Abstract

Colloidal particle lens array (CPLA) proved to be an efficient near-field focusing device for laser nanoprocessing of materials. Within CPLA, spherical particles do not act as independent microlenses. Due to the coupling of the spherical modes, the field near the clusters of spherical microparticles cannot be calculated by means of the superposition of Mie solutions for individual spheres. In the paper, the electromagnetic field distributions near laser-irradiated clusters of dielectric microspheres with configurations that match the fragments of the close-packed CPLA are studied. It is shown that some practically important mode coupling effects can be understood in terms of an effective immersion medium formed for the spherical particle by its surrounding.

© 2012 OSA

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  1. T. C. Chong, M. H. Hong, and L. P. Shi, “Laser precision engineering: from microfabrication to nanoprocessing,” Laser Photonics Rev. 4(1), 123–143 (2010).
    [CrossRef]
  2. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2008).
  3. B. S. Luk'yanchuk, Z. B. Wang, W. D. Song, and M. H. Hong, “Particle on surface: 3D-effects in dry laser cleaning,” Appl. Phys., A Mater. Sci. Process. 79(4-6), 747–751 (2004).
    [CrossRef]
  4. J. Zhang, Y. Li, X. Zhang, and B. Yang, “Colloidal self-assembly meets nanofabrication: from two-dimensional colloidal crystals to nanostructure arrays,” Adv. Mater. (Deerfield Beach Fla.) 22(38), 4249–4269 (2010).
    [CrossRef] [PubMed]
  5. E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008).
    [CrossRef] [PubMed]
  6. E. McLeod and C. B. Arnold, “Optical analysis of time-averaged multiscale Bessel beams generated by a tunable acoustic gradient index of refraction lens,” Appl. Opt. 47(20), 3609–3618 (2008).
    [CrossRef] [PubMed]
  7. A. Pikulin, N. Bityurin, G. Langer, D. Brodoceanu, and D. Bäuerle, “Hexagonal structures on metal-coated two-dimensional microlens arrays,” Appl. Phys. Lett. 91(19), 191106 (2007).
    [CrossRef]
  8. Z. B. Wang, W. Guo, B Luk' yanchuk, D. J. Whitehead, L. Li, and Z. Liu, “Optical near-field interaction between neighbouring micro/nano-particles,” J. Laser Micro/Nanoeng. 3(1), 14–18 (2008).
    [CrossRef]
  9. N. Arnold, “Influence of the substrate, metal overlayer and lattice neighbors on the focusing properties of colloidal microspheres,” Appl. Phys., A Mater. Sci. Process. 92(4), 1005–1012 (2008).
    [CrossRef]
  10. M. Born and E. Wolf, Principles of optics. Electromagnetic theory of propagation, interference and diffraction of light. Seventh (expanded) edition (Cambridge University Press, 2003).
  11. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
    [CrossRef]
  12. Y. L. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. 34(21), 4573–4588 (1995).
    [CrossRef] [PubMed]
  13. Y. Xu, Fortran codes for multi-particle light-scattering calculations, http://diogenes.iwt.uni-bremen.de/vt/laser/codes/Yu-linXu/Yu-linXu-codes.htm .
  14. G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 (2003).
    [CrossRef] [PubMed]
  15. S. Lazare, I. Elaboudi, M. Castillejo, and A. Sionkowska, “Model properties relevant to laser ablation of moderately absorbing polymers,” Appl. Phys., A Mater. Sci. Process. 101(1), 215–224 (2010).
    [CrossRef]
  16. N. Bityurin, “8 Studies on laser ablation of polymers,” Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 101, 216–247 (2005).
    [CrossRef]
  17. A. Selimis, G. J. Tserevelakis, S. Kogou, P. Pouli, G. Filippidis, N. Sapogova, N. Bityurin, and C. Fotakis, “Nonlinear microscopy techniques for assessing the UV laser polymer interactions,” Opt. Express 20(4), 3990–3996 (2012).
    [CrossRef] [PubMed]
  18. N. Bityurin, “Model for laser swelling of a polymer film,” Appl. Surf. Sci. 255(24), 9851–9855 (2009).
    [CrossRef]

