Abstract

We study semi-analytically the light emission and absorption properties of arbitrary stratified photonic structures with embedded two-dimensional magnetoelectric point scattering lattices, as used in recent plasmon-enhanced LEDs and solar cells. By employing dyadic Green’s function for the layered structure in combination with the Ewald lattice summation to deal with the particle lattice, we develop an efficient method to study the coupling between planar 2D scattering lattices of plasmonic, or metamaterial point particles, coupled to layered structures. Using the ‘array scanning method’ we deal with localized sources. Firstly, we apply our method to light emission enhancement of dipole emitters in slab waveguides, mediated by plasmonic lattices. We benchmark the array scanning method against a reciprocity-based approach to find that the calculated radiative rate enhancement in k-space below the light cone shows excellent agreement. Secondly, we apply our method to study absorption-enhancement in thin-film solar cells mediated by periodic Ag nanoparticle arrays. Lastly, we study the emission distribution in k-space of a coupled waveguide-lattice system. In particular, we explore the dark mode excitation on the plasmonic lattice using the so-called array scanning method. Our method could be useful for simulating a broad range of complex nanophotonic structures, i.e., metasurfaces, plasmon-enhanced light emitting systems and photovoltaics.

© 2017 Optical Society of America

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References

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  1. K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58, 267–297 (2007).
    [Crossref]
  2. I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174–2176 (1993).
    [Crossref]
  3. J. Vuckovic, M. Lončar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
    [Crossref]
  4. K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
    [Crossref] [PubMed]
  5. D. M. Yeh, C. F. Huang, C. Y. Chen, Y. C. Lu, and C. C. Yang, “Localized surface plasmon-induced emission enhancement of a green light-emitting diode,” Nanotechnology 19(34), 345201 (2008).
    [Crossref] [PubMed]
  6. J. Henson, J. DiMaria, E. Dimakis, T. D. Moustakas, and R. Paiella, “Plasmon-enhanced light emission based on lattice resonances of silver nanocylinder arrays,” Opt. Lett. 37(1), 79–81 (2012).
    [Crossref] [PubMed]
  7. W. L. Barnes, “Electromagnetic crystals for surface plasmon polaritons and the extraction of light from emissive devices,” J. Lightwave Technol. 17(11), 2170 (1999).
    [Crossref]
  8. H. Rigneault, F. Lemarchand, A. Sentenac, and H. Giovanini, “Extraction of light from sources located inside waveguide grating structures,” Opt. Lett. 24(3), 148–150 (1999).
    [Crossref]
  9. G. Lozano, D. J. Louwers, S. R. K. Rodríguez, S. Murai, O. T. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light Sci. Appl. 2(5), e66 (2013).
    [Crossref]
  10. M. van Lare, F. Lenzmann, M. A. Verschuuren, and A. Polman, “Mode coupling by plasmonic surface scatterers in thin-film silicon solar cells,” Appl. Phys. Lett. 101(22), 221110 (2012).
    [Crossref]
  11. V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express 18(102), A237–A245 (2010).
    [Crossref] [PubMed]
  12. A. H. Schokker and A. F. Koenderink, “Lasing at the band edges of plasmonic lattices,” Phys. Rev. B 90(15), 155452 (2014).
    [Crossref]
  13. M. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
    [Crossref] [PubMed]
  14. P. Törmä and W. L. Barnes, “Strong coupling between surface plasmon polaritons and emitters: a review,” Rep. Prog. Phys. 78(1), 013901 (2015).
    [Crossref]
  15. V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
    [Crossref] [PubMed]
  16. I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
    [Crossref]
  17. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, K V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
    [Crossref] [PubMed]
  18. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
    [Crossref] [PubMed]
  19. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
    [Crossref] [PubMed]
  20. A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9(2), 195–213 (2015).
    [Crossref]
  21. I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magnetoelectric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83(24), 245102 (2011).
    [Crossref]
  22. J. Xu, B. B. Wu, and Y. T. Chen, “Elimination of polarization degeneracy in circularly symmetric bianisotropic waveguides: a decoupled case,” Opt. Express 23(9), 11566–11575 (2015).
    [Crossref] [PubMed]
  23. Y. Ra’di, C. R. Simovski, and S. A. Tretyakov, “Thin perfect absorbers for electromagnetic waves: theory, design, and realizations,” Phys. Rev. Appl. 3(3), 037001 (2015).
    [Crossref]
  24. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
    [Crossref] [PubMed]
  25. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
    [Crossref] [PubMed]
  26. C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
    [Crossref] [PubMed]
  27. A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012).
    [Crossref] [PubMed]
  28. D. Iida, A. Fadil, Y. T. Chen, Y. Y. Ou, O. Kopylov, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Y. Ou, “Internal quantum efficiency enhancement of GaInN/GaN quantum-well structures using Ag nanoparticles,” AIP Adv. 5(9), 097169 (2015).
    [Crossref]
  29. K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
    [Crossref]
  30. K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008).
    [Crossref] [PubMed]
  31. V. A. Fedotov, J. Wallauer, M. Walther, M. Perino, N. Papasimakis, and N. I. Zheludev, “Wavevector selective metasurfaces and tunnel vision filters,” Light Sci. Appl. 4(7), e306 (2015).
    [Crossref]
  32. A. Pors and S. I. Bozhevolnyi, “Plasmonic metasurfaces for efficient phase control in reflection,” Opt. Express 21(22), 27438–27451 (2013).
    [Crossref] [PubMed]
  33. Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
    [Crossref]
  34. Y. T. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18(12), 12489–12498 (2010).
    [Crossref] [PubMed]
  35. A. E. Miroshnichenko, A. B. Evlyukhin, Y. S. Kivshar, and B. N. Chichkov, “Substrated-induced resonant magneto-electric effects for dielectric nanoparticles,” ACS Photonics,  2(10), 1423–1428 (2015).
    [Crossref]
  36. P. Lunnemann, I. Sersic, and A. F. Koenderink, “Optical properties of two-dimensional magnetoelectric point scattering lattices,” Phys. Rev. B 88(24), 245109 (2013).
    [Crossref]
  37. A. Kwadrin and A. F. Koenderink, “Probing the electrodynamic local density of states with magnetoelectric point scatterers,” Phys. Rev. B 87(12), 125123 (2013).
    [Crossref]
  38. A. Kwadrin, C. I. Osorio, and A. F. Koenderink, “Backaction in metasurface etalons,” Phys. Rev. B 93(10), 104301 (2016).
    [Crossref]
  39. A. Eroglu and J. K. Lee, “Simplified formulation of dyadic Green’s functions and their duality relations for general anisotropic media,” Progress in Electromagnetic Research, PIER 77, 391–408 (2007).
    [Crossref]
  40. L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University Press, 2006).
    [Crossref]
  41. V. V. Klimov and M. Ducloy, “Quadrupole transitions near an interface: general theory and application to an atom inside a planar cavity,” Phys. Rev. A 72(4), 043809 (2005).
    [Crossref]
  42. R. L. Hartman, S. M. Cohen, and P. T. Leung, “A note on the Green dyadic calculation of the decay rates for admolecules at multiple planar interfaces,” J. Chem. Phys. 110(4), 2189–2194 (1999).
    [Crossref]
  43. D. H. S. Cheng, “On the formulation of the dyadic Green’s function in a layered medium,” Electromagnetics 6(2), 171–182 (1986).
    [Crossref]
  44. H. P. Urbach and G. L. J. A. Rikken, “Spontaneous emission from a dielectric slab,” Phys. Rev. A 57(5), 3913 (1998).
    [Crossref]
  45. J. Jung, T. Søndergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
    [Crossref]
  46. P. de Vries, D. V. Coevorden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70(2), 447 (1998).
    [Crossref]
  47. C. M. Linton, “Lattice sums for the Helmholtz equation,” SIAM Rev. 52(4), 630–674 (2010).
    [Crossref]
  48. F. Capolino, D. R. Jackson, R. W. Donald, and B. F. Leopold, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propagat. 55(6), 1644–1655 (2007).
    [Crossref]
  49. O. T. A. Janssen, A. J. H. Wachters, and H. P. Urbach, “Efficient optimization method for the light extraction from periodically modulated LEDs using reciprocity,” Opt. Express 18(24), 24522–24535 (2010).
    [Crossref] [PubMed]
  50. S. R. K. Rodriguez, Y. T. Chen, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “From weak to strong coupling of localized surface plasmons to guided modes in a luminescent slab,” Phys. Rev. B 90(23), 235406 (2014).
    [Crossref]
  51. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).
  52. C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
    [Crossref] [PubMed]
  53. A. Kwadrin and A. F. Koenderink, “Diffractive stacks of metamaterial lattices with a complex unit cell: Self-consistent long-range bianisotropic interactions in experiment and theory,” Phys. Rev. B 89(4) 045120 (2014).
    [Crossref]
  54. The matlab scripts of calculating T and R for the slab structure with embedded plasmonic sphere lattice in Appendix A can be requested via www.koenderink.info or yuntian@hust.edu.cn

