Abstract

Using a Green's function technique and the plane-wave spectrum, we formulate a classical theory for the calculation of radiative effects for a source in the presence of a planar interface or structure. The analysis focuses on understanding the roles of radiative and nonradiative energy transfer in the coupling processes and discusses the implications of modal-induced effects. This understanding is important for the design of a class of practical applications, including enhanced-sensitivity optical waveguide sensors.

© 1997 Optical Society of America

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References

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  1. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  2. D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981).
    [CrossRef]
  3. S. Haroche and D. Kleppner, “Cavity quantum electrodynamics,” Phys. Today 42(1), 24–30 (1989).
    [CrossRef]
  4. J. L. Jewell, K. F. Huang, K. Tai, Y. H. Lee, R. J. Fischer, S. L. McCall, and A. Y. Cho, “Vertical cavity single quantum well laser,” Appl. Phys. Lett. 55, 424–426 (1989).
    [CrossRef]
  5. Y. Yamamoto and R. E. Slusher, “Optical processes in microcavities,” Phys. Today 46(6), 66–73 (1993).
    [CrossRef]
  6. See, for example, A. Dodabalapur, L. J. Rothberg, T. M. Miller, and E. W. Kwock, “Microcavity effects in organic semiconductors,” Appl. Phys. Lett. 64, 2486–2488 (1994).
    [CrossRef]
  7. See, for example, E. Yablinovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef]
  8. H. Kuhn, “Classical aspects of energy transfer in molecular systems,” J. Chem. Phys. 53, 101–108 (1970).
    [CrossRef]
  9. K. G. Sullivan and D. G. Hall, “Enhancement and inhibition of electromagnetic radiation in plane-layered media. II. Enhanced fluorescence in optical waveguide sensors,” J. Opt. Soc. Am. B 14, 1161–1167 (1997).
    [CrossRef]
  10. T. Erdogan, K. G. Sullivan, and D. G. Hall, “Enhancement and inhibition of radiation in cylindrically symmetric, periodic structures,” J. Opt. Soc. Am. B 10, 391–398 (1993).
    [CrossRef]
  11. K. G. Sullivan and D. G. Hall, “Radiation in spherically symmetric structures. II. Enhancement and inhibition of dipole radiation in a spherical bragg cavity,” Phys. Rev. A 50, 2708–2718 (1994).
    [CrossRef] [PubMed]
  12. R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an excited molecule near a metal mirror: energy transfer in the Eu3+/silver system,” J. Chem. Phys. 60, 2184–2185 (1974).
    [CrossRef]
  13. R. R. Chance, A. Prock, and R. Silbey, “Frequency shifts of an electric-dipole transition near a partially reflecting surface,” Phys. Rev. A 12, 1448–1452 (1975).
    [CrossRef]
  14. R. R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” in Advances in Chemical Physics, I. Prigogine and S. A. Rice, eds. (Wiley, New York, 1978), Vol. 37, pp. 1–65.
  15. K. H. Drexhage, “Interaction of light with monomolecular dye layers,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1974), Vol. 12, Chap. 4.
  16. W. R. Holland and D. G. Hall, “Frequency shifts of an electric-dipole resonance near a conducting surface,” Phys. Rev. Lett. 52, 1041–1044 (1984).
    [CrossRef]
  17. J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A 30, 1185–1193 (1984).
    [CrossRef]
  18. See, for example, W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1956), Chap. 20 and Eq. (21–3).
  19. See, for example, O. Svelto, Principles of Lasers, 2nd ed. (Plenum, New York, 1982), Chap. 2.
  20. See, for example, J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  21. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953).
  22. C. T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Intext Educational Publishers, Scranton, Penn., 1971).
  23. R. E. Collin, “Dyadic Green’s function,” Electromagnetics 6, 183–207 (1986).
  24. W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).
  25. A. Sommerfeld, Partial Differential Equations (Academic, New York, 1949).
  26. See, for example, H. Kogelnik, “Theory of dielectric waveguides,” in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, Berlin, 1988), Chap. 2.
  27. See, for example, R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, “Mode determination for planar waveguides using the four-sheeted dispersion relation,” IEEE J. Quantum Electron. 28, 1520–1526 (1992).
    [CrossRef]
  28. A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
    [CrossRef]
  29. E. Kröger and E. Kretschmann, “Scattering of light by slightly rough surfaces or thin films including plasma resonance emission,” Z. Phys. 237, 1–15 (1970).
    [CrossRef]
  30. A. A. Maradudin, “Interaction of surface polaritons and plasmons with surface roughness,” in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), Chap. 10.
  31. G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
    [CrossRef]

