Abstract

The radiation of an arbitrarily oriented dipole located above a planarly layered structure is investigated. The dipole is regarded as a tiny light source, and the properties of the layer are varied in order to study the influence on far-field radiation. Topographic contrast is investigated by varying the thickness of the layer, phase contrast is investigated by varying its dielectric constant, and amplitude contrast is investigated by varying its absorption. It is shown that the light emitted into the lower half-space is composed of two major contributions. Radiation emitted into directions within the critical angle of total internal reflection (allowed light) behaves in a classical way, i.e., the contrast mechanisms are similar to those produced by far-field illumination. On the other hand, radiation emitted at supercritical angles (forbidden light) is exponentially dependent on the height of the dipole above the layer, and the contrast mechanisms turn out to depend sensitively on the spatial source spectrum (orientation of the dipole). Because of their different behavior, it is found to be unfavorable to detect both allowed and forbidden light in near-field optical microscopy.

© 1997 Optical Society of America

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1997 (1)

1995 (5)

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

D. A. Christensen, “Analysis of near field tip patterns including object interaction using finite-difference time-domain calculations,” Ultramicroscopy 57, 189–196 (1995).
[CrossRef]

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two-dimensional near-field probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

D. V. 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]

R. Carminati, J. J. Greffet, “Influence of dielectric contrast and topography on the near field scattered by an inhomogeneous surface,” J. Opt. Soc. Am. A 12, 2716–2725 (1995).
[CrossRef]

1994 (3)

1993 (3)

1991 (3)

1990 (2)

C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
[CrossRef]

E. W. Kolk, N. H. G. Baken, H. Blok, “Domain integral equation analysis of intergrated optical channel and ridge waveguides in stratified media,” IEEE Trans. Microwave Theory Tech. 38, 78–85 (1990).
[CrossRef]

1989 (2)

D. Courjon, K. Sarayeddine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–28 (1989).
[CrossRef]

R. C. Reddik, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

1988 (2)

O. H. Crawford, R. H. Ritchie, “Radiation from oscillating dipoles immersed in a solid, and radiation-induced luminescence,” Phys. Rev. A 37, 787–795 (1988).
[CrossRef] [PubMed]

O. H. Crawford, “Radiation from oscillating dipoles embedded in layered system,” J. Chem. Phys. 89, 6017–6027 (1988).
[CrossRef]

1987 (2)

E. H. Hellen, D. Axelrod, “Fluroescence emission at dielectric and metal–film interfaces,” J. Opt. Soc. Am. A 4, 337–350 (1987).
[CrossRef]

E. Betzig, M. Isaacson, A. Lewis, “Collection mode nearfield scanning optical microscopy,” Appl. Phys. Lett. 61, 2088–2090 (1987).
[CrossRef]

1986 (1)

U. Dürig, D. W. Pohl, F. Rohner, “Near-field optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).
[CrossRef]

1984 (1)

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

1983 (1)

J. R. Mosig, F. E. Gardiol, “Analytical and numerical techniques in the Green’s function treatment of microstrip antennas and scatterers,” 130H, 175–182 (1983).

1981 (1)

1979 (2)

1977 (1)

1975 (1)

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

1973 (1)

K. H. Tews, “Zur Variation von Lumineszenz-Lebensdauern,” Ann. Phys. 29, 97–120 (1973).
[CrossRef]

1953 (1)

H. S. Green, E. Wolf, “A scalar representation of electromagnetic fields,” Proc. Phys. Soc. London 66, 1129–1137 (1953).
[CrossRef]

1942 (1)

A. Sommerfeld, F. Renner, “Strahlungsenergie und Erdabsorption bei Dipolantennen,” Ann. Phys. 41, 1–36 (1942).

1937 (1)

K. A. Norton, “The propagation of radio waves over the surface of the earth and in the upper atmosphere,” Proc. IRE 25, 1203–1236 (1937).
[CrossRef]

1930 (1)

B. Van der Pol, K. F. Niessen, “Über die Ausbreitung elektromagnetischer Wellen über einer ebenen Erde,” Ann. Phys. 6, 273–294 (1930).
[CrossRef]

1929 (1)

M. J. O. Strutt, “Strahlung von Antennen unter dem Einfluss der Erdbodeneigen schaften,” Ann. Phys. 1, 721–772 (1929).
[CrossRef]

1926 (1)

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. 81, 1135–1153 (1926).
[CrossRef]

1919 (1)

H. Weyl, “Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter,” Ann. Phys. 60, 481–500 (1919).
[CrossRef]

1911 (1)

H. v. Hörschelmann, “Über die Wirkungsweise des geknickten Marconischen Senders in der drahtlosen Telegraphie,” Jahrb. Drahtl. Telegr. Teleph. 5, 14–34, 188–211 (1911).

1909 (1)

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. 28, 665–736 (1909).
[CrossRef]

1907 (1)

J. Zenneck, “Fortplfanzung ebener elektromagnetischer Wellen längs einer ebenen Leiterfläche,” Ann. Phys. 23, 846–866 (1907).
[CrossRef]

Abramowitz, M.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, 3th ed. (Dover, New York, 1972).

Agarwal, G. S.

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

Arfken, G.

G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, New York, 1985).

Axelrod, D.

E. H. Hellen, D. Axelrod, “Fluroescence emission at dielectric and metal–film interfaces,” J. Opt. Soc. Am. A 4, 337–350 (1987).
[CrossRef]

Baida, F.

Baken, N. H. G.

E. W. Kolk, N. H. G. Baken, H. Blok, “Domain integral equation analysis of intergrated optical channel and ridge waveguides in stratified media,” IEEE Trans. Microwave Theory Tech. 38, 78–85 (1990).
[CrossRef]

Baños, A.