2016 (1)

A. Kwadrin, C. I. Osorio, and A. F. Koenderink, “Backaction in metasurface etalons,” Phys. Rev. B 93(10), 104301 (2016).
[Crossref]

2015 (8)

C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

P. Törmä and W. L. Barnes, “Strong coupling between surface plasmon polaritons and emitters: a review,” Rep. Prog. Phys. 78(1), 013901 (2015).
[Crossref]

J. Xu, B. B. Wu, and Y. T. Chen, “Elimination of polarization degeneracy in circularly symmetric bianisotropic waveguides: a decoupled case,” Opt. Express 23(9), 11566–11575 (2015).
[Crossref] [PubMed]

Y. Ra’di, C. R. Simovski, and S. A. Tretyakov, “Thin perfect absorbers for electromagnetic waves: theory, design, and realizations,” Phys. Rev. Appl. 3(3), 037001 (2015).
[Crossref]

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9(2), 195–213 (2015).
[Crossref]

V. A. Fedotov, J. Wallauer, M. Walther, M. Perino, N. Papasimakis, and N. I. Zheludev, “Wavevector selective metasurfaces and tunnel vision filters,” Light Sci. Appl. 4(7), e306 (2015).
[Crossref]

D. Iida, A. Fadil, Y. T. Chen, Y. Y. Ou, O. Kopylov, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Y. Ou, “Internal quantum efficiency enhancement of GaInN/GaN quantum-well structures using Ag nanoparticles,” AIP Adv. 5(9), 097169 (2015).
[Crossref]

A. E. Miroshnichenko, A. B. Evlyukhin, Y. S. Kivshar, and B. N. Chichkov, “Substrated-induced resonant magneto-electric effects for dielectric nanoparticles,” ACS Photonics,  2(10), 1423–1428 (2015).
[Crossref]

2014 (4)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

A. H. Schokker and A. F. Koenderink, “Lasing at the band edges of plasmonic lattices,” Phys. Rev. B 90(15), 155452 (2014).
[Crossref]

A. Kwadrin and A. F. Koenderink, “Diffractive stacks of metamaterial lattices with a complex unit cell: Self-consistent long-range bianisotropic interactions in experiment and theory,” Phys. Rev. B 89(4) 045120 (2014).
[Crossref]

S. R. K. Rodriguez, Y. T. Chen, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “From weak to strong coupling of localized surface plasmons to guided modes in a luminescent slab,” Phys. Rev. B 90(23), 235406 (2014).
[Crossref]

2013 (4)

G. Lozano, D. J. Louwers, S. R. K. Rodríguez, S. Murai, O. T. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light Sci. Appl. 2(5), e66 (2013).
[Crossref]

P. Lunnemann, I. Sersic, and A. F. Koenderink, “Optical properties of two-dimensional magnetoelectric point scattering lattices,” Phys. Rev. B 88(24), 245109 (2013).
[Crossref]

A. Kwadrin and A. F. Koenderink, “Probing the electrodynamic local density of states with magnetoelectric point scatterers,” Phys. Rev. B 87(12), 125123 (2013).
[Crossref]

A. Pors and S. I. Bozhevolnyi, “Plasmonic metasurfaces for efficient phase control in reflection,” Opt. Express 21(22), 27438–27451 (2013).
[Crossref] [PubMed]

2012 (3)

M. van Lare, F. Lenzmann, M. A. Verschuuren, and A. Polman, “Mode coupling by plasmonic surface scatterers in thin-film silicon solar cells,” Appl. Phys. Lett. 101(22), 221110 (2012).
[Crossref]

J. Henson, J. DiMaria, E. Dimakis, T. D. Moustakas, and R. Paiella, “Plasmon-enhanced light emission based on lattice resonances of silver nanocylinder arrays,” Opt. Lett. 37(1), 79–81 (2012).
[Crossref] [PubMed]

A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012).
[Crossref] [PubMed]

2011 (3)

J. Jung, T. Søndergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magnetoelectric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83(24), 245102 (2011).
[Crossref]

2010 (6)

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref] [PubMed]

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

Y. T. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18(12), 12489–12498 (2010).
[Crossref] [PubMed]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express 18(102), A237–A245 (2010).
[Crossref] [PubMed]

O. T. A. Janssen, A. J. H. Wachters, and H. P. Urbach, “Efficient optimization method for the light extraction from periodically modulated LEDs using reciprocity,” Opt. Express 18(24), 24522–24535 (2010).
[Crossref] [PubMed]

C. M. Linton, “Lattice sums for the Helmholtz equation,” SIAM Rev. 52(4), 630–674 (2010).
[Crossref]

2009 (2)

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[Crossref]

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, K V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

2008 (6)

D. M. Yeh, C. F. Huang, C. Y. Chen, Y. C. Lu, and C. C. Yang, “Localized surface plasmon-induced emission enhancement of a green light-emitting diode,” Nanotechnology 19(34), 345201 (2008).
[Crossref] [PubMed]

M. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[Crossref] [PubMed]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[Crossref] [PubMed]

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[Crossref]

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008).
[Crossref] [PubMed]

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

2007 (3)

K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58, 267–297 (2007).
[Crossref]

F. Capolino, D. R. Jackson, R. W. Donald, and B. F. Leopold, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propagat. 55(6), 1644–1655 (2007).
[Crossref]

A. Eroglu and J. K. Lee, “Simplified formulation of dyadic Green’s functions and their duality relations for general anisotropic media,” Progress in Electromagnetic Research, PIER 77, 391–408 (2007).
[Crossref]

2006 (1)

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

2005 (1)

V. V. Klimov and M. Ducloy, “Quadrupole transitions near an interface: general theory and application to an atom inside a planar cavity,” Phys. Rev. A 72(4), 043809 (2005).
[Crossref]

2004 (1)

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

2000 (1)

J. Vuckovic, M. Lončar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[Crossref]

1999 (3)

1998 (2)

P. de Vries, D. V. Coevorden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70(2), 447 (1998).
[Crossref]

H. P. Urbach and G. L. J. A. Rikken, “Spontaneous emission from a dielectric slab,” Phys. Rev. A 57(5), 3913 (1998).
[Crossref]

1993 (1)

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174–2176 (1993).
[Crossref]

1986 (1)

D. H. S. Cheng, “On the formulation of the dyadic Green’s function in a layered medium,” Electromagnetics 6(2), 171–182 (1986).
[Crossref]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Akasaki, I.

