Abstract

It was recently proposed to put fluorescent molecules at the end of the tip of a scanning near-field optical microscope (SNOM). By measuring lifetime modifications during the tip scanning, one can obtain an image of the sample. We deal with a model of this lifetime SNOM. We propose a theoretical study of the decay rate or the level width of a fluorescent molecule located above a rough interface. When the surface relief is small compared with the wavelength, we determine the electromagnetic decay rate by using a first-order approximation of the Rayleigh–Fano method. Within this approximation the electromagnetic decay rate is composed of two terms: a specular term, which depends only on the distance from the molecule to the sample mean plane, and a diffraction term, which depends on the coordinates of the molecule and on the Fourier transform of the interface profile. It is demonstrated that a kind of linear transfer function can be introduced that connects the Fourier transform of the interface profile to the Fourier transform of the diffraction decay rate. It is independent of the profile but depends on the dielectric constants, on the molecular dipole orientation, and on the molecule–surface distance. We study the properties of this transfer function for a dielectric interface and for various molecular dipole orientations and then present some calculated images. The existence of this transfer function and the good visibility of the calculated images are positive indications for the use of this new kind of SNOM.

© 1999 Optical Society of America

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1998 (2)

D. Van Labeke, F. Baı̈da, J. M. Vigoureux, “A theoretical study of near-field detection and excitation of surface plasmons,” Ultramicroscopy 71, 351–359 (1998).
[CrossRef]

H. Sturmer, J. M. Kohler, T. M. Jovin, “Microstructured polymer tips for scanning near-field optical microscopy,” Ultramicroscopy 71, 107–110 (1998).
[CrossRef]

1997 (5)

1996 (8)

L. Novotny, “Single molecule fluorescence in inhomogeneous environments,” Appl. Phys. Lett. 69, 3806–3808 (1996).
[CrossRef]

D. Barchiesi, “A 3-D multilayer model of scattering by nanostructures: Application to the optimisation of thin coated nano-sources,” Opt. Commun. 126, 7–13 (1996).
[CrossRef]

R. Carminati, J. J. Greffet, N. Garcia, M. Nieto-Vesperinas, “Direct reconstruction of surfaces from near-field intensity under spatially incoherent illumination,” Opt. Lett. 21, 501–503 (1996).
[CrossRef] [PubMed]

J. C. Weeber, F. de Fornel, J. P. Goudonnet, “Numerical study of the tip–sample interaction in the photon scanning tunneling microscope,” Opt. Commun. 126, 285–292 (1996).
[CrossRef]

A. Madrazo, M. Nieto-Vesperinas, “Surface structure and polariton interactions in the scattering of electromagnetic waves from a cylinder in front of a conducting grating: theory for the reflection photon scanning tunneling microscope,” J. Opt. Soc. Am. A 13, 785–795 (1996).
[CrossRef]

D. Barchiesi, C. Girard, O. J. F. Martin, D. Van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[CrossRef]

S. K. Sekatskii, V. S. Letokhov, “Single fluorescent centers on the tips of crystal needles: first observation and prospects for application in scanning one-atom fluorescent microscopy,” Appl. Phys. B: Lasers Opt. 63, 525–530 (1996).
[CrossRef]

A. Dubois, M. Canva, A. Brun, F. Chaput, J.-P. Boilot, “Photostability of dye molecules trapped in solid matrices,” Appl. Opt. 35, 3193–3199 (1996).
[CrossRef] [PubMed]

1995 (8)

A. J. Meixner, D. Zeisel, M. A. Bopp, G. Tarrach, “Super-resolution imaging and detection of fluorescence from single molecules by scanning near-field optical microscopy,” Opt. Eng. (Bellingham) 34, 2324–2332 (1995).
[CrossRef]

J.-J. Greffet, A. Sentenac, R. Carminati, “Surface profile reconstruction using near-field data,” Opt. Commun. 116, 20–24 (1995).
[CrossRef]

