Abstract

We report experimental results of the resonant scattering of light from a prism-glass/Ag/MgF2/air system with use of the attenuated total reflection technique for p and s polarized light. Two MgF2 film thicknesses were used. The system with the thinner dielectric layer supports two transverse magnetic (TM) and two transverse electric (TE) guided modes at a wavelength of 632.8 nm, and the system with the thicker dielectric layer supports three TM and three TE guided modes. In both cases we found dips in the specular reflection as a function of incident angle that is due to excitation of guided modes in the MgF2 film. The scattered light shows peaks at angles corresponding to the measured excitation of the guided modes. These peaks are due to single-order scattering and occur for any angle of the incident light. All features in the scattering response are enhanced in resonance conditions, and the efficiency of injecting light into the guide is reduced.

© 2003 Optical Society of America

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  1. C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
    [CrossRef]
  2. R. Garcı́a-Llamas, L. E. Regalado, “Effects on rough interfaces in a multilayer stack,” in Optical Interference Coatings, F. Abelès ed., Proc. SPIE2253, 1298–1312 (1994).
    [CrossRef]
  3. J. M. Elson, “Multilayer-coated optics: guide-wave coupling and scattering by means of interface random roughness,” J. Opt. Soc. Am. A 12, 729–742 (1995).
    [CrossRef]
  4. R. Garcı́a-Llamas, L. E. Regalado, C. Amra, “Scattering of light from a two-layer system with a rough surface,” J. Opt. Soc. Am. A 16, 2713–2719 (1999).
    [CrossRef]
  5. R. Garcı́a-Llamas, A. S. Ramı́rez-Duverger, J. A. Gaspar-Armenta, “Resonant scattering of light from a bilayer system with a rough surface between dissimilar me-dia. Transmission,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, Washington, D.C., 2001), pp. tuf6-1–tuf6-3.
  6. C. Amra, S. Maure, “Mutual coherence and conical pattern of source optimally excited within multilayer optics,” J. Opt. Soc. Am. A 14, 3114–3124 (1997).
    [CrossRef]
  7. J. Q. Lu, A. A. Maradudin, T. Michel, “Enhanced backscattering from a rough dielectric film on a reflecting substrate,” J. Opt. Soc. Am. B 8, 311–318 (1991).
    [CrossRef]
  8. J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnick, I. Yurkevich, “Scattering of electromagnetic waves from a bounded medium with a random surface,” Phys. Rev. B 50, 15353–15360 (1994).
    [CrossRef]
  9. Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
    [CrossRef]
  10. J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnik, I. Yurkevich, “Satellite peaks in the scattering of p polarized light from a randomly rough film on a perfectly conducting substrate,” J. Mod. Opt. 43, 435–452 (1996).
    [CrossRef]
  11. A. Madrazo, A. A. Maradudin, “Numerical solutions of the reduced Rayleigh equation for the scattering of electromagnetic waves from rough dielectric films on a perfectly conducting substrates,” Opt. Commun. 134, 251–263 (1997).
    [CrossRef]
  12. R. Garcı́a-Llamas, C. Márquez-Beltran, “Scattering of s-polarized electromagnetic plane waves from a film with a shallow random rough surface on a perfect conductor,” Appl. Opt. 39, 4698–4705 (2000).
    [CrossRef]
  13. H. Raether, Surface Plasmon on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  14. N. Mayani, F. Varnier, G. Rasigni, “Experimental study of the relationships between the near-normal reflectance, the optical constants, and the roughness of thin silver films,” J. Opt. Soc. Am. A 7, 191–195 (1990).
    [CrossRef]
  15. Edward D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1991).

2000 (1)

1999 (1)

1997 (2)

C. Amra, S. Maure, “Mutual coherence and conical pattern of source optimally excited within multilayer optics,” J. Opt. Soc. Am. A 14, 3114–3124 (1997).
[CrossRef]

A. Madrazo, A. A. Maradudin, “Numerical solutions of the reduced Rayleigh equation for the scattering of electromagnetic waves from rough dielectric films on a perfectly conducting substrates,” Opt. Commun. 134, 251–263 (1997).
[CrossRef]

1996 (1)

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnik, I. Yurkevich, “Satellite peaks in the scattering of p polarized light from a randomly rough film on a perfectly conducting substrate,” J. Mod. Opt. 43, 435–452 (1996).
[CrossRef]

1995 (2)

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

J. M. Elson, “Multilayer-coated optics: guide-wave coupling and scattering by means of interface random roughness,” J. Opt. Soc. Am. A 12, 729–742 (1995).
[CrossRef]

1994 (2)

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnick, I. Yurkevich, “Scattering of electromagnetic waves from a bounded medium with a random surface,” Phys. Rev. B 50, 15353–15360 (1994).
[CrossRef]

C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11, 197–210 (1994).
[CrossRef]

1991 (1)

1990 (1)

Amra, C.