D. Iida, A. Fadil, Y. T. Chen, Y. Y. Ou, O. Kopylov, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Y. Ou, “Internal quantum efficiency enhancement of GaInN/GaN quantum-well structures using Ag nanoparticles,” AIP Adv. 5(9), 097169 (2015).
[Crossref]

Atwater, H. A.

Auguié, M.

M. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[Crossref] [PubMed]

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, K V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Barnes, W. L.

P. Törmä and W. L. Barnes, “Strong coupling between surface plasmon polaritons and emitters: a review,” Rep. Prog. Phys. 78(1), 013901 (2015).
[Crossref]

M. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[Crossref] [PubMed]

W. L. Barnes, “Electromagnetic crystals for surface plasmon polaritons and the extraction of light from emissive devices,” J. Lightwave Technol. 17(11), 2170 (1999).
[Crossref]

Benisty, H.

A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

Bykov, A. Y.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9(2), 195–213 (2015).
[Crossref]

Caneau, C.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174–2176 (1993).
[Crossref]

Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Capolino, F.

F. Capolino, D. R. Jackson, R. W. Donald, and B. F. Leopold, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propagat. 55(6), 1644–1655 (2007).
[Crossref]

Catchpole, K. R.

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[Crossref]

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008).
[Crossref] [PubMed]

Chen, C. Y.

D. M. Yeh, C. F. Huang, C. Y. Chen, Y. C. Lu, and C. C. Yang, “Localized surface plasmon-induced emission enhancement of a green light-emitting diode,” Nanotechnology 19(34), 345201 (2008).
[Crossref] [PubMed]

Chen, Y.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Chen, Y. T.

J. Xu, B. B. Wu, and Y. T. Chen, “Elimination of polarization degeneracy in circularly symmetric bianisotropic waveguides: a decoupled case,” Opt. Express 23(9), 11566–11575 (2015).
[Crossref] [PubMed]

D. Iida, A. Fadil, Y. T. Chen, Y. Y. Ou, O. Kopylov, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Y. Ou, “Internal quantum efficiency enhancement of GaInN/GaN quantum-well structures using Ag nanoparticles,” AIP Adv. 5(9), 097169 (2015).
[Crossref]

S. R. K. Rodriguez, Y. T. Chen, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “From weak to strong coupling of localized surface plasmons to guided modes in a luminescent slab,” Phys. Rev. B 90(23), 235406 (2014).
[Crossref]

Y. T. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18(12), 12489–12498 (2010).
[Crossref] [PubMed]

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

Cheng, D. H. S.

D. H. S. Cheng, “On the formulation of the dyadic Green’s function in a layered medium,” Electromagnetics 6(2), 171–182 (1986).
[Crossref]

Chichkov, B. N.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. S. Kivshar, and B. N. Chichkov, “Substrated-induced resonant magneto-electric effects for dielectric nanoparticles,” ACS Photonics,  2(10), 1423–1428 (2015).
[Crossref]

Coevorden, D. V.

P. de Vries, D. V. Coevorden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70(2), 447 (1998).
[Crossref]

Cohen, S. M.

R. L. Hartman, S. M. Cohen, and P. T. Leung, “A note on the Green dyadic calculation of the decay rates for admolecules at multiple planar interfaces,” J. Chem. Phys. 110(4), 2189–2194 (1999).
[Crossref]

Dai, N.

C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

David, A.

A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012).
[Crossref] [PubMed]

de Vries, P.

P. de Vries, D. V. Coevorden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70(2), 447 (1998).
[Crossref]

Decker, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, K V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Dimakis, E.

DiMaria, J.

Donald, R. W.

F. Capolino, D. R. Jackson, R. W. Donald, and B. F. Leopold, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propagat. 55(6), 1644–1655 (2007).
[Crossref]

Ducloy, M.

V. V. Klimov and M. Ducloy, “Quadrupole transitions near an interface: general theory and application to an atom inside a planar cavity,” Phys. Rev. A 72(4), 043809 (2005).
[Crossref]

Eroglu, A.

A. Eroglu and J. K. Lee, “Simplified formulation of dyadic Green’s functions and their duality relations for general anisotropic media,” Progress in Electromagnetic Research, PIER 77, 391–408 (2007).
[Crossref]

Evlyukhin, A. B.

A. E. Miroshnichenko, A. B. Evlyukhin, Y. S. Kivshar, and B. N. Chichkov, “Substrated-induced resonant magneto-electric effects for dielectric nanoparticles,” ACS Photonics,  2(10), 1423–1428 (2015).
[Crossref]

Fadil, A.

D. Iida, A. Fadil, Y. T. Chen, Y. Y. Ou, O. Kopylov, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Y. Ou, “Internal quantum efficiency enhancement of GaInN/GaN quantum-well structures using Ag nanoparticles,” AIP Adv. 5(9), 097169 (2015).
[Crossref]

Fedotov, V. A.

V. A. Fedotov, J. Wallauer, M. Walther, M. Perino, N. Papasimakis, and N. I. Zheludev, “Wavevector selective metasurfaces and tunnel vision filters,” Light Sci. Appl. 4(7), e306 (2015).
[Crossref]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Ferry, V. E.

Freymann, G. V.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, K V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Frimmer, M.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[Crossref]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Gansel, J. K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, K V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Giovanini, H.

Gmitter, T. J.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174–2176 (1993).
[Crossref]

Gómez Rivas, J.

S. R. K. Rodriguez, Y. T. Chen, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “From weak to strong coupling of localized surface plasmons to guided modes in a luminescent slab,” Phys. Rev. B 90(23), 235406 (2014).
[Crossref]

G. Lozano, D. J. Louwers, S. R. K. Rodríguez, S. Murai, O. T. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light Sci. Appl. 2(5), e66 (2013).
[Crossref]

Gregersen, N.

Y. T. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18(12), 12489–12498 (2010).
[Crossref] [PubMed]

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

Grigorenko, A. N.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[Crossref] [PubMed]

Hao, J. M.

C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Hartman, R. L.

R. L. Hartman, S. M. Cohen, and P. T. Leung, “A note on the Green dyadic calculation of the decay rates for admolecules at multiple planar interfaces,” J. Chem. Phys. 110(4), 2189–2194 (1999).
[Crossref]

He, Q.

C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University Press, 2006).
[Crossref]

Helgert, C.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref] [PubMed]

Henson, J.

