Abstract

Improving the image quality of small particles is a classic problem and especially challenging when the distance between particles are below the optical diffraction limit. We propose a imaging system illuminated with radially polarized light combined with a suitable substrate that contains a thin dielectric layer to demonstrate that the imaging quality can be enhanced. The coupling between the evanescent wave produced in a designed thin dielectric layer, the small particles and the propagating wave forms a mechanism to transfer sub-wavelength information about the particles to the far field. The smallest distinguished distance reaches to 0.634λ, when the imaging system is composed of a high numerical aperture (NA=0.9) lens and the illumination wavelength λ = 632nm, beyond the diffraction limit 0.678λ. The lateral resolution can be further improved by combining the proposed structure with superresolution microscopy techniques.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  15. O. El Gawhary, N. J. Schilder, A. da Costa Assafrao, S. F. Pereira, and H. P. Urbach, “Restoration of s-polarized evanescent waves and subwavelength imaging by a single dielectric slab,” New J. Phys. 14(5), 053025 (2012).
    [Crossref]
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    [Crossref]
  21. T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarisation microscopes,” Opt. Commun. 141(5-6), 298–313 (1997).
    [Crossref]
  22. P. Török, P. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
    [Crossref]
  23. P. Meng, H. L. Pham, S. F. Pereira, and H. P. Urbach, “Demonstration of lateral resolution enhancement by focusing amplitude modulated radially polarized light in a confocal imaging system,” J. Opt. 22(4), 045605 (2020).
    [Crossref]

2020 (1)

P. Meng, H. L. Pham, S. F. Pereira, and H. P. Urbach, “Demonstration of lateral resolution enhancement by focusing amplitude modulated radially polarized light in a confocal imaging system,” J. Opt. 22(4), 045605 (2020).
[Crossref]

2018 (1)

2017 (1)

S. Roy, S. Pereira, H. Urbach, X. Wei, and O. El Gawhary, “Exploiting evanescent-wave amplification for subwavelength low-contrast particle detection,” Phys. Rev. A 96(1), 013814 (2017).
[Crossref]

2013 (1)

C. J. Regan, D. Dominguez, L. Grave de Peralta, and A. A. Bernussi, “Far-field optical superlenses without metal,” J. Appl. Phys. 113(18), 183105 (2013).
[Crossref]

2012 (1)

O. El Gawhary, N. J. Schilder, A. da Costa Assafrao, S. F. Pereira, and H. P. Urbach, “Restoration of s-polarized evanescent waves and subwavelength imaging by a single dielectric slab,” New J. Phys. 14(5), 053025 (2012).
[Crossref]

2007 (1)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref]

2006 (4)

S. Durant, Z. Liu, J. M. Steele, and X. Zhang, “Theory of the transmission properties of an optical far-field superlens for imaging beyond the diffraction limit,” J. Opt. Soc. Am. B 23(11), 2383–2392 (2006).
[Crossref]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nat. Methods 3(10), 793–796 (2006).
[Crossref]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref]

2005 (1)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref]

2000 (4)

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[Crossref]

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref]

M. Paulus, P. Gay-Balmaz, and O. J. Martin, “Accurate and efficient computation of the green’s tensor for stratified media,” Phys. Rev. E 62(4), 5797–5807 (2000).
[Crossref]

1998 (1)

P. Török, P. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
[Crossref]

1997 (1)

T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarisation microscopes,” Opt. Commun. 141(5-6), 298–313 (1997).
[Crossref]

1994 (1)

1967 (1)

V. Veselago, “Electrodynamics of substances with simultaneously negative ε and μ,” Usp. Fiz. Nauk 92(7), 517 (1967).
[Crossref]

1873 (1)

E. Abbe, “Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Archiv f. mikrosk. Anatomie 9(1), 413–468 (1873).
[Crossref]

Abbe, E.

E. Abbe, “Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Archiv f. mikrosk. Anatomie 9(1), 413–468 (1873).
[Crossref]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nat. Methods 3(10), 793–796 (2006).
[Crossref]

Bernussi, A. A.

C. J. Regan, D. Dominguez, L. Grave de Peralta, and A. A. Bernussi, “Far-field optical superlenses without metal,” J. Appl. Phys. 113(18), 183105 (2013).
[Crossref]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Blaikie, R. J.