1997 (1)

K. G. Sullivan and D. G. Hall, “Enhancement and inhibition of electromagnetic radiation in plane-layered media. II. Enhanced fluorescence in optical waveguide sensors,” J. Opt. Soc. Am. B 14, 1161–1167 (1997).
[CrossRef]

1994 (2)

K. G. Sullivan and D. G. Hall, “Radiation in spherically symmetric structures. II. Enhancement and inhibition of dipole radiation in a spherical bragg cavity,” Phys. Rev. A 50, 2708–2718 (1994).
[CrossRef] [PubMed]

See, for example, A. Dodabalapur, L. J. Rothberg, T. M. Miller, and E. W. Kwock, “Microcavity effects in organic semiconductors,” Appl. Phys. Lett. 64, 2486–2488 (1994).
[CrossRef]

1993 (2)

1992 (1)

See, for example, R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, “Mode determination for planar waveguides using the four-sheeted dispersion relation,” IEEE J. Quantum Electron. 28, 1520–1526 (1992).
[CrossRef]

1989 (2)

S. Haroche and D. Kleppner, “Cavity quantum electrodynamics,” Phys. Today 42(1), 24–30 (1989).
[CrossRef]

J. L. Jewell, K. F. Huang, K. Tai, Y. H. Lee, R. J. Fischer, S. L. McCall, and A. Y. Cho, “Vertical cavity single quantum well laser,” Appl. Phys. Lett. 55, 424–426 (1989).
[CrossRef]

1987 (1)

See, for example, E. Yablinovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

1984 (3)

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

W. R. Holland and D. G. Hall, “Frequency shifts of an electric-dipole resonance near a conducting surface,” Phys. Rev. Lett. 52, 1041–1044 (1984).
[CrossRef]

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

1981 (1)

D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981).
[CrossRef]

1975 (1)

R. R. Chance, A. Prock, and R. Silbey, “Frequency shifts of an electric-dipole transition near a partially reflecting surface,” Phys. Rev. A 12, 1448–1452 (1975).
[CrossRef]

1974 (1)

R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an excited molecule near a metal mirror: energy transfer in the Eu3+/silver system,” J. Chem. Phys. 60, 2184–2185 (1974).
[CrossRef]

1970 (2)

H. Kuhn, “Classical aspects of energy transfer in molecular systems,” J. Chem. Phys. 53, 101–108 (1970).
[CrossRef]

E. Kröger and E. Kretschmann, “Scattering of light by slightly rough surfaces or thin films including plasma resonance emission,” Z. Phys. 237, 1–15 (1970).
[CrossRef]

1968 (1)

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
[CrossRef]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Chance, R. R.

R. R. Chance, A. Prock, and R. Silbey, “Frequency shifts of an electric-dipole transition near a partially reflecting surface,” Phys. Rev. A 12, 1448–1452 (1975).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an excited molecule near a metal mirror: energy transfer in the Eu3+/silver system,” J. Chem. Phys. 60, 2184–2185 (1974).
[CrossRef]

Cho, A. Y.

J. L. Jewell, K. F. Huang, K. Tai, Y. H. Lee, R. J. Fischer, S. L. McCall, and A. Y. Cho, “Vertical cavity single quantum well laser,” Appl. Phys. Lett. 55, 424–426 (1989).
[CrossRef]

Dodabalapur, A.

See, for example, A. Dodabalapur, L. J. Rothberg, T. M. Miller, and E. W. Kwock, “Microcavity effects in organic semiconductors,” Appl. Phys. Lett. 64, 2486–2488 (1994).
[CrossRef]

Erdogan, T.