Huang, C. F.

D. M. Yeh, C. F. Huang, C. Y. Chen, Y. C. Lu, and C. C. Yang, “Localized surface plasmon-induced emission enhancement of a green light-emitting diode,” Nanotechnology 19(34), 345201 (2008).
[Crossref] [PubMed]

Iida, D.

D. Iida, A. Fadil, Y. T. Chen, Y. Y. Ou, O. Kopylov, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Y. Ou, “Internal quantum efficiency enhancement of GaInN/GaN quantum-well structures using Ag nanoparticles,” AIP Adv. 5(9), 097169 (2015).
[Crossref]

Iwaya, M.

D. Iida, A. Fadil, Y. T. Chen, Y. Y. Ou, O. Kopylov, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Y. Ou, “Internal quantum efficiency enhancement of GaInN/GaN quantum-well structures using Ag nanoparticles,” AIP Adv. 5(9), 097169 (2015).
[Crossref]

Jackson, D. R.

F. Capolino, D. R. Jackson, R. W. Donald, and B. F. Leopold, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propagat. 55(6), 1644–1655 (2007).
[Crossref]

Jansen, O. T.

G. Lozano, D. J. Louwers, S. R. K. Rodríguez, S. Murai, O. T. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light Sci. Appl. 2(5), e66 (2013).
[Crossref]

Janssen, O. T. A.

Jung, J.

J. Jung, T. Søndergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

Kamiyama, S.

D. Iida, A. Fadil, Y. T. Chen, Y. Y. Ou, O. Kopylov, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Y. Ou, “Internal quantum efficiency enhancement of GaInN/GaN quantum-well structures using Ag nanoparticles,” AIP Adv. 5(9), 097169 (2015).
[Crossref]

Kampfrath, T.

I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magnetoelectric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83(24), 245102 (2011).
[Crossref]

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Kivshar, Y. S.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9(2), 195–213 (2015).
[Crossref]

A. E. Miroshnichenko, A. B. Evlyukhin, Y. S. Kivshar, and B. N. Chichkov, “Substrated-induced resonant magneto-electric effects for dielectric nanoparticles,” ACS Photonics,  2(10), 1423–1428 (2015).
[Crossref]

Kley, E. B.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref] [PubMed]

Klimov, V. V.

V. V. Klimov and M. Ducloy, “Quadrupole transitions near an interface: general theory and application to an atom inside a planar cavity,” Phys. Rev. A 72(4), 043809 (2005).
[Crossref]

Koenderink, A. F.

A. Kwadrin, C. I. Osorio, and A. F. Koenderink, “Backaction in metasurface etalons,” Phys. Rev. B 93(10), 104301 (2016).
[Crossref]

S. R. K. Rodriguez, Y. T. Chen, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “From weak to strong coupling of localized surface plasmons to guided modes in a luminescent slab,” Phys. Rev. B 90(23), 235406 (2014).
[Crossref]

A. Kwadrin and A. F. Koenderink, “Diffractive stacks of metamaterial lattices with a complex unit cell: Self-consistent long-range bianisotropic interactions in experiment and theory,” Phys. Rev. B 89(4) 045120 (2014).
[Crossref]

A. H. Schokker and A. F. Koenderink, “Lasing at the band edges of plasmonic lattices,” Phys. Rev. B 90(15), 155452 (2014).
[Crossref]

A. Kwadrin and A. F. Koenderink, “Probing the electrodynamic local density of states with magnetoelectric point scatterers,” Phys. Rev. B 87(12), 125123 (2013).
[Crossref]

P. Lunnemann, I. Sersic, and A. F. Koenderink, “Optical properties of two-dimensional magnetoelectric point scattering lattices,” Phys. Rev. B 88(24), 245109 (2013).
[Crossref]

I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magnetoelectric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83(24), 245102 (2011).
[Crossref]

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[Crossref]

Kopylov, O.

D. Iida, A. Fadil, Y. T. Chen, Y. Y. Ou, O. Kopylov, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Y. Ou, “Internal quantum efficiency enhancement of GaInN/GaN quantum-well structures using Ag nanoparticles,” AIP Adv. 5(9), 097169 (2015).
[Crossref]

Kravets, V. G.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[Crossref] [PubMed]

Kwadrin, A.

A. Kwadrin, C. I. Osorio, and A. F. Koenderink, “Backaction in metasurface etalons,” Phys. Rev. B 93(10), 104301 (2016).
[Crossref]

A. Kwadrin and A. F. Koenderink, “Diffractive stacks of metamaterial lattices with a complex unit cell: Self-consistent long-range bianisotropic interactions in experiment and theory,” Phys. Rev. B 89(4) 045120 (2014).
[Crossref]

A. Kwadrin and A. F. Koenderink, “Probing the electrodynamic local density of states with magnetoelectric point scatterers,” Phys. Rev. B 87(12), 125123 (2013).
[Crossref]

Lagendijk, A.

P. de Vries, D. V. Coevorden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70(2), 447 (1998).
[Crossref]

Landy, N. I.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

Larsen, A. N.

J. Jung, T. Søndergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

Lederer, F.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref] [PubMed]

Lee, J. K.

A. Eroglu and J. K. Lee, “Simplified formulation of dyadic Green’s functions and their duality relations for general anisotropic media,” Progress in Electromagnetic Research, PIER 77, 391–408 (2007).
[Crossref]

Lemarchand, F.

Lenzmann, F.

M. van Lare, F. Lenzmann, M. A. Verschuuren, and A. Polman, “Mode coupling by plasmonic surface scatterers in thin-film silicon solar cells,” Appl. Phys. Lett. 101(22), 221110 (2012).
[Crossref]

Leopold, B. F.

F. Capolino, D. R. Jackson, R. W. Donald, and B. F. Leopold, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propagat. 55(6), 1644–1655 (2007).
[Crossref]

Leung, P. T.

R. L. Hartman, S. M. Cohen, and P. T. Leung, “A note on the Green dyadic calculation of the decay rates for admolecules at multiple planar interfaces,” J. Chem. Phys. 110(4), 2189–2194 (1999).
[Crossref]

Li, H. B. T.

Li, X.

C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Linden, S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, K V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Linton, C. M.

C. M. Linton, “Lattice sums for the Helmholtz equation,” SIAM Rev. 52(4), 630–674 (2010).
[Crossref]

Lodahl, P.

Y. T. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18(12), 12489–12498 (2010).
[Crossref] [PubMed]

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

Loncar, M.

J. Vuckovic, M. Lončar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[Crossref]

Louwers, D. J.

G. Lozano, D. J. Louwers, S. R. K. Rodríguez, S. Murai, O. T. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light Sci. Appl. 2(5), e66 (2013).
[Crossref]

Lozano, G.

G. Lozano, D. J. Louwers, S. R. K. Rodríguez, S. Murai, O. T. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light Sci. Appl. 2(5), e66 (2013).
[Crossref]

Lu, Y. C.

D. M. Yeh, C. F. Huang, C. Y. Chen, Y. C. Lu, and C. C. Yang, “Localized surface plasmon-induced emission enhancement of a green light-emitting diode,” Nanotechnology 19(34), 345201 (2008).
[Crossref] [PubMed]

Lunnemann, P.

