responses,” Phys. Rev. X3, 011001 (2013).
[CrossRef]

2012 (3)

F. Papoff and G. Robb, “Rapid coherent optical modulation of atomic momenta via pseudoresonances,” Phys. Rev. Lett.108, 113902 (2012).
[CrossRef] [PubMed]

J. Zhang, K. MacDonald, and N. Zheludev, “Controlling light-with-light without nonlinearity,” Light: Science & Appl.1, e18 (2012).
[CrossRef]

H. Noh, Y. Chomg, A. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett.108, 186805 (2012).
[CrossRef] [PubMed]

2011 (4)

2010 (1)

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

2009 (1)

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]

2008 (1)

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

2007 (3)

M. Durach, A. Rusina, and M. Stockman, “Full spatiotemporal control on the nanoscale,” Nano Lett.7, 3145–3149 (2007).
[CrossRef] [PubMed]

M. Martin Aeschlimann, M. Bauer, D. Bayer, T. Tobias Brixner, F. Garcia de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Felix Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature446, 301–304 (2007).
[CrossRef] [PubMed]

P. C. Waterman, “The T-matrix revisited,” JOSA A24, 2257–2267 (2007).
[CrossRef] [PubMed]

2005 (2)

A. Kubo, K. Onda, H. Petek, Z. Sun, Y. Jung, and H. Kim, “Femtosecond imaging of surface plasmon dynamics in a nanostructured silver film,” Nano Lett.5, 1123–1127 (2005).
[CrossRef] [PubMed]

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 (1)

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and a. J. C. E. Yao, “Simplified measurement of the orbital angular momentum of photons,” Opt. Commun.223, 117–122 (2003).
[CrossRef]

2002 (1)

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

2000 (1)

J. Jeffers, “Interference and the lossless lossy beam splitter,” Journ. Mod. Opt.47, 1819–1824 (2000).

1996 (1)

B. F. Farrell and P. J. Ioannou, “Generalized stability theory. part i: Autonomous operators,” Journ. of Atm. Sc.53, 2025–2040 (1996).
[CrossRef]

1975 (1)

1965 (1)

I. Malitson, “Interspecimen comparison of the refractive index of fused silica,” Journal of the Optical Society of America55, 1205–1209 (1965).
[CrossRef]

1939 (1)

J. A. Stratton and L. J. Chu, “Scattering of light from a two-dimensional array of spherical particles on a substrate,” Phys. Rev.56, 99–107 (1939).
[CrossRef]

Abb, M.

M. Abb, P. Albella, J. Aizpurua, and O. Muskens, “All-optical control of a single plasmonic nanoantenna-ITO hybrid,” Nano Lett.11, 2457–2463 (2011).
[CrossRef] [PubMed]

Aizpurua, J.

M. Abb, P. Albella, J. Aizpurua, and O. Muskens, “All-optical control of a single plasmonic nanoantenna-ITO hybrid,” Nano Lett.11, 2457–2463 (2011).
[CrossRef] [PubMed]

Albella, P.

M. Abb, P. Albella, J. Aizpurua, and O. Muskens, “All-optical control of a single plasmonic nanoantenna-ITO hybrid,” Nano Lett.11, 2457–2463 (2011).
[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,” Journ. of Func. Analys.259, 1323–1345 (2010).
[CrossRef]

Barber, P.

Barnett, S. M.

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and a. J. C. E. Yao, “Simplified measurement of the orbital angular momentum of photons,” Opt. Commun.223, 117–122 (2003).
[CrossRef]

Bauer, M.

M. Martin Aeschlimann, M. Bauer, D. Bayer, T. Tobias Brixner, F. Garcia de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Felix Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature446, 301–304 (2007).
[CrossRef] [PubMed]

Baumgartl, J.

Bayer, D.

M. Martin Aeschlimann, M. Bauer, D. Bayer, T. Tobias Brixner, F. Garcia de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Felix Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature446, 301–304 (2007).
[CrossRef] [PubMed]

Cao, H.

H. Noh, Y. Chomg, A. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett.108, 186805 (2012).
[CrossRef] [PubMed]

Carminati, R.

R. Pierrat, C. Vandenbem, M. Fink, and R. Carminati, “Subwavelength focusing inside an open disordered medium by time reversal at a single point antenna,” Phys. Rev. A87, 041801 (2013).
[CrossRef]

Chomg, Y.

H. Noh, Y. Chomg, A. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett.108, 186805 (2012).
[CrossRef] [PubMed]

Chu, L. J.

