Abstract

We consider an attenuated total reflection prism-coupling geometry used to excite surface-plasmon waves along a metal film, bounded by a substrate with an intensity-dependent dielectric constant. Nonlinear wave theory is developed in the infinite incident plane-wave approximation, assuming a dielectric constant proportional to the square of the electric field normal to the film. We calculate the intensity required to observe bistability in the reflected intensity by excitation of the nonlinear, long-range surface plasmon and find it to be 2 orders of magnitude less than that required for the nonlinear, single-surface plasmon. We compare the nonlinear wave analysis with other approaches and illustrate the effects of the sign of the nonlinearity and of a nonlinear coupling layer.

© 1986 Optical Society of America

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  1. D. Sarid and G. I. Stegeman, “Optimization of the effects of power dependent refractive indices in optical waveguides,” J. Appl. Phys. 52, 5439–5441 (1981).
    [CrossRef]
  2. B. Crosignani, C. H. Papas, and P. Di Porto, “Coupled-mode theory approach to nonlinear pulse propagation in optical fibers,” Opt. Lett. 6, 61–63 (1981).
    [CrossRef] [PubMed]
  3. H. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
    [CrossRef]
  4. D. Sarid, “Intrinsic bistable guided-wave devices: theory and applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 317, 132–135 (1981).
  5. G. I. Stegeman, “Guided wave approaches to optical bistability,” IEEE J. Quantum Electron. QE-18, 1610–1619 (1982).
    [CrossRef]
  6. B. Bosacchi and L. M. Narducci, “Optical bistability in the frustrated-total-reflection optical cavity,” Opt. Lett. 8, 324–326 (1983).
    [CrossRef] [PubMed]
  7. G. M. Wysin, H. J. Simon, and R. T. Deck, “Optical bistability with surface plasmons,” Opt. Lett. 6, 30–32 (1981).
    [CrossRef] [PubMed]
  8. Y. J. Chen and G. M. Carter, “Attenuated total reflection calculations for nonlinear surface plasmon dispersion,” Solid State Commun. 45, 277–280 (1983).
    [CrossRef]
  9. P. Martinot, S. Laval, and A. Koster, “Optical bistability from surface plasmon excitation through a nonlinear medium,” J. Phys. (Paris) 45, 597–600 (1984).
    [CrossRef]
  10. P. Vincent, N. Paraire, M. Neviere, A. Koster, and R. Reinisch, “Gratings in nonlinear optics and optical bistability,” J. Opt. Soc. Am. B 2, 1106–1116 (1985).
    [CrossRef]
  11. P. W. Smith, J.-P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a nonlinear interface,” Appl. Phys. Lett. 35, 846–848 (1979).
    [CrossRef]
  12. A. E. Kaplan, “Hysteresis reflection and refraction by a nonlinear boundary—a new class of effects in nonlinear optics,” JETP Lett. 24, 114–119 (1976).
  13. A. E. Kaplan, “Theory of hysteresis reflection and refraction of light by a boundary of a nonlinear medium,” Sov. Phys. JETP 45, 869–905 (1977).
  14. W. J. Tomlinson, “Surface wave at a nonlinear interface,” Opt. Lett. 5, 323–325 (1980).
    [CrossRef] [PubMed]
  15. A. A. Maradudin, “S-polarized nonlinear surface polaritons,” Z. Phys. B 41, 341–344 (1981).
    [CrossRef]
  16. N. N. Akhmediev, “Novel class of nonlinear surface waves: asymmetric modes in a symmetric layered structure,” Sov. Phys. JETP 56, 299–303 (1982).
  17. U. Langbein, F. Lederer, and H.-E. Ponath, “A new type of nonlinear slab-guided waves,” Opt. Commun. 46, 167–169 (1983).
    [CrossRef]
  18. A. A. Maradudin, “Nonlinear surface electromagnetic waves,” in Optical and Acoustic Waves in Solids—Modern Topics, M. Borissov, ed. (World Scientific, Singapore, 1983), pp. 72–142.
  19. D. J. Robbins, “TE modes in a slab waveguide bounded by nonlinear media,” Opt. Commun. 47, 309–312 (1983).
    [CrossRef]
  20. V. J. Montemayor and R. T. Deck, “Optical bistability with the waveguide mode,” J. Opt. Soc. Am. B 2, 1010–1013 (1985).
    [CrossRef]
  21. V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, “Nonlinear surface polaritons,” JETP Lett. 32, 512–515 (1980).
  22. V. K. Fedyanin and D. Mihalache, “P-polarized nonlinear surface polaritons in layered structures,” Z. Phys. B 47, 167–173 (1982).
    [CrossRef]
  23. F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab, II. TM-polarization,” Appl. Phys. B 31, 187–190 (1983).
    [CrossRef]
  24. D. Mihalache, R. G. Nazmitdinov, and V. K. Fedyanin, “P-polarized nonlinear surface waves in symmetric layered structures,” Phys. Scr. 29, 269–275 (1984).
    [CrossRef]
  25. A. D. Boardman and P. Egan, “Nonlinear surface and guided polaritons of a general layered dielectric structure,” J. Phys. C 5, 291–303 (1984).
  26. C. T. Seaton, J. D. Valera, B. Svenson, and G. I. Stegeman, “Comparison of solutions for TM-polarized nonlinear guided waves,” Opt. Lett. 10, 149–150 (1985).
    [CrossRef] [PubMed]
  27. G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, “Nonlinear electromagnetic waves guided by a single interface,” J. Appl. Phys. 58, 2453–2459 (1985).
    [CrossRef]
  28. J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, “Nonlinear surface polaritons guided by metal films,” J. Appl. Phys. 58, 2460–2466 (1985).
    [CrossRef]
  29. K. M. Leung, “P-polarized nonlinear surface polaritons in materials with intensity-dependent dielectric functions,” Phys. Rev. B 32, 5093–5101 (1985).
    [CrossRef]
  30. C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, and J. D. Valera, “Nonlinear distributed waveguide couplers,” J. Opt. Soc. Am. A 2, 590–594 (1985).
    [CrossRef]
  31. G. J. Kovacs, “Optical excitation of resonant electromagnetic oscillations in thin film,” Ph.D. dissertation (University of Toronto, Toronto, Canada, 1977), p. 69.
  32. D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
    [CrossRef]
  33. A. E. Craig, G. A. Olson, and D. Sarid, “Experimental observation of the long-range surface-plasmon polariton,” Opt. Lett. 8, 380–382.
    [PubMed]
  34. Y. Kuwamura, M. Fukui, and O. Tada, “Experimental observation of long-range surface plasmon polaritons,” J. Phys. Soc. Jpn. 52, 2350–2355 (1983).
    [CrossRef]
  35. J. C. Quail, J. G. Rako, and H. J. Simon, “Long-range surface-plasmon modes in silver and aluminum films,” Opt. Lett. 8, 377–379 (1983).
    [CrossRef] [PubMed]
  36. D. Sarid, R. T. Deck, A. E. Craig, R. K. Hickernell, R. S. Jameson, and J. J. Fasano, “Optical field enhancement by long-range surface-plasma waves,” Appl. Opt. 21, 3993–3995 (1982).
    [CrossRef] [PubMed]
  37. E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Phys. 241, 313–324 (1971).
    [CrossRef]
  38. M. J. Moran, C. Y. She, and R. L. Carman, “Interferometric measurements of the nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-12, 259–263 (1975).
    [CrossRef]
  39. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  40. D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197–200 (1981).
    [CrossRef]
  41. H. E. Bennett and J. M. Bennett, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abèles, ed. (Elsevier North-Holland, New York, 1966), p. 175.
  42. R. T. Deck, D. Sarid, G. A. Olson, and J. M. Elson, “Coupling between finite electromagnetic beam and long-range surface-plasmon mode,” Appl. Opt. 22, 3397–3405 (1983).
    [CrossRef] [PubMed]
  43. C. K. R. T. Jones and J. V. Moloney, “Stability and instability of nonlinear waveguide modes” in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, and S. D. Smith, eds. (Springer-Verlag, Berlin, 1986), pp. 98–101.
    [CrossRef]