P. Lunnemann, I. Sersic, and A. F. Koenderink, “Optical properties of two-dimensional magnetoelectric point scattering lattices,” Phys. Rev. B 88(24), 245109 (2013).
[Crossref]

Ma, S. J.

C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Menzel, C.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref] [PubMed]

Miao, Z. Q.

C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Minovich, A. E.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9(2), 195–213 (2015).
[Crossref]

Miroshnichenko, A. E.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9(2), 195–213 (2015).
[Crossref]

A. E. Miroshnichenko, A. B. Evlyukhin, Y. S. Kivshar, and B. N. Chichkov, “Substrated-induced resonant magneto-electric effects for dielectric nanoparticles,” ACS Photonics,  2(10), 1423–1428 (2015).
[Crossref]

Mladyonov, P. L.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Mock, J. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

Mørk, J.

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

Y. T. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18(12), 12489–12498 (2010).
[Crossref] [PubMed]

Moustakas, T. D.

Mukai, T.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

Murai, S.

G. Lozano, D. J. Louwers, S. R. K. Rodríguez, S. Murai, O. T. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light Sci. Appl. 2(5), e66 (2013).
[Crossref]

Murzina, T. V.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9(2), 195–213 (2015).
[Crossref]

Narukawa, Y.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

Neshev, D. N.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9(2), 195–213 (2015).
[Crossref]

Nielsen, B. B.

J. Jung, T. Søndergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

Nielsen, T. R.

Y. T. Chen, N. Gregersen, T. R. Nielsen, J. Mørk, and P. Lodahl, “Spontaneous decay of a single quantum dot coupled to a metallic slot waveguide in the presence of leaky plasmonic modes,” Opt. Express 18(12), 12489–12498 (2010).
[Crossref] [PubMed]

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

Niki, I.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University Press, 2006).
[Crossref]

Okamoto, K.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

Osorio, C. I.

A. Kwadrin, C. I. Osorio, and A. F. Koenderink, “Backaction in metasurface etalons,” Phys. Rev. B 93(10), 104301 (2016).
[Crossref]

Ou, H. Y.

D. Iida, A. Fadil, Y. T. Chen, Y. Y. Ou, O. Kopylov, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Y. Ou, “Internal quantum efficiency enhancement of GaInN/GaN quantum-well structures using Ag nanoparticles,” AIP Adv. 5(9), 097169 (2015).
[Crossref]

Ou, Y. Y.

D. Iida, A. Fadil, Y. T. Chen, Y. Y. Ou, O. Kopylov, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Y. Ou, “Internal quantum efficiency enhancement of GaInN/GaN quantum-well structures using Ag nanoparticles,” AIP Adv. 5(9), 097169 (2015).
[Crossref]

Padilla, W. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

Paiella, R.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

Papasimakis, N.

V. A. Fedotov, J. Wallauer, M. Walther, M. Perino, N. Papasimakis, and N. I. Zheludev, “Wavevector selective metasurfaces and tunnel vision filters,” Light Sci. Appl. 4(7), e306 (2015).
[Crossref]

Pedersen, K.

J. Jung, T. Søndergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

Pedersen, T. G.

J. Jung, T. Søndergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

Perino, M.

V. A. Fedotov, J. Wallauer, M. Walther, M. Perino, N. Papasimakis, and N. I. Zheludev, “Wavevector selective metasurfaces and tunnel vision filters,” Light Sci. Appl. 4(7), e306 (2015).
[Crossref]

Pertsch, T.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref] [PubMed]

Polman, A.

M. van Lare, F. Lenzmann, M. A. Verschuuren, and A. Polman, “Mode coupling by plasmonic surface scatterers in thin-film silicon solar cells,” Appl. Phys. Lett. 101(22), 221110 (2012).
[Crossref]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express 18(102), A237–A245 (2010).
[Crossref] [PubMed]

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008).
[Crossref] [PubMed]

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[Crossref]

Pors, A.

Prosvirnin, S. L.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Qiu, M.

C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Qu, C.

C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Ra’di, Y.

Y. Ra’di, C. R. Simovski, and S. A. Tretyakov, “Thin perfect absorbers for electromagnetic waves: theory, design, and realizations,” Phys. Rev. Appl. 3(3), 037001 (2015).
[Crossref]

Rigneault, H.

Rikken, G. L. J. A.

H. P. Urbach and G. L. J. A. Rikken, “Spontaneous emission from a dielectric slab,” Phys. Rev. A 57(5), 3913 (1998).
[Crossref]

Rill, M. S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, K V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Rockstuhl, C.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref] [PubMed]

Rodriguez, S. R. K.

S. R. K. Rodriguez, Y. T. Chen, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “From weak to strong coupling of localized surface plasmons to guided modes in a luminescent slab,” Phys. Rev. B 90(23), 235406 (2014).
[Crossref]

Rodríguez, S. R. K.

G. Lozano, D. J. Louwers, S. R. K. Rodríguez, S. Murai, O. T. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light Sci. Appl. 2(5), e66 (2013).
[Crossref]

Rogacheva, A. V.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Saile, K V.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, K V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Sajuyigbe, S.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

Schedin, F.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[Crossref] [PubMed]

Scherer, A.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

J. Vuckovic, M. Lončar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[Crossref]

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174–2176 (1993).
[Crossref]

Schnitzer, I.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174–2176 (1993).
[Crossref]

Schokker, A. H.

A. H. Schokker and A. F. Koenderink, “Lasing at the band edges of plasmonic lattices,” Phys. Rev. B 90(15), 155452 (2014).
[Crossref]

Schropp, R. E. I.

Sentenac, A.

Sersic, I.

P. Lunnemann, I. Sersic, and A. F. Koenderink, “Optical properties of two-dimensional magnetoelectric point scattering lattices,” Phys. Rev. B 88(24), 245109 (2013).
[Crossref]

I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magnetoelectric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83(24), 245102 (2011).
[Crossref]

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[Crossref]

Shvartser, A.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

Simovski, C. R.

Y. Ra’di, C. R. Simovski, and S. A. Tretyakov, “Thin perfect absorbers for electromagnetic waves: theory, design, and realizations,” Phys. Rev. Appl. 3(3), 037001 (2015).
[Crossref]

Smith, D. R.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

Søndergaard, T.

J. Jung, T. Søndergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

Steinbusch, T. P.

S. R. K. Rodriguez, Y. T. Chen, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “From weak to strong coupling of localized surface plasmons to guided modes in a luminescent slab,” Phys. Rev. B 90(23), 235406 (2014).
[Crossref]

Sun, S. L.

C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Takeuchi, T.

D. Iida, A. Fadil, Y. T. Chen, Y. Y. Ou, O. Kopylov, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Y. Ou, “Internal quantum efficiency enhancement of GaInN/GaN quantum-well structures using Ag nanoparticles,” AIP Adv. 5(9), 097169 (2015).
[Crossref]

Tetienne, J. P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Thiel, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, K V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Törmä, P.

P. Törmä and W. L. Barnes, “Strong coupling between surface plasmon polaritons and emitters: a review,” Rep. Prog. Phys. 78(1), 013901 (2015).
[Crossref]

Tretyakov, S. A.

