Abstract

We investigate the inverse-scattering problem that arises in total internal reflection microscopy. An analytic solution to this problem within the weak-scattering approximation is used to develop a novel form of three-dimensional microscopy with subwavelength resolution.

© 2001 Optical Society of America

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References

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  1. M. A. Paesler and P. J. Moyer, Near Field Optics (Wiley, New York, 1996).
  2. D. Courjon and C. Bainier, Rep. Prog. Phys. 57, 989 (1994).
    [CrossRef]
  3. C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
    [CrossRef]
  4. E. Betzig and J. K. Trautman, Science 257, 189 (1992).
    [CrossRef] [PubMed]
  5. C. W. McCutchen, Rev. Sci. Instrum. 35, 1340 (1964).
    [CrossRef]
  6. P. A. Temple, Appl. Opt. 20, 2656 (1981).
    [CrossRef] [PubMed]
  7. D. Van Labeke and D. Barchiesi, J. Opt. Soc. Am. A 9, 732 (1992).
    [CrossRef]
  8. R. Carminati and J. Greffet, Opt. Commun. 116, 316 (1995).
    [CrossRef]
  9. R. Carminati and J. Greffet, J. Opt. Soc. Am. A 12, 2716 (1995).
    [CrossRef]
  10. P. S. Carney and J. C. Schotland, Appl. Phys. Lett. 77, 2798 (2000).
    [CrossRef]
  11. D. G. Fischer, J. Mod. Opt. 47, 1359 (2000).
    [CrossRef]
  12. D. G. Fischer, Opt. Lett. 25, 1529 (2000).
    [CrossRef]
  13. The coefficient Al is given by the expression Al=ibl/[k0(bl-igl)] with bl=jl(nk0a) jl (k0a)-njl(nk0a)jl(k0a) and gl=njl(nk0a)nl(k0a)-jl(nk0× a)nl(k0a).
  14. R. Carminati, M. Nieto-Vesperinas, and J. Greffet, J. Opt. Soc. Am. A 15, 706 (1998).
    [CrossRef]

2000

P. S. Carney and J. C. Schotland, Appl. Phys. Lett. 77, 2798 (2000).
[CrossRef]

D. G. Fischer, J. Mod. Opt. 47, 1359 (2000).
[CrossRef]

D. G. Fischer, Opt. Lett. 25, 1529 (2000).
[CrossRef]

1998

1996

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

1995

R. Carminati and J. Greffet, Opt. Commun. 116, 316 (1995).
[CrossRef]

R. Carminati and J. Greffet, J. Opt. Soc. Am. A 12, 2716 (1995).
[CrossRef]

1994

D. Courjon and C. Bainier, Rep. Prog. Phys. 57, 989 (1994).
[CrossRef]

1992

1981

1964

C. W. McCutchen, Rev. Sci. Instrum. 35, 1340 (1964).
[CrossRef]

Bainier, C.

D. Courjon and C. Bainier, Rep. Prog. Phys. 57, 989 (1994).
[CrossRef]

Barchiesi, D.

Betzig, E.

E. Betzig and J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Carminati, R.

Carney, P. S.

P. S. Carney and J. C. Schotland, Appl. Phys. Lett. 77, 2798 (2000).
[CrossRef]

Courjon, D.

D. Courjon and C. Bainier, Rep. Prog. Phys. 57, 989 (1994).
[CrossRef]

Dereux, A.

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

Fischer, D. G.

D. G. Fischer, J. Mod. Opt. 47, 1359 (2000).
[CrossRef]

D. G. Fischer, Opt. Lett. 25, 1529 (2000).
[CrossRef]

Girard, C.

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

Greffet, J.

McCutchen, C. W.

C. W. McCutchen, Rev. Sci. Instrum. 35, 1340 (1964).
[CrossRef]

Moyer, P. J.

M. A. Paesler and P. J. Moyer, Near Field Optics (Wiley, New York, 1996).

Nieto-Vesperinas, M.

Paesler, M. A.

M. A. Paesler and P. J. Moyer, Near Field Optics (Wiley, New York, 1996).

Schotland, J. C.

P. S. Carney and J. C. Schotland, Appl. Phys. Lett. 77, 2798 (2000).
[CrossRef]

Temple, P. A.

Trautman, J. K.

E. Betzig and J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Van Labeke, D.

Appl. Opt.

Appl. Phys. Lett.

P. S. Carney and J. C. Schotland, Appl. Phys. Lett. 77, 2798 (2000).
[CrossRef]

J. Mod. Opt.

D. G. Fischer, J. Mod. Opt. 47, 1359 (2000).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

R. Carminati and J. Greffet, Opt. Commun. 116, 316 (1995).
[CrossRef]

Opt. Lett.

Rep. Prog. Phys.

D. Courjon and C. Bainier, Rep. Prog. Phys. 57, 989 (1994).
[CrossRef]

C. Girard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996).
[CrossRef]

Rev. Sci. Instrum.

C. W. McCutchen, Rev. Sci. Instrum. 35, 1340 (1964).
[CrossRef]

Science

E. Betzig and J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Other

M. A. Paesler and P. J. Moyer, Near Field Optics (Wiley, New York, 1996).

The coefficient Al is given by the expression Al=ibl/[k0(bl-igl)] with bl=jl(nk0a) jl (k0a)-njl(nk0a)jl(k0a) and gl=njl(nk0a)nl(k0a)-jl(nk0× a)nl(k0a).

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Figures (3)

Fig. 1
Fig. 1

Illustration of the measurement scheme. Evanescent waves are generated at the prism face by total internal reflection. The total internal reflection is then partly frustrated by the presence of the scatterer, scattering evanescent modes to the homogeneous mode that propagate to the far zone.

Fig. 2
Fig. 2

Reconstructed tomographs of the real and imaginary parts of the susceptibility with a prism of refractive index n=10. The signal-to-noise ratio is given in decibels above each column. The images were plotted with the linear color scale indicated to the right. The field of view in each image is λ×λ.

Fig. 3
Fig. 3

Reconstructed tomographs of the real and imaginary parts of the susceptibility with a prism of refractive index n=4. All other parameters are as indicated in Fig.  2.

Equations (11)

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

2Ur+k02Ur=-4πk02ηrUr,
Ur=Uir+k02d3rGr,rUrηr,
Gr,r=expik0r-rr-r,
Usr=k02d3rGr,rUirηr.
Usrexpik0rrAq1,q2,
Aq1,q2=k02d3rexpik1q1-k2q2·rηr,
Aq1,q2=k02d3rKq2,z;q1-q2×expiq1-q2·ρηr,
Kq,z;Q=expikzQ+q-kzqzχq,Q+q,
ηr=1k022π2d2Qexp-iQ·ρd2qd2q×K*q,z;QM-1q,q;Qχq,Q+qAq,Q+q.
Mq,q;Q=0LKq,z;QK*q,z;Qdz.
Ak1,k2=expik1-k2·r0l=02l+1AlPlk^1·k^2,

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