Abstract

In our previous paper [J. Opt. Soc. Am. A 15, 101 (1998)], the integral equations that are suitable for simulations of near-field optics with use of an uncoated dielectric probe were proposed. We extend the integral equations to near-field optical circuits by using a metal-coated dielectric probe with an aperture. The derivation of the integral equations is described in detail for the incident TM mode, because it is impossible to derive them with the same procedures as those used in the case of the uncoated dielectric probe. Simulations of the illumination/collection mode of a two-dimensional scanning near-field optical microscope (2D-SNOM) are performed. All numerical results satisfy the energy conservation law within an accuracy of 1%. One-dimensional scanning images of a 2D-SNOM obtained by using the metal-coated dielectric probe with an aperture and those obtained by using the uncoated dielectric probe are compared, and advantages of the metal-coated dielectric probe are described.

© 2001 Optical Society of America

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References

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  1. J. P. Fillard, Near-Field Optics and Nanoscopy (World Scientific, Singapore, 1996).
  2. M. A. Paesler, P. J. Moyer, Near-Field Optics Theory, Instrumentation and Applications (Wiley-Interscience, New York, 1996).
  3. M. Tanaka, K. Tanaka, “Boundary integral equations for computer aided design of near-field optics,” Trans. Inst. Electron. Inf. Commun. Eng. Jpn. J79-C-I, 101–108 (1996) (in Japanese).
  4. M. Tanaka, K. Tanaka, “Boundary integral equations for computer-aided design and simulations of near-field optics: two-dimensional optical manipulator,” J. Opt. Soc. Am. A 15, 101–108 (1998).
    [CrossRef]
  5. K. Tanaka, M. Tanaka, T. Omoya, “Boundary integral equations for a two-dimensional simulator of a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 15, 1918–1931 (1998).
    [CrossRef]
  6. K. Tanaka, M. Tanaka, K. Katayama, “Simulations of two-dimensional photon scanning tunneling microscope by boundary integral equation method: p-polarization,” Opt. Rev. 6, 249–256 (1999).
    [CrossRef]
  7. A. Roberts, “Small-hole coupling of radiation into a near-field probe,” J. Appl. Phys. 70, 4045–4049 (1991).
    [CrossRef]
  8. L. Novotny, D. W. Pohl, P. Regli, “Light propagation through nanometer-sized structures: the two-dimensional-aperture scanning near-field optical microscope,” J. Opt. Soc. Am. A 11, 1768–1779 (1994).
    [CrossRef]
  9. J. L. Kann, T. D. Milster, F. F. Froehlich, R. W. Ziolkowski, J. B. Judkins, “Linear behavior of a near-field optical scanning system,” J. Opt. Soc. Am. A 12, 1677–1682 (1995).
    [CrossRef]
  10. D. Von Labeke, D. Barchiesi, “Scanning-tunneling optical microscopy: a theoretical macroscopic approach,” J. Opt. Soc. Am. A 9, 732–739 (1992).
    [CrossRef]
  11. D. Von Labeke, D. Barchiese, “Probes for scanning tunneling optical microscopy: a theoretical comparison,” J. Opt. Soc. Am. A 10, 2193–2201 (1993).
    [CrossRef]
  12. A. Castiaux, A. Dereux, J. Vigneron, C. Girard, O. Martin, “Electromagnetic fields in two-dimensional models of near-field optical microscope tips,” Ultramicroscopy 60, 1–9 (1995).
    [CrossRef]
  13. A. Castiaux, Ch. Girard, M. Spajer, S. Davy, “Near-field optical effects inside a photosensitive sample coupled,” Ultramicroscopy 71, 49–58 (1998).
    [CrossRef]
  14. R. Carminati, J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope. Concept of transfer function.” Opt. Commun. 116, 316–321 (1995).
    [CrossRef]
  15. S. Berntsen, E. Bozhevolnarya, S. Bozhevolnyi, “Macroscopic self-consistent model for external-reflection near-field microscopy,” J. Opt. Soc. Am. A 10, 878–885 (1993).
    [CrossRef]
  16. M. Tanaka, K. Tanaka, “Simulation of near-field optical manipulator by boundary element method—aperture-probe coated with metal,” Inst. Electron. Inf. Commun. Eng. Jpn. J82-C-I, 468–476 (1999) (in Japanese).