Y. Ra’di, C. R. Simovski, and S. A. Tretyakov, “Thin perfect absorbers for electromagnetic waves: theory, design, and realizations,” Phys. Rev. Appl. 3(3), 037001 (2015).
[Crossref]

Tuambilangana, C.

I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magnetoelectric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83(24), 245102 (2011).
[Crossref]

Tünnermann, A.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref] [PubMed]

Urbach, H. P.

Van Duyne, R. P.

K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58, 267–297 (2007).
[Crossref]

van Lare, M.

M. van Lare, F. Lenzmann, M. A. Verschuuren, and A. Polman, “Mode coupling by plasmonic surface scatterers in thin-film silicon solar cells,” Appl. Phys. Lett. 101(22), 221110 (2012).
[Crossref]

Verhagen, E.

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express 18(102), A237–A245 (2010).
[Crossref] [PubMed]

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[Crossref]

Verschuuren, M. A.

S. R. K. Rodriguez, Y. T. Chen, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “From weak to strong coupling of localized surface plasmons to guided modes in a luminescent slab,” Phys. Rev. B 90(23), 235406 (2014).
[Crossref]

G. Lozano, D. J. Louwers, S. R. K. Rodríguez, S. Murai, O. T. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light Sci. Appl. 2(5), e66 (2013).
[Crossref]

M. van Lare, F. Lenzmann, M. A. Verschuuren, and A. Polman, “Mode coupling by plasmonic surface scatterers in thin-film silicon solar cells,” Appl. Phys. Lett. 101(22), 221110 (2012).
[Crossref]

V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express 18(102), A237–A245 (2010).
[Crossref] [PubMed]

Vuckovic, J.

J. Vuckovic, M. Lončar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[Crossref]

Wachters, A. J. H.

Wallauer, J.

V. A. Fedotov, J. Wallauer, M. Walther, M. Perino, N. Papasimakis, and N. I. Zheludev, “Wavevector selective metasurfaces and tunnel vision filters,” Light Sci. Appl. 4(7), e306 (2015).
[Crossref]

Walters, R. J.

Walther, M.

V. A. Fedotov, J. Wallauer, M. Walther, M. Perino, N. Papasimakis, and N. I. Zheludev, “Wavevector selective metasurfaces and tunnel vision filters,” Light Sci. Appl. 4(7), e306 (2015).
[Crossref]

Wegener, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, K V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Weisbuch, C.

A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012).
[Crossref] [PubMed]

Willets, K. A.

K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58, 267–297 (2007).
[Crossref]

Wu, B. B.

Xiao, S. Y.

C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

Xu, J.

Yablonovitch, E.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174–2176 (1993).
[Crossref]

Yang, C. C.

D. M. Yeh, C. F. Huang, C. Y. Chen, Y. C. Lu, and C. C. Yang, “Localized surface plasmon-induced emission enhancement of a green light-emitting diode,” Nanotechnology 19(34), 345201 (2008).
[Crossref] [PubMed]

Yeh, D. M.

D. M. Yeh, C. F. Huang, C. Y. Chen, Y. C. Lu, and C. C. Yang, “Localized surface plasmon-induced emission enhancement of a green light-emitting diode,” Nanotechnology 19(34), 345201 (2008).
[Crossref] [PubMed]

Yu, N.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Zheludev, N. I.

V. A. Fedotov, J. Wallauer, M. Walther, M. Perino, N. Papasimakis, and N. I. Zheludev, “Wavevector selective metasurfaces and tunnel vision filters,” Light Sci. Appl. 4(7), e306 (2015).
[Crossref]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Zhou, L.

C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

ACS Photonics (1)

A. E. Miroshnichenko, A. B. Evlyukhin, Y. S. Kivshar, and B. N. Chichkov, “Substrated-induced resonant magneto-electric effects for dielectric nanoparticles,” ACS Photonics,  2(10), 1423–1428 (2015).
[Crossref]

AIP Adv. (1)

D. Iida, A. Fadil, Y. T. Chen, Y. Y. Ou, O. Kopylov, M. Iwaya, T. Takeuchi, S. Kamiyama, I. Akasaki, and H. Y. Ou, “Internal quantum efficiency enhancement of GaInN/GaN quantum-well structures using Ag nanoparticles,” AIP Adv. 5(9), 097169 (2015).
[Crossref]

Annu. Rev. Phys. Chem. (1)

K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58, 267–297 (2007).
[Crossref]

Appl. Phys. Lett. (3)

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, and A. Scherer, “30% external quantum efficiency from surface textured, thin-film light-emitting diodes,” Appl. Phys. Lett. 63(16), 2174–2176 (1993).
[Crossref]

M. van Lare, F. Lenzmann, M. A. Verschuuren, and A. Polman, “Mode coupling by plasmonic surface scatterers in thin-film silicon solar cells,” Appl. Phys. Lett. 101(22), 221110 (2012).
[Crossref]

K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008).
[Crossref]

Electromagnetics (1)

D. H. S. Cheng, “On the formulation of the dyadic Green’s function in a layered medium,” Electromagnetics 6(2), 171–182 (1986).
[Crossref]

IEEE J. Quantum Electron. (1)

J. Vuckovic, M. Lončar, and A. Scherer, “Surface plasmon enhanced light-emitting diode,” IEEE J. Quantum Electron. 36(10), 1131–1144 (2000).
[Crossref]

IEEE Trans. Antennas Propagat. (1)

F. Capolino, D. R. Jackson, R. W. Donald, and B. F. Leopold, “Comparison of methods for calculating the field excited by a dipole near a 2-D periodic material,” IEEE Trans. Antennas Propagat. 55(6), 1644–1655 (2007).
[Crossref]

J. Chem. Phys. (1)

R. L. Hartman, S. M. Cohen, and P. T. Leung, “A note on the Green dyadic calculation of the decay rates for admolecules at multiple planar interfaces,” J. Chem. Phys. 110(4), 2189–2194 (1999).
[Crossref]

J. Lightwave Technol. (1)

Laser Photon. Rev. (1)

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9(2), 195–213 (2015).
[Crossref]

Light Sci. Appl. (2)

G. Lozano, D. J. Louwers, S. R. K. Rodríguez, S. Murai, O. T. Jansen, M. A. Verschuuren, and J. Gómez Rivas, “Plasmonics for solid-state lighting: enhanced excitation and directional emission of highly efficient light sources,” Light Sci. Appl. 2(5), e66 (2013).
[Crossref]

V. A. Fedotov, J. Wallauer, M. Walther, M. Perino, N. Papasimakis, and N. I. Zheludev, “Wavevector selective metasurfaces and tunnel vision filters,” Light Sci. Appl. 4(7), e306 (2015).
[Crossref]

Nanotechnology (1)

D. M. Yeh, C. F. Huang, C. Y. Chen, Y. C. Lu, and C. C. Yang, “Localized surface plasmon-induced emission enhancement of a green light-emitting diode,” Nanotechnology 19(34), 345201 (2008).
[Crossref] [PubMed]

Nat. Mater. (2)

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[Crossref] [PubMed]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. A (2)

H. P. Urbach and G. L. J. A. Rikken, “Spontaneous emission from a dielectric slab,” Phys. Rev. A 57(5), 3913 (1998).
[Crossref]

V. V. Klimov and M. Ducloy, “Quadrupole transitions near an interface: general theory and application to an atom inside a planar cavity,” Phys. Rev. A 72(4), 043809 (2005).
[Crossref]