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Brown, T. G.

da Costa Assafrao, A.

O. El Gawhary, N. J. Schilder, A. da Costa Assafrao, S. F. Pereira, and H. P. Urbach, “Restoration of s-polarized evanescent waves and subwavelength imaging by a single dielectric slab,” New J. Phys. 14(5), 053025 (2012).
[Crossref]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Dominguez, D.

C. J. Regan, D. Dominguez, L. Grave de Peralta, and A. A. Bernussi, “Far-field optical superlenses without metal,” J. Appl. Phys. 113(18), 183105 (2013).
[Crossref]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref]

Durant, S.

El Gawhary, O.

S. Roy, S. Pereira, H. Urbach, X. Wei, and O. El Gawhary, “Exploiting evanescent-wave amplification for subwavelength low-contrast particle detection,” Phys. Rev. A 96(1), 013814 (2017).
[Crossref]

O. El Gawhary, N. J. Schilder, A. da Costa Assafrao, S. F. Pereira, and H. P. Urbach, “Restoration of s-polarized evanescent waves and subwavelength imaging by a single dielectric slab,” New J. Phys. 14(5), 053025 (2012).
[Crossref]

Gay-Balmaz, P.

M. Paulus, P. Gay-Balmaz, and O. J. Martin, “Accurate and efficient computation of the green’s tensor for stratified media,” Phys. Rev. E 62(4), 5797–5807 (2000).
[Crossref]

Girirajan, T. P.

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref]

Grave de Peralta, L.

C. J. Regan, D. Dominguez, L. Grave de Peralta, and A. A. Bernussi, “Far-field optical superlenses without metal,” J. Appl. Phys. 113(18), 183105 (2013).
[Crossref]

Gustafsson, M. G.

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref]

Hecht, B.

L. Novotny and B. Hecht, Principles of nano-optics (Cambridge University, 2012).

Hell, S. W.

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Hess, S. T.

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref]

Higdon, P.

P. Török, P. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
[Crossref]

T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarisation microscopes,” Opt. Commun. 141(5-6), 298–313 (1997).
[Crossref]

Jackson, J. D.

J. D. Jackson, “Classical electrodynamics,” (1999).

Juškaitis, R.

T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarisation microscopes,” Opt. Commun. 141(5-6), 298–313 (1997).
[Crossref]

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref]

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref]

S. Durant, Z. Liu, J. M. Steele, and X. Zhang, “Theory of the transmission properties of an optical far-field superlens for imaging beyond the diffraction limit,” J. Opt. Soc. Am. B 23(11), 2383–2392 (2006).
[Crossref]

Martin, O. J.

M. Paulus, P. Gay-Balmaz, and O. J. Martin, “Accurate and efficient computation of the green’s tensor for stratified media,” Phys. Rev. E 62(4), 5797–5807 (2000).
[Crossref]

Mason, M. D.

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref]

Melville, D. O.

Meng, P.

P. Meng, H. L. Pham, S. F. Pereira, and H. P. Urbach, “Demonstration of lateral resolution enhancement by focusing amplitude modulated radially polarized light in a confocal imaging system,” J. Opt. 22(4), 045605 (2020).
[Crossref]

P. Meng, S. Pereira, and P. Urbach, “Confocal microscopy with a radially polarized focused beam,” Opt. Express 26(23), 29600–29613 (2018).
[Crossref]

Novotny, L.

L. Novotny and B. Hecht, Principles of nano-optics (Cambridge University, 2012).

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Paulus, M.

M. Paulus, P. Gay-Balmaz, and O. J. Martin, “Accurate and efficient computation of the green’s tensor for stratified media,” Phys. Rev. E 62(4), 5797–5807 (2000).
[Crossref]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref]

Pereira, S.

P. Meng, S. Pereira, and P. Urbach, “Confocal microscopy with a radially polarized focused beam,” Opt. Express 26(23), 29600–29613 (2018).
[Crossref]

S. Roy, S. Pereira, H. Urbach, X. Wei, and O. El Gawhary, “Exploiting evanescent-wave amplification for subwavelength low-contrast particle detection,” Phys. Rev. A 96(1), 013814 (2017).
[Crossref]

Pereira, S. F.

