Abstract

We present a theoretical study of a new highly efficient system for optical light collection, designed for ultrasensitive fluorescence detection of surface-bound molecules. The main core of the system is a paraboloid glass segment acting as a mirror for collecting the fluorescence. A special feature of the system is its ability to sample not only fluorescence that is emitted below the angle of total internal reflection (the critical angle) but also particularly the light above the critical angle. As shown, this is especially advantageous for collecting the fluorescence of surface-bound molecules. A comparison is made with conventional high-aperture microscope objectives. Furthermore, it is shown that the system allows not only for highly efficient light collection but also for confocal imaging of the detection region, which is of great importance for rejecting scattered light in potential applications such as the detection of only a few molecules.

© 1999 Optical Society of America

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References

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  1. R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” in Advances in Chemical Physics, I. Prigogine, S. R. Rice, eds. (Wiley, New York, 1978), pp. 1–65.
  2. W. Lukosz, R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power,” J. Opt. Soc. Am. 67, 1607–1615 (1977).
    [CrossRef]
  3. B. Hecht, D. W. Pohl, H. Heinzelmann, L. Novotny, “’Tunnel’ near-field optical microscopy: TNOM-2,” Ultramicroscopy 61, 99–104 (1995).
    [CrossRef]
  4. A. Sommerfeld, Partielle Differentialgleichungen der Physik (Akademische Verlagsges., Leipzig, 1966), Chaps. 32–33, pp. 226–243.
  5. C. Girard, A. Dereux, “Near-field optics theory,” Rep. Prog. Phys. 59, 657–699 (1996).
    [CrossRef]
  6. C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11,344–11,351 (1994).
    [CrossRef]
  7. J. D. Jackson, “Reflection and refraction of electromagnetic waves at a plane interface between dielectrics,” in Classical Electrodynamics (Wiley, New York, 1975), Chap. 7.3, pp. 278–282.
  8. A. L. Huston, C. T. Reimann, “Photochemical bleaching of absorbed rhodamine 6G as a probe of binding geometries on a fused silica surface,” Chem. Phys. 149, 401–407 (1991).
    [CrossRef]
  9. M. Lieberherr, C. Fattinger, W. Lukosz, “Optical environment-dependent effects on the fluorescence of submonomolecular dye layers on interfaces,” Surf. Sci. 189/190, 954–959 (1987).
    [CrossRef]
  10. R. A. Keller, W. P. Ambrose, P. M. Goodwin, J. H. Jett, J. C. Martin, M. Wu, “Single-molecule fluorescence analysis in solution,” Appl. Spectrosc. 50, 12–32A (1996).
    [CrossRef]
  11. S. W. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
    [CrossRef]

1996 (2)

C. Girard, A. Dereux, “Near-field optics theory,” Rep. Prog. Phys. 59, 657–699 (1996).
[CrossRef]

R. A. Keller, W. P. Ambrose, P. M. Goodwin, J. H. Jett, J. C. Martin, M. Wu, “Single-molecule fluorescence analysis in solution,” Appl. Spectrosc. 50, 12–32A (1996).
[CrossRef]

1995 (1)

B. Hecht, D. W. Pohl, H. Heinzelmann, L. Novotny, “’Tunnel’ near-field optical microscopy: TNOM-2,” Ultramicroscopy 61, 99–104 (1995).
[CrossRef]

1994 (1)

C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11,344–11,351 (1994).
[CrossRef]

1993 (1)

S. W. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

1991 (1)

A. L. Huston, C. T. Reimann, “Photochemical bleaching of absorbed rhodamine 6G as a probe of binding geometries on a fused silica surface,” Chem. Phys. 149, 401–407 (1991).
[CrossRef]

1987 (1)

M. Lieberherr, C. Fattinger, W. Lukosz, “Optical environment-dependent effects on the fluorescence of submonomolecular dye layers on interfaces,” Surf. Sci. 189/190, 954–959 (1987).
[CrossRef]

1977 (1)

Ambrose, W. P.

R. A. Keller, W. P. Ambrose, P. M. Goodwin, J. H. Jett, J. C. Martin, M. Wu, “Single-molecule fluorescence analysis in solution,” Appl. Spectrosc. 50, 12–32A (1996).
[CrossRef]

Chance, R. R.