Phys. Rev. Appl. (1)

Y. Ra’di, C. R. Simovski, and S. A. Tretyakov, “Thin perfect absorbers for electromagnetic waves: theory, design, and realizations,” Phys. Rev. Appl. 3(3), 037001 (2015).
[Crossref]

Phys. Rev. B (9)

I. Sersic, C. Tuambilangana, T. Kampfrath, and A. F. Koenderink, “Magnetoelectric point scattering theory for metamaterial scatterers,” Phys. Rev. B 83(24), 245102 (2011).
[Crossref]

Y. T. Chen, T. R. Nielsen, N. Gregersen, P. Lodahl, and J. Mørk, “Finite-element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides,” Phys. Rev. B 81(12), 125431 (2010).
[Crossref]

P. Lunnemann, I. Sersic, and A. F. Koenderink, “Optical properties of two-dimensional magnetoelectric point scattering lattices,” Phys. Rev. B 88(24), 245109 (2013).
[Crossref]

A. Kwadrin and A. F. Koenderink, “Probing the electrodynamic local density of states with magnetoelectric point scatterers,” Phys. Rev. B 87(12), 125123 (2013).
[Crossref]

A. Kwadrin, C. I. Osorio, and A. F. Koenderink, “Backaction in metasurface etalons,” Phys. Rev. B 93(10), 104301 (2016).
[Crossref]

A. H. Schokker and A. F. Koenderink, “Lasing at the band edges of plasmonic lattices,” Phys. Rev. B 90(15), 155452 (2014).
[Crossref]

A. Kwadrin and A. F. Koenderink, “Diffractive stacks of metamaterial lattices with a complex unit cell: Self-consistent long-range bianisotropic interactions in experiment and theory,” Phys. Rev. B 89(4) 045120 (2014).
[Crossref]

J. Jung, T. Søndergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: applications within plasmonic solar cells,” Phys. Rev. B 83(8), 085419 (2011).
[Crossref]

S. R. K. Rodriguez, Y. T. Chen, T. P. Steinbusch, M. A. Verschuuren, A. F. Koenderink, and J. Gómez Rivas, “From weak to strong coupling of localized surface plasmons to guided modes in a luminescent slab,” Phys. Rev. B 90(23), 235406 (2014).
[Crossref]

Phys. Rev. Lett. (7)

C. Qu, S. J. Ma, J. M. Hao, M. Qiu, X. Li, S. Y. Xiao, Z. Q. Miao, N. Dai, Q. He, S. L. Sun, and L. Zhou, “Tailor the functionalities of metasurfaces based on a complete phase diagram,” Phys. Rev. Lett. 115(23), 235503 (2015).
[Crossref] [PubMed]

M. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[Crossref] [PubMed]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, “Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles,” Phys. Rev. Lett. 101(8), 087403 (2008).
[Crossref] [PubMed]

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[Crossref]

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[Crossref] [PubMed]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref] [PubMed]

Progress in Electromagnetic Research, PIER (1)

A. Eroglu and J. K. Lee, “Simplified formulation of dyadic Green’s functions and their duality relations for general anisotropic media,” Progress in Electromagnetic Research, PIER 77, 391–408 (2007).
[Crossref]

Rep. Prog. Phys. (2)

A. David, H. Benisty, and C. Weisbuch, “Photonic crystal light-emitting sources,” Rep. Prog. Phys. 75(12), 126501 (2012).
[Crossref] [PubMed]

P. Törmä and W. L. Barnes, “Strong coupling between surface plasmon polaritons and emitters: a review,” Rep. Prog. Phys. 78(1), 013901 (2015).
[Crossref]

Rev. Mod. Phys. (1)

P. de Vries, D. V. Coevorden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys. 70(2), 447 (1998).
[Crossref]

Science (2)

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, K V. Saile, G. V. Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

SIAM Rev. (1)

C. M. Linton, “Lattice sums for the Helmholtz equation,” SIAM Rev. 52(4), 630–674 (2010).
[Crossref]

Other (3)

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

The matlab scripts of calculating T and R for the slab structure with embedded plasmonic sphere lattice in Appendix A can be requested via www.koenderink.info or yuntian@hust.edu.cn

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University Press, 2006).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Sketches of canonical scenarios that our theory can address. (a) Plasmonic lattice patterned on a GaN material based LED structure to improve outcoupling; (b) Remote phosphor for white light emission from LED systems, pumped by a blue LED. Plasmonic texturing can improve absorption, and redirect emission. (c) Thin film solar cell with texturing to improve light incoupling.
Fig. 2
Fig. 2 Angle-dependent far-field emission enhancement of an electric dipole located insidea slab waveguide coupled to a plasmonic lattice, as sketched in Fig. 1 (a). The host medium of the lattice is air, below which a waveguiding layer (index 1.6, thickness 0.2λ0) is placed on a perfect reflector. a–d (e–h) shows emission pattern calculated from ASM method (reciprocity method) at four lattice constants, i.e., 1/4λ0, 1/2λ0, 3/4λ0, λ0 respectively. λ0 is the vacuum wavelength. White lines are the folded slab waveguide inside the light cone. In (b,c,d), the white number pairs denote the diffraction order. The nanoparticle is taken as metallic sphere defined through an electrostatic polarizability of ( 3.78 + 0.135 i ) 10 3 λ 0 3 (typical for, e.g., a 80 nm aluminum particle in the green). The calculation is done for a single frequency determined by 2π/λ0, and taking a source height Z0 = 1/10λ0.
Fig. 3
Fig. 3 (a) Calculated reflection from the layer geometry shown in the inset, which reflects the cell geometry of a realistic photovoltaic cell based on amorphous silicon [10]. (b) Calculated absorption in the a-Si:H i-layer. Red line for the bare layer geometry without plasmonic lattice, blue line for the plasmonic lattice with particle radius of 70 nm, black line for the plasmonic lattice with particle radius of 120 nm. (c) Absorption as function of incident angle and photon energy. In (a–b), light is illuminated at normal incidence. In (c), the incident light has TE polarization.
Fig. 4
Fig. 4 Emission rate of a dipole coupled to an aluminum sphere array embedded in a GaAs slab waveguide for an x-oriented dipole (black curves, left y-axis), and for a z-oriented dipole (blue curves, righthand y-axis). Solid (dashed) curves are for a lattice pitch of 145 (173) nm. (b) Contour plot of the integrand of a bare slab Green’s function log 10 | Im [ G z z s ] |. (c–g) Contour plot of Im[Gzz], i.e., Ī(k, r, r0) in Eq. (10) for the special points, as marked by C,D, E, F, G in (a). In (b–g), the blue (black) dotted lines indicate the folded light line in air (GaAs), the white and magenta (red) dotted lines for TE (TM) bound modes.
Fig. 5
Fig. 5 (a) Polarizability α0 and αeff for free space(1), single interface(2) and slab(3) respectively. (b)–(d) Reflectivity and transmissivity of point dipole theory and COMSOL. Red and blue line indicate the reflectivity and transmissivity calculated using point theory, while red and blue circles indicate the reflectivity and transmissivity of Multiphysics COMSOL 5.2 simulation. (b), (c) and (d) indicate the structure of free space, single interface and slab respectively.