A. Baños, Dipole Radiation in the Presence of a Conducting Half-Space, 1st ed. (Pergamon, Oxford, 1966).

Barber, P. W.

Barchiesi, D.

Betzig, E.

E. Betzig, M. Isaacson, A. Lewis, “Collection mode nearfield scanning optical microscopy,” Appl. Phys. Lett. 61, 2088–2090 (1987).
[CrossRef]

Bickel, W. S.

Blok, H.

E. W. Kolk, N. H. G. Baken, H. Blok, “Domain integral equation analysis of intergrated optical channel and ridge waveguides in stratified media,” IEEE Trans. Microwave Theory Tech. 38, 78–85 (1990).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1970).

Bozhevolnyi, S.

O. Keller, M. Xiao, S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217–230 (1993).
[CrossRef]

Brekhovskikh, L. M.

L. M. Brekhovskikh, O. A. Godin, Acoustics of Layered Media, 1st ed. (Springer, Berlin, 1990).

L. M. Brekhovskikh, Waves in Layered Media, 2nd ed. (Academic, New York, 1980).

Carminati, R.

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. A. Rice, eds. (Wiley, New York, 1978), Vol. 37, pp. 1–65.

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media, 2nd ed. (Institute of Electrical and Electronics Engineers, New York, 1995).

Christensen, D. A.

D. A. Christensen, “Analysis of near field tip patterns including object interaction using finite-difference time-domain calculations,” Ultramicroscopy 57, 189–196 (1995).
[CrossRef]

Courjon, D.

C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
[CrossRef]

D. Courjon, K. Sarayeddine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–28 (1989).
[CrossRef]

Crawford, O. H.

O. H. Crawford, “Radiation from oscillating dipoles embedded in layered system,” J. Chem. Phys. 89, 6017–6027 (1988).
[CrossRef]

O. H. Crawford, R. H. Ritchie, “Radiation from oscillating dipoles immersed in a solid, and radiation-induced luminescence,” Phys. Rev. A 37, 787–795 (1988).
[CrossRef] [PubMed]

de Fornel, F.

F. de Fornel, J. P. Goudonnet, L. Salomon, E. Lesniewska, “An evanescent field optical microscope,” in Optical Storage and Scanning Technology, T. Wilson, ed., Proc. SPIE1139, 77–84 (1989).

Denk, W.

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

Dereux, A.

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

O. J. F. Martin, A. Dereux, C. Girard, “Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape,” J. Opt. Soc. Am. A 11, 1073–1080 (1994).
[CrossRef]

Devel, M.

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

Dürig, U.

U. Dürig, D. W. Pohl, F. Rohner, “Near-field optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).
[CrossRef]

Efrima, S.

S. Efrima, H. Metiu, “Resonant Raman scattering by adsorbed molecules,” J. Chem. Phys. 70, 1939–1947 (1979).
[CrossRef]

Ferrell, T. L.

R. C. Reddik, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

Froehlich, F.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two-dimensional near-field probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

Gardiol, F. E.

J. R. Mosig, F. E. Gardiol, “Analytical and numerical techniques in the Green’s function treatment of microstrip antennas and scatterers,” 130H, 175–182 (1983).

F. E. Gardiol, Microstrip Circuits, 1st ed. (Wiley, New York, 1994).

Girard, C.

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

O. J. F. Martin, A. Dereux, C. Girard, “Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape,” J. Opt. Soc. Am. A 11, 1073–1080 (1994).
[CrossRef]

C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
[CrossRef]

Godin, O. A.

L. M. Brekhovskikh, O. A. Godin, Acoustics of Layered Media, 1st ed. (Springer, Berlin, 1990).

Goudonnet, J. P.

F. de Fornel, J. P. Goudonnet, L. Salomon, E. Lesniewska, “An evanescent field optical microscope,” in Optical Storage and Scanning Technology, T. Wilson, ed., Proc. SPIE1139, 77–84 (1989).

Green, H. S.

H. S. Green, E. Wolf, “A scalar representation of electromagnetic fields,” Proc. Phys. Soc. London 66, 1129–1137 (1953).
[CrossRef]

Greffet, J. J.

Hecht, B.

B. Hecht, D. W. Pohl, H. Heinzelmann, L. Novotny, “ ‘Tunnel’ near-field optical microscopy: TNOM-2,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO Advanced Study Institute, Series E (Kluwer, Dordrecht, The Netherlands, 1995), pp. 93–107.

Heinzelmann, H.

H. Heinzelmann, D. W. Pohl, “Scanning near-field optical microscopy,” Appl. Phys. A 59, 89–101 (1994).
[CrossRef]

B. Hecht, D. W. Pohl, H. Heinzelmann, L. Novotny, “ ‘Tunnel’ near-field optical microscopy: TNOM-2,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO Advanced Study Institute, Series E (Kluwer, Dordrecht, The Netherlands, 1995), pp. 93–107.

Hellen, E. H.

E. H. Hellen, D. Axelrod, “Fluroescence emission at dielectric and metal–film interfaces,” J. Opt. Soc. Am. A 4, 337–350 (1987).
[CrossRef]

Hörschelmann, H. v.

H. v. Hörschelmann, “Über die Wirkungsweise des geknickten Marconischen Senders in der drahtlosen Telegraphie,” Jahrb. Drahtl. Telegr. Teleph. 5, 14–34, 188–211 (1911).

Iafelice, V. J.

Isaacson, M.