Elson, J. M.

Freilikher, V. D.

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnik, I. Yurkevich, “Satellite peaks in the scattering of p polarized light from a randomly rough film on a perfectly conducting substrate,” J. Mod. Opt. 43, 435–452 (1996).
[CrossRef]

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnick, I. Yurkevich, “Scattering of electromagnetic waves from a bounded medium with a random surface,” Phys. Rev. B 50, 15353–15360 (1994).
[CrossRef]

Garci´a-Llamas, R.

R. Garcı́a-Llamas, C. Márquez-Beltran, “Scattering of s-polarized electromagnetic plane waves from a film with a shallow random rough surface on a perfect conductor,” Appl. Opt. 39, 4698–4705 (2000).
[CrossRef]

R. Garcı́a-Llamas, L. E. Regalado, C. Amra, “Scattering of light from a two-layer system with a rough surface,” J. Opt. Soc. Am. A 16, 2713–2719 (1999).
[CrossRef]

R. Garcı́a-Llamas, L. E. Regalado, “Effects on rough interfaces in a multilayer stack,” in Optical Interference Coatings, F. Abelès ed., Proc. SPIE2253, 1298–1312 (1994).
[CrossRef]

R. Garcı́a-Llamas, A. S. Ramı́rez-Duverger, J. A. Gaspar-Armenta, “Resonant scattering of light from a bilayer system with a rough surface between dissimilar me-dia. Transmission,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, Washington, D.C., 2001), pp. tuf6-1–tuf6-3.

Gaspar-Armenta, J. A.

R. Garcı́a-Llamas, A. S. Ramı́rez-Duverger, J. A. Gaspar-Armenta, “Resonant scattering of light from a bilayer system with a rough surface between dissimilar me-dia. Transmission,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, Washington, D.C., 2001), pp. tuf6-1–tuf6-3.

Lu, J. Q.

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnik, I. Yurkevich, “Satellite peaks in the scattering of p polarized light from a randomly rough film on a perfectly conducting substrate,” J. Mod. Opt. 43, 435–452 (1996).
[CrossRef]

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnick, I. Yurkevich, “Scattering of electromagnetic waves from a bounded medium with a random surface,” Phys. Rev. B 50, 15353–15360 (1994).
[CrossRef]

J. Q. Lu, A. A. Maradudin, T. Michel, “Enhanced backscattering from a rough dielectric film on a reflecting substrate,” J. Opt. Soc. Am. B 8, 311–318 (1991).
[CrossRef]

Madrazo, A.

A. Madrazo, A. A. Maradudin, “Numerical solutions of the reduced Rayleigh equation for the scattering of electromagnetic waves from rough dielectric films on a perfectly conducting substrates,” Opt. Commun. 134, 251–263 (1997).
[CrossRef]

Maradudin, A. A.

A. Madrazo, A. A. Maradudin, “Numerical solutions of the reduced Rayleigh equation for the scattering of electromagnetic waves from rough dielectric films on a perfectly conducting substrates,” Opt. Commun. 134, 251–263 (1997).
[CrossRef]

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnik, I. Yurkevich, “Satellite peaks in the scattering of p polarized light from a randomly rough film on a perfectly conducting substrate,” J. Mod. Opt. 43, 435–452 (1996).
[CrossRef]

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnick, I. Yurkevich, “Scattering of electromagnetic waves from a bounded medium with a random surface,” Phys. Rev. B 50, 15353–15360 (1994).
[CrossRef]

J. Q. Lu, A. A. Maradudin, T. Michel, “Enhanced backscattering from a rough dielectric film on a reflecting substrate,” J. Opt. Soc. Am. B 8, 311–318 (1991).
[CrossRef]

Márquez-Beltran, C.

Maure, S.

Mayani, N.