1985 (7)

P. Vincent, N. Paraire, M. Neviere, A. Koster, and R. Reinisch, “Gratings in nonlinear optics and optical bistability,” J. Opt. Soc. Am. B 2, 1106–1116 (1985).
[CrossRef]

V. J. Montemayor and R. T. Deck, “Optical bistability with the waveguide mode,” J. Opt. Soc. Am. B 2, 1010–1013 (1985).
[CrossRef]

C. T. Seaton, J. D. Valera, B. Svenson, and G. I. Stegeman, “Comparison of solutions for TM-polarized nonlinear guided waves,” Opt. Lett. 10, 149–150 (1985).
[CrossRef] [PubMed]

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

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, “Nonlinear surface polaritons guided by metal films,” J. Appl. Phys. 58, 2460–2466 (1985).
[CrossRef]

K. M. Leung, “P-polarized nonlinear surface polaritons in materials with intensity-dependent dielectric functions,” Phys. Rev. B 32, 5093–5101 (1985).
[CrossRef]

C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, and J. D. Valera, “Nonlinear distributed waveguide couplers,” J. Opt. Soc. Am. A 2, 590–594 (1985).
[CrossRef]

1984 (3)

D. Mihalache, R. G. Nazmitdinov, and V. K. Fedyanin, “P-polarized nonlinear surface waves in symmetric layered structures,” Phys. Scr. 29, 269–275 (1984).
[CrossRef]

A. D. Boardman and P. Egan, “Nonlinear surface and guided polaritons of a general layered dielectric structure,” J. Phys. C 5, 291–303 (1984).