E. Betzig, M. Isaacson, A. Lewis, “Collection mode nearfield scanning optical microscopy,” Appl. Phys. Lett. 61, 2088–2090 (1987).
[CrossRef]

Judkins, J.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two-dimensional near-field probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

Kann, J. L.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two-dimensional near-field probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

Keller, O.

O. Keller, M. Xiao, S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217–230 (1993).
[CrossRef]

Kolk, E. W.

E. W. Kolk, N. H. G. Baken, H. Blok, “Domain integral equation analysis of intergrated optical channel and ridge waveguides in stratified media,” IEEE Trans. Microwave Theory Tech. 38, 78–85 (1990).
[CrossRef]

Kunz, R. E.

Labeke, D. V.

Lanz, M.

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

Lesniewska, E.

F. de Fornel, J. P. Goudonnet, L. Salomon, E. Lesniewska, “An evanescent field optical microscope,” in Optical Storage and Scanning Technology, T. Wilson, ed., Proc. SPIE1139, 77–84 (1989).

Lewis, A.

E. Betzig, M. Isaacson, A. Lewis, “Collection mode nearfield scanning optical microscopy,” Appl. Phys. Lett. 61, 2088–2090 (1987).
[CrossRef]

Lindell, I. V.

Lukosz, W.

Lumme, K. A.

Martin, O. J. F.

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

O. J. F. Martin, A. Dereux, C. Girard, “Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape,” J. Opt. Soc. Am. A 11, 1073–1080 (1994).
[CrossRef]

Metiu, H.

S. Efrima, H. Metiu, “Resonant Raman scattering by adsorbed molecules,” J. Chem. Phys. 70, 1939–1947 (1979).
[CrossRef]

H. Metiu, “Surface enhanced spectroscopy,” in Progress in Surface Science, I. Prigogine, S. A. Rice, eds. (Pergamon, New York, 1984), Vol. 17, pp. 153–320.

Milster, T. D.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two-dimensional near-field probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

Mosig, J. R.

J. R. Mosig, F. E. Gardiol, “Analytical and numerical techniques in the Green’s function treatment of microstrip antennas and scatterers,” 130H, 175–182 (1983).

Muinonen, K. O.

Niessen, K. F.

B. Van der Pol, K. F. Niessen, “Über die Ausbreitung elektromagnetischer Wellen über einer ebenen Erde,” Ann. Phys. 6, 273–294 (1930).
[CrossRef]

Norton, K. A.

K. A. Norton, “The propagation of radio waves over the surface of the earth and in the upper atmosphere,” Proc. IRE 25, 1203–1236 (1937).
[CrossRef]

Novotny, L.

L. Novotny, “Allowed and forbidden light in near-field optics. II. Interacting dipolar particles,” J. Opt. Soc. Am. A 14, 105–113 (1997).
[CrossRef]

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]

L. Novotny, D. W. Pohl, “Light propagation in scanning near-field optical microscopy,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO Advanced Study Institute, Series E (Kluwer, Dordrecht, The Netherlands, 1995), pp. 21–33.

B. Hecht, D. W. Pohl, H. Heinzelmann, L. Novotny, “ ‘Tunnel’ near-field optical microscopy: TNOM-2,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO Advanced Study Institute, Series E (Kluwer, Dordrecht, The Netherlands, 1995), pp. 93–107.

Pohl, D. W.

H. Heinzelmann, D. W. Pohl, “Scanning near-field optical microscopy,” Appl. Phys. A 59, 89–101 (1994).
[CrossRef]

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]

U. Dürig, D. W. Pohl, F. Rohner, “Near-field optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).
[CrossRef]

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

B. Hecht, D. W. Pohl, H. Heinzelmann, L. Novotny, “ ‘Tunnel’ near-field optical microscopy: TNOM-2,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO Advanced Study Institute, Series E (Kluwer, Dordrecht, The Netherlands, 1995), pp. 93–107.

L. Novotny, D. W. Pohl, “Light propagation in scanning near-field optical microscopy,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO Advanced Study Institute, Series E (Kluwer, Dordrecht, The Netherlands, 1995), pp. 21–33.

Prock, A.

R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” in Advances in Chemical Physics, I. Prigogine, S. A. Rice, eds. (Wiley, New York, 1978), Vol. 37, pp. 1–65.

Reddik, R. C.

R. C. Reddik, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

Regli, P.

Renner, F.

A. Sommerfeld, F. Renner, “Strahlungsenergie und Erdabsorption bei Dipolantennen,” Ann. Phys. 41, 1–36 (1942).

Ritchie, R. H.

O. H. Crawford, R. H. Ritchie, “Radiation from oscillating dipoles immersed in a solid, and radiation-induced luminescence,” Phys. Rev. A 37, 787–795 (1988).
[CrossRef] [PubMed]

Rohner, F.

U. Dürig, D. W. Pohl, F. Rohner, “Near-field optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).
[CrossRef]

Salomon, L.

F. de Fornel, J. P. Goudonnet, L. Salomon, E. Lesniewska, “An evanescent field optical microscope,” in Optical Storage and Scanning Technology, T. Wilson, ed., Proc. SPIE1139, 77–84 (1989).

Sarayeddine, K.

D. Courjon, K. Sarayeddine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–28 (1989).
[CrossRef]

Sihvola, A. H.

Silbey, R.

R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” in Advances in Chemical Physics, I. Prigogine, S. A. Rice, eds. (Wiley, New York, 1978), Vol. 37, pp. 1–65.

Sommerfeld, A.