2012

2010

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

S. Lazare, I. Elaboudi, M. Castillejo, and A. Sionkowska, “Model properties relevant to laser ablation of moderately absorbing polymers,” Appl. Phys., A Mater. Sci. Process. 101(1), 215–224 (2010).
[CrossRef]

J. Zhang, Y. Li, X. Zhang, and B. Yang, “Colloidal self-assembly meets nanofabrication: from two-dimensional colloidal crystals to nanostructure arrays,” Adv. Mater. (Deerfield Beach Fla.) 22(38), 4249–4269 (2010).
[CrossRef] [PubMed]

T. C. Chong, M. H. Hong, and L. P. Shi, “Laser precision engineering: from microfabrication to nanoprocessing,” Laser Photonics Rev. 4(1), 123–143 (2010).
[CrossRef]

2009

N. Bityurin, “Model for laser swelling of a polymer film,” Appl. Surf. Sci. 255(24), 9851–9855 (2009).
[CrossRef]

2008

Z. B. Wang, W. Guo, B Luk' yanchuk, D. J. Whitehead, L. Li, and Z. Liu, “Optical near-field interaction between neighbouring micro/nano-particles,” J. Laser Micro/Nanoeng. 3(1), 14–18 (2008).
[CrossRef]

N. Arnold, “Influence of the substrate, metal overlayer and lattice neighbors on the focusing properties of colloidal microspheres,” Appl. Phys., A Mater. Sci. Process. 92(4), 1005–1012 (2008).
[CrossRef]

E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008).
[CrossRef] [PubMed]

E. McLeod and C. B. Arnold, “Optical analysis of time-averaged multiscale Bessel beams generated by a tunable acoustic gradient index of refraction lens,” Appl. Opt. 47(20), 3609–3618 (2008).
[CrossRef] [PubMed]

2007

A. Pikulin, N. Bityurin, G. Langer, D. Brodoceanu, and D. Bäuerle, “Hexagonal structures on metal-coated two-dimensional microlens arrays,” Appl. Phys. Lett. 91(19), 191106 (2007).
[CrossRef]

2005

N. Bityurin, “8 Studies on laser ablation of polymers,” Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 101, 216–247 (2005).
[CrossRef]

2004

B. S. Luk'yanchuk, Z. B. Wang, W. D. Song, and M. H. Hong, “Particle on surface: 3D-effects in dry laser cleaning,” Appl. Phys., A Mater. Sci. Process. 79(4-6), 747–751 (2004).
[CrossRef]

2003

G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 (2003).
[CrossRef] [PubMed]

1995

Arnold, C. B.

E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008).
[CrossRef] [PubMed]

E. McLeod and C. B. Arnold, “Optical analysis of time-averaged multiscale Bessel beams generated by a tunable acoustic gradient index of refraction lens,” Appl. Opt. 47(20), 3609–3618 (2008).
[CrossRef] [PubMed]

Arnold, N.

N. Arnold, “Influence of the substrate, metal overlayer and lattice neighbors on the focusing properties of colloidal microspheres,” Appl. Phys., A Mater. Sci. Process. 92(4), 1005–1012 (2008).
[CrossRef]

Bäuerle, D.

A. Pikulin, N. Bityurin, G. Langer, D. Brodoceanu, and D. Bäuerle, “Hexagonal structures on metal-coated two-dimensional microlens arrays,” Appl. Phys. Lett. 91(19), 191106 (2007).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

Bityurin, N.

A. Selimis, G. J. Tserevelakis, S. Kogou, P. Pouli, G. Filippidis, N. Sapogova, N. Bityurin, and C. Fotakis, “Nonlinear microscopy techniques for assessing the UV laser polymer interactions,” Opt. Express 20(4), 3990–3996 (2012).
[CrossRef] [PubMed]

N. Bityurin, “Model for laser swelling of a polymer film,” Appl. Surf. Sci. 255(24), 9851–9855 (2009).
[CrossRef]

A. Pikulin, N. Bityurin, G. Langer, D. Brodoceanu, and D. Bäuerle, “Hexagonal structures on metal-coated two-dimensional microlens arrays,” Appl. Phys. Lett. 91(19), 191106 (2007).
[CrossRef]

N. Bityurin, “8 Studies on laser ablation of polymers,” Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 101, 216–247 (2005).
[CrossRef]

Brodoceanu, D.