P. Martinot, S. Laval, and A. Koster, “Optical bistability from surface plasmon excitation through a nonlinear medium,” J. Phys. (Paris) 45, 597–600 (1984).
[CrossRef]

1983 (8)

Y. J. Chen and G. M. Carter, “Attenuated total reflection calculations for nonlinear surface plasmon dispersion,” Solid State Commun. 45, 277–280 (1983).
[CrossRef]

B. Bosacchi and L. M. Narducci, “Optical bistability in the frustrated-total-reflection optical cavity,” Opt. Lett. 8, 324–326 (1983).
[CrossRef] [PubMed]

U. Langbein, F. Lederer, and H.-E. Ponath, “A new type of nonlinear slab-guided waves,” Opt. Commun. 46, 167–169 (1983).
[CrossRef]

D. J. Robbins, “TE modes in a slab waveguide bounded by nonlinear media,” Opt. Commun. 47, 309–312 (1983).
[CrossRef]

Y. Kuwamura, M. Fukui, and O. Tada, “Experimental observation of long-range surface plasmon polaritons,” J. Phys. Soc. Jpn. 52, 2350–2355 (1983).
[CrossRef]

J. C. Quail, J. G. Rako, and H. J. Simon, “Long-range surface-plasmon modes in silver and aluminum films,” Opt. Lett. 8, 377–379 (1983).
[CrossRef] [PubMed]

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab, II. TM-polarization,” Appl. Phys. B 31, 187–190 (1983).
[CrossRef]

R. T. Deck, D. Sarid, G. A. Olson, and J. M. Elson, “Coupling between finite electromagnetic beam and long-range surface-plasmon mode,” Appl. Opt. 22, 3397–3405 (1983).
[CrossRef] [PubMed]

1982 (4)

V. K. Fedyanin and D. Mihalache, “P-polarized nonlinear surface polaritons in layered structures,” Z. Phys. B 47, 167–173 (1982).
[CrossRef]

D. Sarid, R. T. Deck, A. E. Craig, R. K. Hickernell, R. S. Jameson, and J. J. Fasano, “Optical field enhancement by long-range surface-plasma waves,” Appl. Opt. 21, 3993–3995 (1982).
[CrossRef] [PubMed]

N. N. Akhmediev, “Novel class of nonlinear surface waves: asymmetric modes in a symmetric layered structure,” Sov. Phys. JETP 56, 299–303 (1982).

G. I. Stegeman, “Guided wave approaches to optical bistability,” IEEE J. Quantum Electron. QE-18, 1610–1619 (1982).
[CrossRef]

1981 (7)

D. Sarid, “Intrinsic bistable guided-wave devices: theory and applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 317, 132–135 (1981).

D. Sarid and G. I. Stegeman, “Optimization of the effects of power dependent refractive indices in optical waveguides,” J. Appl. Phys. 52, 5439–5441 (1981).
[CrossRef]

B. Crosignani, C. H. Papas, and P. Di Porto, “Coupled-mode theory approach to nonlinear pulse propagation in optical fibers,” Opt. Lett. 6, 61–63 (1981).
[CrossRef] [PubMed]

G. M. Wysin, H. J. Simon, and R. T. Deck, “Optical bistability with surface plasmons,” Opt. Lett. 6, 30–32 (1981).
[CrossRef] [PubMed]

A. A. Maradudin, “S-polarized nonlinear surface polaritons,” Z. Phys. B 41, 341–344 (1981).
[CrossRef]

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
[CrossRef]

D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197–200 (1981).
[CrossRef]

1980 (2)

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, “Nonlinear surface polaritons,” JETP Lett. 32, 512–515 (1980).

W. J. Tomlinson, “Surface wave at a nonlinear interface,” Opt. Lett. 5, 323–325 (1980).
[CrossRef] [PubMed]

1979 (2)

P. W. Smith, J.-P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a nonlinear interface,” Appl. Phys. Lett. 35, 846–848 (1979).
[CrossRef]

H. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

1977 (1)

A. E. Kaplan, “Theory of hysteresis reflection and refraction of light by a boundary of a nonlinear medium,” Sov. Phys. JETP 45, 869–905 (1977).

1976 (1)

A. E. Kaplan, “Hysteresis reflection and refraction by a nonlinear boundary—a new class of effects in nonlinear optics,” JETP Lett. 24, 114–119 (1976).

1975 (1)

M. J. Moran, C. Y. She, and R. L. Carman, “Interferometric measurements of the nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-12, 259–263 (1975).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1971 (1)

E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, “Nonlinear surface polaritons,” JETP Lett. 32, 512–515 (1980).

Akhmediev, N. N.

N. N. Akhmediev, “Novel class of nonlinear surface waves: asymmetric modes in a symmetric layered structure,” Sov. Phys. JETP 56, 299–303 (1982).

Ariyasu, J.

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

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, “Nonlinear surface polaritons guided by metal films,” J. Appl. Phys. 58, 2460–2466 (1985).
[CrossRef]

Babichenko, V. S.

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, “Nonlinear surface polaritons,” JETP Lett. 32, 512–515 (1980).

Bennett, H. E.

H. E. Bennett and J. M. Bennett, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abèles, ed. (Elsevier North-Holland, New York, 1966), p. 175.