Fischer, R. J.

J. L. Jewell, K. F. Huang, K. Tai, Y. H. Lee, R. J. Fischer, S. L. McCall, and A. Y. Cho, “Vertical cavity single quantum well laser,” Appl. Phys. Lett. 55, 424–426 (1989).
[CrossRef]

Forbes, G. W.

See, for example, R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, “Mode determination for planar waveguides using the four-sheeted dispersion relation,” IEEE J. Quantum Electron. 28, 1520–1526 (1992).
[CrossRef]

Ford, G. W.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Hall, D. G.

K. G. Sullivan and D. G. Hall, “Enhancement and inhibition of electromagnetic radiation in plane-layered media. II. Enhanced fluorescence in optical waveguide sensors,” J. Opt. Soc. Am. B 14, 1161–1167 (1997).
[CrossRef]

K. G. Sullivan and D. G. Hall, “Radiation in spherically symmetric structures. II. Enhancement and inhibition of dipole radiation in a spherical bragg cavity,” Phys. Rev. A 50, 2708–2718 (1994).
[CrossRef] [PubMed]

T. Erdogan, K. G. Sullivan, and D. G. Hall, “Enhancement and inhibition of radiation in cylindrically symmetric, periodic structures,” J. Opt. Soc. Am. B 10, 391–398 (1993).
[CrossRef]

W. R. Holland and D. G. Hall, “Frequency shifts of an electric-dipole resonance near a conducting surface,” Phys. Rev. Lett. 52, 1041–1044 (1984).
[CrossRef]

Haroche, S.

S. Haroche and D. Kleppner, “Cavity quantum electrodynamics,” Phys. Today 42(1), 24–30 (1989).
[CrossRef]

Holland, W. R.

W. R. Holland and D. G. Hall, “Frequency shifts of an electric-dipole resonance near a conducting surface,” Phys. Rev. Lett. 52, 1041–1044 (1984).
[CrossRef]

Houde-Walter, S. N.

See, for example, R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, “Mode determination for planar waveguides using the four-sheeted dispersion relation,” IEEE J. Quantum Electron. 28, 1520–1526 (1992).
[CrossRef]

Huang, K. F.

J. L. Jewell, K. F. Huang, K. Tai, Y. H. Lee, R. J. Fischer, S. L. McCall, and A. Y. Cho, “Vertical cavity single quantum well laser,” Appl. Phys. Lett. 55, 424–426 (1989).
[CrossRef]

Jewell, J. L.

J. L. Jewell, K. F. Huang, K. Tai, Y. H. Lee, R. J. Fischer, S. L. McCall, and A. Y. Cho, “Vertical cavity single quantum well laser,” Appl. Phys. Lett. 55, 424–426 (1989).
[CrossRef]

Kleppner, D.

S. Haroche and D. Kleppner, “Cavity quantum electrodynamics,” Phys. Today 42(1), 24–30 (1989).
[CrossRef]

D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981).
[CrossRef]

Kretschmann, E.

E. Kröger and E. Kretschmann, “Scattering of light by slightly rough surfaces or thin films including plasma resonance emission,” Z. Phys. 237, 1–15 (1970).
[CrossRef]

Kröger, E.

E. Kröger and E. Kretschmann, “Scattering of light by slightly rough surfaces or thin films including plasma resonance emission,” Z. Phys. 237, 1–15 (1970).
[CrossRef]

Kuhn, H.

H. Kuhn, “Classical aspects of energy transfer in molecular systems,” J. Chem. Phys. 53, 101–108 (1970).
[CrossRef]

Kwock, E. W.

See, for example, A. Dodabalapur, L. J. Rothberg, T. M. Miller, and E. W. Kwock, “Microcavity effects in organic semiconductors,” Appl. Phys. Lett. 64, 2486–2488 (1994).
[CrossRef]

Lee, Y. H.

