Abstract

Surface plasmons (SP’s) are electromagnetic surface waves that propagate along the interface between conductors and dielectrics. The k vector of these waves is larger than the free-space wave vector. The importance of SP’s lies in the fact that they are extremely sensitive to small changes in the dielectric properties of substances that are in contact with the conductors. This property means that SP’s have many sensor applications; however, when they are used in microscopic applications the lateral resolution is limited to several micrometers. We discuss how this limit can be overcome by use of defocused high-numerical-aperture liquid-immersion objectives. We also present SP images that demonstrate a resolution comparable with that expected from high-numerical-aperture optical microscopes. Finally, we discuss how ultrahigh-numerical-aperture objectives with numerical apertures greater than 1.5 can be expected to have considerable influence on biological imaging.

© 2000 Optical Society of America

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References

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  1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1998).
  2. R. J. Green, S. Tasker, J. Davies, M. C. Davies, C. J. Roberts, S. J. B. Tendler, “Adsorption of PEO–PPO–PEO triblock copolymers at the solid–liquid interface,” Langmuir 13, 6510–6515 (1997).
    [CrossRef]
  3. M. T. Flanagan, R. H. Pantell, “Surface plasmon resonance and immunosensors,” Electron. Lett. 20, 969–970 (1984).
    [CrossRef]
  4. B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
    [CrossRef] [PubMed]
  5. T. Velinov, M. G. Somekh, S. Liu, “Direct far-field observation of surface-plasmon propagation by photoinduced scattering,” Appl. Phys. Lett. 75, 3908–3910 (1999).
    [CrossRef]
  6. E. M. Yeatman, E. A. Ash, “Surface plasmon microscopy,” Electron. Lett. 23, 1091–1092 (1987).
    [CrossRef]
  7. B. Rothenhausler, W. Knoll, “Surface-plasmon microscopy,” Nature 332, 615–617 (1988).
    [CrossRef]
  8. E. M. Yeatman, “Resolution and sensitivity in surface plasmon microscopy and sensing,” Biosens. Bioelectron. 11, 635–649 (1996).
    [CrossRef]
  9. K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, M. Bastmeyer, “Imaging of cell–substrate contacts of living cells,” Biophys. J. 76, 509–516 (1999).
    [CrossRef] [PubMed]
  10. C. E. H. Berger, R. P. H. Kooyman, J. Greve, “Resolution in surface plasmon microscopy,” Rev. Sci. Instrum. 65, 2829–2835 (1994).
    [CrossRef]
  11. H. Kano, S. Mizuguchi, S. Kawata, “Excitation of surface-plasmon polaritons by a focused laser beam,” J. Opt. Soc. Am. B 15, 1381–1386 (1998).
    [CrossRef]
  12. M. G. Somekh, S. Liu, T. S. Velinov, C. W. See, “Optical V(z) for high-resolution 2π surface plasmon microscopy,” Opt. Lett. 25, 823–825 (2000).
    [CrossRef]
  13. A. L. Migdall, B. Roop, Y. C. Zheng, J. E. Hardis, G. J. Xia, “Use of heterodyne detection to measure optical transmittance over a wide range,” Appl. Opt. 29, 5136–5144 (1990).
    [CrossRef] [PubMed]
  14. H. Zhou, C. J. R. Sheppard, “Aberration measurement in confocal microscopy: phase retrieval from a single intensity measurement,” J. Mod. Opt. 44, 1553–1561 (1997).
    [CrossRef]
  15. W. Parmon, H. L. Bertoni, “Ray interpretation of the material signature in the acoustic microscope,” Electron. Lett. 15, 684–686 (1979).
    [CrossRef]
  16. A. Atalar, C. F. Quate, H. K. Wickramasinghe, “Phase imaging in reflection with the acoustic microscope,” Appl. Phys. Lett. 31, 791–793 (1977).
    [CrossRef]
  17. C. Ilett, M. G. Somekh, G. A. D. Briggs, “Acoustic microscopy of elastic discontinuities,” Proc. R. Soc. London Ser. A 393, 171–183 (1984).
    [CrossRef]
  18. M. Schrader, S. W. Hell, “4 pi-confocal images with axial superresolution,” J. Microsc. 183, 189–193 (1996).
    [CrossRef]

2000 (1)

1999 (2)

T. Velinov, M. G. Somekh, S. Liu, “Direct far-field observation of surface-plasmon propagation by photoinduced scattering,” Appl. Phys. Lett. 75, 3908–3910 (1999).
[CrossRef]