R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” in Advances in Chemical Physics, I. Prigogine, S. R. Rice, eds. (Wiley, New York, 1978), pp. 1–65.

Cremer, C.

S. W. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Dereux, A.

C. Girard, A. Dereux, “Near-field optics theory,” Rep. Prog. Phys. 59, 657–699 (1996).
[CrossRef]

C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11,344–11,351 (1994).
[CrossRef]

Fattinger, C.

M. Lieberherr, C. Fattinger, W. Lukosz, “Optical environment-dependent effects on the fluorescence of submonomolecular dye layers on interfaces,” Surf. Sci. 189/190, 954–959 (1987).
[CrossRef]

Girard, C.

C. Girard, A. Dereux, “Near-field optics theory,” Rep. Prog. Phys. 59, 657–699 (1996).
[CrossRef]

C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11,344–11,351 (1994).
[CrossRef]

Goodwin, P. M.

R. A. Keller, W. P. Ambrose, P. M. Goodwin, J. H. Jett, J. C. Martin, M. Wu, “Single-molecule fluorescence analysis in solution,” Appl. Spectrosc. 50, 12–32A (1996).
[CrossRef]

Hecht, B.

B. Hecht, D. W. Pohl, H. Heinzelmann, L. Novotny, “’Tunnel’ near-field optical microscopy: TNOM-2,” Ultramicroscopy 61, 99–104 (1995).
[CrossRef]

Heinzelmann, H.

B. Hecht, D. W. Pohl, H. Heinzelmann, L. Novotny, “’Tunnel’ near-field optical microscopy: TNOM-2,” Ultramicroscopy 61, 99–104 (1995).
[CrossRef]

Hell, S. W.

S. W. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Huston, A. L.

A. L. Huston, C. T. Reimann, “Photochemical bleaching of absorbed rhodamine 6G as a probe of binding geometries on a fused silica surface,” Chem. Phys. 149, 401–407 (1991).
[CrossRef]

Jackson, J. D.

J. D. Jackson, “Reflection and refraction of electromagnetic waves at a plane interface between dielectrics,” in Classical Electrodynamics (Wiley, New York, 1975), Chap. 7.3, pp. 278–282.

Jett, J. H.

R. A. Keller, W. P. Ambrose, P. M. Goodwin, J. H. Jett, J. C. Martin, M. Wu, “Single-molecule fluorescence analysis in solution,” Appl. Spectrosc. 50, 12–32A (1996).
[CrossRef]

Keller, R. A.

R. A. Keller, W. P. Ambrose, P. M. Goodwin, J. H. Jett, J. C. Martin, M. Wu, “Single-molecule fluorescence analysis in solution,” Appl. Spectrosc. 50, 12–32A (1996).
[CrossRef]

Kunz, R. E.

Lieberherr, M.

M. Lieberherr, C. Fattinger, W. Lukosz, “Optical environment-dependent effects on the fluorescence of submonomolecular dye layers on interfaces,” Surf. Sci. 189/190, 954–959 (1987).
[CrossRef]

Lukosz, W.

M. Lieberherr, C. Fattinger, W. Lukosz, “Optical environment-dependent effects on the fluorescence of submonomolecular dye layers on interfaces,” Surf. Sci. 189/190, 954–959 (1987).
[CrossRef]

W. Lukosz, R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power,” J. Opt. Soc. Am. 67, 1607–1615 (1977).
[CrossRef]

Martin, J. C.

R. A. Keller, W. P. Ambrose, P. M. Goodwin, J. H. Jett, J. C. Martin, M. Wu, “Single-molecule fluorescence analysis in solution,” Appl. Spectrosc. 50, 12–32A (1996).
[CrossRef]

Novotny, L.

B. Hecht, D. W. Pohl, H. Heinzelmann, L. Novotny, “’Tunnel’ near-field optical microscopy: TNOM-2,” Ultramicroscopy 61, 99–104 (1995).
[CrossRef]

Pohl, D. W.

B. Hecht, D. W. Pohl, H. Heinzelmann, L. Novotny, “’Tunnel’ near-field optical microscopy: TNOM-2,” Ultramicroscopy 61, 99–104 (1995).
[CrossRef]

Prock, A.

