Abstract

An analysis of the radiative properties of an electric dipole placed near planar, Kerr-type nonlinear waveguides is presented. Four fundamental geometries are discussed with emphasis on a linear–nonlinear interface and a Fabry–Perot cavity. A comparison is made with a dipole near a linear waveguide for which the interaction with nearby bound modes influences the damping rate and angular distribution of the dipole’s radiation. The magnitude of the influence, which is readily quantified, depends on the properties of the waveguide modes. Unlike its linear counterpart, the nonlinear waveguide supports different modes when pumped at different intensities. Rather than having properties that are fixed at the time of sample fabrication, a dipole near a nonlinear waveguide is found to have a dynamically tunable, intensity-dependent damping rate.

© 2002 Optical Society of America

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References

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  1. 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.
  2. A. Sommerfeld, “Uber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. Leipz. 28, 665 (1909).
    [CrossRef]
  3. A. Sommerfeld, Partial Differential Equations in Physics (Academic, New York, 1949), Chap. 6.
  4. G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
    [CrossRef]
  5. A. D. Boardman and P. Egan, “Optically nonlinear waves in thin films,” IEEE J. Quantum Electron. QE-22, 319–324 (1986).
    [CrossRef]
  6. G. Stegeman, C. Seaton, J. Ariyasu, R. Wallis, and A. Maradudin, “Nonlinear electromagnetic waves guided by a single interface,” J. Appl. Phys. 58, 2453–2459 (1985).
    [CrossRef]
  7. W. Tomlinson, “Surface wave at a nonlinear interface,” Opt. Lett. 5, 323–325 (1980).
    [CrossRef] [PubMed]
  8. W. R. Holland, “Nonlinear guided waves in low-index, self-focusing thin films: transverse electric case,” J. Opt. Soc. Am. B 3, 1529–1534 (1986).
    [CrossRef]
  9. K. H. Drexhage, “Interaction of light with monomolecular dye layers,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1974), Vol. 12, pp. 163–232.
  10. W. Weber and C. Eagen, “Energy transfer from an excited dye molecule to the surface plasmons of an adjacent metal,” Opt. Lett. 4, 236–238 (1979).
    [CrossRef] [PubMed]
  11. P. Worthing, R. Amos, and W. Barnes, “Modification of the spontaneous emission rate of Eu3+ ions embedded within a dielectric layer above a silver mirror,” Phys. Rev. A 59, 865–872 (1999).
    [CrossRef]
  12. T. Durhuus, C. Joergensen, B. Mikkelsen, R. Pedersen, and K. Stubkjaer, “All optical wavelength conversion by SOAs in a Mach–Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
    [CrossRef]
  13. D. Maywar, Y. Nakano, and G. Agrawal, “1.31-to-1.55 μm wavelength conversion by optically pumping a distributed feedback amplifier,” IEEE Photonics Technol. Lett. 12, 858–860 (2000).
    [CrossRef]
  14. R. Y. Chiao, P. L. Kelley, and E. Garmire, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rev. Lett. 17, 1158 (1966).
    [CrossRef]
  15. G. Carter and Y. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
    [CrossRef]
  16. F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab. I. TE-polarization,” Appl. Phys. B B31, 69–73 (1983).
    [CrossRef]
  17. F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab. II. TM-polarization,” Appl. Phys. B B31, 187–190 (1983).
    [CrossRef]
  18. A. D. Boardman and P. Egan, “S-polarized waves in a thin dielectric film asymmetrically bounded by optically nonlinear media,” IEEE J. Quantum Electron. QE-21, 1701–1713 (1985).
    [CrossRef]
  19. A. Boardman, A. Maradudin, G. Stegeman, T. Twardowski, and E. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
    [CrossRef] [PubMed]
  20. H. A. Macleod, Thin Film Optical Filters, 2nd ed. (Macmillan, New York, 1986).
  21. A. Kaplan, “Theory of hysteresis reflection and refraction of light at the boundary of a nonlinear medium,” Zh. Eksp. Teor. Fiz. 72, 1710–1726 (1977).
  22. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985), Vol. 1.
  23. K. Sullivan and D. Hall, “Enhancement and inhibition of electromagnetic radiation in plane-layered media. I. Plane-wave spectrum approach to modeling classical effects,” J. Opt. Soc. Am. B 14, 1149–1159 (1997).
    [CrossRef]
  24. H. Bingler, H. Brunner, M. Klenke, A. Leitner, F. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
    [CrossRef]
  25. R. W. Boyd, Nonlinear Optics (Academic, New York, 1992), Chap. 4.
  26. Y. J. Chen and G. M. Carter, “Measurement of third order nonlinear susceptibilities by surface plasmons,” Appl. Phys. Lett. 41, 307–309 (1982).
    [CrossRef]
  27. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).
  28. 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]