A. Pikulin, N. Bityurin, G. Langer, D. Brodoceanu, and D. Bäuerle, “Hexagonal structures on metal-coated two-dimensional microlens arrays,” Appl. Phys. Lett. 91(19), 191106 (2007).
[CrossRef]

Castillejo, M.

S. Lazare, I. Elaboudi, M. Castillejo, and A. Sionkowska, “Model properties relevant to laser ablation of moderately absorbing polymers,” Appl. Phys., A Mater. Sci. Process. 101(1), 215–224 (2010).
[CrossRef]

Chong, T. C.

T. C. Chong, M. H. Hong, and L. P. Shi, “Laser precision engineering: from microfabrication to nanoprocessing,” Laser Photonics Rev. 4(1), 123–143 (2010).
[CrossRef]

Dyer, P. E.

G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 (2003).
[CrossRef] [PubMed]

Elaboudi, I.

S. Lazare, I. Elaboudi, M. Castillejo, and A. Sionkowska, “Model properties relevant to laser ablation of moderately absorbing polymers,” Appl. Phys., A Mater. Sci. Process. 101(1), 215–224 (2010).
[CrossRef]

Filippidis, G.

Fotakis, C.

Guo, W.

Z. B. Wang, W. Guo, B Luk' yanchuk, D. J. Whitehead, L. Li, and Z. Liu, “Optical near-field interaction between neighbouring micro/nano-particles,” J. Laser Micro/Nanoeng. 3(1), 14–18 (2008).
[CrossRef]

Hong, M. H.

T. C. Chong, M. H. Hong, and L. P. Shi, “Laser precision engineering: from microfabrication to nanoprocessing,” Laser Photonics Rev. 4(1), 123–143 (2010).
[CrossRef]

B. S. Luk'yanchuk, Z. B. Wang, W. D. Song, and M. H. Hong, “Particle on surface: 3D-effects in dry laser cleaning,” Appl. Phys., A Mater. Sci. Process. 79(4-6), 747–751 (2004).
[CrossRef]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

Kogou, S.

Langer, G.

A. Pikulin, N. Bityurin, G. Langer, D. Brodoceanu, and D. Bäuerle, “Hexagonal structures on metal-coated two-dimensional microlens arrays,” Appl. Phys. Lett. 91(19), 191106 (2007).
[CrossRef]

Lazare, S.

S. Lazare, I. Elaboudi, M. Castillejo, and A. Sionkowska, “Model properties relevant to laser ablation of moderately absorbing polymers,” Appl. Phys., A Mater. Sci. Process. 101(1), 215–224 (2010).
[CrossRef]

Li, L.

Z. B. Wang, W. Guo, B Luk' yanchuk, D. J. Whitehead, L. Li, and Z. Liu, “Optical near-field interaction between neighbouring micro/nano-particles,” J. Laser Micro/Nanoeng. 3(1), 14–18 (2008).
[CrossRef]

Li, Y.

J. Zhang, Y. Li, X. Zhang, and B. Yang, “Colloidal self-assembly meets nanofabrication: from two-dimensional colloidal crystals to nanostructure arrays,” Adv. Mater. (Deerfield Beach Fla.) 22(38), 4249–4269 (2010).
[CrossRef] [PubMed]

Liu, Z.

Z. B. Wang, W. Guo, B Luk' yanchuk, D. J. Whitehead, L. Li, and Z. Liu, “Optical near-field interaction between neighbouring micro/nano-particles,” J. Laser Micro/Nanoeng. 3(1), 14–18 (2008).
[CrossRef]

Luk' yanchuk, B

Z. B. Wang, W. Guo, B Luk' yanchuk, D. J. Whitehead, L. Li, and Z. Liu, “Optical near-field interaction between neighbouring micro/nano-particles,” J. Laser Micro/Nanoeng. 3(1), 14–18 (2008).
[CrossRef]

Luk'yanchuk, B. S.

B. S. Luk'yanchuk, Z. B. Wang, W. D. Song, and M. H. Hong, “Particle on surface: 3D-effects in dry laser cleaning,” Appl. Phys., A Mater. Sci. Process. 79(4-6), 747–751 (2004).
[CrossRef]

McLeod, E.

