Abstract

The imaging principle of the scanning surface plasmon microscope (SSPM) springs from the high sensitivity of surface plasmons to modifications of material properties near the dielectric–metal interface. In this paper, we show that tomographic techniques can be applied to SSPM imaging of dielectric objects to reach resolutions beyond the diffraction-limited half-wavelength scale. Furthermore, this high resolution is not limited to the multiple scattering regime. Finally, we conclude that SSPM is less sensitive to noise because it provides higher contrast ratio than other far-field microscopies.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).
  2. A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
    [CrossRef]
  3. Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
    [CrossRef]
  4. J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801(R) (2010).
    [CrossRef]
  5. H. Kano, S. Mizuguchi, and S. Kawata, “Excitation of surface-plasmon polaritons by a focused laser beam,” J. Opt. Soc. Am. B 15, 1381–1386 (1998).
    [CrossRef]
  6. M. G. Somekh, S. Liu, and T. S. Velinov, “Optical V(z) for high-resolution 2π surface plasmon microscopy,” Opt. Lett. 25, 823–825 (2000).
    [CrossRef]
  7. L. Berguiga, S.-J. Zhang, F. Argoul, and J. Elezgaray, “High-resolution surface-plasmon imaging in air and in water: V(z) curve and operating conditions,” Opt. Lett. 32, 509–511 (2007).
    [CrossRef]
  8. L. Berguiga, E. Boyer-Provera, C. Martinez-Torres, J. Elezgaray, A. Arneodo, and F. Argoul, “Guided wave microscopy: mastering the inverse problem,” Opt. Lett. 38, 4269–4272 (2013).
    [CrossRef]
  9. C. E. H. Berger, R. P. H. Kooyman, and J. Greve, “Resolution in surface plasmon microscopy,” Rev. Sci. Instrum. 65, 2829–2836 (1994).
    [CrossRef]
  10. M. G. Somekh, “Surface plasmon and surface wave microscopy,” in Optical imaging and Microscopy, A. Török and A. Tao, eds., Vol. 87, Springer Series in Optical Sciences (Springer-Verlag, 2003), pp. 275–307.
  11. E. M. Yeatman and E. A. Ash, “Surface plasmon microscopy,” Electron. Lett. 23, 1091–1092 (1987).
    [CrossRef]
  12. B. Rothenhausler and W. Knoll, “Surface-plasmon microscopy,” Nature 332, 615–617 (1988).
    [CrossRef]
  13. K. Belkebir and A. Sentenac, “High-resolution optical diffraction microscopy,” J. Opt. Soc. Am. 20, 1223–1229 (2003).
    [CrossRef]
  14. J. Elezgaray, T. Roland, L. Berguiga, and F. Argoul, “Modeling of the scanning surface plasmon microscope,” J. Opt. Soc. Am. A 27, 450–457 (2010).
    [CrossRef]
  15. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef]
  16. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
    [CrossRef]
  17. T. Roland, L. Berguiga, J. Elezgaray, and F. Argoul, “Scanning surface plasmon imaging of nanoparticles,” Phys. Rev. B 81, 235419 (2010).
    [CrossRef]
  18. J. Elezgaray, L. Berguiga, and F. Argoul, “Optimization of branched resonant nanostructures illuminated by a strongly focused beam,” Appl. Phys. Lett. 97, 243103 (2010).
    [CrossRef]
  19. W. C. Chew and Y. M. Wang, “Efficient ways to compute the vector addition theorem,” J. Electromagn. Waves. Appl. 7, 651–665 (1993).
    [CrossRef]
  20. G. Videen, “Light scattering from a sphere behind a surface,” J. Opt. Soc. Am. 10, 110–117 (1993).
    [CrossRef]
  21. A. Doicu, Y. A. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266–277 (1999).
    [CrossRef]
  22. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 1986).
  23. P. S. Carney and J. C. Schotland, “Theory of total-internal-reflection tomography,” J. Opt. Soc. Am. A 20, 542–547 (2003).
    [CrossRef]

2013

2012

2010

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801(R) (2010).
[CrossRef]