2000

D. Maywar, Y. Nakano, and G. Agrawal, “1.31-to-1.55 μm wavelength conversion by optically pumping a distributed feedback amplifier,” IEEE Photonics Technol. Lett. 12, 858–860 (2000).
[CrossRef]

1999

P. Worthing, R. Amos, and W. Barnes, “Modification of the spontaneous emission rate of Eu3+ ions embedded within a dielectric layer above a silver mirror,” Phys. Rev. A 59, 865–872 (1999).
[CrossRef]

1997

1994

T. Durhuus, C. Joergensen, B. Mikkelsen, R. Pedersen, and K. Stubkjaer, “All optical wavelength conversion by SOAs in a Mach–Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

1993

H. Bingler, H. Brunner, M. Klenke, A. Leitner, F. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

1987

A. Boardman, A. Maradudin, G. Stegeman, T. Twardowski, and E. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[CrossRef] [PubMed]

1986

W. R. Holland, “Nonlinear guided waves in low-index, self-focusing thin films: transverse electric case,” J. Opt. Soc. Am. B 3, 1529–1534 (1986).
[CrossRef]

A. D. Boardman and P. Egan, “Optically nonlinear waves in thin films,” IEEE J. Quantum Electron. QE-22, 319–324 (1986).
[CrossRef]

1985

G. Stegeman, C. Seaton, J. Ariyasu, R. Wallis, and A. Maradudin, “Nonlinear electromagnetic waves guided by a single interface,” J. Appl. Phys. 58, 2453–2459 (1985).
[CrossRef]

A. D. Boardman and P. Egan, “S-polarized waves in a thin dielectric film asymmetrically bounded by optically nonlinear media,” IEEE J. Quantum Electron. QE-21, 1701–1713 (1985).
[CrossRef]

1984

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]

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

1983

G. Carter and Y. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
[CrossRef]

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab. I. TE-polarization,” Appl. Phys. B B31, 69–73 (1983).
[CrossRef]

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab. II. TM-polarization,” Appl. Phys. B B31, 187–190 (1983).
[CrossRef]

1982

Y. J. Chen and G. M. Carter, “Measurement of third order nonlinear susceptibilities by surface plasmons,” Appl. Phys. Lett. 41, 307–309 (1982).
[CrossRef]

1980

1979

1977

A. Kaplan, “Theory of hysteresis reflection and refraction of light at the boundary of a nonlinear medium,” Zh. Eksp. Teor. Fiz. 72, 1710–1726 (1977).

1966

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

1909

A. Sommerfeld, “Uber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. Leipz. 28, 665 (1909).
[CrossRef]

Agrawal, G.

D. Maywar, Y. Nakano, and G. Agrawal, “1.31-to-1.55 μm wavelength conversion by optically pumping a distributed feedback amplifier,” IEEE Photonics Technol. Lett. 12, 858–860 (2000).
[CrossRef]

Amos, R.

P. Worthing, R. Amos, and W. Barnes, “Modification of the spontaneous emission rate of Eu3+ ions embedded within a dielectric layer above a silver mirror,” Phys. Rev. A 59, 865–872 (1999).
[CrossRef]

Ariyasu, J.

G. Stegeman, C. Seaton, J. Ariyasu, R. Wallis, and A. Maradudin, “Nonlinear electromagnetic waves guided by a single interface,” J. Appl. Phys. 58, 2453–2459 (1985).
[CrossRef]

Aussenegg, F.

H. Bingler, H. Brunner, M. Klenke, A. Leitner, F. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

Barnes, W.