E. McLeod and C. B. Arnold, “Optical analysis of time-averaged multiscale Bessel beams generated by a tunable acoustic gradient index of refraction lens,” Appl. Opt. 47(20), 3609–3618 (2008).
[CrossRef] [PubMed]

E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008).
[CrossRef] [PubMed]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

Paltauf, G.

G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 (2003).
[CrossRef] [PubMed]

Pikulin, A.

A. Pikulin, N. Bityurin, G. Langer, D. Brodoceanu, and D. Bäuerle, “Hexagonal structures on metal-coated two-dimensional microlens arrays,” Appl. Phys. Lett. 91(19), 191106 (2007).
[CrossRef]

Pouli, P.

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

Sapogova, N.

Selimis, A.

Shi, L. P.

T. C. Chong, M. H. Hong, and L. P. Shi, “Laser precision engineering: from microfabrication to nanoprocessing,” Laser Photonics Rev. 4(1), 123–143 (2010).
[CrossRef]

Sionkowska, A.

S. Lazare, I. Elaboudi, M. Castillejo, and A. Sionkowska, “Model properties relevant to laser ablation of moderately absorbing polymers,” Appl. Phys., A Mater. Sci. Process. 101(1), 215–224 (2010).
[CrossRef]

Song, W. D.

B. S. Luk'yanchuk, Z. B. Wang, W. D. Song, and M. H. Hong, “Particle on surface: 3D-effects in dry laser cleaning,” Appl. Phys., A Mater. Sci. Process. 79(4-6), 747–751 (2004).
[CrossRef]

Tserevelakis, G. J.

Wang, Z. B.

Z. B. Wang, W. Guo, B Luk' yanchuk, D. J. Whitehead, L. Li, and Z. Liu, “Optical near-field interaction between neighbouring micro/nano-particles,” J. Laser Micro/Nanoeng. 3(1), 14–18 (2008).
[CrossRef]

B. S. Luk'yanchuk, Z. B. Wang, W. D. Song, and M. H. Hong, “Particle on surface: 3D-effects in dry laser cleaning,” Appl. Phys., A Mater. Sci. Process. 79(4-6), 747–751 (2004).
[CrossRef]

Whitehead, D. J.

Z. B. Wang, W. Guo, B Luk' yanchuk, D. J. Whitehead, L. Li, and Z. Liu, “Optical near-field interaction between neighbouring micro/nano-particles,” J. Laser Micro/Nanoeng. 3(1), 14–18 (2008).
[CrossRef]

Xu, Y. L.

Yang, B.

J. Zhang, Y. Li, X. Zhang, and B. Yang, “Colloidal self-assembly meets nanofabrication: from two-dimensional colloidal crystals to nanostructure arrays,” Adv. Mater. (Deerfield Beach Fla.) 22(38), 4249–4269 (2010).
[CrossRef] [PubMed]

Zhang, J.

J. Zhang, Y. Li, X. Zhang, and B. Yang, “Colloidal self-assembly meets nanofabrication: from two-dimensional colloidal crystals to nanostructure arrays,” Adv. Mater. (Deerfield Beach Fla.) 22(38), 4249–4269 (2010).
[CrossRef] [PubMed]

Zhang, X.

J. Zhang, Y. Li, X. Zhang, and B. Yang, “Colloidal self-assembly meets nanofabrication: from two-dimensional colloidal crystals to nanostructure arrays,” Adv. Mater. (Deerfield Beach Fla.) 22(38), 4249–4269 (2010).
[CrossRef] [PubMed]

Adv. Mater. (Deerfield Beach Fla.)

J. Zhang, Y. Li, X. Zhang, and B. Yang, “Colloidal self-assembly meets nanofabrication: from two-dimensional colloidal crystals to nanostructure arrays,” Adv. Mater. (Deerfield Beach Fla.) 22(38), 4249–4269 (2010).
[CrossRef] [PubMed]

Annu. Rep. Prog. Chem., Sect. C: Phys. Chem.

N. Bityurin, “8 Studies on laser ablation of polymers,” Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 101, 216–247 (2005).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

A. Pikulin, N. Bityurin, G. Langer, D. Brodoceanu, and D. Bäuerle, “Hexagonal structures on metal-coated two-dimensional microlens arrays,” Appl. Phys. Lett. 91(19), 191106 (2007).
[CrossRef]

Appl. Phys., A Mater. Sci. Process.