J. A. Stratton and L. J. Chu, “Scattering of light from a two-dimensional array of spherical particles on a substrate,” Phys. Rev.56, 99–107 (1939).
[CrossRef]

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]

Dawson, P.

M. Doherty, A. Murphy, R. Pollard, and P. Dawson, “Surface-enhanced raman scattering from metallic nanostructures: Bridging the gap between the near-field and far-field responses,” Phys. Rev. X3, 011001 (2013).
[CrossRef]

Dholakia, K.

Doherty, M.

M. Doherty, A. Murphy, R. Pollard, and P. Dawson, “Surface-enhanced raman scattering from metallic nanostructures: Bridging the gap between the near-field and far-field responses,” Phys. Rev. X3, 011001 (2013).
[CrossRef]

Doicu, A.

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

A. Doicu, Y. Eremin, and T. Wreidt, Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources(Accademic Press, 2000).

Durach, M.

M. Durach, A. Rusina, and M. Stockman, “Full spatiotemporal control on the nanoscale,” Nano Lett.7, 3145–3149 (2007).
[CrossRef] [PubMed]

Eremin, Y.

A. Doicu, Y. Eremin, and T. Wreidt, Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources(Accademic Press, 2000).

Farrell, B. F.

B. F. Farrell and P. J. Ioannou, “Generalized stability theory. part i: Autonomous operators,” Journ. of Atm. Sc.53, 2025–2040 (1996).
[CrossRef]

Felix Steeb, F.

M. Martin Aeschlimann, M. Bauer, D. Bayer, T. Tobias Brixner, F. Garcia de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Felix Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature446, 301–304 (2007).
[CrossRef] [PubMed]

Fink, M.

R. Pierrat, C. Vandenbem, M. Fink, and R. Carminati, “Subwavelength focusing inside an open disordered medium by time reversal at a single point antenna,” Phys. Rev. A87, 041801 (2013).
[CrossRef]

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]

Franke-Arnold, S.

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and a. J. C. E. Yao, “Simplified measurement of the orbital angular momentum of photons,” Opt. Commun.223, 117–122 (2003).
[CrossRef]

Garcia de Abajo, F.

M. Martin Aeschlimann, M. Bauer, D. Bayer, T. Tobias Brixner, F. Garcia de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Felix Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature446, 301–304 (2007).
[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]

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]

Hourahine, B.

F. Papoff and B. Hourahine, “Geometrical mie theory for resonances in nanoparticles of any shape,” Opt.Express19, 21432–21444 (2011).
[CrossRef] [PubMed]

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]

Ioannou, P. J.

B. F. Farrell and P. J. Ioannou, “Generalized stability theory. part i: Autonomous operators,” Journ. of Atm. Sc.53, 2025–2040 (1996).
[CrossRef]

Jeffers, J.

J. Jeffers, “Interference and the lossless lossy beam splitter,” Journ. Mod. Opt.47, 1819–1824 (2000).

Jujusnashvili, A.

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

Jung, Y.

A. Kubo, K. Onda, H. Petek, Z. Sun, Y. Jung, and H. Kim, “Femtosecond imaging of surface plasmon dynamics in a nanostructured silver film,” Nano Lett.5, 1123–1127 (2005).
[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. Electromag. Res.38, 47–95 (2002).
[CrossRef]

Kim, H.

A. Kubo, K. Onda, H. Petek, Z. Sun, Y. Jung, and H. Kim, “Femtosecond imaging of surface plasmon dynamics in a nanostructured silver film,” Nano Lett.5, 1123–1127 (2005).
[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,” Journ. of Func. Analys.259, 1323–1345 (2010).
[CrossRef]

Kosmeier, S.

Kubo, A.

A. Kubo, K. Onda, H. Petek, Z. Sun, Y. Jung, and H. Kim, “Femtosecond imaging of surface plasmon dynamics in a nanostructured silver film,” Nano Lett.5, 1123–1127 (2005).
[CrossRef] [PubMed]

Leach, J.

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and a. J. C. E. Yao, “Simplified measurement of the orbital angular momentum of photons,” Opt. Commun.223, 117–122 (2003).
[CrossRef]

MacDonald, K.

J. Zhang, K. MacDonald, and N. Zheludev, “Controlling light-with-light without nonlinearity,” Light: Science & Appl.1, e18 (2012).
[CrossRef]

Malitson, I.

I. Malitson, “Interspecimen comparison of the refractive index of fused silica,” Journal of the Optical Society of America55, 1205–1209 (1965).
[CrossRef]

Martin Aeschlimann, M.