A. Sommerfeld, F. Renner, “Strahlungsenergie und Erdabsorption bei Dipolantennen,” Ann. Phys. 41, 1–36 (1942).

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. 81, 1135–1153 (1926).
[CrossRef]

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. 28, 665–736 (1909).
[CrossRef]

Spajer, M.

D. Courjon, K. Sarayeddine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–28 (1989).
[CrossRef]

Stegun, I. A.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, 3th ed. (Dover, New York, 1972).

Strutt, M. J. O.

M. J. O. Strutt, “Strahlung von Antennen unter dem Einfluss der Erdbodeneigen schaften,” Ann. Phys. 1, 721–772 (1929).
[CrossRef]

Tews, K. H.

K. H. Tews, “Zur Variation von Lumineszenz-Lebensdauern,” Ann. Phys. 29, 97–120 (1973).
[CrossRef]

Toledo-Crow, R.

M. Vaez-Iravani, R. Toledo-Crow, “Amplitude, phase contrast and polarization imaging in near-field scanning optical microscopy,” in Near Field Optics, D. W. Pohl, D. Courjon, eds., Vol. 242 of NATO Advanced Study Institute, Series E (Kluwer, Dordrecht, The Netherlands, 1993), pp. 25–34.

Turner, M. G.

Vaez-Iravani, M.

M. Vaez-Iravani, R. Toledo-Crow, “Amplitude, phase contrast and polarization imaging in near-field scanning optical microscopy,” in Near Field Optics, D. W. Pohl, D. Courjon, eds., Vol. 242 of NATO Advanced Study Institute, Series E (Kluwer, Dordrecht, The Netherlands, 1993), pp. 25–34.

Van der Pol, B.

B. Van der Pol, K. F. Niessen, “Über die Ausbreitung elektromagnetischer Wellen über einer ebenen Erde,” Ann. Phys. 6, 273–294 (1930).
[CrossRef]

Videen, G.

Warmack, R. J.

R. C. Reddik, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

Weyl, H.

H. Weyl, “Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter,” Ann. Phys. 60, 481–500 (1919).
[CrossRef]

Wolf, E.

H. S. Green, E. Wolf, “A scalar representation of electromagnetic fields,” Proc. Phys. Soc. London 66, 1129–1137 (1953).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1970).

Wolfe, W. L.

Xiao, M.

O. Keller, M. Xiao, S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217–230 (1993).
[CrossRef]

Zenneck, J.

J. Zenneck, “Fortplfanzung ebener elektromagnetischer Wellen längs einer ebenen Leiterfläche,” Ann. Phys. 23, 846–866 (1907).
[CrossRef]

Ziolkowski, R. W.

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two-dimensional near-field probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

Analytical and numerical techniques in the Green’s function treatment of microstrip antennas and scatterers (1)

J. R. Mosig, F. E. Gardiol, “Analytical and numerical techniques in the Green’s function treatment of microstrip antennas and scatterers,” 130H, 175–182 (1983).

Ann. Phys. (8)

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. 81, 1135–1153 (1926).
[CrossRef]

H. Weyl, “Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter,” Ann. Phys. 60, 481–500 (1919).
[CrossRef]

M. J. O. Strutt, “Strahlung von Antennen unter dem Einfluss der Erdbodeneigen schaften,” Ann. Phys. 1, 721–772 (1929).
[CrossRef]

B. Van der Pol, K. F. Niessen, “Über die Ausbreitung elektromagnetischer Wellen über einer ebenen Erde,” Ann. Phys. 6, 273–294 (1930).
[CrossRef]

K. H. Tews, “Zur Variation von Lumineszenz-Lebensdauern,” Ann. Phys. 29, 97–120 (1973).
[CrossRef]

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. 28, 665–736 (1909).
[CrossRef]

J. Zenneck, “Fortplfanzung ebener elektromagnetischer Wellen längs einer ebenen Leiterfläche,” Ann. Phys. 23, 846–866 (1907).
[CrossRef]

A. Sommerfeld, F. Renner, “Strahlungsenergie und Erdabsorption bei Dipolantennen,” Ann. Phys. 41, 1–36 (1942).

Appl. Phys. A (1)

H. Heinzelmann, D. W. Pohl, “Scanning near-field optical microscopy,” Appl. Phys. A 59, 89–101 (1994).
[CrossRef]

Appl. Phys. Lett. (2)

D. W. Pohl, W. Denk, M. Lanz, “Optical stethoscopy: image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

E. Betzig, M. Isaacson, A. Lewis, “Collection mode nearfield scanning optical microscopy,” Appl. Phys. Lett. 61, 2088–2090 (1987).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

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[CrossRef]

J. Appl. Phys. (1)

U. Dürig, D. W. Pohl, F. Rohner, “Near-field optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).
[CrossRef]

J. Chem. Phys. (2)

S. Efrima, H. Metiu, “Resonant Raman scattering by adsorbed molecules,” J. Chem. Phys. 70, 1939–1947 (1979).
[CrossRef]

O. H. Crawford, “Radiation from oscillating dipoles embedded in layered system,” J. Chem. Phys. 89, 6017–6027 (1988).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (11)

G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991).
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G. Videen, “Light scattering from a sphere behind a surface,” J. Opt. Soc. Am. A 10, 110–117 (1993).
[CrossRef]

G. Videen, M. G. Turner, V. J. Iafelice, W. S. Bickel, W. L. Wolfe, “Scattering from a small sphere near a surface,” J. Opt. Soc. Am. A 10, 118–126 (1993).
[CrossRef]

I. V. Lindell, A. H. Sihvola, K. O. Muinonen, P. W. Barber, “Scattering by a small object close to an interface. I. Exact-image theory formulation,” J. Opt. Soc. Am. A 8, 472–476 (1991).
[CrossRef]