Michel, T.

Ogura, H.

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

Palik, Edward D.

Edward D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1991).

Pustilnick, M.

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnick, I. Yurkevich, “Scattering of electromagnetic waves from a bounded medium with a random surface,” Phys. Rev. B 50, 15353–15360 (1994).
[CrossRef]

Pustilnik, M.

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnik, I. Yurkevich, “Satellite peaks in the scattering of p polarized light from a randomly rough film on a perfectly conducting substrate,” J. Mod. Opt. 43, 435–452 (1996).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmon on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

Rami´rez-Duverger, A. S.

R. Garcı́a-Llamas, A. S. Ramı́rez-Duverger, J. A. Gaspar-Armenta, “Resonant scattering of light from a bilayer system with a rough surface between dissimilar me-dia. Transmission,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, Washington, D.C., 2001), pp. tuf6-1–tuf6-3.

Rasigni, G.

Regalado, L. E.

R. Garcı́a-Llamas, L. E. Regalado, C. Amra, “Scattering of light from a two-layer system with a rough surface,” J. Opt. Soc. Am. A 16, 2713–2719 (1999).
[CrossRef]

R. Garcı́a-Llamas, L. E. Regalado, “Effects on rough interfaces in a multilayer stack,” in Optical Interference Coatings, F. Abelès ed., Proc. SPIE2253, 1298–1312 (1994).
[CrossRef]

Sánchez-Gil, J. A.

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnik, I. Yurkevich, “Satellite peaks in the scattering of p polarized light from a randomly rough film on a perfectly conducting substrate,” J. Mod. Opt. 43, 435–452 (1996).
[CrossRef]

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnick, I. Yurkevich, “Scattering of electromagnetic waves from a bounded medium with a random surface,” Phys. Rev. B 50, 15353–15360 (1994).
[CrossRef]

Takahashi, N.

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

Varnier, F.

Wang, Z. L.

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

Yurkevich, I.

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnik, I. Yurkevich, “Satellite peaks in the scattering of p polarized light from a randomly rough film on a perfectly conducting substrate,” J. Mod. Opt. 43, 435–452 (1996).
[CrossRef]

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnick, I. Yurkevich, “Scattering of electromagnetic waves from a bounded medium with a random surface,” Phys. Rev. B 50, 15353–15360 (1994).
[CrossRef]

Appl. Opt. (1)

J. Mod. Opt. (1)

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnik, I. Yurkevich, “Satellite peaks in the scattering of p polarized light from a randomly rough film on a perfectly conducting substrate,” J. Mod. Opt. 43, 435–452 (1996).
[CrossRef]

J. Opt. Soc. Am. A (5)

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

Opt. Commun. (1)

A. Madrazo, A. A. Maradudin, “Numerical solutions of the reduced Rayleigh equation for the scattering of electromagnetic waves from rough dielectric films on a perfectly conducting substrates,” Opt. Commun. 134, 251–263 (1997).
[CrossRef]

Phys. Rev. B (2)

J. A. Sánchez-Gil, A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnick, I. Yurkevich, “Scattering of electromagnetic waves from a bounded medium with a random surface,” Phys. Rev. B 50, 15353–15360 (1994).
[CrossRef]

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

Other (4)

R. Garcı́a-Llamas, L. E. Regalado, “Effects on rough interfaces in a multilayer stack,” in Optical Interference Coatings, F. Abelès ed., Proc. SPIE2253, 1298–1312 (1994).
[CrossRef]

R. Garcı́a-Llamas, A. S. Ramı́rez-Duverger, J. A. Gaspar-Armenta, “Resonant scattering of light from a bilayer system with a rough surface between dissimilar me-dia. Transmission,” in Optical Interference Coatings, OSA Technical Digest (Optical Society of America, Washington, D.C., 2001), pp. tuf6-1–tuf6-3.

H. Raether, Surface Plasmon on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

Edward D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1991).

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Figures (5)

Fig. 1
Fig. 1

Reflection as a function of angle of incidence for a wavelength of 632.8 nm and for a thickness of the MgF2 film dMgF2(1)=665 nm. The system is described in Section 2. The circles and the triangles represent the experimental results for p and s polarization of the incident light, respectively. The solid and dashed curves correspond to the theoretical data for p and s polarization, respectively, and were calculated with Eq. (4). The minima (circles) at θ12(p)=42.2° and θ11(p)=56.8° correspond to excitation of the second and the first TM guided mode, respectively. The dips (triangles) at θ12(s)=49.1° and θ11(s)=61.0° are related to excitation of the second and the first TE guided mode, respectively.