D. Barchiesi, D. Van Labeke, “The inverse scanning tunneling near-field microscope (ISTOM) or tunnel scanning near-field optical microscope (TSNOM) 3D simulations and application to nano-sources,” Ultramicroscopy 61, 17–20 (1995).
[CrossRef]

D. Van Labeke, D. Barchiesi, F. Baida, “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am. A 12, 695–703 (1995).
[CrossRef]

D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope (ISTOM),” Opt. Commun. 114, 470–480 (1995).
[CrossRef]

D. Barchiesi, D. Van Labeke, “A perturbative diffraction theory of a multilayer system, applications to near-field optical microscopy SNOM and STOM,” Ultramicroscopy 57, 196–203 (1995).
[CrossRef]

R. X. Bian, R. C. Dunn, X. S. Xie, P. T. Leung, “Single molecule emission characteristics in near-field microscopy,” Phys. Rev. Lett. 75, 4772–4775 (1995).
[CrossRef] [PubMed]

C. Girard, O. J. F. Martin, A. Dereux, “Molecular lifetime changes induced by nanometer scale optical fields,” Phys. Rev. Lett. 75, 3098–3101 (1995).
[CrossRef] [PubMed]

1994 (7)

D. Courjon, C. Bainier, “Near-field microscopy and near-field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

H. F. Hess, E. Betzig, T. D. Harris, L. N. Pfeiffer, K. W. West, “Near-field spectroscopy of the quantum constituents of a luminescent system,” Science 264, 1740–1745 (1994).
[CrossRef] [PubMed]

J. K. Trautman, J. J. Macklin, L. E. Brus, E. Betzig, “Near-field spectroscopy of single molecules at room temperature,” Nature (London) 369, 40–42 (1994).
[CrossRef]

X. S. Xie, R. C. Dunn, “Probing single molecule dynamics,” Science 265, 361–364 (1994).
[CrossRef] [PubMed]

W. P. Ambrose, P. M. Goodwin, J. C. Martin, R. A. Keller, “Alterations of single molecule fluorescence lifetimes in near-field optical microscopy,” Science 265, 364–367 (1994).
[CrossRef] [PubMed]

R. C. Dunn, G. R. Holtom, L. Mets, X. S. Xie, “Near-field fluorescence imaging and fluorescence lifetime measurement of light harvesting complexes in intact photosynthetic membranes,” J. Phys. Chem. 98, 3094–3098 (1994).
[CrossRef]

P. Ambrose, P. M. Goodwin, J. C. Martin, R. A. Keller, “Single molecule detection and photochemistry on a surface using near-field optical excitation,” Phys. Rev. Lett. 72, 160–163 (1994).
[CrossRef] [PubMed]

1993 (2)

E. Betzig, R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1993).
[CrossRef] [PubMed]

D. Van Labeke, D. Barchiesi, “Probes for scanning tunneling optical microscopy: a theoretical comparison,” J. Opt. Soc. Am. A 10, 2193–2201 (1993).
[CrossRef]

1992 (1)

1991 (1)

A. Lewis, K. Lieberman, “Near-field optical imaging with a non-evanescently excited high-brightness light source of sub-wavelength dimensions,” Nature (London) 354, 214–216 (1991).
[CrossRef]

1990 (1)

K. Lieberman, S. Harush, A. Lewis, R. Kopelman, “A light source smaller than the optical wavelength,” Science 24, 59–61 (1990).
[CrossRef]

1988 (1)

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[CrossRef] [PubMed]

1987 (2)

P. T. Leung, Z. C. Wu, D. A. Jelski, T. F. George, “Molecular lifetime in the presence of periodically roughened metallic surfaces,” Phys. Rev. B 36, 1475–1479 (1987).
[CrossRef]

P. T. Leung, T. F. George, “Energy-transfer theory for the classical decay rates of molecules at rough metallic surfaces,” Phys. Rev. B 36, 4664–4671 (1987).
[CrossRef]