Bennett, J. M.

H. E. Bennett and J. M. Bennett, in Optical Properties and Electronic Structure of Metals and Alloys, F. Abèles, ed. (Elsevier North-Holland, New York, 1966), p. 175.

Boardman, A. D.

A. D. Boardman and P. Egan, “Nonlinear surface and guided polaritons of a general layered dielectric structure,” J. Phys. C 5, 291–303 (1984).

Bosacchi, B.

Carman, R. L.

M. J. Moran, C. Y. She, and R. L. Carman, “Interferometric measurements of the nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-12, 259–263 (1975).
[CrossRef]

Carter, G. M.

Y. J. Chen and G. M. Carter, “Attenuated total reflection calculations for nonlinear surface plasmon dispersion,” Solid State Commun. 45, 277–280 (1983).
[CrossRef]

Chen, Y. J.

Y. J. Chen and G. M. Carter, “Attenuated total reflection calculations for nonlinear surface plasmon dispersion,” Solid State Commun. 45, 277–280 (1983).
[CrossRef]

Chernyak, V. Y.

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, “Nonlinear surface polaritons,” JETP Lett. 32, 512–515 (1980).

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Craig, A. E.

Crosignani, B.

Deck, R. T.

Di Porto, P.

Egan, P.

A. D. Boardman and P. Egan, “Nonlinear surface and guided polaritons of a general layered dielectric structure,” J. Phys. C 5, 291–303 (1984).

Elson, J. M.

Fasano, J. J.

Fedyanin, V. K.

D. Mihalache, R. G. Nazmitdinov, and V. K. Fedyanin, “P-polarized nonlinear surface waves in symmetric layered structures,” Phys. Scr. 29, 269–275 (1984).
[CrossRef]

V. K. Fedyanin and D. Mihalache, “P-polarized nonlinear surface polaritons in layered structures,” Z. Phys. B 47, 167–173 (1982).
[CrossRef]

Fukui, M.

Y. Kuwamura, M. Fukui, and O. Tada, “Experimental observation of long-range surface plasmon polaritons,” J. Phys. Soc. Jpn. 52, 2350–2355 (1983).
[CrossRef]

Garmire, E.

H. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Hermann, J.-P.

P. W. Smith, J.-P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a nonlinear interface,” Appl. Phys. Lett. 35, 846–848 (1979).
[CrossRef]

Hickernell, R. K.

Jameson, R. S.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Jones, C. K. R. T.

C. K. R. T. Jones and J. V. Moloney, “Stability and instability of nonlinear waveguide modes” in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, and S. D. Smith, eds. (Springer-Verlag, Berlin, 1986), pp. 98–101.
[CrossRef]

Kaplan, A. E.

A. E. Kaplan, “Theory of hysteresis reflection and refraction of light by a boundary of a nonlinear medium,” Sov. Phys. JETP 45, 869–905 (1977).

A. E. Kaplan, “Hysteresis reflection and refraction by a nonlinear boundary—a new class of effects in nonlinear optics,” JETP Lett. 24, 114–119 (1976).

Koster, A.

P. Vincent, N. Paraire, M. Neviere, A. Koster, and R. Reinisch, “Gratings in nonlinear optics and optical bistability,” J. Opt. Soc. Am. B 2, 1106–1116 (1985).
[CrossRef]

P. Martinot, S. Laval, and A. Koster, “Optical bistability from surface plasmon excitation through a nonlinear medium,” J. Phys. (Paris) 45, 597–600 (1984).
[CrossRef]

Kovacs, G. J.

G. J. Kovacs, “Optical excitation of resonant electromagnetic oscillations in thin film,” Ph.D. dissertation (University of Toronto, Toronto, Canada, 1977), p. 69.

Kretschmann, E.

E. Kretschmann, “The determination of the optical constants of metals by excitation of surface plasmons,” Z. Phys. 241, 313–324 (1971).
[CrossRef]

Kuwamura, Y.

Y. Kuwamura, M. Fukui, and O. Tada, “Experimental observation of long-range surface plasmon polaritons,” J. Phys. Soc. Jpn. 52, 2350–2355 (1983).
[CrossRef]

Langbein, U.

U. Langbein, F. Lederer, and H.-E. Ponath, “A new type of nonlinear slab-guided waves,” Opt. Commun. 46, 167–169 (1983).
[CrossRef]

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab, II. TM-polarization,” Appl. Phys. B 31, 187–190 (1983).
[CrossRef]

Laval, S.

P. Martinot, S. Laval, and A. Koster, “Optical bistability from surface plasmon excitation through a nonlinear medium,” J. Phys. (Paris) 45, 597–600 (1984).
[CrossRef]

Lederer, F.

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab, II. TM-polarization,” Appl. Phys. B 31, 187–190 (1983).
[CrossRef]

U. Langbein, F. Lederer, and H.-E. Ponath, “A new type of nonlinear slab-guided waves,” Opt. Commun. 46, 167–169 (1983).
[CrossRef]

Leung, K. M.