K. O. Muinonen, A. H. Sihvola, I. V. Lindell, K. A. Lumme, “Scattering by a small object close to an interface. II. Study of backscattering,” J. Opt. Soc. Am. A 8, 477–482 (1991).
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D. V. 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]

L. Novotny, “Allowed and forbidden light in near-field optics. II. Interacting dipolar particles,” J. Opt. Soc. Am. A 14, 105–113 (1997).
[CrossRef]

O. J. F. Martin, A. Dereux, C. Girard, “Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape,” J. Opt. Soc. Am. A 11, 1073–1080 (1994).
[CrossRef]

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]

R. Carminati, J. J. Greffet, “Influence of dielectric contrast and topography on the near field scattered by an inhomogeneous surface,” J. Opt. Soc. Am. A 12, 2716–2725 (1995).
[CrossRef]

Jahrb. Drahtl. Telegr. Teleph. (1)

H. v. Hörschelmann, “Über die Wirkungsweise des geknickten Marconischen Senders in der drahtlosen Telegraphie,” Jahrb. Drahtl. Telegr. Teleph. 5, 14–34, 188–211 (1911).

Opt. Commun. (1)

D. Courjon, K. Sarayeddine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–28 (1989).
[CrossRef]

Phys. Rev. A (2)

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

O. H. Crawford, R. H. Ritchie, “Radiation from oscillating dipoles immersed in a solid, and radiation-induced luminescence,” Phys. Rev. A 37, 787–795 (1988).
[CrossRef] [PubMed]

Phys. Rev. B (3)

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

R. C. Reddik, R. J. Warmack, T. L. Ferrell, “New form of scanning optical microscopy,” Phys. Rev. B 39, 767–770 (1989).
[CrossRef]

C. Girard, D. Courjon, “Model for scanning tunneling optical microscopy: a microscopic self-consistent approach,” Phys. Rev. B 42, 9340–9349 (1990).
[CrossRef]

Proc. IRE (1)

K. A. Norton, “The propagation of radio waves over the surface of the earth and in the upper atmosphere,” Proc. IRE 25, 1203–1236 (1937).
[CrossRef]

Proc. Phys. Soc. London (1)

H. S. Green, E. Wolf, “A scalar representation of electromagnetic fields,” Proc. Phys. Soc. London 66, 1129–1137 (1953).
[CrossRef]

Surf. Sci. (1)

O. Keller, M. Xiao, S. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217–230 (1993).
[CrossRef]

Ultramicroscopy (2)

D. A. Christensen, “Analysis of near field tip patterns including object interaction using finite-difference time-domain calculations,” Ultramicroscopy 57, 189–196 (1995).
[CrossRef]

J. L. Kann, T. D. Milster, F. Froehlich, R. W. Ziolkowski, J. Judkins, “Numerical analysis of a two-dimensional near-field probe,” Ultramicroscopy 57, 251–256 (1995).
[CrossRef]

Other (14)

L. Novotny, D. W. Pohl, “Light propagation in scanning near-field optical microscopy,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO Advanced Study Institute, Series E (Kluwer, Dordrecht, The Netherlands, 1995), pp. 21–33.

F. de Fornel, J. P. Goudonnet, L. Salomon, E. Lesniewska, “An evanescent field optical microscope,” in Optical Storage and Scanning Technology, T. Wilson, ed., Proc. SPIE1139, 77–84 (1989).

M. Vaez-Iravani, R. Toledo-Crow, “Amplitude, phase contrast and polarization imaging in near-field scanning optical microscopy,” in Near Field Optics, D. W. Pohl, D. Courjon, eds., Vol. 242 of NATO Advanced Study Institute, Series E (Kluwer, Dordrecht, The Netherlands, 1993), pp. 25–34.

A. Baños, Dipole Radiation in the Presence of a Conducting Half-Space, 1st ed. (Pergamon, Oxford, 1966).

R. R. Chance, A. Prock, R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” in Advances in Chemical Physics, I. Prigogine, S. A. Rice, eds. (Wiley, New York, 1978), Vol. 37, pp. 1–65.

B. Hecht, D. W. Pohl, H. Heinzelmann, L. Novotny, “ ‘Tunnel’ near-field optical microscopy: TNOM-2,” in Photons and Local Probes, O. Marti, R. Möller, eds., Vol. 300 of NATO Advanced Study Institute, Series E (Kluwer, Dordrecht, The Netherlands, 1995), pp. 93–107.

H. Metiu, “Surface enhanced spectroscopy,” in Progress in Surface Science, I. Prigogine, S. A. Rice, eds. (Pergamon, New York, 1984), Vol. 17, pp. 153–320.

F. E. Gardiol, Microstrip Circuits, 1st ed. (Wiley, New York, 1994).

L. M. Brekhovskikh, O. A. Godin, Acoustics of Layered Media, 1st ed. (Springer, Berlin, 1990).

W. C. Chew, Waves and Fields in Inhomogeneous Media, 2nd ed. (Institute of Electrical and Electronics Engineers, New York, 1995).

L. M. Brekhovskikh, Waves in Layered Media, 2nd ed. (Academic, New York, 1980).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1970).

G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, New York, 1985).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, 3th ed. (Dover, New York, 1972).

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Figures (8)

Fig. 1
Fig. 1

Configuration of the problem.

Fig. 2
Fig. 2

Illustration of allowed and forbidden light. The three media fulfill 3>1>2. The incident wave hits the upper interface in such a way that (a) a transmitted wave exists and (b) the wave is totally reflected.