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, M. Bastmeyer, “Imaging of cell–substrate contacts of living cells,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

1998 (1)

1997 (2)

H. Zhou, C. J. R. Sheppard, “Aberration measurement in confocal microscopy: phase retrieval from a single intensity measurement,” J. Mod. Opt. 44, 1553–1561 (1997).
[CrossRef]

R. J. Green, S. Tasker, J. Davies, M. C. Davies, C. J. Roberts, S. J. B. Tendler, “Adsorption of PEO–PPO–PEO triblock copolymers at the solid–liquid interface,” Langmuir 13, 6510–6515 (1997).
[CrossRef]

1996 (3)

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

M. Schrader, S. W. Hell, “4 pi-confocal images with axial superresolution,” J. Microsc. 183, 189–193 (1996).
[CrossRef]

E. M. Yeatman, “Resolution and sensitivity in surface plasmon microscopy and sensing,” Biosens. Bioelectron. 11, 635–649 (1996).
[CrossRef]

1994 (1)

C. E. H. Berger, R. P. H. Kooyman, J. Greve, “Resolution in surface plasmon microscopy,” Rev. Sci. Instrum. 65, 2829–2835 (1994).
[CrossRef]

1990 (1)

1988 (1)

B. Rothenhausler, W. Knoll, “Surface-plasmon microscopy,” Nature 332, 615–617 (1988).
[CrossRef]

1987 (1)

E. M. Yeatman, E. A. Ash, “Surface plasmon microscopy,” Electron. Lett. 23, 1091–1092 (1987).
[CrossRef]

1984 (2)

M. T. Flanagan, R. H. Pantell, “Surface plasmon resonance and immunosensors,” Electron. Lett. 20, 969–970 (1984).
[CrossRef]

C. Ilett, M. G. Somekh, G. A. D. Briggs, “Acoustic microscopy of elastic discontinuities,” Proc. R. Soc. London Ser. A 393, 171–183 (1984).
[CrossRef]

1979 (1)

W. Parmon, H. L. Bertoni, “Ray interpretation of the material signature in the acoustic microscope,” Electron. Lett. 15, 684–686 (1979).
[CrossRef]

1977 (1)

A. Atalar, C. F. Quate, H. K. Wickramasinghe, “Phase imaging in reflection with the acoustic microscope,” Appl. Phys. Lett. 31, 791–793 (1977).
[CrossRef]

Ash, E. A.

E. M. Yeatman, E. A. Ash, “Surface plasmon microscopy,” Electron. Lett. 23, 1091–1092 (1987).
[CrossRef]

Atalar, A.

A. Atalar, C. F. Quate, H. K. Wickramasinghe, “Phase imaging in reflection with the acoustic microscope,” Appl. Phys. Lett. 31, 791–793 (1977).
[CrossRef]

Bastmeyer, M.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, M. Bastmeyer, “Imaging of cell–substrate contacts of living cells,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Bechinger, C.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, M. Bastmeyer, “Imaging of cell–substrate contacts of living cells,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Berger, C. E. H.

C. E. H. Berger, R. P. H. Kooyman, J. Greve, “Resolution in surface plasmon microscopy,” Rev. Sci. Instrum. 65, 2829–2835 (1994).
[CrossRef]

Bertoni, H. L.

W. Parmon, H. L. Bertoni, “Ray interpretation of the material signature in the acoustic microscope,” Electron. Lett. 15, 684–686 (1979).
[CrossRef]

Bielefeldt, H.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

Briggs, G. A. D.

C. Ilett, M. G. Somekh, G. A. D. Briggs, “Acoustic microscopy of elastic discontinuities,” Proc. R. Soc. London Ser. A 393, 171–183 (1984).
[CrossRef]

Davies, J.

R. J. Green, S. Tasker, J. Davies, M. C. Davies, C. J. Roberts, S. J. B. Tendler, “Adsorption of PEO–PPO–PEO triblock copolymers at the solid–liquid interface,” Langmuir 13, 6510–6515 (1997).
[CrossRef]

Davies, M. C.

R. J. Green, S. Tasker, J. Davies, M. C. Davies, C. J. Roberts, S. J. B. Tendler, “Adsorption of PEO–PPO–PEO triblock copolymers at the solid–liquid interface,” Langmuir 13, 6510–6515 (1997).
[CrossRef]

Flanagan, M. T.