P. Worthing, R. Amos, and W. Barnes, “Modification of the spontaneous emission rate of Eu3+ ions embedded within a dielectric layer above a silver mirror,” Phys. Rev. A 59, 865–872 (1999).
[CrossRef]

Bingler, H.

H. Bingler, H. Brunner, M. Klenke, A. Leitner, F. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

Boardman, A.

A. Boardman, A. Maradudin, G. Stegeman, T. Twardowski, and E. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[CrossRef] [PubMed]

Boardman, A. D.

A. D. Boardman and P. Egan, “Optically nonlinear waves in thin films,” IEEE J. Quantum Electron. QE-22, 319–324 (1986).
[CrossRef]

A. D. Boardman and P. Egan, “S-polarized waves in a thin dielectric film asymmetrically bounded by optically nonlinear media,” IEEE J. Quantum Electron. QE-21, 1701–1713 (1985).
[CrossRef]

Brunner, H.

H. Bingler, H. Brunner, M. Klenke, A. Leitner, F. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

Carter, G.

G. Carter and Y. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
[CrossRef]

Carter, G. M.

Y. J. Chen and G. M. Carter, “Measurement of third order nonlinear susceptibilities by surface plasmons,” Appl. Phys. Lett. 41, 307–309 (1982).
[CrossRef]

Chen, Y.

G. Carter and Y. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
[CrossRef]

Chen, Y. J.

Y. J. Chen and G. M. Carter, “Measurement of third order nonlinear susceptibilities by surface plasmons,” Appl. Phys. Lett. 41, 307–309 (1982).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

Durhuus, T.

T. Durhuus, C. Joergensen, B. Mikkelsen, R. Pedersen, and K. Stubkjaer, “All optical wavelength conversion by SOAs in a Mach–Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

Eagen, C.

Egan, P.

A. D. Boardman and P. Egan, “Optically nonlinear waves in thin films,” IEEE J. Quantum Electron. QE-22, 319–324 (1986).
[CrossRef]

A. D. Boardman and P. Egan, “S-polarized waves in a thin dielectric film asymmetrically bounded by optically nonlinear media,” IEEE J. Quantum Electron. QE-21, 1701–1713 (1985).
[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]

Garmire, E.

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

Hall, D.

Hall, D. G.

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]

Holland, W. R.

W. R. Holland, “Nonlinear guided waves in low-index, self-focusing thin films: transverse electric case,” J. Opt. Soc. Am. B 3, 1529–1534 (1986).
[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]

Joergensen, C.

T. Durhuus, C. Joergensen, B. Mikkelsen, R. Pedersen, and K. Stubkjaer, “All optical wavelength conversion by SOAs in a Mach–Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

Kaplan, A.

A. Kaplan, “Theory of hysteresis reflection and refraction of light at the boundary of a nonlinear medium,” Zh. Eksp. Teor. Fiz. 72, 1710–1726 (1977).

Kelley, P. L.

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rev. Lett. 17, 1158 (1966).
[CrossRef]

Klenke, M.

H. Bingler, H. Brunner, M. Klenke, A. Leitner, F. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

Langbein, U.

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab. I. TE-polarization,” Appl. Phys. B B31, 69–73 (1983).
[CrossRef]

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab. II. TM-polarization,” Appl. Phys. B B31, 187–190 (1983).
[CrossRef]

Lederer, F.

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab. II. TM-polarization,” Appl. Phys. B B31, 187–190 (1983).
[CrossRef]

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab. I. TE-polarization,” Appl. Phys. B B31, 69–73 (1983).
[CrossRef]

Leitner, A.

H. Bingler, H. Brunner, M. Klenke, A. Leitner, F. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

Maradudin, A.

A. Boardman, A. Maradudin, G. Stegeman, T. Twardowski, and E. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[CrossRef] [PubMed]

G. Stegeman, C. Seaton, J. Ariyasu, R. Wallis, and A. Maradudin, “Nonlinear electromagnetic waves guided by a single interface,” J. Appl. Phys. 58, 2453–2459 (1985).
[CrossRef]

Maywar, D.