J. L. Jewell, K. F. Huang, K. Tai, Y. H. Lee, R. J. Fischer, S. L. McCall, and A. Y. Cho, “Vertical cavity single quantum well laser,” Appl. Phys. Lett. 55, 424–426 (1989).
[CrossRef]

McCall, S. L.

J. L. Jewell, K. F. Huang, K. Tai, Y. H. Lee, R. J. Fischer, S. L. McCall, and A. Y. Cho, “Vertical cavity single quantum well laser,” Appl. Phys. Lett. 55, 424–426 (1989).
[CrossRef]

Miller, T. M.

See, for example, A. Dodabalapur, L. J. Rothberg, T. M. Miller, and E. W. Kwock, “Microcavity effects in organic semiconductors,” Appl. Phys. Lett. 64, 2486–2488 (1994).
[CrossRef]

Otto, A.

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
[CrossRef]

Prock, A.

R. R. Chance, A. Prock, and R. Silbey, “Frequency shifts of an electric-dipole transition near a partially reflecting surface,” Phys. Rev. A 12, 1448–1452 (1975).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an excited molecule near a metal mirror: energy transfer in the Eu3+/silver system,” J. Chem. Phys. 60, 2184–2185 (1974).
[CrossRef]

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Rothberg, L. J.

See, for example, A. Dodabalapur, L. J. Rothberg, T. M. Miller, and E. W. Kwock, “Microcavity effects in organic semiconductors,” Appl. Phys. Lett. 64, 2486–2488 (1994).
[CrossRef]

Silbey, R.

R. R. Chance, A. Prock, and R. Silbey, “Frequency shifts of an electric-dipole transition near a partially reflecting surface,” Phys. Rev. A 12, 1448–1452 (1975).
[CrossRef]

R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an excited molecule near a metal mirror: energy transfer in the Eu3+/silver system,” J. Chem. Phys. 60, 2184–2185 (1974).
[CrossRef]

Sipe, J. E.

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

Slusher, R. E.

Y. Yamamoto and R. E. Slusher, “Optical processes in microcavities,” Phys. Today 46(6), 66–73 (1993).
[CrossRef]

Smith, R. E.

See, for example, R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, “Mode determination for planar waveguides using the four-sheeted dispersion relation,” IEEE J. Quantum Electron. 28, 1520–1526 (1992).
[CrossRef]

Sullivan, K. G.

K. G. Sullivan and D. G. Hall, “Enhancement and inhibition of electromagnetic radiation in plane-layered media. II. Enhanced fluorescence in optical waveguide sensors,” J. Opt. Soc. Am. B 14, 1161–1167 (1997).
[CrossRef]

K. G. Sullivan and D. G. Hall, “Radiation in spherically symmetric structures. II. Enhancement and inhibition of dipole radiation in a spherical bragg cavity,” Phys. Rev. A 50, 2708–2718 (1994).
[CrossRef] [PubMed]

T. Erdogan, K. G. Sullivan, and D. G. Hall, “Enhancement and inhibition of radiation in cylindrically symmetric, periodic structures,” J. Opt. Soc. Am. B 10, 391–398 (1993).
[CrossRef]

Tai, K.

J. L. Jewell, K. F. Huang, K. Tai, Y. H. Lee, R. J. Fischer, S. L. McCall, and A. Y. Cho, “Vertical cavity single quantum well laser,” Appl. Phys. Lett. 55, 424–426 (1989).
[CrossRef]

Weber, W. H.

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Wylie, J. M.

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

Yablinovitch, E.

See, for example, E. Yablinovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

Yamamoto, Y.