M. Martin Aeschlimann, M. Bauer, D. Bayer, T. Tobias Brixner, F. Garcia de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Felix Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature446, 301–304 (2007).
[CrossRef] [PubMed]

Mazilu, M.

Murphy, A.

M. Doherty, A. Murphy, R. Pollard, and P. Dawson, “Surface-enhanced raman scattering from metallic nanostructures: Bridging the gap between the near-field and far-field responses,” Phys. Rev. X3, 011001 (2013).
[CrossRef]

Muskens, O.

M. Abb, P. Albella, J. Aizpurua, and O. Muskens, “All-optical control of a single plasmonic nanoantenna-ITO hybrid,” Nano Lett.11, 2457–2463 (2011).
[CrossRef] [PubMed]

Noh, H.

H. Noh, Y. Chomg, A. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett.108, 186805 (2012).
[CrossRef] [PubMed]

Onda, K.

A. Kubo, K. Onda, H. Petek, Z. Sun, Y. Jung, and H. Kim, “Femtosecond imaging of surface plasmon dynamics in a nanostructured silver film,” Nano Lett.5, 1123–1127 (2005).
[CrossRef] [PubMed]

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]

Padgett, M. J.

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and a. J. C. E. Yao, “Simplified measurement of the orbital angular momentum of photons,” Opt. Commun.223, 117–122 (2003).
[CrossRef]

Papoff, F.

F. Papoff and G. Robb, “Rapid coherent optical modulation of atomic momenta via pseudoresonances,” Phys. Rev. Lett.108, 113902 (2012).
[CrossRef] [PubMed]

F. Papoff and B. Hourahine, “Geometrical mie theory for resonances in nanoparticles of any shape,” Opt.Express19, 21432–21444 (2011).
[CrossRef] [PubMed]

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]

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

Petek, H.

A. Kubo, K. Onda, H. Petek, Z. Sun, Y. Jung, and H. Kim, “Femtosecond imaging of surface plasmon dynamics in a nanostructured silver film,” Nano Lett.5, 1123–1127 (2005).
[CrossRef] [PubMed]

Pfeiffer, W.

M. Martin Aeschlimann, M. Bauer, D. Bayer, T. Tobias Brixner, F. Garcia de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Felix Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature446, 301–304 (2007).
[CrossRef] [PubMed]

Pierrat, R.

R. Pierrat, C. Vandenbem, M. Fink, and R. Carminati, “Subwavelength focusing inside an open disordered medium by time reversal at a single point antenna,” Phys. Rev. A87, 041801 (2013).
[CrossRef]

Pollard, R.

M. Doherty, A. Murphy, R. Pollard, and P. Dawson, “Surface-enhanced raman scattering from metallic nanostructures: Bridging the gap between the near-field and far-field responses,” Phys. Rev. X3, 011001 (2013).
[CrossRef]

Robb, G.

F. Papoff and G. Robb, “Rapid coherent optical modulation of atomic momenta via pseudoresonances,” Phys. Rev. Lett.108, 113902 (2012).
[CrossRef] [PubMed]

Rodríguez-Oliveros, R.

Rohmer, M.

M. Martin Aeschlimann, M. Bauer, D. Bayer, T. Tobias Brixner, F. Garcia de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Felix Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature446, 301–304 (2007).
[CrossRef] [PubMed]

Rother, T.

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

Rusina, A.

M. Durach, A. Rusina, and M. Stockman, “Full spatiotemporal control on the nanoscale,” Nano Lett.7, 3145–3149 (2007).
[CrossRef] [PubMed]

Sanchez-Gil, J. A.

Spindler, C.

M. Martin Aeschlimann, M. Bauer, D. Bayer, T. Tobias Brixner, F. Garcia de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Felix Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature446, 301–304 (2007).
[CrossRef] [PubMed]

Stockman, M.

M. Durach, A. Rusina, and M. Stockman, “Full spatiotemporal control on the nanoscale,” Nano Lett.7, 3145–3149 (2007).
[CrossRef] [PubMed]

Stone, A.

H. Noh, Y. Chomg, A. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett.108, 186805 (2012).
[CrossRef] [PubMed]

Stratton, J. A.

J. A. Stratton and L. J. Chu, “Scattering of light from a two-dimensional array of spherical particles on a substrate,” Phys. Rev.56, 99–107 (1939).
[CrossRef]

Sun, Z.

A. Kubo, K. Onda, H. Petek, Z. Sun, Y. Jung, and H. Kim, “Femtosecond imaging of surface plasmon dynamics in a nanostructured silver film,” Nano Lett.5, 1123–1127 (2005).
[CrossRef] [PubMed]

Taflove, A.