R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” in Advances in Chemical Physics, I. Prigogine, S. R. Rice, eds. (Wiley, New York, 1978), pp. 1–65.

Reimann, C. T.

A. L. Huston, C. T. Reimann, “Photochemical bleaching of absorbed rhodamine 6G as a probe of binding geometries on a fused silica surface,” Chem. Phys. 149, 401–407 (1991).
[CrossRef]

Reiner, G.

S. W. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Silbey, R.

R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” in Advances in Chemical Physics, I. Prigogine, S. R. Rice, eds. (Wiley, New York, 1978), pp. 1–65.

Sommerfeld, A.

A. Sommerfeld, Partielle Differentialgleichungen der Physik (Akademische Verlagsges., Leipzig, 1966), Chaps. 32–33, pp. 226–243.

Stelzer, E. H. K.

S. W. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Wu, M.

R. A. Keller, W. P. Ambrose, P. M. Goodwin, J. H. Jett, J. C. Martin, M. Wu, “Single-molecule fluorescence analysis in solution,” Appl. Spectrosc. 50, 12–32A (1996).
[CrossRef]

Appl. Spectrosc. (1)

R. A. Keller, W. P. Ambrose, P. M. Goodwin, J. H. Jett, J. C. Martin, M. Wu, “Single-molecule fluorescence analysis in solution,” Appl. Spectrosc. 50, 12–32A (1996).
[CrossRef]

Chem. Phys. (1)

A. L. Huston, C. T. Reimann, “Photochemical bleaching of absorbed rhodamine 6G as a probe of binding geometries on a fused silica surface,” Chem. Phys. 149, 401–407 (1991).
[CrossRef]

J. Microsc. (1)

S. W. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

Phys. Rev. B (1)

C. Girard, A. Dereux, “Optical spectroscopy of a surface at the nanometer scale: a theoretical study in real space,” Phys. Rev. B 49, 11,344–11,351 (1994).
[CrossRef]

Rep. Prog. Phys. (1)

C. Girard, A. Dereux, “Near-field optics theory,” Rep. Prog. Phys. 59, 657–699 (1996).
[CrossRef]

Surf. Sci. (1)

M. Lieberherr, C. Fattinger, W. Lukosz, “Optical environment-dependent effects on the fluorescence of submonomolecular dye layers on interfaces,” Surf. Sci. 189/190, 954–959 (1987).
[CrossRef]

Ultramicroscopy (1)

B. Hecht, D. W. Pohl, H. Heinzelmann, L. Novotny, “’Tunnel’ near-field optical microscopy: TNOM-2,” Ultramicroscopy 61, 99–104 (1995).
[CrossRef]

Other (3)

A. Sommerfeld, Partielle Differentialgleichungen der Physik (Akademische Verlagsges., Leipzig, 1966), Chaps. 32–33, pp. 226–243.

R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” in Advances in Chemical Physics, I. Prigogine, S. R. Rice, eds. (Wiley, New York, 1978), pp. 1–65.

J. D. Jackson, “Reflection and refraction of electromagnetic waves at a plane interface between dielectrics,” in Classical Electrodynamics (Wiley, New York, 1975), Chap. 7.3, pp. 278–282.

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Figures (8)

Fig. 1
Fig. 1

Geometry of the reflected and transmitted electromagnetic field at the phase boundary dividing regions of different refractive index.

Fig. 2
Fig. 2

(a) Angular distribution of the radiation of an electric dipole with vertical orientation to a surface with refractive index n 1 = 1.33 above the surface and n 2 = 1.5 below it. (b) As in (a) but with n 1 = n 2 = 1.33.

Fig. 3
Fig. 3

(a) Angular distribution of the radiation of an electric dipole with parallel orientation to a surface with refractive index n 1 = 1.33 above the surface and n 2 = 1.5 below it. (b) As in (a) but with n 1 = n 2 = 1.33.

Fig. 4
Fig. 4

Schematic of the paraboloid light collector.