Y. Yamamoto and R. E. Slusher, “Optical processes in microcavities,” Phys. Today 46(6), 66–73 (1993).
[CrossRef]

Appl. Phys. Lett. (2)

J. L. Jewell, K. F. Huang, K. Tai, Y. H. Lee, R. J. Fischer, S. L. McCall, and A. Y. Cho, “Vertical cavity single quantum well laser,” Appl. Phys. Lett. 55, 424–426 (1989).
[CrossRef]

See, for example, A. Dodabalapur, L. J. Rothberg, T. M. Miller, and E. W. Kwock, “Microcavity effects in organic semiconductors,” Appl. Phys. Lett. 64, 2486–2488 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

See, for example, R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, “Mode determination for planar waveguides using the four-sheeted dispersion relation,” IEEE J. Quantum Electron. 28, 1520–1526 (1992).
[CrossRef]

J. Chem. Phys. (2)

R. R. Chance, A. Prock, and R. Silbey, “Lifetime of an excited molecule near a metal mirror: energy transfer in the Eu3+/silver system,” J. Chem. Phys. 60, 2184–2185 (1974).
[CrossRef]

H. Kuhn, “Classical aspects of energy transfer in molecular systems,” J. Chem. Phys. 53, 101–108 (1970).
[CrossRef]

J. Opt. Soc. Am. B (2)

K. G. Sullivan and D. G. Hall, “Enhancement and inhibition of electromagnetic radiation in plane-layered media. II. Enhanced fluorescence in optical waveguide sensors,” J. Opt. Soc. Am. B 14, 1161–1167 (1997).
[CrossRef]

T. Erdogan, K. G. Sullivan, and D. G. Hall, “Enhancement and inhibition of radiation in cylindrically symmetric, periodic structures,” J. Opt. Soc. Am. B 10, 391–398 (1993).
[CrossRef]

Phys. Rep. (1)

G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Phys. Rev. (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Phys. Rev. A (3)

K. G. Sullivan and D. G. Hall, “Radiation in spherically symmetric structures. II. Enhancement and inhibition of dipole radiation in a spherical bragg cavity,” Phys. Rev. A 50, 2708–2718 (1994).
[CrossRef] [PubMed]

R. R. Chance, A. Prock, and R. Silbey, “Frequency shifts of an electric-dipole transition near a partially reflecting surface,” Phys. Rev. A 12, 1448–1452 (1975).
[CrossRef]

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

Phys. Rev. Lett. (3)

W. R. Holland and D. G. Hall, “Frequency shifts of an electric-dipole resonance near a conducting surface,” Phys. Rev. Lett. 52, 1041–1044 (1984).
[CrossRef]

D. Kleppner, “Inhibited spontaneous emission,” Phys. Rev. Lett. 47, 233–236 (1981).
[CrossRef]

See, for example, E. Yablinovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

Phys. Today (2)

S. Haroche and D. Kleppner, “Cavity quantum electrodynamics,” Phys. Today 42(1), 24–30 (1989).
[CrossRef]

Y. Yamamoto and R. E. Slusher, “Optical processes in microcavities,” Phys. Today 46(6), 66–73 (1993).
[CrossRef]

Z. Phys. (2)

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398–410 (1968).
[CrossRef]

E. Kröger and E. Kretschmann, “Scattering of light by slightly rough surfaces or thin films including plasma resonance emission,” Z. Phys. 237, 1–15 (1970).
[CrossRef]

Other (12)

A. A. Maradudin, “Interaction of surface polaritons and plasmons with surface roughness,” in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), Chap. 10.

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

K. H. Drexhage, “Interaction of light with monomolecular dye layers,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1974), Vol. 12, Chap. 4.

See, for example, W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1956), Chap. 20 and Eq. (21–3).

See, for example, O. Svelto, Principles of Lasers, 2nd ed. (Plenum, New York, 1982), Chap. 2.

See, for example, J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953).

C. T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Intext Educational Publishers, Scranton, Penn., 1971).

R. E. Collin, “Dyadic Green’s function,” Electromagnetics 6, 183–207 (1986).

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990).

A. Sommerfeld, Partial Differential Equations (Academic, New York, 1949).

See, for example, H. Kogelnik, “Theory of dielectric waveguides,” in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, Berlin, 1988), Chap. 2.

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Figures (4)

Fig. 1
Fig. 1

Radiating dipole in the presence of an interface or a structure. The specific case of region 2 as a metal-clad waveguide is examined.

Fig. 2
Fig. 2

Generalized geometry of a radiating dipole in a planar cavity. The structures denoted by regions 2 and 3 have associated amplitude-reflection coefficients ρ12 and ρ13.