D. Maywar, Y. Nakano, and G. Agrawal, “1.31-to-1.55 μm wavelength conversion by optically pumping a distributed feedback amplifier,” IEEE Photonics Technol. Lett. 12, 858–860 (2000).
[CrossRef]

Mikkelsen, B.

T. Durhuus, C. Joergensen, B. Mikkelsen, R. Pedersen, and K. Stubkjaer, “All optical wavelength conversion by SOAs in a Mach–Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

Nakano, Y.

D. Maywar, Y. Nakano, and G. Agrawal, “1.31-to-1.55 μm wavelength conversion by optically pumping a distributed feedback amplifier,” IEEE Photonics Technol. Lett. 12, 858–860 (2000).
[CrossRef]

Pedersen, R.

T. Durhuus, C. Joergensen, B. Mikkelsen, R. Pedersen, and K. Stubkjaer, “All optical wavelength conversion by SOAs in a Mach–Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

Ponath, H.-E.

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab. I. TE-polarization,” Appl. Phys. B B31, 69–73 (1983).
[CrossRef]

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab. II. TM-polarization,” Appl. Phys. B B31, 187–190 (1983).
[CrossRef]

Seaton, C.

G. Stegeman, C. Seaton, J. Ariyasu, R. Wallis, and A. Maradudin, “Nonlinear electromagnetic waves guided by a single interface,” J. Appl. Phys. 58, 2453–2459 (1985).
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, “Uber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. Leipz. 28, 665 (1909).
[CrossRef]

Stegeman, G.

A. Boardman, A. Maradudin, G. Stegeman, T. Twardowski, and E. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[CrossRef] [PubMed]

G. Stegeman, C. Seaton, J. Ariyasu, R. Wallis, and A. Maradudin, “Nonlinear electromagnetic waves guided by a single interface,” J. Appl. Phys. 58, 2453–2459 (1985).
[CrossRef]

Stubkjaer, K.

T. Durhuus, C. Joergensen, B. Mikkelsen, R. Pedersen, and K. Stubkjaer, “All optical wavelength conversion by SOAs in a Mach–Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

Sullivan, K.

Tomlinson, W.

Twardowski, T.

A. Boardman, A. Maradudin, G. Stegeman, T. Twardowski, and E. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[CrossRef] [PubMed]

Wallis, R.

G. Stegeman, C. Seaton, J. Ariyasu, R. Wallis, and A. Maradudin, “Nonlinear electromagnetic waves guided by a single interface,” J. Appl. Phys. 58, 2453–2459 (1985).
[CrossRef]

Weber, W.

Weber, W. H.

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

Wokaun, A.

H. Bingler, H. Brunner, M. Klenke, A. Leitner, F. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

Worthing, P.

P. Worthing, R. Amos, and W. Barnes, “Modification of the spontaneous emission rate of Eu3+ ions embedded within a dielectric layer above a silver mirror,” Phys. Rev. A 59, 865–872 (1999).
[CrossRef]

Wright, E.

A. Boardman, A. Maradudin, G. Stegeman, T. Twardowski, and E. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[CrossRef] [PubMed]

Ann. Phys. Leipz.

A. Sommerfeld, “Uber die ausbreitung der wellen in der drahtlosen telegraphie,” Ann. Phys. Leipz. 28, 665 (1909).
[CrossRef]

Appl. Phys. B

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab. I. TE-polarization,” Appl. Phys. B B31, 69–73 (1983).
[CrossRef]

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab. II. TM-polarization,” Appl. Phys. B B31, 187–190 (1983).
[CrossRef]

Appl. Phys. Lett.

G. Carter and Y. Chen, “Nonlinear optical coupling between radiation and confined modes,” Appl. Phys. Lett. 42, 643–645 (1983).
[CrossRef]

Y. J. Chen and G. M. Carter, “Measurement of third order nonlinear susceptibilities by surface plasmons,” Appl. Phys. Lett. 41, 307–309 (1982).
[CrossRef]

IEEE J. Quantum Electron.

A. D. Boardman and P. Egan, “S-polarized waves in a thin dielectric film asymmetrically bounded by optically nonlinear media,” IEEE J. Quantum Electron. QE-21, 1701–1713 (1985).
[CrossRef]

A. D. Boardman and P. Egan, “Optically nonlinear waves in thin films,” IEEE J. Quantum Electron. QE-22, 319–324 (1986).
[CrossRef]

IEEE Photonics Technol. Lett.