P. Meng, H. L. Pham, S. F. Pereira, and H. P. Urbach, “Demonstration of lateral resolution enhancement by focusing amplitude modulated radially polarized light in a confocal imaging system,” J. Opt. 22(4), 045605 (2020).
[Crossref]

O. El Gawhary, N. J. Schilder, A. da Costa Assafrao, S. F. Pereira, and H. P. Urbach, “Restoration of s-polarized evanescent waves and subwavelength imaging by a single dielectric slab,” New J. Phys. 14(5), 053025 (2012).
[Crossref]

Pham, H. L.

P. Meng, H. L. Pham, S. F. Pereira, and H. P. Urbach, “Demonstration of lateral resolution enhancement by focusing amplitude modulated radially polarized light in a confocal imaging system,” J. Opt. 22(4), 045605 (2020).
[Crossref]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref]

Regan, C. J.

C. J. Regan, D. Dominguez, L. Grave de Peralta, and A. A. Bernussi, “Far-field optical superlenses without metal,” J. Appl. Phys. 113(18), 183105 (2013).
[Crossref]

Roy, S.

S. Roy, S. Pereira, H. Urbach, X. Wei, and O. El Gawhary, “Exploiting evanescent-wave amplification for subwavelength low-contrast particle detection,” Phys. Rev. A 96(1), 013814 (2017).
[Crossref]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nat. Methods 3(10), 793–796 (2006).
[Crossref]

Schilder, N. J.

O. El Gawhary, N. J. Schilder, A. da Costa Assafrao, S. F. Pereira, and H. P. Urbach, “Restoration of s-polarized evanescent waves and subwavelength imaging by a single dielectric slab,” New J. Phys. 14(5), 053025 (2012).
[Crossref]

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

Steele, J. M.

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref]

Török, P.

P. Török, P. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
[Crossref]

Urbach, H.

S. Roy, S. Pereira, H. Urbach, X. Wei, and O. El Gawhary, “Exploiting evanescent-wave amplification for subwavelength low-contrast particle detection,” Phys. Rev. A 96(1), 013814 (2017).
[Crossref]

Urbach, H. P.

P. Meng, H. L. Pham, S. F. Pereira, and H. P. Urbach, “Demonstration of lateral resolution enhancement by focusing amplitude modulated radially polarized light in a confocal imaging system,” J. Opt. 22(4), 045605 (2020).
[Crossref]

O. El Gawhary, N. J. Schilder, A. da Costa Assafrao, S. F. Pereira, and H. P. Urbach, “Restoration of s-polarized evanescent waves and subwavelength imaging by a single dielectric slab,” New J. Phys. 14(5), 053025 (2012).
[Crossref]

Urbach, P.

Veselago, V.

V. Veselago, “Electrodynamics of substances with simultaneously negative ε and μ,” Usp. Fiz. Nauk 92(7), 517 (1967).
[Crossref]

Wei, X.

S. Roy, S. Pereira, H. Urbach, X. Wei, and O. El Gawhary, “Exploiting evanescent-wave amplification for subwavelength low-contrast particle detection,” Phys. Rev. A 96(1), 013814 (2017).
[Crossref]

Wichmann, J.

Wilson, T.

P. Török, P. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
[Crossref]

T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarisation microscopes,” Opt. Commun. 141(5-6), 298–313 (1997).
[Crossref]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref]

Youngworth, K. S.

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref]

S. Durant, Z. Liu, J. M. Steele, and X. Zhang, “Theory of the transmission properties of an optical far-field superlens for imaging beyond the diffraction limit,” J. Opt. Soc. Am. B 23(11), 2383–2392 (2006).
[Crossref]

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nat. Methods 3(10), 793–796 (2006).
[Crossref]

Archiv f. mikrosk. Anatomie (1)

E. Abbe, “Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Archiv f. mikrosk. Anatomie 9(1), 413–468 (1873).
[Crossref]

Biophys. J. (1)

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref]

J. Appl. Phys. (1)

C. J. Regan, D. Dominguez, L. Grave de Peralta, and A. A. Bernussi, “Far-field optical superlenses without metal,” J. Appl. Phys. 113(18), 183105 (2013).
[Crossref]

J. Microsc. (1)

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref]

J. Mod. Opt. (1)

P. Török, P. Higdon, and T. Wilson, “Theory for confocal and conventional microscopes imaging small dielectric scatterers,” J. Mod. Opt. 45(8), 1681–1698 (1998).
[Crossref]