K. M. Leung, “P-polarized nonlinear surface polaritons in materials with intensity-dependent dielectric functions,” Phys. Rev. B 32, 5093–5101 (1985).
[CrossRef]

Liao, C.

Maloney, P. J.

P. W. Smith, J.-P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a nonlinear interface,” Appl. Phys. Lett. 35, 846–848 (1979).
[CrossRef]

Maradudin, A. A.

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, “Nonlinear surface polaritons guided by metal films,” J. Appl. Phys. 58, 2460–2466 (1985).
[CrossRef]

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

A. A. Maradudin, “S-polarized nonlinear surface polaritons,” Z. Phys. B 41, 341–344 (1981).
[CrossRef]

A. A. Maradudin, “Nonlinear surface electromagnetic waves,” in Optical and Acoustic Waves in Solids—Modern Topics, M. Borissov, ed. (World Scientific, Singapore, 1983), pp. 72–142.

Marburger, J. H.

H. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Martinot, P.

P. Martinot, S. Laval, and A. Koster, “Optical bistability from surface plasmon excitation through a nonlinear medium,” J. Phys. (Paris) 45, 597–600 (1984).
[CrossRef]

Mihalache, D.

D. Mihalache, R. G. Nazmitdinov, and V. K. Fedyanin, “P-polarized nonlinear surface waves in symmetric layered structures,” Phys. Scr. 29, 269–275 (1984).
[CrossRef]

V. K. Fedyanin and D. Mihalache, “P-polarized nonlinear surface polaritons in layered structures,” Z. Phys. B 47, 167–173 (1982).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197–200 (1981).
[CrossRef]

Moloney, J. V.

C. K. R. T. Jones and J. V. Moloney, “Stability and instability of nonlinear waveguide modes” in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, and S. D. Smith, eds. (Springer-Verlag, Berlin, 1986), pp. 98–101.
[CrossRef]

Montemayor, V. J.

Moran, M. J.

M. J. Moran, C. Y. She, and R. L. Carman, “Interferometric measurements of the nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-12, 259–263 (1975).
[CrossRef]

Narducci, L. M.

Nazmitdinov, R. G.

D. Mihalache, R. G. Nazmitdinov, and V. K. Fedyanin, “P-polarized nonlinear surface waves in symmetric layered structures,” Phys. Scr. 29, 269–275 (1984).
[CrossRef]

Neviere, M.

Olson, G. A.

Papas, C. H.

Paraire, N.

Ponath, H.-E.

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab, II. TM-polarization,” Appl. Phys. B 31, 187–190 (1983).
[CrossRef]

U. Langbein, F. Lederer, and H.-E. Ponath, “A new type of nonlinear slab-guided waves,” Opt. Commun. 46, 167–169 (1983).
[CrossRef]

Prise, M. E.

D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197–200 (1981).
[CrossRef]

Quail, J. C.

Rako, J. G.

Reinisch, R.

Robbins, D. J.

D. J. Robbins, “TE modes in a slab waveguide bounded by nonlinear media,” Opt. Commun. 47, 309–312 (1983).
[CrossRef]

Sarid, D.

R. T. Deck, D. Sarid, G. A. Olson, and J. M. Elson, “Coupling between finite electromagnetic beam and long-range surface-plasmon mode,” Appl. Opt. 22, 3397–3405 (1983).
[CrossRef] [PubMed]

D. Sarid, R. T. Deck, A. E. Craig, R. K. Hickernell, R. S. Jameson, and J. J. Fasano, “Optical field enhancement by long-range surface-plasma waves,” Appl. Opt. 21, 3993–3995 (1982).
[CrossRef] [PubMed]

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
[CrossRef]

D. Sarid, “Intrinsic bistable guided-wave devices: theory and applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 317, 132–135 (1981).

D. Sarid and G. I. Stegeman, “Optimization of the effects of power dependent refractive indices in optical waveguides,” J. Appl. Phys. 52, 5439–5441 (1981).
[CrossRef]

A. E. Craig, G. A. Olson, and D. Sarid, “Experimental observation of the long-range surface-plasmon polariton,” Opt. Lett. 8, 380–382.
[PubMed]

Seaton, C. T.

C. T. Seaton, J. D. Valera, B. Svenson, and G. I. Stegeman, “Comparison of solutions for TM-polarized nonlinear guided waves,” Opt. Lett. 10, 149–150 (1985).
[CrossRef] [PubMed]

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

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, “Nonlinear surface polaritons guided by metal films,” J. Appl. Phys. 58, 2460–2466 (1985).
[CrossRef]

C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, and J. D. Valera, “Nonlinear distributed waveguide couplers,” J. Opt. Soc. Am. A 2, 590–594 (1985).
[CrossRef]

D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197–200 (1981).
[CrossRef]

She, C. Y.

M. J. Moran, C. Y. She, and R. L. Carman, “Interferometric measurements of the nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-12, 259–263 (1975).
[CrossRef]

Shoemaker, R. L.