T. Durhuus, C. Joergensen, B. Mikkelsen, R. Pedersen, and K. Stubkjaer, “All optical wavelength conversion by SOAs in a Mach–Zehnder configuration,” IEEE Photonics Technol. Lett. 6, 53–55 (1994).
[CrossRef]

D. Maywar, Y. Nakano, and G. Agrawal, “1.31-to-1.55 μm wavelength conversion by optically pumping a distributed feedback amplifier,” IEEE Photonics Technol. Lett. 12, 858–860 (2000).
[CrossRef]

J. Appl. Phys.

G. Stegeman, C. Seaton, J. Ariyasu, R. Wallis, and A. Maradudin, “Nonlinear electromagnetic waves guided by a single interface,” J. Appl. Phys. 58, 2453–2459 (1985).
[CrossRef]

J. Chem. Phys.

H. Bingler, H. Brunner, M. Klenke, A. Leitner, F. Aussenegg, and A. Wokaun, “Enhanced second harmonic generation in a silver-spacer-islands multilayer system,” J. Chem. Phys. 99, 7499–7505 (1993).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rep.

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

Phys. Rev. A

P. Worthing, R. Amos, and W. Barnes, “Modification of the spontaneous emission rate of Eu3+ ions embedded within a dielectric layer above a silver mirror,” Phys. Rev. A 59, 865–872 (1999).
[CrossRef]

A. Boardman, A. Maradudin, G. Stegeman, T. Twardowski, and E. Wright, “Exact theory of nonlinear p-polarized optical waves,” Phys. Rev. A 35, 1159–1164 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett.

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rev. Lett. 17, 1158 (1966).
[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]

Zh. Eksp. Teor. Fiz.

A. Kaplan, “Theory of hysteresis reflection and refraction of light at the boundary of a nonlinear medium,” Zh. Eksp. Teor. Fiz. 72, 1710–1726 (1977).

Other

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985), Vol. 1.

R. W. Boyd, Nonlinear Optics (Academic, New York, 1992), Chap. 4.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).

H. A. Macleod, Thin Film Optical Filters, 2nd ed. (Macmillan, New York, 1986).

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.

A. Sommerfeld, Partial Differential Equations in Physics (Academic, New York, 1949), Chap. 6.

K. H. Drexhage, “Interaction of light with monomolecular dye layers,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1974), Vol. 12, pp. 163–232.

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Figures (11)

Fig. 1
Fig. 1

Structure of a nonlinear planar waveguide and the geometry for its decomposition for numerical analysis.

Fig. 2
Fig. 2

Normalized damping rate of an isotropic distribution of dipoles embedded 1/4 of the way across three different three-layer structures, the all-dielectric waveguide (ADWG), the singly metal-clad waveguide (SMCWG), and the doubly metal-clad waveguides (DMCWG), plotted as a function of the normalized thickness coefficient εz/λ. Permittivity profiles for each of the structure are (1, 2, 1), (1, 2,-8.50+i0.759) and (-8.50+i0.759, 2,-8.50+i0.759), respectively.

Fig. 3
Fig. 3

Selected mode profiles of varying mode parameter D as a function of the normalized position z/λ with respect to the interface. The maximum separation between the mode peak and the interface, z/λ0.431, occurs for D2.27.

Fig. 4
Fig. 4

Normalized damping rate as a function of D, a measure of mode index, for an isotropic distribution of dipoles near the interface between linear and nonlinear half-spaces. Also shown is the value of D for which the mode peak is a maximum distance from the interface (zmax) and the power per unit width in the y direction carried in the mode as a function of D. Several dipole positions are shown on both the linear (z<0) and the nonlinear (z>0) sides of the interface.

Fig. 5
Fig. 5

Inset, complete power spectrum of a dipole at a linear–nonlinear interface in the presence of a mode (of mode parameter D=1.01) supported at the interface. Large plot, details of the power spectra for dipoles near similar modes and around the peak in the damping rate shown in Fig. 4, illustrating differences in coupling efficiency to the bound modes (represented by the region uc<u<1).