1986 (1)

W. Ekardt, Z. Penzar, “Nonradiative lifetime of excited states near a small metal particle,” Phys. Rev. B 34, 8444–8448 (1986).
[CrossRef]

1984 (1)

J. M. Wylie, J. E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A 30, 1185–1193 (1984).
[CrossRef]

1982 (2)

R. Rossetti, L. E. Brus, “Time resolved energy transfer from electronically excited B3U pyrazine molecules to planar Ag and Au surfaces,” J. Chem. Phys. 76, 1146–1149 (1982).
[CrossRef]

R. Ruppin, “Decay of an excited molecule near a small metal sphere,” J. Chem. Phys. 76, 1681–1687 (1982).
[CrossRef]

1981 (1)

J. Gersten, A. Nitzan, “Spectroscopic properties of molecules interacting with small dielectric particles,” J. Chem. Phys. 75, 1139–1152 (1981).
[CrossRef]

1980 (3)

A. Adams, R. W. Rendell, W. P. West, H. P. Broida, P. K. Hansma, H. Metiu, “Luminescence and nonradiative energy transfer to surfaces,” Phys. Rev. B 21, 5565–5571 (1980).
[CrossRef]

A. Campion, A. R. Gallo, C. B. Harris, H. J. Robota, P. M. Whitmore, “Electronic energy transfer to metal surfaces: a test of classical image dipole theory at short distances,” Chem. Phys. Lett. 73, 447–450 (1980).
[CrossRef]

P. K. Aravind, H. Metiu, “The enhancement of Raman and fluorescent intensity by small surface roughness. Changes in dipole emission,” Chem. Phys. Lett. 74, 301–305 (1980).
[CrossRef]

1977 (1)

W. Lukosz, R. E. Kunz, “Fluorescence lifetime of magnetic and electric dipoles near a dielectric interface,” Opt. Commun. 20, 195–199 (1977).
[CrossRef]

1975 (5)

G. S. Agarwal, “Quantum electrodynamics in the presence of dielectrics and conductors. IV. General theory for spontaneous emission in finite geometries,” Phys. Rev. A 12, 1475–1497 (1975).
[CrossRef]

G. S. Agarwal, “Quantum electrodynamics in the presence of dielectrics and conductors. I. Electromagnetic-field response functions and black-body fluctuations in finite geometries,” Phys. Rev. A 11, 230–242 (1975).
[CrossRef]

M. R. Philpott, “Effect of surface plasmons on transitions in molecules,” J. Chem. Phys. 62, 1812–1817 (1975).
[CrossRef]

R. R. Chance, A. H. Miller, A. Prock, R. Silbey, “Fluorescence and energy transfer near interfaces: the complete and quantitative description of the Eu+3 mirror systems,” J. Chem. Phys. 63, 1589–1595 (1975).
[CrossRef]

R. R. Chance, A. H. Miller, A. Prock, R. Silbey, “Luminescent lifetimes near multiple interfaces: a quantitative comparison of theory and experiment,” Chem. Phys. Lett. 33, 590–592 (1975).
[CrossRef]

1974 (1)

R. R. Chance, A. Prock, R. Silbey, “Lifetime of an emitting molecule near a partially reflecting surface,” J. Chem. Phys. 60, 2744–2748 (1974).
[CrossRef]

Adams, A.

A. Adams, R. W. Rendell, W. P. West, H. P. Broida, P. K. Hansma, H. Metiu, “Luminescence and nonradiative energy transfer to surfaces,” Phys. Rev. B 21, 5565–5571 (1980).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, “Quantum electrodynamics in the presence of dielectrics and conductors. IV. General theory for spontaneous emission in finite geometries,” Phys. Rev. A 12, 1475–1497 (1975).
[CrossRef]

G. S. Agarwal, “Quantum electrodynamics in the presence of dielectrics and conductors. I. Electromagnetic-field response functions and black-body fluctuations in finite geometries,” Phys. Rev. A 11, 230–242 (1975).
[CrossRef]

Ambrose, P.