1999 (2)

K. Tanaka, M. Tanaka, K. Katayama, “Simulations of two-dimensional photon scanning tunneling microscope by boundary integral equation method: p-polarization,” Opt. Rev. 6, 249–256 (1999).
[CrossRef]

M. Tanaka, K. Tanaka, “Simulation of near-field optical manipulator by boundary element method—aperture-probe coated with metal,” Inst. Electron. Inf. Commun. Eng. Jpn. J82-C-I, 468–476 (1999) (in Japanese).

1998 (3)

1996 (1)

M. Tanaka, K. Tanaka, “Boundary integral equations for computer aided design of near-field optics,” Trans. Inst. Electron. Inf. Commun. Eng. Jpn. J79-C-I, 101–108 (1996) (in Japanese).

1995 (3)

J. L. Kann, T. D. Milster, F. F. Froehlich, R. W. Ziolkowski, J. B. Judkins, “Linear behavior of a near-field optical scanning system,” J. Opt. Soc. Am. A 12, 1677–1682 (1995).
[CrossRef]

R. Carminati, J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope. Concept of transfer function.” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

A. Castiaux, A. Dereux, J. Vigneron, C. Girard, O. Martin, “Electromagnetic fields in two-dimensional models of near-field optical microscope tips,” Ultramicroscopy 60, 1–9 (1995).
[CrossRef]

1994 (1)

1993 (2)

1992 (1)

1991 (1)

A. Roberts, “Small-hole coupling of radiation into a near-field probe,” J. Appl. Phys. 70, 4045–4049 (1991).
[CrossRef]

Barchiese, D.

Barchiesi, D.

Berntsen, S.

Bozhevolnarya, E.

Bozhevolnyi, S.

Carminati, R.

R. Carminati, J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope. Concept of transfer function.” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

Castiaux, A.

A. Castiaux, Ch. Girard, M. Spajer, S. Davy, “Near-field optical effects inside a photosensitive sample coupled,” Ultramicroscopy 71, 49–58 (1998).
[CrossRef]

A. Castiaux, A. Dereux, J. Vigneron, C. Girard, O. Martin, “Electromagnetic fields in two-dimensional models of near-field optical microscope tips,” Ultramicroscopy 60, 1–9 (1995).
[CrossRef]

Davy, S.

A. Castiaux, Ch. Girard, M. Spajer, S. Davy, “Near-field optical effects inside a photosensitive sample coupled,” Ultramicroscopy 71, 49–58 (1998).
[CrossRef]

Dereux, A.

A. Castiaux, A. Dereux, J. Vigneron, C. Girard, O. Martin, “Electromagnetic fields in two-dimensional models of near-field optical microscope tips,” Ultramicroscopy 60, 1–9 (1995).
[CrossRef]

Fillard, J. P.

J. P. Fillard, Near-Field Optics and Nanoscopy (World Scientific, Singapore, 1996).

Froehlich, F. F.

Girard, C.

A. Castiaux, A. Dereux, J. Vigneron, C. Girard, O. Martin, “Electromagnetic fields in two-dimensional models of near-field optical microscope tips,” Ultramicroscopy 60, 1–9 (1995).
[CrossRef]

Girard, Ch.

A. Castiaux, Ch. Girard, M. Spajer, S. Davy, “Near-field optical effects inside a photosensitive sample coupled,” Ultramicroscopy 71, 49–58 (1998).
[CrossRef]

Greffet, J.

R. Carminati, J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope. Concept of transfer function.” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

Judkins, J. B.

Kann, J. L.

Katayama, K.

K. Tanaka, M. Tanaka, K. Katayama, “Simulations of two-dimensional photon scanning tunneling microscope by boundary integral equation method: p-polarization,” Opt. Rev. 6, 249–256 (1999).
[CrossRef]

Martin, O.

A. Castiaux, A. Dereux, J. Vigneron, C. Girard, O. Martin, “Electromagnetic fields in two-dimensional models of near-field optical microscope tips,” Ultramicroscopy 60, 1–9 (1995).
[CrossRef]

Milster, T. D.

Moyer, P. J.

M. A. Paesler, P. J. Moyer, Near-Field Optics Theory, Instrumentation and Applications (Wiley-Interscience, New York, 1996).

Novotny, L.

Omoya, T.

Paesler, M. A.

M. A. Paesler, P. J. Moyer, Near-Field Optics Theory, Instrumentation and Applications (Wiley-Interscience, New York, 1996).

Pohl, D. W.

Regli, P.

Roberts, A.