Fig. 3
Fig. 3

Power flux through horizontal planes in upper and lower half-spaces.

Fig. 4
Fig. 4

Dipole with orientation θ=60° approaching a planar waveguide. λ=488 nm, d=80 nm, 1=1, 2=5, and 3=2.25. (a) Total transmitted light Pn (solid curve), allowed light Pna (dotted curve), and forbidden light Pnf (dashed line). (b) Total radiated power P (solid curve), wide-angle interferences plus direct radiation (dotted curve), evanescent losses (dashed curve), and power coupled to waveguide modes P1-Pn (dashed–dotted curve). All curves are normalized with the total free-space radiation Po.

Fig. 5
Fig. 5

Power density of a dipole above a slab waveguide depicted at a certain time. There is a factor of 2 between successive contour lines. The dipole is located at h=20 nm, and its axis is in the (x, z) plane. θ=60°, λ=488 nm, d =80 nm, 1=1, 2=5, and 3=2.25.

Fig. 6
Fig. 6

Pna (dashed curve), Pnf (solid curve), and Pw=P1 -Pn (dashed–dotted curve) as a function of the thickness d of the slab waveguide characterized in Fig. 5. The discontinuities correspond to the cutoffs of the TE0, TM0, TE1, and TM1 modes.

Fig. 7
Fig. 7

Topographic contrast for allowed light (dashed curves), forbidden light (solid curves), and a plane wave at normal incidence (dotted curves). The light source is an electric dipole at 45° from the normal axis (h=5 nm) radiating at λ=488 nm. The upper medium is vacuum, and the substrate is glass (s=2.25). (a) =1.5, (b) =3, and (c) =-9.13+0.31i. The forbidden light and the allowed light are normalized with the corresponding intensity in the absence of the layer.

Fig. 8
Fig. 8

(a) Phase contrast and (b) amplitude contrast for allowed light (dashed curves), forbidden light (solid curves), and a plane wave at normal incidence (dotted curves). The light source is an electric dipole at 45° from the normal axis (h=5 nm) radiating at λ=488 nm. The layer thickness is d=10 nm. The upper medium is vacuum, and the substrate is glass (s=2.25). In (a) is real, and in (b) the real part of is =s. The forbidden light and the allowed light are normalized with the corresponding intensity in the absence of the layer.

Tables (1)

Tables Icon

Table 1 Dependence of Allowed/Forbidden Light on the Properties of the Layera

Equations (113)