Fig. 5
Fig. 5

(a) Collection efficiency of the paraboloid light collector for a parallel (solid curve) and vertically (dashed curve) oriented dipole positioned on the optical axis at the front face of the paraboloid segment. The dotted line divides the classical light region (emission angle below the critical angle) on the right side from the evanescent light region (emission angle above the critical angle) on the left side. (b) Collection efficiency of a microscope objective for a parallel (solid curve) and vertically (dashed curve) oriented dipole positioned on the optical axis. The dotted line divides the classical light region (emission angle below the critical angle) on the left side from the evanescent light region (emission angle above the critical angle) on the right side.

Fig. 6
Fig. 6

Total emission of a parallel (solid curve) and vertically (dashed curve) oriented dipole into the glass half-space (n 2 = 1.5), depending on its distance from the glass surface. The refractive index of the half-space over the glass surface is equal to n 1 = 1.33 (water).

Fig. 7
Fig. 7

(a) Paths of light rays near the focus of the focusing lens for a fluorescing source on the optical axis and on the front face of the paraboloid segment, with the front face at position z front = -11 µm. (b) As in (a) but with the front face at position z front = -21 µm. (c) As in (a) but with the front face at position z front = -31 µm.

Fig. 8
Fig. 8

Spatial dependence of the CEF for a paraboloid plus lens system as described in the text. The paraboloid front face position is set equal to z front = -21 µm. The CEF is normalized by its maximum value.

Equations (30)

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EDr=1ε1  d3k2π2k2p-kk·pexpik·Rk12-k2,
ED=i2πε1  d2qw1k12p-k1k1·pexpiq·ρ-ρ0+iw1|z-z0|,
Rp=w1ε2-w2ε1w1ε2+w2ε1,  Rs=w1-w2w1+w2,
Tp=2n1n2w1w1ε2+w2ε1,  Ts=2w1w1+w2,
k1k1-k12Iˆ=k12κˆp1κˆp1+κˆsκˆs,
κˆp1=1k1w1ˆq, q,  κˆs=zˆ×qˆ, 0,
ED=ik122πε  d2qw1κˆp1κˆp1·p+κˆsκˆs·p×expiq·ρ-ρ0+iw1|z-z0|.
ER=ik122πε  d2qw1κˆp1Rpκˆp1·p+κˆsRsκˆs·p×expiq·ρ-ρ0+iw1z+z0,
κˆp1=1k1-w1qˆ, q
ET=ik122πε  d2qw1κˆp2Tpκˆp1·p+κˆsTsκˆs·p×expiq·ρ-ρ0+iw1z0+iw2|z|,
κˆp2=1k2w2qˆ, q,
S=c8πReE*×B.
d2SdΩ2=c8πε12k12p-k1k1·p×ck1ω×k12p-k1k1·p=ck028πn1k12p2-k1·p2,
dSdθ=cn1k04p28πsin2 θ,
2π 0π dθ sin θ dSdθ=13 cn1k04p2.
S=cn18π |E|2.
d2S1dΩ12=C1n1k132πε12|κˆp1κˆp1·p+κˆp1Rp expi2w1z0×κˆp1·p+κˆs1+Rs expi2w1z0κˆs·p|2=C1n1k132πε12|κˆp1+Rp expi2w1z0κˆp1·p|2+|1+Rs expi2w1z0κˆs·p|2.
d2qw1k1=dΩ12.
C1n1k144π2ε12=ck028πn1
C1=πc2k12.
d2S2dΩ22=C2n2k12k2w22πε1w12|Tpκˆp1·p|2+|Tsκˆs·p|2×exp-2 Imw1z0,
C2=πc2k22,
dΩ22=d2qk2w2.
d2S1dΩ2=cn1k12p24πε12 q2|1+Rp exp2iw1z0|2, d2S2dΩ2=cn2k12w22p24πε12|w1|2 q2|Tp|2 exp-2 Imw1z0,
d2S1dΩ12=cn1k04p24πw12k12cos2 ϕ|1-Rp|2+sin2 ϕ|1+Rs|2, d2S2dΩ22=cn2k04w22p24π|w1|2|w1|2k12cos2 ϕ|Tp|2+sin2 ϕ|Ts|2×exp-2 Imw1z0.
z=-αx2+y2,  0>zfrontzzrear,
CE=2π π/2θmax dθ sin θd2S2dΩ22,
θmax=π2+arctanzfront-zrear|zrear/α|1/2.
CE=2π θminπ dθ sin θd2S2dΩ22,
θmin=π-arcsinNAng,

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