A. Roberts, “Small-hole coupling of radiation into a near-field probe,” J. Appl. Phys. 70, 4045–4049 (1991).
[CrossRef]

Spajer, M.

A. Castiaux, Ch. Girard, M. Spajer, S. Davy, “Near-field optical effects inside a photosensitive sample coupled,” Ultramicroscopy 71, 49–58 (1998).
[CrossRef]

Tanaka, K.

K. Tanaka, M. Tanaka, K. Katayama, “Simulations of two-dimensional photon scanning tunneling microscope by boundary integral equation method: p-polarization,” Opt. Rev. 6, 249–256 (1999).
[CrossRef]

M. Tanaka, K. Tanaka, “Simulation of near-field optical manipulator by boundary element method—aperture-probe coated with metal,” Inst. Electron. Inf. Commun. Eng. Jpn. J82-C-I, 468–476 (1999) (in Japanese).

M. Tanaka, K. Tanaka, “Boundary integral equations for computer-aided design and simulations of near-field optics: two-dimensional optical manipulator,” J. Opt. Soc. Am. A 15, 101–108 (1998).
[CrossRef]

K. Tanaka, M. Tanaka, T. Omoya, “Boundary integral equations for a two-dimensional simulator of a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 15, 1918–1931 (1998).
[CrossRef]

M. Tanaka, K. Tanaka, “Boundary integral equations for computer aided design of near-field optics,” Trans. Inst. Electron. Inf. Commun. Eng. Jpn. J79-C-I, 101–108 (1996) (in Japanese).

Tanaka, M.

K. Tanaka, M. Tanaka, K. Katayama, “Simulations of two-dimensional photon scanning tunneling microscope by boundary integral equation method: p-polarization,” Opt. Rev. 6, 249–256 (1999).
[CrossRef]

M. Tanaka, K. Tanaka, “Simulation of near-field optical manipulator by boundary element method—aperture-probe coated with metal,” Inst. Electron. Inf. Commun. Eng. Jpn. J82-C-I, 468–476 (1999) (in Japanese).

M. Tanaka, K. Tanaka, “Boundary integral equations for computer-aided design and simulations of near-field optics: two-dimensional optical manipulator,” J. Opt. Soc. Am. A 15, 101–108 (1998).
[CrossRef]

K. Tanaka, M. Tanaka, T. Omoya, “Boundary integral equations for a two-dimensional simulator of a photon scanning tunneling microscope,” J. Opt. Soc. Am. A 15, 1918–1931 (1998).
[CrossRef]

M. Tanaka, K. Tanaka, “Boundary integral equations for computer aided design of near-field optics,” Trans. Inst. Electron. Inf. Commun. Eng. Jpn. J79-C-I, 101–108 (1996) (in Japanese).

Vigneron, J.

A. Castiaux, A. Dereux, J. Vigneron, C. Girard, O. Martin, “Electromagnetic fields in two-dimensional models of near-field optical microscope tips,” Ultramicroscopy 60, 1–9 (1995).
[CrossRef]

Von Labeke, D.

Ziolkowski, R. W.

Inst. Electron. Inf. Commun. Eng. Jpn. (1)

M. Tanaka, K. Tanaka, “Simulation of near-field optical manipulator by boundary element method—aperture-probe coated with metal,” Inst. Electron. Inf. Commun. Eng. Jpn. J82-C-I, 468–476 (1999) (in Japanese).

J. Appl. Phys. (1)

A. Roberts, “Small-hole coupling of radiation into a near-field probe,” J. Appl. Phys. 70, 4045–4049 (1991).
[CrossRef]

J. Opt. Soc. Am. A (7)

Opt. Commun. (1)

R. Carminati, J. Greffet, “Two-dimensional numerical simulation of the photon scanning tunneling microscope. Concept of transfer function.” Opt. Commun. 116, 316–321 (1995).
[CrossRef]

Opt. Rev. (1)

K. Tanaka, M. Tanaka, K. Katayama, “Simulations of two-dimensional photon scanning tunneling microscope by boundary integral equation method: p-polarization,” Opt. Rev. 6, 249–256 (1999).
[CrossRef]

Trans. Inst. Electron. Inf. Commun. Eng. Jpn. (1)

M. Tanaka, K. Tanaka, “Boundary integral equations for computer aided design of near-field optics,” Trans. Inst. Electron. Inf. Commun. Eng. Jpn. J79-C-I, 101–108 (1996) (in Japanese).

