Abstract

We observed enhanced reflected second-harmonic generation (SHG) that was due to coupled surface-plasmon modes in thin silver films separated with a liquid dielectric layer whose thickness may be continuously varied. The observed angular SHG spectra resulting from excitation of the coupled fundamental surface-plasmon modes are in reasonable agreement with a multilayer plane-wave theory. In contrast to the highly resonant SHG associated with the familiar long-range surface-plasmon mode, here the coupling of the surface modes decreases the SHG resonance because of the lossy nature of these new coupled modes.

© 1999 Optical Society of America

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References

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  1. J. E. Sipe and G. I. Stegeman, “Nonlinear optical response of metal surfaces,” in Surface Polaritons Electromagnetic Waves at Surfaces and Interfaces, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), pp. 661–701.
  2. H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531–1533 (1974).
    [CrossRef]
  3. D. Sarid, “Long-range surface plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
    [CrossRef]
  4. 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]
  5. J. C. Quail, J. G. Rako, H. J. Simon, and R. T. Deck, “Optical second-harmonic generation with long-range surface plasmons,” Phys. Rev. Lett. 50, 1987–1989 (1983).
    [CrossRef]
  6. C. C. Tzeng and J. T. Lue, “Optical second-harmonic generation from silver films with long-range surface-plasmon excitation,” Surf. Sci. 216, 579–583 (1989).
    [CrossRef]
  7. K. R. Welford and J. R. Sambles, “Coupled surface plasmons in a symmetric system,” J. Mod. Opt. 35, 1467–1483 (1988).
    [CrossRef]
  8. Q. Chen, “Attenuated total reflectance due to coupled surface plasmon modes in thin Ag/dielectric/Ag layers,” M.S. thesis (The University of Toledo, Toledo, Ohio, 1997).
  9. J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980).
    [CrossRef]
  10. D. Maystre and M. Nevière, “Nonlinear polarization inside metals: a mathematical study of the free-electron model,” Appl. Phys. A 39, 115–121 (1986).
    [CrossRef]
  11. V. M. Agranovich and S. A. Darmanyan, “Theory of second-harmonic generation upon reflection of light from a medium with a central of inversion,” JETP Lett. 35, 80–82 (1982).
  12. J. Rudnick and E. A. Stern, “Second-harmonic radiation from metal surfaces,” Phys. Rev. B 4, 4274–4290 (1971).
    [CrossRef]
  13. E. D. Palik, Handbook of Optical Constants of Solids (Academic, London, 1985).
  14. A. A. Maradudin, “Interaction of surface polaritons and plasmons with surface roughness,” in Surface Polaritons Electromagnetic Waves at Surfaces and Interfaces, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), pp. 405–510.
  15. J. C. Quail and H. J. Simon, “Second-harmonic generation with phase-matched long-range and short-range surface plasmons,” J. Appl. Phys. 56, 2589–2591 (1984).
    [CrossRef]

1989 (1)

C. C. Tzeng and J. T. Lue, “Optical second-harmonic generation from silver films with long-range surface-plasmon excitation,” Surf. Sci. 216, 579–583 (1989).
[CrossRef]

1988 (1)

K. R. Welford and J. R. Sambles, “Coupled surface plasmons in a symmetric system,” J. Mod. Opt. 35, 1467–1483 (1988).
[CrossRef]

1986 (1)

D. Maystre and M. Nevière, “Nonlinear polarization inside metals: a mathematical study of the free-electron model,” Appl. Phys. A 39, 115–121 (1986).
[CrossRef]

1984 (1)

J. C. Quail and H. J. Simon, “Second-harmonic generation with phase-matched long-range and short-range surface plasmons,” J. Appl. Phys. 56, 2589–2591 (1984).
[CrossRef]

1983 (2)

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]

J. C. Quail, J. G. Rako, H. J. Simon, and R. T. Deck, “Optical second-harmonic generation with long-range surface plasmons,” Phys. Rev. Lett. 50, 1987–1989 (1983).
[CrossRef]

1982 (1)

V. M. Agranovich and S. A. Darmanyan, “Theory of second-harmonic generation upon reflection of light from a medium with a central of inversion,” JETP Lett. 35, 80–82 (1982).

1981 (1)

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

1980 (1)

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980).
[CrossRef]

1974 (1)

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531–1533 (1974).
[CrossRef]

1971 (1)

J. Rudnick and E. A. Stern, “Second-harmonic radiation from metal surfaces,” Phys. Rev. B 4, 4274–4290 (1971).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich and S. A. Darmanyan, “Theory of second-harmonic generation upon reflection of light from a medium with a central of inversion,” JETP Lett. 35, 80–82 (1982).

Darmanyan, S. A.

