Abstract

This paper is to present a model and analysis of a common-path surface plasmon interferometer from the aspect of the electrical field distribution, which excellently supplements the currently applied simplified ray model. We apply radial polarization to show the principle. Firstly, we study the electric field distribution in the vicinity of the focal spot and show how the defocusing properties behave on the far-field imaging plane. The diffraction orders on the far-field image plane with an axially-scanned sample contains the common-path interferometric V(z) effect and quantitatively interprets the plasmonic properties of the materials. The implementation refers to extracting the interferometric V(z) SP signals from intensity-based SPM by applying a confocal annulus on the image plane. Secondly, we specifically analyze the impact of annulus parameters, e.g. inner radius and width, on the acquisition of the interferometric V(z) curves. We also discuss the acquisition conditions of the plasmonic V(z) effect. Finally, we discuss the advantages of using radially polarized illumination and make a comparison with a conventional linearly polarized system. The established model is experimentally verified.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2018 (1)

. Zhang, C. Zhang, J. Wang, and P. Yan, “Modeling and analysis of surface plasmon microscopy with radial polarization,” Opt. Commun. 427, 369–373 (2018).
[Crossref]

2016 (1)

2014 (1)

2013 (2)

2012 (1)

2011 (1)

2007 (2)

2006 (1)

2002 (1)

M. G. Somekh, “Surface plasmon fluorescence microscopy: an analysis,” J. Microsc. 206(2), 120–131 (2002).
[Crossref] [PubMed]

2000 (2)

1998 (2)

H. Kano and W. Knoll, “Locally excited surface-plasmon-polaritons for thickness measurement of LBK films,” Opt. Commun. 153(4–6), 235–239 (1998).
[Crossref]

H. Kano, S. Mizuguchi, and S. Kawata, “Excitation of surface-plasmon polaritons by a focused laser beam,” J. Opt. Soc. Am. B 15(4), 1381–1386 (1998).
[Crossref]

1981 (1)

C. J. R. Sheppard and T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38(11), 858–859 (1981).
[Crossref]

Argoul, F.

Arneodo, A.

Berguiga, L.

Boyer-Provera, E.

Dumontet, C.

Elezgaray, J.

Horiguchi, N.

Kano, H.

Kawata, S.

Knoll, W.

H. Kano and W. Knoll, “Locally excited surface-plasmon-polaritons for thickness measurement of LBK films,” Opt. Commun. 153(4–6), 235–239 (1998).
[Crossref]

Liu, S.

Liu, S. G.

Martinez-Torres, C.

Mizuguchi, S.

Monier, K.

Oriol, L.

Pechprasarn, S.

Plesa, A.

Roland, T.

Rossi, A.

Schaeffer, L.

See, C. W.

Sheppard, C. J. R.

C. J. R. Sheppard and T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38(11), 858–859 (1981).
[Crossref]

Somekh, M. G.

Streppa, L.

Velinov, T. S.

Wang, J.

. Zhang, C. Zhang, J. Wang, and P. Yan, “Modeling and analysis of surface plasmon microscopy with radial polarization,” Opt. Commun. 427, 369–373 (2018).
[Crossref]

Watanabe, K.

Wilson, T.

C. J. R. Sheppard and T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38(11), 858–859 (1981).
[Crossref]

Yan, P.

. Zhang, C. Zhang, J. Wang, and P. Yan, “Modeling and analysis of surface plasmon microscopy with radial polarization,” Opt. Commun. 427, 369–373 (2018).
[Crossref]

Zhan, Q.

Zhang, .

. Zhang, C. Zhang, J. Wang, and P. Yan, “Modeling and analysis of surface plasmon microscopy with radial polarization,” Opt. Commun. 427, 369–373 (2018).
[Crossref]

Zhang, B.

Zhang, C.

. Zhang, C. Zhang, J. Wang, and P. Yan, “Modeling and analysis of surface plasmon microscopy with radial polarization,” Opt. Commun. 427, 369–373 (2018).
[Crossref]

Zhang, J.