Simon, H. J.

Smith, P. W.

P. W. Smith, J.-P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a nonlinear interface,” Appl. Phys. Lett. 35, 846–848 (1979).
[CrossRef]

Smith, S. D.

D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197–200 (1981).
[CrossRef]

Stegeman, G. I.

C. Liao, G. I. Stegeman, C. T. Seaton, R. L. Shoemaker, and J. D. Valera, “Nonlinear distributed waveguide couplers,” J. Opt. Soc. Am. A 2, 590–594 (1985).
[CrossRef]

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, “Nonlinear surface polaritons guided by metal films,” J. Appl. Phys. 58, 2460–2466 (1985).
[CrossRef]

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

C. T. Seaton, J. D. Valera, B. Svenson, and G. I. Stegeman, “Comparison of solutions for TM-polarized nonlinear guided waves,” Opt. Lett. 10, 149–150 (1985).
[CrossRef] [PubMed]

G. I. Stegeman, “Guided wave approaches to optical bistability,” IEEE J. Quantum Electron. QE-18, 1610–1619 (1982).
[CrossRef]

D. Sarid and G. I. Stegeman, “Optimization of the effects of power dependent refractive indices in optical waveguides,” J. Appl. Phys. 52, 5439–5441 (1981).
[CrossRef]

Svenson, B.

Tada, O.

Y. Kuwamura, M. Fukui, and O. Tada, “Experimental observation of long-range surface plasmon polaritons,” J. Phys. Soc. Jpn. 52, 2350–2355 (1983).
[CrossRef]

Tomlinson, W. J.

W. J. Tomlinson, “Surface wave at a nonlinear interface,” Opt. Lett. 5, 323–325 (1980).
[CrossRef] [PubMed]

P. W. Smith, J.-P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a nonlinear interface,” Appl. Phys. Lett. 35, 846–848 (1979).
[CrossRef]

Valera, J. D.

Vincent, P.

Wallis, R. F.

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

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, “Nonlinear surface polaritons guided by metal films,” J. Appl. Phys. 58, 2460–2466 (1985).
[CrossRef]

Winful, H.

H. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Wysin, G. M.

Appl. Opt. (2)

Appl. Phys. B (1)

F. Lederer, U. Langbein, and H.-E. Ponath, “Nonlinear waves guided by a dielectric slab, II. TM-polarization,” Appl. Phys. B 31, 187–190 (1983).
[CrossRef]

Appl. Phys. Lett. (2)

H. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

P. W. Smith, J.-P. Hermann, W. J. Tomlinson, and P. J. Maloney, “Optical bistability at a nonlinear interface,” Appl. Phys. Lett. 35, 846–848 (1979).
[CrossRef]

IEEE J. Quantum Electron. (2)

G. I. Stegeman, “Guided wave approaches to optical bistability,” IEEE J. Quantum Electron. QE-18, 1610–1619 (1982).
[CrossRef]

M. J. Moran, C. Y. She, and R. L. Carman, “Interferometric measurements of the nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-12, 259–263 (1975).
[CrossRef]

J. Appl. Phys. (3)

D. Sarid and G. I. Stegeman, “Optimization of the effects of power dependent refractive indices in optical waveguides,” J. Appl. Phys. 52, 5439–5441 (1981).
[CrossRef]

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

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, “Nonlinear surface polaritons guided by metal films,” J. Appl. Phys. 58, 2460–2466 (1985).
[CrossRef]

J. Opt. Soc. Am. A (1)

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

J. Phys. (Paris) (1)

P. Martinot, S. Laval, and A. Koster, “Optical bistability from surface plasmon excitation through a nonlinear medium,” J. Phys. (Paris) 45, 597–600 (1984).
[CrossRef]

J. Phys. C (1)

A. D. Boardman and P. Egan, “Nonlinear surface and guided polaritons of a general layered dielectric structure,” J. Phys. C 5, 291–303 (1984).

J. Phys. Soc. Jpn. (1)

Y. Kuwamura, M. Fukui, and O. Tada, “Experimental observation of long-range surface plasmon polaritons,” J. Phys. Soc. Jpn. 52, 2350–2355 (1983).
[CrossRef]

JETP Lett. (2)

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, “Nonlinear surface polaritons,” JETP Lett. 32, 512–515 (1980).

A. E. Kaplan, “Hysteresis reflection and refraction by a nonlinear boundary—a new class of effects in nonlinear optics,” JETP Lett. 24, 114–119 (1976).