Fig. 6
Fig. 6

(a) Allowed effective indices, N, of the modes of a symmetric, nonlinear, dielectric waveguide and their corresponding αI at the interface. (b) Damping rate of a dipole placed at the same interface. The damping rate branches as the mode profile branches into symmetric (middle branch) and asymmetric (top and bottom branch) components. Three representative modes a, b, and c (depicted in Fig. 7) with a common intensity at the dipole position are chosen to illustrate that the dipole–mode overlap does not uniquely specify the damping rate.

Fig. 7
Fig. 7

Selected electric field profiles for modes a, b, and c identified in Fig. 6.

Fig. 8
Fig. 8

Damping rate for several dipole positions throughout the waveguide. For the dipole in the center of the waveguide, the upper branch of the curve is the asymmetric one.

Fig. 9
Fig. 9

Inset, thickness dependence of the damping rate of the DMCWG. Large plot, magnified view of the steepest (dotted) region, showing the starting (zero-intensity) values for the thickness of the nonlinear Fabry–Perot cavity coupled to a dipole.

Fig. 10
Fig. 10

Intensity-induced damping rate change for the DMCWG plotted versus αI (minor axes) for both positive and negative nonlinearities and fitted to the thickness dependence of the linear DMCWG for three different nonlinear waveguide starting thicknesses. The top two curves have been vertically offset to separate the curves.

Fig. 11
Fig. 11

For a starting value of εAg=-16.0+i0.6, the effect of modifications to the magnitude of the real (left) and imaginary (right) parts of the permittivity on the form and position of the damping-rate curves.

Equations (29)

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P=VJ·EdV.
J·E=12Re(J*·E).
J(r, t)=-iωp0 exp(-iωt)δ(3)(r-zˆd),
E=Etotal exp(-iωt),
P=-ωp02·Im[Etotal(r=zˆd)].
b=P/ω.
u=kmdρkmd=1-(kmdz/kmd)2=sin θmd.
sin θm=uεmd/εm.
lm=εm-εmdu2.
Em=1εm[km2Πm+(·Πm)].
Πm(r, z)=eˆzp0kεmd0J0(ur) ulmd[δm,md×exp(iklm|z-zs|)+fm- exp(-iklmz)+fm+ exp(+iklmz)]du,
EtotalVED=eˆz p0k3εmdεmd 0 u31-u2 [1+ρmd,0TM exp(i2klmdzs)][1+ρmd,M+1TM exp(i2klmdzc)]1-ρmd,0TMρmd,M+1TM exp[i2klmd(zs+zc)] du.
EtotalVED=eˆz p0k3εmdεmd 0 u1-u2 [1+ρmd,0TE exp(i2klmdzs)][1+ρmd,M+1TE exp(i2klmdzc)]1-ρmd,0TEρmd,M+1TE exp[i2klmd(zs+zc)]+(1-u2) [1-ρmd,0TM exp(i2klmdzs)][1-ρmd,M+1TM exp(i2klmdzc)]1-ρmd,0TMρmd,M+1TM exp[i2klmd(zs+zc)]du,
rα,βTE=lα-lβlα+lβ,
rα,βTM=εβlα-εαlβεβlα+εαlβ,
ρα,γ=rα,β+rβ,γ exp(i2klβzβ)1+rα,βrβ,γ exp(i2klβzβ),
Em(z)=Em+ expiklmz-μ=1mzμ+Em- exp-iklmz-μ=1mzμ,
Em±=exp(iklmzm)rm,m+1TEEm+1+Em+1±1+rm,m+1TE
Hm±=exp(iklmzm)rm,m+1TMHm+1+Hm+1±1+rm,m+1TM
εm=εm0+(α/2)(Im-1+Im),
Im=|Em+1++Em+1-|2
N=εmd sin θmd=uεmd
EM+1(z)=EM+1+ exp[iklM+1(z-Z)],
E0(z)=E0- exp(-i2kl0z)
HM+1(z)=HM+1+ exp[iklM+1(z-Z)],
H0(z)=H0- exp(-i2kl0z)
Z=m=1Mzm.
D=N2-εlin|Δε|.
q=ε(ω)sp+εhε(ω)sp-2εh,

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