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

(2+k2)Π(r)=0,
Jn(kρρ)exp(ikzz+inϕ).
E=(k2+·)Π,
H=-iωo×Π.
Π(r)=iωoV dV j(r)Go(r, r),
Π(r)=po4πo1exp(ik|r-ro|)|r-ro|.
exp(ikRo)Ro=i 0 dkρkρkzJ0(kρρ)exp(ikz|z-h|).
kz=k2-kρ2withIm(kz)>0.
F=(cos θ)F+(sin θ)F.
1z=poz4πo1exp(ik1Ro)Ro+poz4πo10 dkρ J0(kρρ)×exp[ik1z(z+h)]A1(kρ),
2z=poz4πo10 dkρ J0(kρρ)exp(ik1zh)[A2(kρ)×exp(-ik2zz)+A3(kρ)exp(ik2zz)],
3z=poz4πo10 dkρ J0(kρρ)exp(ik1zh)A4(kρ)×exp(-ik3zz),
A1(kρ)=ikρk1zr(p)(kρ),
A4(kρ)=ikρk1z13exp(-ik3zd)t(p)(kρ).
r(p,s)=r1,2(p,s)+r2,3(p,s) exp(2ik2zd)1+r1,2(p,s)r2,3(p,s) exp(2ik2zd),
t(p,s)=t1,2(p,s)t2,3(p,s) exp(ik2zd)1+r1,2(p,s)r2,3(p,s) exp(2ik2zd),
1+r1,2(p)(kρ)r2,3(p)(kρ)exp(2ik2zd)=0.
1x=pox4πo1exp(ik1Ro)Ro+pox4πo1×0 dkρ J0(kρρ)exp[ik1z(z+h)]B1(kρ),
1z=pox4πo1(cos ϕ) 0 dkρ J1(kρρ)×exp[ik1z(z+h)]C1(kρ),
2x=pox4πo10 dkρ J0(kρρ)exp(ik1zh)×[B2(kρ)exp(-ik2zz)+B3(kρ)exp(ik2zz)],
2z=pox4πo1(cos ϕ) 0 dkρ J1(kρρ)exp(ik1zh)×[C2(kρ)exp(-ik2zz)+C3(kρ)exp(ik2zz)],
3x=pox4πo10 dkρ J0(kρρ)exp(ik1zh)B4(kρ)×exp(-ik3zz),
3z=pox4πo1(cos ϕ) 0 dkρ J1(kρρ)×exp(ik1zh)C4(kρ)exp(-ik3zz).
B1(kρ)=ikρk1zr(s)(kρ),
B4(kρ)=ikρk1zk12k32exp(-ik3zd)t(s)(kρ),
C1(kρ)=-[r(s)(kρ)+r(p)(kρ)],
C4kρ=k12k32k3zk1ztskρ-13tpkρexp-ik3zd.
1+r1,2(s)(kρ)r2,3(s)(kρ)exp(2ik2zd)=0.
Pj=±12Re0 dρ ρ 02π dϕE×H*·nz,
z=poz4πo10 dkρ J0(kρρ)X(kρ),
Xkρ=ikρk1zexpik1zz-h+rp expik1zz+hz>hikρk1zexp-ik1zz-h+rp expik1zz+h0<z<hikρk1z1ntp expik1zh-knzz+δz<-δ.
Pj=±12Re 0 (dρ ρ 02π dϕ EρHϕ*).
Eρ=ρzz=-poz4πo10 dkρ kρJ1(kρρ)X(kρ)z,
Hϕ*=-iωojρz*=iωjpoz4π10 dk˜ρ k˜ρJ1(k˜ρρ)X*(k˜ρ).
0 dρ ρJm(k˜ρρ)Jm(kρρ)=1kρδ(kρ-k˜ρ),
Po=po212πωo1k13,
PjPo=±34j11k13Im 0 dkρ kρXzX*.
P1Po=12+341k13Re 0k1 dkρkρ3k1z|rp|2+321k13Re 0k1 dkρkρ3k1zrp exp2ik1zh,
P1Po=12-341k13Re 0k1 dkρkρ3k1z|rp|2+321k13Re k1 dkρkρ3k1zrp exp2ik1zh.
PPo=1+321k13Re 0k1 dkρkρ3k1zrp exp2ik1zh+321k13Re k1 dkρkρ3k1zrp exp2ik1zh.
PnPo=341n1k13Re 0kn dkρkρ3knzknzk1ztp2×exp-2k1zh,
kρ=kn sin α,knz=-kn cos α
αc=αkρ=k1=arcsink1kn.
x=pox4πo10 dkρ J0(kρρ)X(kρ),
z=(cos ϕ)pox4πo10 dkρ J1(kρρ)Y(kρ),
Xkρ=ikρk1zexpik1zz-h+rs expik1zz+hz>hikρk1zexp-ik1zz-h+rs expik1zz+h0<z<hikρk1zk12kn2ts expik1zh-knzz+δz<-δ,
Ykρ=-rp+rsexpik1zz+hz>0-1ntp-knzk1zk12kn2tsexpik1zh-knzz+δz<-δ.
Pj=±12Re 0 dρ ρ 02π dϕ EρHϕ*-EϕHρ*.
Eρ=kj2cos ϕjx+cos ϕ2/ρ2jx+/ρ×/zjz=cos ϕpox4πo10 dkρkj2J0kρρXkρ+kρ2J2kρρ-J0kρρkρXkρ±ikjzYkρ,
Hϕ*=iωojcos ϕ/zjx*-/ρjz*=cos ϕiωpoxj4π10 dk˜ρJ0k˜ρρX*k˜ρz+k˜ρ2J2k˜ρρ-J0k˜ρρY*k˜ρ,
Ejϕ=-kj2sin ϕjx-1/ρsin ϕ/ρjx-1/ρtan ϕ/zjz=sin ϕpox4πo10 dkρkj2J0kρρXkρ-kρ2J2kρρ+J0kρρkρXkρ±ikjzYkρ,
Hρ*=iωojsin ϕ/zjx*-1/ρtan ϕjz*=sin ϕ-iωpoxj4π10 dk˜ρJ0k˜ρρX*k˜ρz-k˜ρ2J2k˜ρρ+J0k˜ρρY*k˜ρ.
PjPo=34j11k13Im0 dkρk12kρXX*z-k122XY*-12kρX±ikjzYX*z+kρ2kρX±ikjzYY*.
P1Po=12+381k13Re 0k1 dkρkρk1zk12|rs|2+k1z2|rp|2+341k13Re 0k1 dkρ×kρk1zk12rs-k1z2rpexp2ik1zh,
P1Po=12-381k13Re 0k1 dkρkρk1zk12|rs|2+k1z2|rp|2+341k13Re k10 dkρkρk1zk12rs-k1z2rpexp2ik1zh.
PPo=1+341k13Re 0k1 dkρkρk1z×k12rs-k1z2rpexp2ik1zh+341k13Re k1 dkρkρk1z×k12rs-k1z2rpexp2ik1zh.
PnPo=381n1k13Re 0kn dkρ kρknzkn2knz2μ12μn2knzk1zts2+|tp|2exp-2k1zh,