P. Ambrose, P. M. Goodwin, J. C. Martin, R. A. Keller, “Single molecule detection and photochemistry on a surface using near-field optical excitation,” Phys. Rev. Lett. 72, 160–163 (1994).
[CrossRef] [PubMed]

Ambrose, W. P.

W. P. Ambrose, P. M. Goodwin, J. C. Martin, R. A. Keller, “Alterations of single molecule fluorescence lifetimes in near-field optical microscopy,” Science 265, 364–367 (1994).
[CrossRef] [PubMed]

Aravind, P. K.

P. K. Aravind, H. Metiu, “The enhancement of Raman and fluorescent intensity by small surface roughness. Changes in dipole emission,” Chem. Phys. Lett. 74, 301–305 (1980).
[CrossRef]

Bai¨da, F.

D. Van Labeke, F. Baı̈da, J. M. Vigoureux, “A theoretical study of near-field detection and excitation of surface plasmons,” Ultramicroscopy 71, 351–359 (1998).
[CrossRef]

Baida, F.

D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope (ISTOM),” Opt. Commun. 114, 470–480 (1995).
[CrossRef]

D. Van Labeke, D. Barchiesi, F. Baida, “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am. A 12, 695–703 (1995).
[CrossRef]

Bainier, C.

D. Courjon, C. Bainier, “Near-field microscopy and near-field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

Barchiesi, D.

D. Barchiesi, “A 3-D multilayer model of scattering by nanostructures: Application to the optimisation of thin coated nano-sources,” Opt. Commun. 126, 7–13 (1996).
[CrossRef]

D. Barchiesi, C. Girard, O. J. F. Martin, D. Van Labeke, D. Courjon, “Computing the optical near-field distributions around complex subwavelength surface structures: a comparative study of different methods,” Phys. Rev. E 54, 4285–4292 (1996).
[CrossRef]

D. Van Labeke, F. Baida, D. Barchiesi, D. Courjon, “A theoretical model for the inverse scanning tunneling optical microscope (ISTOM),” Opt. Commun. 114, 470–480 (1995).
[CrossRef]

D. Barchiesi, D. Van Labeke, “The inverse scanning tunneling near-field microscope (ISTOM) or tunnel scanning near-field optical microscope (TSNOM) 3D simulations and application to nano-sources,” Ultramicroscopy 61, 17–20 (1995).
[CrossRef]

D. Van Labeke, D. Barchiesi, F. Baida, “Optical characterization of nanosources used in scanning near-field optical microscopy,” J. Opt. Soc. Am. A 12, 695–703 (1995).
[CrossRef]

D. Barchiesi, D. Van Labeke, “A perturbative diffraction theory of a multilayer system, applications to near-field optical microscopy SNOM and STOM,” Ultramicroscopy 57, 196–203 (1995).
[CrossRef]

D. Van Labeke, D. Barchiesi, “Probes for scanning tunneling optical microscopy: a theoretical comparison,” J. Opt. Soc. Am. A 10, 2193–2201 (1993).
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W. P. Ambrose, P. M. Goodwin, J. C. Martin, R. A. Keller, “Alterations of single molecule fluorescence lifetimes in near-field optical microscopy,” Science 265, 364–367 (1994).
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[CrossRef]

P. T. Leung, T. F. George, “Energy-transfer theory for the classical decay rates of molecules at rough metallic surfaces,” Phys. Rev. B 36, 4664–4671 (1987).
[CrossRef]

W. L. Blacke, P. T. Leung, “Molecular fluorescence at a rough surface: the orientation effects,” Phys. Rev. B 56, 12625–12631 (1997).
[CrossRef]

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Phys. Rev. E (1)