M. T. Flanagan, R. H. Pantell, “Surface plasmon resonance and immunosensors,” Electron. Lett. 20, 969–970 (1984).
[CrossRef]

Giebel, K. F.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, M. Bastmeyer, “Imaging of cell–substrate contacts of living cells,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Green, R. J.

R. J. Green, S. Tasker, J. Davies, M. C. Davies, C. J. Roberts, S. J. B. Tendler, “Adsorption of PEO–PPO–PEO triblock copolymers at the solid–liquid interface,” Langmuir 13, 6510–6515 (1997).
[CrossRef]

Greve, J.

C. E. H. Berger, R. P. H. Kooyman, J. Greve, “Resolution in surface plasmon microscopy,” Rev. Sci. Instrum. 65, 2829–2835 (1994).
[CrossRef]

Hardis, J. E.

Hecht, B.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

Hell, S. W.

M. Schrader, S. W. Hell, “4 pi-confocal images with axial superresolution,” J. Microsc. 183, 189–193 (1996).
[CrossRef]

Herminghaus, S.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, M. Bastmeyer, “Imaging of cell–substrate contacts of living cells,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Ilett, C.

C. Ilett, M. G. Somekh, G. A. D. Briggs, “Acoustic microscopy of elastic discontinuities,” Proc. R. Soc. London Ser. A 393, 171–183 (1984).
[CrossRef]

Inouye, Y.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

Kano, H.

Kawata, S.

Knoll, W.

B. Rothenhausler, W. Knoll, “Surface-plasmon microscopy,” Nature 332, 615–617 (1988).
[CrossRef]

Kooyman, R. P. H.

C. E. H. Berger, R. P. H. Kooyman, J. Greve, “Resolution in surface plasmon microscopy,” Rev. Sci. Instrum. 65, 2829–2835 (1994).
[CrossRef]

Leiderer, P.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, M. Bastmeyer, “Imaging of cell–substrate contacts of living cells,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Liu, S.

M. G. Somekh, S. Liu, T. S. Velinov, C. W. See, “Optical V(z) for high-resolution 2π surface plasmon microscopy,” Opt. Lett. 25, 823–825 (2000).
[CrossRef]

T. Velinov, M. G. Somekh, S. Liu, “Direct far-field observation of surface-plasmon propagation by photoinduced scattering,” Appl. Phys. Lett. 75, 3908–3910 (1999).
[CrossRef]

Migdall, A. L.

Mizuguchi, S.

Novotny, L.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

Pantell, R. H.

M. T. Flanagan, R. H. Pantell, “Surface plasmon resonance and immunosensors,” Electron. Lett. 20, 969–970 (1984).
[CrossRef]

Parmon, W.

W. Parmon, H. L. Bertoni, “Ray interpretation of the material signature in the acoustic microscope,” Electron. Lett. 15, 684–686 (1979).
[CrossRef]

Pohl, D. W.

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

Quate, C. F.

A. Atalar, C. F. Quate, H. K. Wickramasinghe, “Phase imaging in reflection with the acoustic microscope,” Appl. Phys. Lett. 31, 791–793 (1977).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1998).

Riedel, M.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, M. Bastmeyer, “Imaging of cell–substrate contacts of living cells,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Roberts, C. J.

R. J. Green, S. Tasker, J. Davies, M. C. Davies, C. J. Roberts, S. J. B. Tendler, “Adsorption of PEO–PPO–PEO triblock copolymers at the solid–liquid interface,” Langmuir 13, 6510–6515 (1997).
[CrossRef]

Roop, B.

Rothenhausler, B.

B. Rothenhausler, W. Knoll, “Surface-plasmon microscopy,” Nature 332, 615–617 (1988).
[CrossRef]

Schrader, M.

M. Schrader, S. W. Hell, “4 pi-confocal images with axial superresolution,” J. Microsc. 183, 189–193 (1996).
[CrossRef]

See, C. W.

Sheppard, C. J. R.

H. Zhou, C. J. R. Sheppard, “Aberration measurement in confocal microscopy: phase retrieval from a single intensity measurement,” J. Mod. Opt. 44, 1553–1561 (1997).
[CrossRef]

Somekh, M. G.

M. G. Somekh, S. Liu, T. S. Velinov, C. W. See, “Optical V(z) for high-resolution 2π surface plasmon microscopy,” Opt. Lett. 25, 823–825 (2000).
[CrossRef]

T. Velinov, M. G. Somekh, S. Liu, “Direct far-field observation of surface-plasmon propagation by photoinduced scattering,” Appl. Phys. Lett. 75, 3908–3910 (1999).
[CrossRef]

C. Ilett, M. G. Somekh, G. A. D. Briggs, “Acoustic microscopy of elastic discontinuities,” Proc. R. Soc. London Ser. A 393, 171–183 (1984).
[CrossRef]

Tasker, S.