T. Roland, L. Berguiga, J. Elezgaray, and F. Argoul, “Scanning surface plasmon imaging of nanoparticles,” Phys. Rev. B 81, 235419 (2010).
[CrossRef]

J. Elezgaray, L. Berguiga, and F. Argoul, “Optimization of branched resonant nanostructures illuminated by a strongly focused beam,” Appl. Phys. Lett. 97, 243103 (2010).
[CrossRef]

J. Elezgaray, T. Roland, L. Berguiga, and F. Argoul, “Modeling of the scanning surface plasmon microscope,” J. Opt. Soc. Am. A 27, 450–457 (2010).
[CrossRef]

2007

2006

A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
[CrossRef]

2003

P. S. Carney and J. C. Schotland, “Theory of total-internal-reflection tomography,” J. Opt. Soc. Am. A 20, 542–547 (2003).
[CrossRef]

K. Belkebir and A. Sentenac, “High-resolution optical diffraction microscopy,” J. Opt. Soc. Am. 20, 1223–1229 (2003).
[CrossRef]

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

2000

1999

A. Doicu, Y. A. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266–277 (1999).
[CrossRef]

1998

1994

C. E. H. Berger, R. P. H. Kooyman, and J. Greve, “Resolution in surface plasmon microscopy,” Rev. Sci. Instrum. 65, 2829–2836 (1994).
[CrossRef]

1993

W. C. Chew and Y. M. Wang, “Efficient ways to compute the vector addition theorem,” J. Electromagn. Waves. Appl. 7, 651–665 (1993).
[CrossRef]

G. Videen, “Light scattering from a sphere behind a surface,” J. Opt. Soc. Am. 10, 110–117 (1993).
[CrossRef]

1988

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

1987

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

1959

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
[CrossRef]

Argoul, F.

Arneodo, A.

Ash, E. A.

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

Belkebir, K.

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[CrossRef]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801(R) (2010).
[CrossRef]

A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
[CrossRef]

K. Belkebir and A. Sentenac, “High-resolution optical diffraction microscopy,” J. Opt. Soc. Am. 20, 1223–1229 (2003).
[CrossRef]

Berger, C. E. H.

C. E. H. Berger, R. P. H. Kooyman, and J. Greve, “Resolution in surface plasmon microscopy,” Rev. Sci. Instrum. 65, 2829–2836 (1994).
[CrossRef]

Berguiga, L.

Bon, P.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

Boyer-Provera, E.

Carney, P. S.

Chaumet, P. C.

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[CrossRef]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801(R) (2010).
[CrossRef]

A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
[CrossRef]

Chew, W. C.

W. C. Chew and Y. M. Wang, “Efficient ways to compute the vector addition theorem,” J. Electromagn. Waves. Appl. 7, 651–665 (1993).
[CrossRef]

Doicu, A.

A. Doicu, Y. A. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266–277 (1999).
[CrossRef]

Dorn, R.

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

Elezgaray, J.

Eremin, Y. A.

A. Doicu, Y. A. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266–277 (1999).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 1986).

Giovannini, H.

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[CrossRef]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801(R) (2010).
[CrossRef]

Girard, J.

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801(R) (2010).
[CrossRef]

Greve, J.

C. E. H. Berger, R. P. H. Kooyman, and J. Greve, “Resolution in surface plasmon microscopy,” Rev. Sci. Instrum. 65, 2829–2836 (1994).
[CrossRef]

Kano, H.

Kawata, S.

Knoll, W.

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

Kooyman, R. P. H.

C. E. H. Berger, R. P. H. Kooyman, and J. Greve, “Resolution in surface plasmon microscopy,” Rev. Sci. Instrum. 65, 2829–2836 (1994).
[CrossRef]

Leuchs, G.

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

Liu, S.

Maire, G.

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[CrossRef]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801(R) (2010).
[CrossRef]

Martinez-Torres, C.

Mizuguchi, S.

Monneret, S.

Mudry, E.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 1986).

Quabis, S.

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

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
[CrossRef]

Roland, T.