A. Taflove, Computational Electrodynamics: The Finite Difference Time-Domain Method (Artech House Publishers , Boston, MA, 1995).

Tobias Brixner, T.

M. Martin Aeschlimann, M. Bauer, D. Bayer, T. Tobias Brixner, F. Garcia de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Felix Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature446, 301–304 (2007).
[CrossRef] [PubMed]

Vandenbem, C.

R. Pierrat, C. Vandenbem, M. Fink, and R. Carminati, “Subwavelength focusing inside an open disordered medium by time reversal at a single point antenna,” Phys. Rev. A87, 041801 (2013).
[CrossRef]

Waterman, P. C.

P. C. Waterman, “The T-matrix revisited,” JOSA A24, 2257–2267 (2007).
[CrossRef] [PubMed]

Wauer, J.

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

Wei, H.

H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and a. J. C. E. Yao, “Simplified measurement of the orbital angular momentum of photons,” Opt. Commun.223, 117–122 (2003).
[CrossRef]

Wreidt, T.

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Figures (5)

Fig. 1
Fig. 1

Suggested experimental geometries for control of optical channels. a) Monochromatic incident light fields approaching a disc shaped nanostructure to change the amplitudes of a specified principal mode, two independent light sources with amplitudes A and A1 and a specified relative phase ΔΦ are used. b) A more general spatial-light modulator approach for changing phase and/or amplitude over a range of wavelengths for a broadband source or an applied pulse of light. Here the incident light is split into two paths, with one being dispersed and its complex amplitude modified as a function of wavelenth, before being re-combined and applied to the nanostructure together with the light which followed the second path. c) Generation of phase controlled light from an internal source within a nano-particle or nanostructure. This is driven by the blue by incident light, and re-radiates through a coherent process, such as two photon decay or parametric down conversion, in the red. This then interacts with external light incident at the emission wavelength (again in red). By exchanging the roles of the red and blue light sources, the same scheme can be used for control in the context of second harmonic generation.

Fig. 2
Fig. 2

Schematic of one pair of principal modes of a nanostructure interacting with different incident fields. The modes and incident fields have been normalized to unit magnitude (the marked circle). The amplitude, a n s, of the scattered mode, sn, is given by the intersection of straight lines parallel to in and passing through the extrema of the incident field and a line containing sn. From this construction, we can see that a unit magnitude field with fn parallel to sn induces amplitudes a n s = 1, a n i = 0 (shown in red, corresponding to Eq. (1)), while a unit field with fn parallel to s′n (and orthogonal to in) induces the largest amplitude possible a n s from a unit magnitude incident field along with a non-vanishing internal amplitude a n i (blue, matching Eq. (2)). Equivalently [17], the amplitudes are proportional to the scalar products of the incident field with the biorthogonal modes {i′n} and {s′n}, as shown in Eq. (6).

Fig. 3
Fig. 3

Internal and scattered mode amplitudes of a rounded rod-shaped dielectric (n = 1.5) particle, of 2 μm length and 0.7 μm diameter around one of its (many) resonances at ∼ 630 nm. The height of this landscape is sin−1(ξ), i.e. the largest value of amplitude possible for |fn| = 1; while the shading of the traces overlaid on top show, for each wavelength (λ), the amplitude of mode induced by the incident combinations for the first n most aligned principle modes. For fields which obey Eq. (3), the internal and scattered modes can be independently addressed. Here we use two plane-polarized incident fields, either incident with their k-vector along the axis of the particle or at 60° to this direction. Figures a) and b) show the resulting internal amplitude for the two fields, while c) and d) are the scattered amplitudes. Both fields are linearly independent and both interact with the resonant feature at the back of the landscape (the fields also causes appreciable amplitude in several of the more poorly aligned modes further down the landscape). Figures e) and g) show the corresponding amplitudes for a field combination constructed to only cancel the internal component of the resonance (while leaving the scattered unchanged at the value caused by the axially incident light) for the resonant feature. f) and h) show the converse case of removing the amplitude of the resonance in the scattered space while leaving the internal unchanged. In both cases, the unchanged resonant mode is seem to retain exactly the same amplitude at its peak as the corresponding axial incident case; a) vs. f) and c) vs. g), whilst the paired mode in the other space is lost. Modes which are not controlled further down the landscape are also seen to acquire large amplitudes from these combinations of the incident field.