R. J. Green, S. Tasker, J. Davies, M. C. Davies, C. J. Roberts, S. J. B. Tendler, “Adsorption of PEO–PPO–PEO triblock copolymers at the solid–liquid interface,” Langmuir 13, 6510–6515 (1997).
[CrossRef]

Tendler, S. J. B.

R. J. Green, S. Tasker, J. Davies, M. C. Davies, C. J. Roberts, S. J. B. Tendler, “Adsorption of PEO–PPO–PEO triblock copolymers at the solid–liquid interface,” Langmuir 13, 6510–6515 (1997).
[CrossRef]

Velinov, T.

T. Velinov, M. G. Somekh, S. Liu, “Direct far-field observation of surface-plasmon propagation by photoinduced scattering,” Appl. Phys. Lett. 75, 3908–3910 (1999).
[CrossRef]

Velinov, T. S.

Weiland, U.

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, M. Bastmeyer, “Imaging of cell–substrate contacts of living cells,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Wickramasinghe, H. K.

A. Atalar, C. F. Quate, H. K. Wickramasinghe, “Phase imaging in reflection with the acoustic microscope,” Appl. Phys. Lett. 31, 791–793 (1977).
[CrossRef]

Xia, G. J.

Yeatman, E. M.

E. M. Yeatman, “Resolution and sensitivity in surface plasmon microscopy and sensing,” Biosens. Bioelectron. 11, 635–649 (1996).
[CrossRef]

E. M. Yeatman, E. A. Ash, “Surface plasmon microscopy,” Electron. Lett. 23, 1091–1092 (1987).
[CrossRef]

Zheng, Y. C.

Zhou, H.

H. Zhou, C. J. R. Sheppard, “Aberration measurement in confocal microscopy: phase retrieval from a single intensity measurement,” J. Mod. Opt. 44, 1553–1561 (1997).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. Atalar, C. F. Quate, H. K. Wickramasinghe, “Phase imaging in reflection with the acoustic microscope,” Appl. Phys. Lett. 31, 791–793 (1977).
[CrossRef]

T. Velinov, M. G. Somekh, S. Liu, “Direct far-field observation of surface-plasmon propagation by photoinduced scattering,” Appl. Phys. Lett. 75, 3908–3910 (1999).
[CrossRef]

Biophys. J. (1)

K. F. Giebel, C. Bechinger, S. Herminghaus, M. Riedel, P. Leiderer, U. Weiland, M. Bastmeyer, “Imaging of cell–substrate contacts of living cells,” Biophys. J. 76, 509–516 (1999).
[CrossRef] [PubMed]

Biosens. Bioelectron. (1)

E. M. Yeatman, “Resolution and sensitivity in surface plasmon microscopy and sensing,” Biosens. Bioelectron. 11, 635–649 (1996).
[CrossRef]

Electron. Lett. (3)

W. Parmon, H. L. Bertoni, “Ray interpretation of the material signature in the acoustic microscope,” Electron. Lett. 15, 684–686 (1979).
[CrossRef]

E. M. Yeatman, E. A. Ash, “Surface plasmon microscopy,” Electron. Lett. 23, 1091–1092 (1987).
[CrossRef]

M. T. Flanagan, R. H. Pantell, “Surface plasmon resonance and immunosensors,” Electron. Lett. 20, 969–970 (1984).
[CrossRef]

J. Microsc. (1)

M. Schrader, S. W. Hell, “4 pi-confocal images with axial superresolution,” J. Microsc. 183, 189–193 (1996).
[CrossRef]

J. Mod. Opt. (1)

H. Zhou, C. J. R. Sheppard, “Aberration measurement in confocal microscopy: phase retrieval from a single intensity measurement,” J. Mod. Opt. 44, 1553–1561 (1997).
[CrossRef]

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

Langmuir (1)

R. J. Green, S. Tasker, J. Davies, M. C. Davies, C. J. Roberts, S. J. B. Tendler, “Adsorption of PEO–PPO–PEO triblock copolymers at the solid–liquid interface,” Langmuir 13, 6510–6515 (1997).
[CrossRef]

Nature (1)

B. Rothenhausler, W. Knoll, “Surface-plasmon microscopy,” Nature 332, 615–617 (1988).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A (1)

C. Ilett, M. G. Somekh, G. A. D. Briggs, “Acoustic microscopy of elastic discontinuities,” Proc. R. Soc. London Ser. A 393, 171–183 (1984).
[CrossRef]

Rev. Sci. Instrum. (1)

C. E. H. Berger, R. P. H. Kooyman, J. Greve, “Resolution in surface plasmon microscopy,” Rev. Sci. Instrum. 65, 2829–2835 (1994).
[CrossRef]

Other (1)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1998).