Opt. Commun. (2)

U. Langbein, F. Lederer, and H.-E. Ponath, “A new type of nonlinear slab-guided waves,” Opt. Commun. 46, 167–169 (1983).
[CrossRef]

D. J. Robbins, “TE modes in a slab waveguide bounded by nonlinear media,” Opt. Commun. 47, 309–312 (1983).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

K. M. Leung, “P-polarized nonlinear surface polaritons in materials with intensity-dependent dielectric functions,” Phys. Rev. B 32, 5093–5101 (1985).
[CrossRef]

Phys. Rev. Lett. (2)

D. A. B. Miller, C. T. Seaton, M. E. Prise, and S. D. Smith, “Band-gap-resonant nonlinear refraction in III–V semiconductors,” Phys. Rev. Lett. 47, 197–200 (1981).
[CrossRef]

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
[CrossRef]

Phys. Scr. (1)

D. Mihalache, R. G. Nazmitdinov, and V. K. Fedyanin, “P-polarized nonlinear surface waves in symmetric layered structures,” Phys. Scr. 29, 269–275 (1984).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

D. Sarid, “Intrinsic bistable guided-wave devices: theory and applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 317, 132–135 (1981).

Solid State Commun. (1)

Y. J. Chen and G. M. Carter, “Attenuated total reflection calculations for nonlinear surface plasmon dispersion,” Solid State Commun. 45, 277–280 (1983).
[CrossRef]

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A. E. Kaplan, “Theory of hysteresis reflection and refraction of light by a boundary of a nonlinear medium,” Sov. Phys. JETP 45, 869–905 (1977).

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Z. Phys. (1)

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[CrossRef]

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[CrossRef]

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[CrossRef]

Other (4)

A. A. Maradudin, “Nonlinear surface electromagnetic waves,” in Optical and Acoustic Waves in Solids—Modern Topics, M. Borissov, ed. (World Scientific, Singapore, 1983), pp. 72–142.

G. J. Kovacs, “Optical excitation of resonant electromagnetic oscillations in thin film,” Ph.D. dissertation (University of Toronto, Toronto, Canada, 1977), p. 69.

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C. K. R. T. Jones and J. V. Moloney, “Stability and instability of nonlinear waveguide modes” in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, and S. D. Smith, eds. (Springer-Verlag, Berlin, 1986), pp. 98–101.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Prism-coupling geometry.

Fig. 2
Fig. 2

Theoretical reflectance versus incident intensity of 1.06-μm radiation coupled to surface plasmons in silver with CS2 nonlinearity in substrate [n3 = 1.5 + (3 × 10−18 cm2/W)I, n1 = 1.5]. Single-surface plasmon curve is for Kretschmann geometry (d1 = 0) and d = 625 Å; long-range surface-plasmon curve is for d1 = 3.8 μm and d2 = 200 Å.

Fig. 3
Fig. 3

Theoretical parameters of uncoupled, freely propagating long-range surface plasmon (solid lines), prism-coupled long-range surface plasmon (dashed lines), and single-surface plasmon (→) versus silver-film thickness at low 1.06-μm incident intensity (n1 = n3 = 1.5). Single-surface-plasmon parameters are shown with arrows for the geometry of Fig. 2. Im(βu) is the absorptive part of the effective, uncoupled mode index, [Im(q3u)]−1 is the inverse of the imaginary part of the uncoupled mode’s transverse decay constant, δθ is the reflectance resonance’s angular FWHM in the prism, and Ix3/Iin is the on-resonance intensity enhancement in the substrate.

Fig. 4
Fig. 4

Switch-up (long-dashed line) and switch-down (long- and short-dashed line) intensity (in watts per square centimeter) for bistability in prism-coupled long-range surface plasmon [λ0 = 1.06 μm, n3 = 1.5 + (3 × 10−18 cm2/W)I], and parameter Im(βu)Im(q3u) × 1016 (solid line) predicting switching-intensity dependence, for varying silver-film thickness.

Fig. 5
Fig. 5

Comparison of switching characteristics of long-range surface plasmon for positive (long- and short-dashed line) and negative (solid line) substrate nonlinearities of the magnitude of InSb at λ0 = 5.6 μm and 77 K (n = 4.0 + i0.00016, n2,I = 7 × 10−5 cm2/W). Silver-film thickness is 200 Å, coupling-layer thickness is 6 μm, and prism index is 5.0.

Fig. 6
Fig. 6

Reflectance versus incident intensity predicted by nonlinear wave theory for thinner-than-optimum coupling layer (d1 = 3.4 μm) in long-range surface-plasmon geometry [λ0 = 5.6 μm, n1 = 4.0 + i0.00016, n3 = 4.0 + i0.00016 + (7 × 10−5 cm2/W)I, d2 = 200 Å, detuning = 0.05° in prism]. Power limiting is indicated.

Fig. 7
Fig. 7

Theoretical guided intensity profile for geometry of Fig. 6 at Iin = 0.27 W/cm2 on the upper branch. Both depth and intensity in the metal film are expanded × 100. Self-focusing in the nonlinear substrate is evident.

Fig. 8
Fig. 8

Reflectance versus incident intensity of long-range surface plasmon for 150-Å silver film and InSb-like positive nonlinearity in the substrate at 5.6 μm and 77 K. Solid line is based on nonlinear wave theory, and long- and short-dashed line is based on first-order perturbation theory.