J. Elezgaray, T. Roland, L. Berguiga, and F. Argoul, “Modeling of the scanning surface plasmon microscope,” J. Opt. Soc. Am. A 27, 450–457 (2010).
[CrossRef]

T. Roland, L. Berguiga, J. Elezgaray, and F. Argoul, “Scanning surface plasmon imaging of nanoparticles,” Phys. Rev. B 81, 235419 (2010).
[CrossRef]

Rothenhausler, B.

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

Ruan, Y.

Schotland, J. C.

Sentenac, A.

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[CrossRef]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801(R) (2010).
[CrossRef]

A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
[CrossRef]

K. Belkebir and A. Sentenac, “High-resolution optical diffraction microscopy,” J. Opt. Soc. Am. 20, 1223–1229 (2003).
[CrossRef]

Somekh, M. G.

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

M. G. Somekh, “Surface plasmon and surface wave microscopy,” in Optical imaging and Microscopy, A. Török and A. Tao, eds., Vol. 87, Springer Series in Optical Sciences (Springer-Verlag, 2003), pp. 275–307.

Talneau, A.

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[CrossRef]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801(R) (2010).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 1986).

Velinov, T. S.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 1986).

Videen, G.

G. Videen, “Light scattering from a sphere behind a surface,” J. Opt. Soc. Am. 10, 110–117 (1993).
[CrossRef]

Wang, Y. M.

W. C. Chew and Y. M. Wang, “Efficient ways to compute the vector addition theorem,” J. Electromagn. Waves. Appl. 7, 651–665 (1993).
[CrossRef]

Wattellier, B.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
[CrossRef]

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

Wriedt, T.

A. Doicu, Y. A. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266–277 (1999).
[CrossRef]

Yeatman, E. M.

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

Zhang, S.-J.

Appl. Phys. Lett.

J. Elezgaray, L. Berguiga, and F. Argoul, “Optimization of branched resonant nanostructures illuminated by a strongly focused beam,” Appl. Phys. Lett. 97, 243103 (2010).
[CrossRef]

Electron. Lett.

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

J. Electromagn. Waves. Appl.

W. C. Chew and Y. M. Wang, “Efficient ways to compute the vector addition theorem,” J. Electromagn. Waves. Appl. 7, 651–665 (1993).
[CrossRef]

J. Opt. Soc. Am.

G. Videen, “Light scattering from a sphere behind a surface,” J. Opt. Soc. Am. 10, 110–117 (1993).
[CrossRef]

K. Belkebir and A. Sentenac, “High-resolution optical diffraction microscopy,” J. Opt. Soc. Am. 20, 1223–1229 (2003).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nature

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

Opt. Commun.

A. Doicu, Y. A. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266–277 (1999).
[CrossRef]

Opt. Lett.

Phys. Rev. A

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801(R) (2010).
[CrossRef]

Phys. Rev. B

T. Roland, L. Berguiga, J. Elezgaray, and F. Argoul, “Scanning surface plasmon imaging of nanoparticles,” Phys. Rev. B 81, 235419 (2010).
[CrossRef]

Phys. Rev. Lett.

A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
[CrossRef]

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

Proc. R. Soc. London, Ser. A

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253, 358–379 (1959).
[CrossRef]

Rev. Sci. Instrum.

C. E. H. Berger, R. P. H. Kooyman, and J. Greve, “Resolution in surface plasmon microscopy,” Rev. Sci. Instrum. 65, 2829–2836 (1994).
[CrossRef]

Other

M. G. Somekh, “Surface plasmon and surface wave microscopy,” in Optical imaging and Microscopy, A. Török and A. Tao, eds., Vol. 87, Springer Series in Optical Sciences (Springer-Verlag, 2003), pp. 275–307.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 1986).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Schematic representation of the system: an arbitrary object (here a bead) in a medium with optical index n2 is illuminated by a focused beam, incoming from the objective immersed in an adapting oil medium (index n0), going through a gold layer (index n1), and finally reaching the bead. O denotes the position of the focus.

Fig. 2.
Fig. 2.