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H. F. Hess, E. Betzig, T. D. Harris, L. N. Pfeiffer, K. W. West, “Near-field spectroscopy of the quantum constituents of a luminescent system,” Science 264, 1740–1745 (1994).
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[CrossRef] [PubMed]

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[CrossRef]

D. Van Labeke, F. Baı̈da, J. M. Vigoureux, “A theoretical study of near-field detection and excitation of surface plasmons,” Ultramicroscopy 71, 351–359 (1998).
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D. Barchiesi, T. Pagnot, C. Pieralli, D. Van Labeke, “Fluorescence scanning near-field microscopy (FSNOM) by measuring the decay-time of a fluorescent particle,” in Scanning Probe Microscopies III, M. Vaez-Iravani, ed., Proc. SPIE2384, 90–100 (1995).
[CrossRef]

D. Van Labeke, Ph. Grossel, J. M. Vigoureux, “Decay of an excited molecule near small roughness,” in Optical Storage and Scanning Technology, T. Wilson, ed., Proc. SPIE1139, 73–75 (1989).
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Figures (9)

Fig. 1
Fig. 1

Geometry of the problem. The molecule is modeled by its transition moment M. The molecule is in medium 1, the dielectric constant of which is 1, and is above medium 2, the dielectric constant of which is 2.

Fig. 2
Fig. 2

Variations of the reduced lifetime versus the distance z0 for a dipole in air above a glass surface. (a) Dipole parallel to the surface, (b) dipole perpendicular to the surface.

Fig. 3
Fig. 3

Variations of the filtering function versus k for a dipole perpendicular to a glass surface: zr=zA(2π/λ)=0.3 (solid curve), zr=0.5 (dashed curve), zr=0.7 (dotted–dashed curve), zr=1 (dotted curve).

Fig. 4
Fig. 4

Variations of the filtering function versus k for a dipole parallel to a glass surface: zr=zA(2π/λ)=0.3 (solid curve), zr=0.5 (dashed curve), zr=0.7 (dotted–dashed curve), zr=1 (dotted curve). (a) Dipole parallel to k, (b) dipole perpendicular to k.

Fig. 5
Fig. 5

2D variations of the filtering function versus k for a dipole parallel to a glass surface with zr=0.5.

Fig. 6
Fig. 6

Geometry of the object: five square-shaped glass (2=2.25) dots with 10-nm height. The width of the squares and the gap between them are given by the parameter d.

Fig. 7
Fig. 7

Gray-level representation of the reduced level width Γ/Γ0 obtained with a perpendicular dipole above the object described in Fig. 6. (a) d=200 nm, zA=50 nm; (b) d=100 nm, zA=50 nm; (c) d=200 nm, zA=30 nm; (d) d=100 nm, zA=30 nm.

Fig. 8
Fig. 8

Gray-level representation of the reduced level width Γ/Γ0 obtained with a parallel dipole above the object described in Fig. 6 (the arrow indicates the orientation of the dipole). (a) d=200 nm, zA=50 nm; (b) d=100 nm, zA=50 nm; (c) d=200 nm, zA=30 nm; (d) d=100 nm, zA=30 nm.

Fig. 9
Fig. 9

Normalized lifetime τ/(τ0+τsp) variations for a scan in the x direction above a glass disk-shaped dot of 100-nm diameter and 40-nm height. The altitude of the scan is 50 nm above the surface, i.e., 10 nm above the dot (x is in nanometers). (a) Dipole along the z axis, (b) dipole along the y axis, (c) dipole along the x axis.