Fig. 3
Fig. 3

Geometry of the dipole–waveguide coupled system.

Fig. 4
Fig. 4

Normalized damping rate versus LiF film thickness for a dipole on the surface of an Ag/LiF/air waveguide structure. (a) Damping rate is plotted for the VED case, the HED case, and the case of an isotropic distribution of dipoles. (b) HED damping rate is plotted, with the TE and the TM contributions, which sum to form the HED damping rate, plotted separately.

Tables (1)

Tables Icon

Table 1 Cutoff Film Thicknesses for Bound Modes of the Metal-Clad Waveguide Structure a

Equations (67)

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

·D=0,
·B=0,
×1(x)D=iωB,
×B=-iμωD,
(x)=0n2(x)=0[n02+Δn2(x)].
××B-μ(x)ω2B=1(x)ddx[xˆ×(×B)],
××1(x)D-μω2D=0.
(2+n02k02)[xˆ·B(r)]=-Δn2(x)k02[xˆ·B(r)],
(2+n02k02)[xˆ·D(r)]=-Δn2(x)k02- ddx1 ddx×[xˆ·D(r)],
xˆ·B(r)=0,xˆ·D(r)forTMpolarization,
xˆ·D(r)=0,xˆ·B(r)forTEpolarization.
t×xˆDx+xxˆ×Dt=iωBt,
t×xˆBx+xxˆ×Bt=-iωμDt,
Dt=1μω2-kx2t Dxx-iωxˆ×tBx.
Bt=1μω2-kx2t Bxx+iωμxˆ×tDx.
p¨+ω02p=q2mER-b0p˙,
p=p0 exp(-iΩt)=p0 exp[-(iω+b/2)t],
ER=E0 exp(-iΩt),
bb0=1+q2mωp0b0Im(E0),
ω2-ω02=b24-bb02-q2mp0Re(E0).
Δωb28ω0-bb04ω0-q22mω0p0Re(E0).
b0=n0q2ω026π0mc3 1γ,
ES=-μ0n0ω02J06πc=iμ0n0ω03p06πc.
bb0=1+γ ReE0ES=1+γ Re(Γ),
Δω=b028ω0ReE0ES2-1+b02ImE0ES.
Δωb02ImE0ES=b02Im(Γ).
××DS(r)-ω02μ0DS(r)=iμ0ω0J(r),
J(r)=αˆδ(x-xS)δ(y-yS)δ(z-zS)J0=αˆδ(r-rS)J0,
DS(r)=iω0μ0VG¯¯·J(r)d3r,
××G¯¯(r, r)-k2G¯¯(r,r)=I¯¯δ(r-r),
G¯¯(r, r)=I¯¯+1k2g(r, r),
g(r, r)=exp(ik|r-r|)4π|r-r|.
DS(r)=iω0μ0J0I¯¯+1k2·αˆg(r, rS).
BS(r)=μ0J0×αˆg(r, rS).
g(r, rS)=exp(ik|r-rS|)4π|r-rS|=i4π0dkρ kρkxJ0(kρ|ρ-ρS|)×exp(ikx|x-xS|).
[Dx(r)]VED=-ωμ0J04πk20dkρ kρ3kxJ0(kρρ)×exp(ikx|x-xS|),
[Bx(r)]VED=0,
[Dx(r)]HED=sgn(x-xS) iJ04πωcos φ0dkρkρ2J1(kρρ)×exp(ikx|x-xS|),
[Bx(r)]HED=iμ0J04πsin φ0dkρ kρ2kxJ1(kρρ)×exp(ikx|x-xS|),
I(e)(x, xS)=exp(ikx|x-xS|),
I(o)(x, xS)=sgn(x-xS)exp(ikx|x-xS|),