po=poznz+poxnx=(cos θ)ponz+(sin θ)ponx.
E=(cos θ)E+(sin θ)E,
H=(cos θ)H+(sin θ)H.
(E×H*)·nz=(cos2 θ)(E×H*)·nz+(sin2 θ)(E×H*)·nz+(cos θ sin θ)[(E×H*)·nz+(E×H*)·nz].
P=(cos2 θ)P+(sin2 θ)P.
P=13P+23P.
f1=2k1z-1k2z,g1=μ2k1z-μ1k2z,
f2=2k1z+1k2z,g2=μ2k1z+μ1k2z,
f3=3k2z-2k3z,g3=μ3k2z-μ2k3z,
f4=3k2z+2k3z,g4=μ3k2z+μ2k3z
A1(kρ)=ikρ[f1f4+f2f3 exp(2ik2zd)]k1z[f2f4+f1f3 exp(2ik2zd)],
A2(kρ)=i21kρf4f2f4+f1f3 exp(2ik2zd),
A3(kρ)=i21kρf3 exp(2ik2zd)f2f4+f1f3 exp(2ik2zd),
A4(kρ)=i412kρk2z exp[i(k2z-k3z)d]f2f4+f1f3 exp(2ik2zd),
B1(kρ)=ikρ[g1g4+g2g3 exp(2ik2zd)]k1z[g2g4+g1g3 exp(2ik2zd)],
B2(kρ)=i122μ1kρg4g2g4+g1g3 exp(2ik2zd),
B3(kρ)=i122μ1kρg3 exp(2ik2zd)g2g4+g1g3 exp(2ik2zd),
B4(kρ)=i134μ1μ2kρk2z exp[i(k2z-k3z)d]g2g4+g1g3 exp(2ik2zd),
C1(kρ)=2kρ2{[f4+f3 exp(2ik2zd)]×[g4+g3 exp(2ik2zd)](1μ1-2μ2)+41μ1k2z2(2μ2-3μ3)exp(2ik2zd)}/{[g2g4+g1g3 exp(2ik2zd)]×[f2f4+f1f3 exp(2ik2zd)]},
C2(kρ)=2kρ212{f4[g4+g3 exp(2ik2zd)]×(1μ1-2μ2)-2μ1k2zf1(2μ2-3μ3)×exp(2ik2zd)}/{[g2g4+g1g3×exp(2ik2zd)][f2f4+f1f3 exp(2ik2zd)]},
C3(kρ)=2kρ212{f3[g4+g3 exp(2ik2zd)]×(1μ1-2μ2)exp(2ik2zd)+2μ1k2zf2(2μ2-3μ3)exp(2ik2zd)}/{[g2g4+g1g3 exp(2ik2zd)]×[f2f4+f1f3 exp(2ik2zd)]},
C4(kρ)=4kρ2k2z13exp[i(k2z-k3z)d]×{3[g4+g3 exp(2ik2zd)](1μ1-2μ2)+μ1[f2-f1 exp(2ik2zd)](2μ2-3μ3)}/{[g2g4+g1g3 exp(2ik2zd)]×[f2f4+f1f3 exp(2ik2zd)]}.
A1(kρ)=ikρk1zf1f2=kρk1zr1,2(p),
A2(kρ)=i2kρ1f2=kρk1z12t1,2(p),
B1(kρ)=ikρk1zg1g2=kρk1zr1,2(s),
B2(kρ)=i2kρ1f2=kρk1z1μ12μ2t1,2(s),
C1(kρ)=2kρ2(1μ1-2μ2)f2g2=-[r1,2(s)+r1,2(p)],
C2(kρ)=12C1(kρ)=-12[r1,2(s)+r1,2(p)]=k12k22k2zk1zt1,2(s)-12t1,2(p).
kjz=kj2-kρ2,j{1, 2, 3}
EjρEjzHjϕ=(/ρ)(/z)jz,=(kj2+2/z2)jz,=iωoj(/ρ)jz,Ejϕ=0,Hjρ=0,Hjz=0.
Ejρ=kj2(cos ϕ)jx+(cos ϕ)(2/ρ2)jx+(/ρ)(/z)jz,
Ejϕ=-kj2(sin ϕ)jx-(1/ρ)(sin ϕ)(/ρ)jx-(1/ρ)(tan ϕ)(/z)jz,
Ejz=(cos ϕ)(/ρ)(/z)jx+kj2jz+(2/z2)jz,
Hjρ=-iωoj[(sin ϕ)(/z)jx-(1/ρ)(tan ϕ)jz],
Hjϕ=-iωoj[(cos ϕ)(/z)jx-(/ρ)jz],
Hjz=iωoj(sin ϕ)(/ρ)jx.
E1,ρ=-poz4πo10 dkρ J0kρ2r(p) exp[ik1z(z+h)],
E1z=ipoz4πo10 dkρ J0kρ3k1zr(p) exp[ik1z(z+h)],
H1ϕ=-ωpoz4π0 dkρ J0kρ2k1zr(p) exp[ik1z(z+h)],
Enρ=poz4πon0 dkρ J0kρ2knzk1zt(p)×exp{i[k1zh-knz(z+δ)]},
Enz=ipoz4πo10 dkρ J0kρ3k1zt(p)×exp{i[k1zh-knz(z+δ)]},
Hnϕ=-ωpoz4π0 dkρ J0kρ2k1zt(p)×exp{i[k1zh-knz(z+δ)]}.
E1ρ=cos ϕipox4πo10 dkρ expik1zz+h×J0kρk1zrp-J0ρk12k1zrs,
E1ϕ=sin ϕ-ipox4πo10 dkρ expik1zz+h×J0ρk1zrp-J0kpk12k1zrs,
E1z=(cos ϕ)pox4πo10 dkρ exp[ik1z(z+h)]×J0kρ2r(p),
H1ρ=sin ϕiωpox4π0 dkρ expik1zz+h×J0ρrp-J0kρrs,
H1ϕ=cos ϕiωpox4π0 dkρ expik1zz+h×J0kρrp-J0ρrs,
H1z=(sin ϕ)-ωpox4π0dkρ exp[ik1z(z+h)]×J0kρ2k1zr(s),
Enρ=cos ϕ-ipox4π010 dkρ×expik1zh-knzz+δ×J0kρknz1ntp+J0ρk12k1zts,
Enϕ=sin ϕipox4πo10 dkρ×expik1zh-knzz+δ×J0ρknz1ntp+J0kρk12k1zts,
Enz=(cos ϕ)ipox4πo10 dkρ×exp{i[k1zh-knz(z+δ)]}J0kρ21nt(p),
Hnρ=sin ϕiωpox4π0 dkρ×expik1zh-knzz+δ×J0ρtp+J0kρknzk1zμ1μnts,
Hnϕ=cos ϕiωpox4π0 dkρ×expik1zh-knzz+δ×J0kρtp+J0ρknzk1zμ1μnts,
Hnz=(sin ϕ)-ωpox4π0 dkρ×exp{i[k1zh-knz(z+δ)]}×J0kρ2k1zμ1μnt(s).
J0=J0(kρρ),J0=-J1(kρρ),
J0=1kρρJ1(kρρ)-J0(kρρ).

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