Ultramicroscopy (2)

A. Castiaux, A. Dereux, J. Vigneron, C. Girard, O. Martin, “Electromagnetic fields in two-dimensional models of near-field optical microscope tips,” Ultramicroscopy 60, 1–9 (1995).
[CrossRef]

A. Castiaux, Ch. Girard, M. Spajer, S. Davy, “Near-field optical effects inside a photosensitive sample coupled,” Ultramicroscopy 71, 49–58 (1998).
[CrossRef]

Other (2)

J. P. Fillard, Near-Field Optics and Nanoscopy (World Scientific, Singapore, 1996).

M. A. Paesler, P. J. Moyer, Near-Field Optics Theory, Instrumentation and Applications (Wiley-Interscience, New York, 1996).

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Figures (3)

Fig. 1
Fig. 1

(a) Model of NFO circuit and (b) boundaries on integral equations.

Fig. 2
Fig. 2

1D output images obtained by a 2D-SNOM with use of the metal-coated dielectric probe for the incident TE and TM modes. The separation of the two objects is s=0.16λ (solid curves), s=0.80λ (dotted curves), and s=0.02λ (dashed curves).

Fig. 3
Fig. 3

Same as Fig. 2, but using the uncoated dielectric probe.

Tables (1)

Tables Icon

Table 1 Reflection Energy (ΓR), Scattering Energy (ΓS), and Their Total Energy (Γtotal) for the Incident TE and TM Modes

Equations (27)

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2Hz(x)+n22k02Hz(x)=0,
2G2(x|x)+n22k02G2(x|x)=-δ(x|x),
G2(x|x)=-j4H0(2)(n2k0|x-x|)
12Hz(x)=CtG2(x|x)Hz(x)n-Hz(x)G2(x|x)ndl-CinHz(x)G2(x|x)ndl,
Hz(x)=HzC(x)+RHz+(1)(x)+Hz-(1)(x)
(x onC3 andC4),
Hz(x)=HzC(x)(x onCt,C1,andC2).
12HzC(x)=CtG2(x|x)HzC(x)n-HzC(x)G2(x|x)ndl-CinHzC(x)G2(x|x)ndl-RU+(1)(x)-U-(1)(x),
U±(1)(x)=C20G2(x|x)Hz±(1)(x)n-Hz±(1)(x)G2(x|x)ndl
G2(x|x)=A2(r)g2(θ|x),
A2(r)=-j42jπn2k0r1/2exp(-jn2k0r),
g2(θ|x)=exp[jn2k0(x cos θ+y sin θ)].
12HzC(r, θ)A2(r)=Ctg2(θ|x)HzC(x)n-HzC(x)g2(θ|x)ndl-CinHzC(x)g2(θ|x)ndl-Ru+(1)(θ)-u-(1)(θ),
u±(1)(θ)=C20g2(θ|x)H±(1)(x)n-Hz±(1)(x)g2(θ|x)ndl
HC(r, π/2)/A2(r)=0(r).
12HzC(r, θ)θA2(r)=Cth2(θ|x)HzC(x)n-HzC(x)h2(θ|x)ndl-CinHzC(x)h2(θ|x)ndl-Rv+(1)(θ)-v-(1)(θ),
h2(θ|x)=g2(θ|x)θ,
v±(1)(θ)=C20h2(θ|x)Hz±(1)(x)n-Hz±(1)(x)h2(θ|x)ndl.
HzC(r, θ)θθ=π/2A2(r)=0(r).
R=Cth2(π/2|x)HzC(x)n-HzC(x)h2(π/2|x)ndl-CinHzC(x)h2(π/2|x)ndl-v-(1)(π/2)v+(1)(π/2).
12HzC(x)=CtP(x|x)HzC(x)n-HzC(x)P(x|x)ndl-CinHzC(x)P(x|x)ndl-S(x),
P(x|x)=G2(x|x)-h2π2xU+(1)(x)v+(1)(π/2),
S(x)=U+(1)(x)v-(1)(π/2)v+(1)(π/2)-U-(1)(x).
Hz(x)=HzC(x)(x onC5 andC6).
12HzC(x)=-CtG1(x|x)HzC(x)n-HzC(x)G1(x|x)ndl+C5+C6HzC(x)G1(x|x)ndl-Cp1+Cp2G1(x|x)HzC(x)n-HzC(x)G1(x|x)ndl,
Hz(x)=HzC(x)(x onCp1 andCp2).
12HzC(x)=-Cp1+Cp2G3(x|x)HzC(x)n-HzC(x)G3(x|x)ndl.

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