V. M. Agranovich and S. A. Darmanyan, “Theory of second-harmonic generation upon reflection of light from a medium with a central of inversion,” JETP Lett. 35, 80–82 (1982).

Deck, R. T.

J. C. Quail, J. G. Rako, H. J. Simon, and R. T. Deck, “Optical second-harmonic generation with long-range surface plasmons,” Phys. Rev. Lett. 50, 1987–1989 (1983).
[CrossRef]

Fukui, M.

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980).
[CrossRef]

Lue, J. T.

C. C. Tzeng and J. T. Lue, “Optical second-harmonic generation from silver films with long-range surface-plasmon excitation,” Surf. Sci. 216, 579–583 (1989).
[CrossRef]

Maystre, D.

D. Maystre and M. Nevière, “Nonlinear polarization inside metals: a mathematical study of the free-electron model,” Appl. Phys. A 39, 115–121 (1986).
[CrossRef]

Mitchell, D. E.

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531–1533 (1974).
[CrossRef]

Nevière, M.

D. Maystre and M. Nevière, “Nonlinear polarization inside metals: a mathematical study of the free-electron model,” Appl. Phys. A 39, 115–121 (1986).
[CrossRef]

Quail, J. C.

J. C. Quail and H. J. Simon, “Second-harmonic generation with phase-matched long-range and short-range surface plasmons,” J. Appl. Phys. 56, 2589–2591 (1984).
[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]

J. C. Quail, J. G. Rako, H. J. Simon, and R. T. Deck, “Optical second-harmonic generation with long-range surface plasmons,” Phys. Rev. Lett. 50, 1987–1989 (1983).
[CrossRef]

Rako, J. G.

J. C. Quail, J. G. Rako, H. J. Simon, and R. T. Deck, “Optical second-harmonic generation with long-range surface plasmons,” Phys. Rev. Lett. 50, 1987–1989 (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]

Rudnick, J.

J. Rudnick and E. A. Stern, “Second-harmonic radiation from metal surfaces,” Phys. Rev. B 4, 4274–4290 (1971).
[CrossRef]

Sambles, J. R.

K. R. Welford and J. R. Sambles, “Coupled surface plasmons in a symmetric system,” J. Mod. Opt. 35, 1467–1483 (1988).
[CrossRef]

Sarid, D.

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

Simon, H. J.

J. C. Quail and H. J. Simon, “Second-harmonic generation with phase-matched long-range and short-range surface plasmons,” J. Appl. Phys. 56, 2589–2591 (1984).
[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]

J. C. Quail, J. G. Rako, H. J. Simon, and R. T. Deck, “Optical second-harmonic generation with long-range surface plasmons,” Phys. Rev. Lett. 50, 1987–1989 (1983).
[CrossRef]

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531–1533 (1974).
[CrossRef]

Sipe, J. E.

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980).
[CrossRef]

So, V. C. Y.

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980).
[CrossRef]

Stegeman, G. I.

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980).
[CrossRef]

Stern, E. A.

J. Rudnick and E. A. Stern, “Second-harmonic radiation from metal surfaces,” Phys. Rev. B 4, 4274–4290 (1971).
[CrossRef]

Tzeng, C. C.

C. C. Tzeng and J. T. Lue, “Optical second-harmonic generation from silver films with long-range surface-plasmon excitation,” Surf. Sci. 216, 579–583 (1989).
[CrossRef]

Watson, J. G.

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531–1533 (1974).
[CrossRef]

Welford, K. R.

K. R. Welford and J. R. Sambles, “Coupled surface plasmons in a symmetric system,” J. Mod. Opt. 35, 1467–1483 (1988).
[CrossRef]

Appl. Phys. A (1)

D. Maystre and M. Nevière, “Nonlinear polarization inside metals: a mathematical study of the free-electron model,” Appl. Phys. A 39, 115–121 (1986).
[CrossRef]

J. Appl. Phys. (1)

J. C. Quail and H. J. Simon, “Second-harmonic generation with phase-matched long-range and short-range surface plasmons,” J. Appl. Phys. 56, 2589–2591 (1984).
[CrossRef]

J. Mod. Opt. (1)

K. R. Welford and J. R. Sambles, “Coupled surface plasmons in a symmetric system,” J. Mod. Opt. 35, 1467–1483 (1988).
[CrossRef]

JETP Lett. (1)

V. M. Agranovich and S. A. Darmanyan, “Theory of second-harmonic generation upon reflection of light from a medium with a central of inversion,” JETP Lett. 35, 80–82 (1982).