N. Arnold, “Influence of the substrate, metal overlayer and lattice neighbors on the focusing properties of colloidal microspheres,” Appl. Phys., A Mater. Sci. Process. 92(4), 1005–1012 (2008).
[CrossRef]

B. S. Luk'yanchuk, Z. B. Wang, W. D. Song, and M. H. Hong, “Particle on surface: 3D-effects in dry laser cleaning,” Appl. Phys., A Mater. Sci. Process. 79(4-6), 747–751 (2004).
[CrossRef]

S. Lazare, I. Elaboudi, M. Castillejo, and A. Sionkowska, “Model properties relevant to laser ablation of moderately absorbing polymers,” Appl. Phys., A Mater. Sci. Process. 101(1), 215–224 (2010).
[CrossRef]

Appl. Surf. Sci.

N. Bityurin, “Model for laser swelling of a polymer film,” Appl. Surf. Sci. 255(24), 9851–9855 (2009).
[CrossRef]

Chem. Rev.

G. Paltauf and P. E. Dyer, “Photomechanical processes and effects in ablation,” Chem. Rev. 103(2), 487–518 (2003).
[CrossRef] [PubMed]

Comput. Phys. Commun.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

J. Laser Micro/Nanoeng.

Z. B. Wang, W. Guo, B Luk' yanchuk, D. J. Whitehead, L. Li, and Z. Liu, “Optical near-field interaction between neighbouring micro/nano-particles,” J. Laser Micro/Nanoeng. 3(1), 14–18 (2008).
[CrossRef]

Laser Photonics Rev.

T. C. Chong, M. H. Hong, and L. P. Shi, “Laser precision engineering: from microfabrication to nanoprocessing,” Laser Photonics Rev. 4(1), 123–143 (2010).
[CrossRef]

Nat. Nanotechnol.

E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008).
[CrossRef] [PubMed]

Opt. Express

Other

Y. Xu, Fortran codes for multi-particle light-scattering calculations, http://diogenes.iwt.uni-bremen.de/vt/laser/codes/Yu-linXu/Yu-linXu-codes.htm .

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2008).

M. Born and E. Wolf, Principles of optics. Electromagnetic theory of propagation, interference and diffraction of light. Seventh (expanded) edition (Cambridge University Press, 2003).

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Figures (4)

Fig. 1
Fig. 1

Modeling setup: a closely packed cluster of seven transparent dielectric spheres on a dielectric transparent substrate. The spheres are irradiated by a plane monochromatic wave normal to the substrate boundary plane.

Fig. 2
Fig. 2

Calculated distributions of | E | 2 at the central y-z plane of the sphere (a, c) and the cluster of seven spheres (b, d) irradiated by a plane wave. The spheres are either located in free space (a, b) or placed on substrate (c, d). Both the central sphere and the substrate are indicated with white lines. Axial (e) field distribution at the center line (x = 0, y = 0) and lateral (f) field distribution near the substrate surface (at x = 0, z/dsp = 0.525) are plotted in the bottom graphs. The field distributions are normalized by the value of | E 0 | 2 in the incident wave. In graph (f), the field distributions are normalized by their values in the maximum. Polarization of the incident wave is linear along x. Refractive indices of the spheres and the substrate are 1.59 and 1.46, respectively. The diameter of the spheres is 1000 nm, and the wavelength is 800 nm.

Fig. 3
Fig. 3

Scattered fields at the central z-axis calculated for the cluster of 7 spheres on the substrate (black line) and for a single sphere on the substrate (blue line). Coherent superposition of scattered field solutions for 7 individual spheres that constitute the cluster on the substrate (magenta line). The parameters of the setup are the same as in Fig. 2.

Fig. 4
Fig. 4

Calculated field distributions at the central z-axis of the cluster of seven PMMA spheres on glass substrate (black), the cluster of seven polystyrene spheres on glass substrate (black dashed), the single PMMA sphere in vacuum (red), and the single PMMA sphere in immersion media with refractive indices of 1.1 (green), and 1.2 (blue). The diameter of the spheres is dsp = 2700 nm, the wavelength is 800 nm, refractive indices of PMMA, polystyrene, and glass are 1.49, 1.59 and 1.46, respectively.

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