Far-field image of two cubes of side 150 nm, separated by 50 nm. The black (resp. red) curves were computed with M1 metallic (resp. dielectric). Continuous (resp. dashed) lines correspond to |R(vl(F))| (resp. |I(vl(F))|), F=(x,0,2) x[0.2,0.2](nm). For each situation, one can distinguish the symmetric and slightly asymmetric cases, corresponding to two cubes with ϵ=2.25 [resp. ϵ=2.25 (left) and ϵ=2 (right)].

Fig. 3.
Fig. 3.

Reconstructed dielectric distribution from two dielectric cubes with ϵ=2 (left) and ϵ=2.25 (right). (b) and (d) [resp. (a) and (c)] have been obtained with M1 being a gold slab [resp. no slab (n1=n0)]. (a) and (b) have been reconstructed with no external noise on the far-field data v(Fl), but different mesh. (c) and (d) have been obtained by reconstruction with the far-field data corrupted by 10% noise. In all cases, θ[42°,45°].

Fig. 4.
Fig. 4.

Reconstructed dielectric distribution from two dielectric cubes one on top of each other, with ϵ=1.5 (upper) and ϵ=2.5 (lower). The incident beam is characterized by θ[10°,50°]. Dashed line: M1 is filled with gold. Continuous line: M1 is made of the same material as M0. Dotted line: n0=n1, but this time θ[40°,50°]. Real values ϵ(x,y,z).

Fig. 5.
Fig. 5.

Reconstructed dielectric distribution from two dielectric cubes, with ϵ=2 (left) and ϵ=2.25 (right). The z coordinate of the center of the two cubes is successively 100nm (continuous line), 200nm (dashed line), and 300nm (dotted line). Thick bars give the real values ϵ(x,y,z).

Fig. 6.
Fig. 6.

(a) Variation of the fb,0(0,0,z) coefficients (real part is the continuous line, imaginary part is the dashed line) as a function of z. Both the case of a metallic (lines) and a dielectric slab (lines+squares) are represented. (b) Variation of the ratio tPb(metal)/tPb(diel) between the trasmittance coefficients for plane waves incident from the M2 region when the slab is either metallic or dielectric.

Equations (19)

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

Einc(X)=dΩ(θ,φ)cos(θ)E0e^ρ(θ,φ)eiK0·XeiK0·F,
K0=kn0(sinθcosφ,sinθsinφ,cosθ),
Eincr(X)=E0cos(θ)e^θrP(θ)eiK0·(XF)eik0z(z2z1+2Fz)dΩ.
Esc(X)=b,n,meb,n,mMn,m3(n2k(Xb))+b,n,mfb,n,mNn,m3(n2k(Xb)).
fb,mb,mTbMm,m(b,b)fb,m=TbRb,m.
Tb2i3(2πλn2rb)3μ21μ2+2,μ=nbn2,
E,0(θ,φ,r)=2πirk0eik0re2ik0(δFz)rP(θ)cosθe^θ.
δE(r,θ,φ)r˜e^θb,meikrikreimφtPb(θ)[τ1|m|fb,m]eiK0Xfb.
V({b},F)=[E,0+δE]·e^θRobjsin(θ)cos(θ)dθdφ.
I0=maxFz|E,0·e^θRobjsin(θ)cos(θ)dθdφ|,
v({b},F)=(V({b},F)V(,F))/I0=b,mVb,mfb,m,
F({Tb})=l|vlm,bVb,mfb,m|2.
φb,mb,mTbMm,m(b,b)φb,m=Rb,m.
F({Tbn})=l|vlim,bVb,m(Tbn1+andbn)φb,m|2.
Rlhln1·m,bVb,m(Fl)*dbn,*φbm*=anl|b,mVb,m(Fl)dbnφb,m|2,
gbn=R(lhln*mVb,m(Fl)φb,m).
dbn=gbn+bgbn(gbngbn1)b|gbn1|2dbn1,
vl(ran)=vl+A(δvRξr+iδvIξi),|ξr|<1,|ξi|<1,A<1,
δE(r,θ,φ)r˜e^θeikrikrmtPb(θ)τ1|m|eimφbTbeiK0Xfb,

Metrics