Tables (1)

Tables Icon

Table 1 Theoretically Calculated Switching Intensities for Prism-Coupled Nonlinear Long-Range Surface Plasmon in 200-Å Silver Film Bound by InSb-like Nonlinearity at 5.6 μm, 77 K

Equations (28)

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A = 1 2 A ( z ) exp [ i ( ω t k 0 β x ) ] + c . c . ,
× H = 0 · E t = i ω 0 · E
× E = μ · H t = i ω μ 0 · H ,
E x ( z ) = i ω 0 x H y ( z ) z ,
E z ( z ) = β c 0 z H y ( z ) ,
H y ( z ) = 1 ω μ 0 [ i E x ( z ) z k 0 β E z ( z ) ] .
z = z o + α j E z 2 ( z ) = j + Δ z , x = x o = z o j ,
E z ( z ) [ j + α j E z 2 ( z ) ] = β c 0 H y ( z ) , E z ( z ) = 1 j [ β c 0 H y ( z ) + α j E z 3 ( z ) ] = 1 j β c 0 H y ( z ) [ 1 β 2 α j c 2 0 2 z 2 H y 2 ( z ) ] .
2 H y ( z ) z 2 k 0 2 q j 2 H y ( z ) + k 0 2 α j H y 3 = 0 ,
H y ( z ) = | 2 α j | 1 / 2 q j cosh [ k 0 q j ( z z j ζ j ) ] for α j > 0 , H y ( z ) = | 2 α j | 1 / 2 q j sinh [ k 0 q j ( z z j ζ j ) ] for α j < 0
H y j ( z ) = H y j + exp [ k 0 q j ( z z j ) ] + H y j exp [ k 0 q j ( z z j + 1 ) ] ,
H y 3 ( z ) = H y 3 + ( z ) = | 2 α 3 | 1 / 2 q 3 cosh [ k 0 q 3 ( z z 3 ζ 3 ) ] , E x 3 ( z ) = i q 3 c 0 n 3 2 tanh [ k 0 q 3 ( z z 3 ζ 3 ) ] H y 3 ( z ) , E z 3 ( z ) = β c 0 n 3 2 [ 1 α i β 2 H y 3 2 ( z ) ] H y 3 ( z ) .
H y + c 0 E x + = i n j 2 q j 1 Q j ,
Q 3 q 3 i n 3 2 tanh ( k 0 q 3 ζ 3 ) .
H y j + = 1 2 Q j exp ( + γ j ) [ ( Q j + Q j + 1 ) H y , j + 1 + + ( Q j Q j + 1 ) H y , j + 1 ] , H y j = 1 2 Q j exp ( γ j ) [ ( Q j Q j + 1 ) H y , j + 1 + + ( Q j + Q j + 1 ) H y , j + 1 ]
r j , j + 1 = Q j Q j + 1 Q j + Q j + 1
ρ j = H y j H y j + = exp ( 2 γ j ) [ r j , j + 1 + ρ j + 1 1 + r j , j + 1 ρ j + 1 ] .
R 0 = | r 01 [ 1 + r 12 r 23 exp ( 2 γ 2 ) ] + exp ( 2 γ 1 ) [ r 12 + r 23 exp ( 2 γ 2 ) ] 1 + r 12 r 23 exp ( 2 γ 2 ) + r 01 exp ( 2 γ 1 ) [ r 12 + r 23 exp ( 2 γ 2 ) ] | 2 .
E x j + = i q j c 0 n j 2 H y j + , E z j + = β c 0 n j 2 H y j + , E x j = i q j c 0 n j 2 ρ j H y j + , E z j = β c 0 n j 2 ρ j H y j + ,
I in = 1 2 c 0 n 0 2 | H y 0 + | 2 .
I x 1 = β 2 c 0 1 | H y 1 ( z 2 ) | 2
I x 3 = β 2 c 0 3 | H y 3 ( z 3 ) | 2
| E x 3 ( z ) | 2 | E z 3 ( z ) | 2 1.
| E x 3 ( z ) | 2 | E z 3 ( z ) | 2 = | q 3 tanh [ k 0 q 3 ( z z 3 ζ 3 ) ] H y 3 ( z ) | 2 | β { 1 2 q 3 2 β 2 cosh 2 [ k 0 q 3 ( z z 3 ζ 3 ) ] } H y 3 ( z ) | 2 .
| E x 3 ( z ) | 2 | E z 3 ( z ) | 2 < q 3 2 β 2 1 ,
3 Δ z 3 = 3 α 3 3 E z 3 2 ( z ) = 6 q 3 2 β 2 cosh 2 [ k 0 q 3 ( z z 3 ζ 3 ) ] × { 1 2 q 3 2 β 2 cosh 2 [ k 0 q 3 ( z z 3 ζ 3 ) ] }
q 3 2 β 2 0.16.
Δ n j = n j β Δ β = π c 2 0 2 n j 2 n 2 , I 4 P j d z { 2 3 [ | E x j ( z ) | 2 + | E z j ( z ) | 2 ] 2 + 1 3 | E x j 2 ( z ) + E z j 2 ( z ) | 2 } ,

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