Tables (1)

Tables Icon

Table 1 Fraction of emission of z-dipole coupled to waveguide-lattice system in k-space. C, D, E, F, G denote the special points marked in Fig. 4 (a).

Equations (22)

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[ × × k 0 2 ε ¯ r ( r ) μ ¯ r ( r ) ] G ¯ e e ( r , r ) = I ¯ 0 δ ( r , r ) ,
[ × × k 0 2 ε ¯ r ( r ) μ ¯ r ( r ) ] G ¯ h e ( r , r ) = I ¯ 0 × δ ( r r ) ,
[ × × k 0 2 ε ¯ r ( r ) μ ¯ r ( r ) ] G ¯ h h ( r , r ) = I ¯ 0 δ ( r r ) ,
[ × × k 0 2 ε ¯ r ( r ) μ ¯ r ( r ) ] G ¯ e h ( r , r ) = I ¯ 0 × δ ( r r ) ,
E ( r ) = i ω 0 μ 0 G ¯ e e ( r , r ) μ ¯ r ( r ) j e ( r ) d r + 1 ¯ r ( r ) G ¯ e h ( r , r ) ¯ r ( r ) j h ( r ) d r H ( r ) = i ω 0 ε 0 G ¯ h h ( r , r ) ε ¯ r ( r ) j h ( r ) d r + 1 μ ¯ r ( r ) G ¯ h e ( r , r ) μ ¯ r ( r ) j e ( r ) d r .
( e h ) = 4 π k 0 ( k 0 μ ¯ r e G ¯ e e i ¯ ( r 0 ) ¯ ( r ) G ¯ e h i μ ¯ ( r 0 ) μ ¯ ( r ) G ¯ h e k 0 ε ¯ r e G ¯ h h ) ( p m ) .
( p l m l ) = α ¯ [ ( e k ( R l ) h k ( R l ) ) + l l g ¯ ( R l , R l ) ( p l m l ) ] .
( p 0 m 0 ) = [ α ¯ 1 g ] 1 ( E in ( R 0 ) H in ( R 0 ) ) ,
α ¯ 1 g ¯ ( k ) = α ¯ static 1 2 i k 3 3 l g ¯ s ( R 0 , R l ) e i k R l { l g ¯ 0 ( R 0 , R l ) e i k R l g ¯ 0 ( R 0 , R 0 ) } .
l G ¯ s e e ( R 0 , R l ) e i k R l = l d q x d q y i 8 π 2 k z 1 [ M + γ s 1 , 23 M + + N + γ p 1 , 23 N + ] e i q ( R l R 0 ) e i k R l .
l G ¯ s e e ( R 0 , R l ) e i k R l = ( 2 π ) 2 A l i 8 π 2 k z 2 [ M + γ s 1 , 23 M + + N + γ p 1 , 23 N + ] e i k R 0 | ( q = k + 𝒢 l ) .
( E total k ( r ) H total k ( r ) ) = ( E slab k ( r ) H slab k ( r ) ) + l g ¯ ( r , R l ) e i k R l ( p 0 m 0 ) .
G ¯ ( r , r ) = g ¯ b ( r , r ) + A ( 2 π ) 2 B Z d k I ¯ ( k , r , r 0 )
G ¯ slab E E , 21 ( r 0 , r ) = d k x d k y i 8 π 2 { 1 Δ s { [ M ( k ) + γ s , 23 ( k ) M + ( k ) ] T s , 12 e i ψ } [ M + ( k ) ] 1 Δ p { [ N ( k ) + γ p , 23 ( k ) N + ( k ) ] T p , 12 e i ψ } [ N + ( k ) ] }
E ( s x , s y , s z ) = 2 i π k z E ( k x , k y ; z = z r ) e i k r r
g ¯ far ( [ k x , k y , z = z r ] , r ) = g ¯ b ( [ k x , k y , z = z r ] , r ) + A ( 2 π 2 ) g l = 0 = ( [ k x , k y , z = z r ] , r 0 ) Q ¯ ( r 0 , r 0 ) g = ( r 0 , r )
M ( k , ± 1 , ± 2 ) = e i ± 2 k z z ( x ^ k y k + y ^ k x k ) ,
N ( k , ± 1 , ± 2 ) = e i ± 2 k z z [ z ^ i k k 0 x ^ i ( ± 1 ) k z k x k k 0 y ^ i ( ± 1 ) k z k y k k 0 ] ,
× [ e i k r M ( k , ± , ± ) ] = e i k r k 0 N ( k , ± , ± ) . × [ e i k r N ( k , ± , ± ) ] = e i k r k 0 M ( k , ± , ± ) .
G ¯ 0 e e ( r , r ) = i 8 π 2 d k x d k y e i θ k z [ M + M N + N ] G ¯ 0 h e ( r , r ) = i k 0 8 π 2 d k x d k y e i θ k z [ N + M M + N ] , G ¯ 0 h h ( r , r ) = i 8 π 2 d k x d k y e i θ k z [ N + N + M + M ] , G ¯ 0 h e ( r , r ) = i k 0 8 π 2 d k x d k y e i θ k z [ M + N + N + M ] .
G ¯ s , e e if = i 8 π 2 d k e i θ k z { γ s M + M + γ p N + N + } G ¯ s , h e if = i k 0 8 π 2 d k e i θ k z { γ s N + M + γ p M + N + } , G ¯ s , h h if = i 8 π 2 d k e i θ k z { γ p M + M + γ s N + N + } , G ¯ s , e h if = i k 0 8 π 2 d k e i θ k z { γ p N + M + γ s M + N + } .
G ¯ 2 , 2 e e ( r , r ) = d k i e i θ 8 π 2 k z 2 { 1 Δ s [ M + + γ s , 21 ( k ) M ( ) η ] [ M ( ) + γ s , 23 ( k ) M ( + ) ] 1 Δ p [ N ( + ) + γ p , 21 ( k ) N ( ) η ] [ N ( ) + γ p , 23 ( k ) N ( + ) ] } , G ¯ 2 , 2 h e ( r , r ) = d k i e i θ k 0 8 π 2 k z 2 { 1 Δ s [ N + + γ s , 21 ( k ) N ( ) η ] [ M ( ) + γ s , 23 ( k ) M ( + ) ] 1 Δ p [ M ( + ) + γ p , 21 ( k ) M ( ) η ] [ N ( ) + γ p , 23 ( k ) N ( + ) ] } , G ¯ 2 , 2 h h ( r , r ) = d k i e i θ 8 π 2 k z 2 { 1 Δ s [ N + + γ s , 21 ( k ) N ( ) η ] [ N ( ) + γ s , 23 ( k ) N ( + ) ] 1 Δ p [ M ( + ) + γ p , 21 ( k ) M ( ) η ] [ M ( + ) + γ p , 23 ( k ) M ( ) ] } , G ¯ 2 , 2 e h ( r , r ) = d k i e i θ k 0 8 π 2 k z 2 { 1 Δ s [ M ( + ) + γ s , 21 ( k ) M ( ) η ] [ N ( ) + γ s , 23 ( k ) N ( + ) ] 1 Δ p [ N ( + ) + γ p , 21 ( k ) N ( ) η ] [ M ( ) + γ p , 23 ( k ) M ( + ) ] } .

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