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram showing the Kretschmann configuration of thin conducting layers deposited on a dielectric film that exhibits many properties of SP’s.

Fig. 2
Fig. 2

Schematic diagram of the scanning heterodyne interferometer used in the experiments.

Fig. 3
Fig. 3

Diagram showing the relations between different polarization components in the field that is reflected in the back focal plane of the microscope objective.

Fig. 4
Fig. 4

(a) Amplitude (thick curve) and phase (thin curve) of the Fresnel coefficients for a liquid with a refractive index of n = 1.52, a 44-nm layer of gold with a refractive index of n = 0.1721 + i3.5156, and air with a refractive index of n = 1. The incident light is s polarized. (b) Amplitude (thick curve) and phase (thin curve) of the Fresnel coefficients with the same parameters as for (a) but with an incident p polarization. (c) Comparison of the amplitude reflection coefficients for p-polarized incident light. The thick curve represents the sample described in (a), and the thin curve represents a sample with a 20-nm layer of silica deposited on the gold. (d) Comparison of the phase of the reflection coefficients. The thick curve represents the sample of (a), and the thin curve that of a sample with a 20-nm layer of silica deposited on the gold.

Fig. 5
Fig. 5

(a) Theoretical V(z) curve obtained with the reflection coefficients of Fig. 4. The thick curve represents p-polarized incident light, and the thin curve represents s-polarized incident light. (b) Theoretical V(z) curve obtained with equal contributions from the s- and the p-polarized incident light. The units of the x axis are free-space wavelengths.

Fig. 6
Fig. 6

(a) Ray paths that show the principal ray paths for the V(z) effect. (b) Diagram that shows the ring excitation and focusing of SP’s.

Fig. 7
Fig. 7

Experimental V(z) curves for a coverslip that is coated with chromium and gold (thick curve) and chromium and gold layers that are overlaid with a dielectric (thin curve).

Fig. 8
Fig. 8

Relative strength of SP excitation for slits that are oriented parallel to (thick curve) and normal to (thin curve) the incident polarization plotted as functions of a normalized slit width; θ p = 44°.

Fig. 9
Fig. 9

V(z) curves obtained for samples with 2-mm slits. The thick curve represents a slit that is at a right angle to the input polarization; the thin curve represents a slit that is oriented parallel to the input polarization.

Fig. 10
Fig. 10

Schematic diagram of the sample structure that was used for the imaging experiments. Bare metal strips of 2-µm width are followed by a 6-µm width of a dielectric-coated metal. The chromium film is approximately 1 nm thick; the gold film is approximately 50 nm thick; the silicon dioxide dielectric is approximately 20 nm thick.

Fig. 11
Fig. 11

SP microscope images of the structured sample: (a) Left-hand side: image taken with a SP microscope of a sample with a defocus of z = 0. Right-hand side: horizontal line trace taken from a position starting 1.6 µm below the top left-hand corner. (b) Images and line traces of the same region for a defocus of z = -1.5 µm. (c) Images and line traces of the same region for a defocus of z = -1.85 µm. The image dimensions are 9 µm × 12 µm.

Fig. 12
Fig. 12

SP images obtained with a slit in the back focal plane: (a) The slit is normal to the incident polarization. (b) The slit is parallel to the incident polarization. The image dimensions are 9 µm × 9 µm, and the sample defocus is -2.5 µm.

Fig. 13
Fig. 13

(a) Amplitude (thick curve) and phase (thin curve) of the p-polarization reflection coefficient, as in Fig. 4(b), except that air (n = 1) is replaced with water with a refractive index of n = 1.33. (b) Same as for (a) except that oil with a refractive index of n = 1.52 is replaced with oil with a refractive index of n = 1.78.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Ereflected=P2sin θRpsin θcos2 ϕ+Rssin θsin2 ϕexpj2nk cos θ z.
2ReEreflectedEo*.
Vz=lens apertureP2sin θRpsin θcos2 ϕ+Rssin θsin2 ϕexpj2nk cos θ zdsin θdϕ.
Δz=λfree2n1-cos θp,

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