Equations (35)

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P(x, y)=P(r)=14π2-+P(k)exp(ik·r)dk.
Γ=1τ=Γi+ΓEM=Γi+Im[M·G(RA, RA, ω)·M],
ΓEM=Im[M·E(RA)].
[G0(R, RA, ω)]i,j=11ij+1ω2c2δij×exp(i1ωc|R-RA|)|R-RA|.
Γ0=231ω3c3|M|2.
Einc(R)=G0(R, RA, ω)·M.
Einc(R)=14π2-+Einc(k)exp{i[k·r-zw1(k)]}dk,
E1(R)=14π2-+E1(k)exp{i[k·r+zw1(k)]}dk,
E2(R)=14π2-+E2(k)exp{i[k·r-zw2(k)]}dk.
w1(k)=1ω2c2-u2-v21/2,
w2(k)=2ω2c2-u2-v21/2.
expi1ωc|R-RA||R-RA|
=i2π-+dkw1(k)exp[ik·(r-rA)+i|z-zA|w1(k)].
Einc(k)=exp[-ik·rA+izA·w1(k)]G(k)·M,
G(k)=2iπ1w1(k)1ω2c2-u2-uvuw1(k)-uv1ω2c2-v2vw1(k)uw1(k)vw1(k)k2.
exp[iP(r)w1(k)]1+iP(r)w1(k).
E1(k)=Er(k)+Ed1(k),
E2(k)=Et(k)+Ed2(k).
Er(k)=R(k)·Einc(k),
Et(k)=T(k)·Einc(k),
R(k)=2w1(k)w1(k)+w2(k)02uw1(k)(2-1)[2w1(k)+1w2(k)][w1(k)+w2(k)]02w1(k)w1(k)+w2(k)2vw1(k)(2-1)[2w1(k)+1w2(k)][w1(k)+w2(k)]0021w1(k)2w1(k)+1w2(k),
T(k)=w1(k)-w2(k)w1(k)+w2(k)02uw1(k)(2-1)[2w1(k)+1w2(k)][w1(k)+w2(k)]0w1(k)-w2(k)w1(k)+w2(k)2vw1(k)(2-1)[2w1(k)+1w2(k)][w1(k)+w2(k)]002w1(k)-1w2(k)2w1(k)+1w2(k).
Ed1(k)=i1-24π2P(k-k0)D1(k)·T(k0)·Einc(k0)dk0,
D1(k)=12w1(k)+1w2(k)-v2-w1(k)w2(k)uv21uw1(k)uv-u2-w1(k)w2(k)21vw1(k)uw2(k)vw2(k)-21k2.
Γ=Γi+Γ0+Γsp(zA)+ΓD1(RA).
Γsp(zA)=3Γ021Re0exp2iωcμ1(κ)zAμ1(κ)1×κ32μ1(κ)-1μ2(κ)2μ1(κ)+1μ2(κ)dκ,
κ=kcω,μα=wα(k)cω=α-κ2(α=1, 2).
Γsp(zA)=3Γ021Re0κ exp2iωcμ1(κ)zAμ1(κ)1×κ21-21μ1(k)2μ1(κ)+1μ2(κ)-21μ2(κ)-μ1(κ)μ2(κ)+μ1(κ)dκ.
ΓD1(RA)=14π2Im-+M·ED1(k)exp{i[k·rA+zAw1(k)]}dk,
ED1(k)=i1-24π2-+ exp[-ik0·rA+iw1(k0)zA]×P(k-k0)D1(k)·T(k0)·G(k0)·M dk0.
ΓD1(RA)=Im14π2-+dk0 exp(+ik0·rA)×P(k0)Fˆ(k0, zA),
Fˆ(k0, zA)=i1-24π2-+dk×[M·D(k)·T(k-k0)·G(k-k0)·M]×exp{i[w1(k)+w1(k-k0)]zA}.
ΓD1(RA)=14π2-+dk0 exp(+ik0·rA)×P(k0)F(k0, zA),
F(k0, zA)=cos2(θ)F1(k0, zA)+sin2(θ)F2(k0, zA),
I(r, z)=|E(r, z)|2=|E0(r, z)+Ediff(r, z)|2|E0(r, z)|2+2 Re[E0(r, z)·Ediff(r, z)]

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