I(e)(x, xS)=exp(ik1x|x-xS|)+(A-)(e) exp(-ik1xx)+(A+)(e) exp(ik1xx),
(A-)(e) exp[-ik1x(xS+xD)]
=ρ13{exp(ik1xxD)+(A+)(e) exp[ik1x(xS+xD)]}.
(A+)(e)=ρ12[exp(ik1xxS)+(A-)(e)].
(A-)(e)=ρ13 exp[ik1x(xS+xD)]{exp(ik1xxD)+ρ12 exp[ik1x(2xS+xD)]}1-ρ12ρ13 exp[2ik1x(xS+xD)],
(A+)(e)=ρ12{exp(ik1xxS)+ρ13 exp[ik1x(2xD+xS)]}1-ρ12ρ13 exp[2ik1x(xS+xD)].
(A-)(o)=ρ13 exp[ik1x(xS+xD)]{exp(ik1xxD)-ρ12 exp[ik1x(2xS+xD)]}1-ρ12ρ13 exp[2ik1x(xS+xD)],
(A+)(o)=ρ12{-exp(ik1xxS)+ρ13 exp[ik1x(2xD+xS)]}1-ρ12ρ13 exp[2ik1x(xS+xD)].
ΓVED(E0)VEDES=11ESlimxxS(xˆ·DRTM)VED,
IR(e)=(A-)(e) exp(-ik1xxS)+(A+)(e) exp(ik1xxS).
IR(e)={ρ12 exp(2ik1xxS)+ρ13 exp(2ik1xxD)+2ρ12ρ13 exp[2ik1x(xS+xD)]}1-ρ12ρ13 exp[2ik1x(xS+xD)].
IR(e)=[1+ρ12 exp(2ik1xxS)][1+ρ13 exp(2ik1xxD)]1-ρ12ρ13 exp[2ik1x(xS+xD)]-1.
(E0)VED=11[xˆ·DRTM(x=xS)]VED=32ES0du u31-u2[IR(e)]TM,
ΓVED=320du u31-u2[1+ρ12TM exp(2ik1xxS)][1+ρ13TM exp(2ik1xxD)]1-ρ12TMρ13TM exp[2ik1x(xS+xD)]-1.
ΓHED=11ESlimxxS{zˆ·[DRTM(r)+DRTE(r)]HED}.
[xˆ·BTTE(r)]HED=iμ0J04πsin φ0dkρ kρ2k1xJ1(kρρ)×[exp(ik1x|x-xS|)+(A(-))TE(e) exp(-ik1xx)+(A(+))TE(e) exp(ik1xx)].
[zˆ·DRTE(x=xS)]HED=341ES0du u1-u2[(A-)TE(e) exp(-ik1xxS)+(A+)TE(e) exp(ik1xxS)].
(ΓHED)TE=340du u1-u2[1+ρ12TE exp(2ik1xxS)][1+ρ13TE exp(2ik1xxD)]1-ρ12TEρ13TE exp[2ik1x(xS+xD)]-1.
[zˆ·DRTE(x=xS)]HED=-341ES0du u(1-u2)1-u2[(A-)TM(o) exp(-ik1xxS)-(A+)TM(o) exp(ik1xxS)].
(ΓHED)TM=340du u1-u2(1-u2)[1-ρ12TM exp(2ik1xxS)][1-ρ13TM exp(2ik1xxD)]1-ρ12TMρ13TM exp[2ik1x(xS+xD)]-1.
ΓHED=340du u1-u2(1-u2)[1-ρ12TM exp(2ik1xxS)][1-ρ13TM exp(2ik1xxD)]1-ρ12TMρ13TM exp[2ik1x(xS+xD)]-1+[1+ρ12TE exp(2ik1xxS)][1+ρ13TE exp(2ik1xxD)]1-ρ12TEρ13TE exp[2ik1x(xS+xD)]-1 .
bb0VED=1-γ+32γ Re0du u31-u2×[1+ρ12TM exp(2ik1xxS)],
bb0HED=1-γ+34γ Re0du u1-u2×{(1-u2)[1-ρ12TM exp(2ik1xxS)]+[1+ρ12TE exp(2ik1xxS)]}.
ρ12=r12+r23 exp(2ik2xd)1+r12r23 exp(2ik2xd),
bb0=23bb0HED+13bb0VED.
1+r12r23 exp(2ik2xd)=0.

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