Fig. 4
Fig. 4

Differential scattering for a rounded disc shaped (20 nm thickness and 60 nm radius) gold disc, with a dominant single pair mode modes showing a dipolar resonance at 697 nm (in a surrounding medium [19] with εr scaled by 0.75 to emulate support of the disc by a silica surface in air.) a) Scattering from an incident plane wave, with the square of the electric near field shown inset. This system clearly shows a dipole radiation pattern for axially incident light, which consists of light with both m = ±1 angular momentum. By introducing a second and then third field with chosen complex amplitudes, the light in the m = −1 and then both m ± 1 channels can be removed, eventually leaving relatively little interaction with the incident light. b) Illustration of the effect of scanning for the condition to remove the m = −1 channel by adjusting the magnitude and phase of a second incident planewave. Experimentally, this example requires monitoring the orbital angular momentum of light emitted along the particle axis [20], to determine the relative amplitudes and phase where only the m = −1 dipolar resonance is active. Here we show the effect of scanning the relative amplitude and phase of light incident along the axis and an additional 45° direction (with respect to the particle axis) plane-polarized light. The scan is between the light consiting purely of the axially incident field A (x = 1) and field incident at 45° (A1 at x = 0) and over the range of relative phases of the two incident light sources.

Fig. 5
Fig. 5

Cross sections of the gold disc from Figure 4 with standard axial incidence, leading to a broad feature in the extinction (red) and scattering (blue). These are compared against its response to illumination of light from three directions (axial, 45 and 90° incident) with their relative phases (but not amplitudes) modulated to cause constructive interference only at a chosen wavelength, then rotating the phase to cause destructive interference according to a gaussian envelope, producing a specified location and line width feature within the envelope of the original broad peak.

Equations (17)

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f n = s n a n s = 1 , a n i = 0 ,
f n = s n a n s = 1 sin ( ξ n ) , a n i = cos ( ξ n ) sin ( ξ n ) .
s n f s n f 1 i n f i n f 1 .
A 1 = A i n f i n f 1 ,
A 1 = A i n f i n f 1 ,
a n i = i n f i n i n , a n s = s n f s n s n ,
i n = i n ( i n s n ) s n 1 ( i n s n ) 2 , s n = s n ( i n s n ) i n 1 ( i n s n ) 2
i l m = e i ϕ l ( | i l E ( r ) | 2 + | i l H ( r ) | 2 ) 1 / 2 [ m l m ( Ω ) i l E ( r ) , n l m ( Ω ) i l H ( r ) ] T ,
s l m = 1 ( | s l E ( r ) | 2 + | s l H ( r ) | 2 ) 1 / 2 [ m l m ( Ω ) s l E ( r ) , n l m ( Ω ) s l H ( r ) ] T
i l m s l m = | i l E ( r ) * s l E ( r ) + i l H ( r ) * s l H ( r ) | ( | i l E ( r ) | 2 + | i l H ( r ) | 2 ) 1 / 2 ( | s l E ( r ) | 2 + | s l H ( r ) | 2 ) 1 / 2 .
A 1 = A f l E * i l E + f l H * i l H f l 1 E * i l E + f l 1 H * i l H ,
A 1 = A f l E * ( e i ϕ l i l E cos ( ξ n ) s l E ) + f l H * ( e i ϕ l i l H cos ( ξ n ) s l E ) f l 1 E * ( e i ϕ l i l E cos ( ξ n ) s l E ) + f l 1 H * ( e i ϕ l i l H cos ( ξ n ) s l E ) .
[ i ω μ ( n × S n H ) × ( n × S n E ) ( n S n E ) ] g ( x , y ) d σ = 0
[ i ω μ ( n × F n H ) × ( n × F n E ) ( n F n E ) ] g ( x , y ) d σ = F n E ( x ) ,
n ( x ) × ( n ( x ) × [ i ω μ ( n × I n H ) × ( n × I n E ) ε i ε ( n I n E ) ] g ( x , y ) d σ ) = a n s a n i s n ( x ) i n ( x )
W n = | a n i | 2 W n i | a n s | 2 W n s + 1 2 Re [ n ( a n i a s * n i n E × s n H * + a i * n a n s s n E × i n H * ) d σ ] = 0 ,
[ i 1 f 1 sin ( ξ 1 ) i 1 f m + l + 1 sin ( ξ 1 ) s l f 1 sin ( ξ l ) s l f m + l + 1 sin ( ξ l ) ] [ A 1 A m + l + 1 ] = [ A i 1 f sin ( ξ 1 ) c A i 2 f sin ( ξ 2 ) A s l f sin ( ξ l ) ] .

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