Opt. Lett. (1)

Phys. Rev. B (2)

J. E. Sipe, V. C. Y. So, M. Fukui, and G. I. Stegeman, “Analysis of second-harmonic generation at metal surfaces,” Phys. Rev. B 21, 4389–4402 (1980).
[CrossRef]

J. Rudnick and E. A. Stern, “Second-harmonic radiation from metal surfaces,” Phys. Rev. B 4, 4274–4290 (1971).
[CrossRef]

Phys. Rev. Lett. (3)

J. C. Quail, J. G. Rako, H. J. Simon, and R. T. Deck, “Optical second-harmonic generation with long-range surface plasmons,” Phys. Rev. Lett. 50, 1987–1989 (1983).
[CrossRef]

H. J. Simon, D. E. Mitchell, and J. G. Watson, “Optical second-harmonic generation with surface plasmons in silver films,” Phys. Rev. Lett. 33, 1531–1533 (1974).
[CrossRef]

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

Surf. Sci. (1)

C. C. Tzeng and J. T. Lue, “Optical second-harmonic generation from silver films with long-range surface-plasmon excitation,” Surf. Sci. 216, 579–583 (1989).
[CrossRef]

Other (4)

Q. Chen, “Attenuated total reflectance due to coupled surface plasmon modes in thin Ag/dielectric/Ag layers,” M.S. thesis (The University of Toledo, Toledo, Ohio, 1997).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, London, 1985).

A. A. Maradudin, “Interaction of surface polaritons and plasmons with surface roughness,” in Surface Polaritons Electromagnetic Waves at Surfaces and Interfaces, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), pp. 405–510.

J. E. Sipe and G. I. Stegeman, “Nonlinear optical response of metal surfaces,” in Surface Polaritons Electromagnetic Waves at Surfaces and Interfaces, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), pp. 661–701.

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Figures (4)

Fig. 1
Fig. 1

Diagram of prism-coupled multilayer geometry.

Fig. 2
Fig. 2

Reflected SHG versus internal angle of incidence. Solid dots are experimental points, and the dotted curve with triangles is the theoretical calculation. The liquid-dielectric-layer thickness is 3675 nm.

Fig. 3
Fig. 3

Same as Fig. 2 but with a layer thickness of 2645 nm.

Fig. 4
Fig. 4

Same as Fig. 2 but with a layer thickness of 1550 nm.

Equations (19)

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ER(2ω)=AaEzR(2ω)+2bExR(2ω)+12EBR(2ω).
EzR(2ω)=T21M(1)1/2 sin θ1((cos Θ2)-1{1+[R23+R34 exp(i2Δ3)]exp(i2Δ2)+R23R34 exp(i2Δ3)}[(f12+f12)sin θ2]2+T32(cos Θ3)-1[1+R34 exp(i2Δ3)]exp(iΔ2)×[(f23+f23)sin θ2]2+T43T32(cos Θ4)-1 exp[i(Δ2+Δ3)]×(f34 sin θ4)2),
ExR(2ω)=T21M((E2)-1/2{1-[R23+R34 exp(i2Δ3)]exp(i2Δ2)+R23R34 exp(i2Δ3)}[(f122-f122)cos θ2 sin θ2]+T32(E3)-1/2{[1-R34 exp(i2Δ3)]exp(iΔ2)}×[(f232-f232)cos θ2 sin θ2]+T43T32(E4)-1/2 exp[i(Δ2+Δ3)]×(f342 cos θ4 sin θ4)),
EBR(2ω)=T21M(1)1/2 sin θ1((E2 cos Θ2)-1{1+[R23+R34 exp(i2Δ3)]exp(i2Δ2)+R23R34 exp(i2Δ3)}[f122+f122+2 f12f12(sin2 θ2-cos2 θ2)]-(E2 cos θ3)-1{T32[1+R34 exp(i2Δ3)]×exp(iΔ2)}[f232+f232+2 f23f23(sin2 θ2-cos2 θ2)]+(E4 cos Θ4)-1T43T32 exp[i(Δ2+Δ3)]f342).
f12=m1234t12,
f12=f12r234 exp(i2δ2),
f23=f12 exp(iδ2),
f23=f23r234,
f34=m1234m234t12t23t34 exp[i(δ2+δ3)],
rij=j cos θi-i cos θjj cos θi+i cos θj,
tij=2i cos θij cos θi+i cos θj,
rijk=rij+rjk exp(i2δj)1+rijrjk exp(i2δj),
δj=2πλj cos θjdj.
m1234=[1+r12r234 exp(i2δ2)]-1,
m234=[1+r23r34 exp(i2δ3)]-1.
Ei sin Θi=1 sin θ1,
M=([1+R12R234 exp(i2Δ2)]×[1+R23R34 exp(i2Δ3)])-1,
Δi=4πλEi cos Θidi.
IR(2ω)=|ER(2ω)|2,

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