Zhang, S.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

C. J. R. Sheppard and T. Wilson, “Effects of high angles of convergence on V(z) in the scanning acoustic microscope,” Appl. Phys. Lett. 38(11), 858–859 (1981).
[Crossref]

Biomed. Opt. Express (1)

J. Microsc. (1)

M. G. Somekh, “Surface plasmon fluorescence microscopy: an analysis,” J. Microsc. 206(2), 120–131 (2002).
[Crossref] [PubMed]

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

Opt. Commun. (2)

H. Kano and W. Knoll, “Locally excited surface-plasmon-polaritons for thickness measurement of LBK films,” Opt. Commun. 153(4–6), 235–239 (1998).
[Crossref]

. Zhang, C. Zhang, J. Wang, and P. Yan, “Modeling and analysis of surface plasmon microscopy with radial polarization,” Opt. Commun. 427, 369–373 (2018).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

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Figures (7)

Fig. 1
Fig. 1 (a) Diagram that showing structure of surface plasmons excitation; (b) Diagram that showing surface plasmons excitation by a high NA objective lens with the sample at defocus.
Fig. 2
Fig. 2 (a) Diagram of a reflecting SPs system with radial polarization. a(kr) refers to the entrance pupil and provides illumination for the objective; the beam reflects back through the BFP and focuses on the imaging plane; (b) The meridional plane of a simplified reflecting SPM in radially polarized mode.
Fig. 3
Fig. 3 (a) Intensity distribution of the ρ-z plane in imaging plane. (b) Simulated focal distribution in x-y plane; the red circle represents the virtual annulus we take for the I(z) intensity. For consistency between the figures and the text, the scales of the x-y axis are in λ/NA unity and the z axis is in micron.
Fig. 4
Fig. 4 (a) V(z) curve with whole Airy disk; (b) V(z) curves with inner radii of 0 (blue), 0.6 (red), 1 (black), 1.2 (cyan), 1.7 (pink) and 2(grey) of the Airy disk. The width of the annulus is 0.1 of Airy disk. The curves are shifted along the y-axis by 0.1 for clarity.
Fig. 5
Fig. 5 (a)(c) BFPs without and with apodized pupil with non-plasmonic samples; (b)(d) The captured electric field distribution in the vicinity of focus on imaging plane focused by (a) and (c) respectively; the region between the lines is defined as the virtual confocal annulus taking for V(z), which is shown in (i). (e)(g) BFPs without and with apodized pupil with plasmonic samples; (f)(h) The captured electric field distribution in the vicinity of focus on imaging plane focused by (e) and (g) respectively; (j) The corresponding of V(z) curves when using a plasmonic sample.
Fig. 6
Fig. 6 (a) Diagram of the principle of the SP common-path interferometer with radially polarized illumination; (b) The sample structure; (c) Simulated V(z) curves of different samples. (d) Experimental V(z) curves of different samples.
Fig. 7
Fig. 7 (a) The focal spot of radial system; (b)The focal spot of linear system; the red circles refer to the defined virtual annulus; The scales of the figure (a) and (b) are 1μm; (c)-(f)V(z) curves for different annulus with limits between (c) 0-1; (d) 0-0.1; (e) 0.7-0.8; (f) 1.1-1.2 of the Airy disk.

Equations (4)

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k x = w c ε sin θ sp = k sp
E r =A 0 θ 1 P(θ) cos 1/2 (θ)sinθcosθ t p (θ) J 1 ( k c ρ 1 sinθ)exp(i k z z) dθ E z =iA 0 θ 1 P(θ) cos 1/2 (θ) sin 2 θ t p (θ) J 0 ( k c ρ 1 sinθ)exp(i k z z) dθ
E det rad (ρ,z)=2πi 0 k max P 2 ( k r ) r p ( k r ) J 1 ( k r ρ) k r exp2i k z zd k r
I(z)= ρ min ρ max | E det rad (ρ,z) | 2 ρdρ

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