J. Opt. (1)

P. Meng, H. L. Pham, S. F. Pereira, and H. P. Urbach, “Demonstration of lateral resolution enhancement by focusing amplitude modulated radially polarized light in a confocal imaging system,” J. Opt. 22(4), 045605 (2020).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Methods (1)

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nat. Methods 3(10), 793–796 (2006).
[Crossref]

New J. Phys. (1)

O. El Gawhary, N. J. Schilder, A. da Costa Assafrao, S. F. Pereira, and H. P. Urbach, “Restoration of s-polarized evanescent waves and subwavelength imaging by a single dielectric slab,” New J. Phys. 14(5), 053025 (2012).
[Crossref]

Opt. Commun. (1)

T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarisation microscopes,” Opt. Commun. 141(5-6), 298–313 (1997).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (1)

S. Roy, S. Pereira, H. Urbach, X. Wei, and O. El Gawhary, “Exploiting evanescent-wave amplification for subwavelength low-contrast particle detection,” Phys. Rev. A 96(1), 013814 (2017).
[Crossref]

Phys. Rev. E (1)

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Figures (6)

Fig. 1.
Fig. 1. Schematic diagram of the imaging system. (a) A complete imaging setup with the illumination of radially polarized beam at the wavelength $\lambda =632nm$. (b) The mechanism of enhancement of evanescent waves by considering a sample on the glass substrate with a thin dielectric film on the top. Abbreviations: beam splitter (BS), spatial light modulator (SLM), polarization convertor (Pol.con), nanoparticle (NP).
Fig. 2.
Fig. 2. Schematic geometry of a dipole placed above the substrate.
Fig. 3.
Fig. 3. The comparison on the modulus of the reflection coefficient for $s$ (a) and $p$ (b) polarized light at the interface of air and three kinds of substrates: without enhanced slab (solid line), with TiO$_2$ slab (dashed line) and with InSb slab (dot line) on top of the glass substrate.
Fig. 4.
Fig. 4. The comparison of total intensity distributions in the near field of $xz$ plane with the illumination radially polarized beams on the top of the nanosphere without (a), with TiO$_2$ (b) and with InSb (c) slab.
Fig. 5.
Fig. 5. Imaging of one sphere in the $xy$ plane without ($a$) and with (($b$)-TiO$_2$, ($c$)-InSb) the enhanced layer under the illumination of radially polarized light. (d) is the cross section of the normalized scattering intensity.
Fig. 6.
Fig. 6. Profile of the imaging of two separated nanospheres supported on different substrates with various distances between the spheres: $d=600nm$ , $d=500nm$, $d=400nm$ and $d=200nm$. ($\textrm{a}_1$)-($\textrm{d}_1$): with the enhancing TiO$_2$ slab on the top of glass, ($\textrm{a}_2$)-($\textrm{d}_2$): without enhancing slab.

Equations (11)

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U dipole ( r ) = ( G 0 ( r , r p ) + G r ( r , r p ) ) p ,
G 0 ( r ) = 1 4 π e i k 0 | r r p | | r r p | k 0 2 ϵ 0 ,
p = α U tot i n ( r p ) + α G r ( r , r p ) p ,
p = α U tot i n ( r p ) 1 α G r ( r , r p ) ,
G r ( r , r p = 1 4 π 2 R ( k ) F ( G 0 ) ( k x 2 π , k y 2 π , z p ) e i [ k x ( x x p ) + k y ( y y p ) + k z z ] d k x d k y ,
F ( G 0 ( r , r p ) ) = e i ( k x x p + k y y p k z | z z p | ) 2 i k z d k x d k y ,
r i , j = k z , i k z , j k z , i + k z , j ,
R ( k ) = r 1 , 2 + t 2 , 1 r 2 , 3 t 1 , 2 e 2 i k z , 2 d { 1 + r 2 , 3 r 2 , 1 e 2 i k z , 2 d + } ,
E img = R 0 1 L 2 L 1 1 R 0 U dipole ,
R 0 = [ cos ϕ sin ϕ 0 sin ϕ cos ϕ 0 0 0 1 ] ,
L n = [ cos θ n 0 sin θ n 0 1 0 sin θ n 0 cos θ n ] ,