Fig. 2
Fig. 2

(a) Light scattering as a function of scattering angle for an incidence angle θi=θ12(p)=-42.2° for p polarization and for a wavelength of 632.8 nm. Both experimental (circles) and theoretical (solid curve) data are displayed. This angle corresponds to the direct excitation of the second TM guided mode in the Kretschmann ATR device. We observed peaks at θs=±θ11(p)=±56.8° that were due to the single-scattering effect; they are related to the indirect excitation of the first TM guided mode via the roughness of the system. (b) Same as Fig. 2(a) but for θi=θ12(p)=-56.8°. The angle corresponds to the resonance condition of the excitation of the first TM guided mode. We observed peaks at θs=±θ12(p)=±42.2°, related to the indirect excitation of the second TM guided mode. (c) Same as Fig. 2(a) but for θi=-49.7°. The angle does not correspond to the excitation of any mode. We observed weak peaks at θs=±θ11(p)=±56.8° and at θs=±θ11(p)=±42.2° that were due to the single-scattering effect; they are related to the indirect excitation of the first and second TM guided modes.

Fig. 3
Fig. 3

(a) Same as Fig. 2(a) but for θi=θ12(s)=-49.1° and for s polarization. This angle corresponds to the direct excitation of the second TE guided mode. As in the case of p polarization, we observed peaks at θs=±θ11(s)=±61.0° that were due to the single-scattering effect; they are related to the indirect excitation of the first TE guided mode. (b) Same as Fig. 3(a) but for θi=-55.3°. The angle does not correspond to the excitation of any mode. We observed peaks of low intensity at θs=±θ11(s)=±56.8° and at θs=±θ11(s)=±42.2° that were due to the single-scattering effect; they are related to the indirect excitation of the first and second TE guided modes. The background scattering is lower than in resonant excitation.

Fig. 4
Fig. 4

Reflection versus angle of incidence for a wavelength of 632.8 nm; the thickness of the MgF2 film is increased to dMgF2(2)=965 nm. The dashed and solid curves correspond to the theoretical data for s and p polarization, respectively. The curves with triangles and circles represent the experimental results for s and p polarization, respectively. The dips (circles) at θ23(p)=41.3°, θ22(p)=51.5°, and θ21(p)=61.6° correspond to excitation of the third, second, and first TM guided modes, respectively. The minima (triangles) at θ23(s)=45.8°, θ22(s)=55.6°, and θ21(s)=62.6° are related to the excitation of the third, second, and first TE guided modes, respectively.

Fig. 5
Fig. 5

Light scattering versus scattering angle for θi=θ21(p)=-61.6° for p polarization and for a wavelength of 632.8 nm. The angle of incidence corresponds to the direct excitation of the first TM guided mode in the ATR device. The experimental curve (circles) displays four peaks at θ22(p)=±51.5° and θ23(p)=±41.3° that are related to the indirect excitation of the second and third TE guided modes. The remaining two peaks at θ21(p)=±51.5° are shown only on the theoretical (solid) curve.

Tables (1)

Tables Icon

Table 1 Wave Numbers of the Guided Modes Obtained from the Angular Positions of the Minima of the Reflection Curves (Figs. 1 and 4 )

Equations (4)

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

R(θi)=-π/2π/2dRdθscohdθs,
dRdθscoh=|r(0)(γ)|2+2 Re[r(0)*(γ)r(2)(γ)],
r(2)(γ)=δ(γ-αi)1G3a(0)(γ, γ)-dαG3a(1)(γ, α)×H3a(1)(α, αi)-G3a(1)(α, αi)r(0)(αi)G3a(0)(α, α)×g(α-αi)-12H3a(2)(γ, αi)-G3a(2)(γ, αi)r(0)(αi)G3a(0)(γ, γ),
R(θi)=H3a(0)(αi, αi)G3a(0)(αi, αi)2+2 ReH3a(0)(αi, αi)*|G3a(0)(αi, αi)|2-dαG3a(1)(αi, α)H3a(1)(α, αi)-G3a(1)(α, αi)r(0)(αi)G3a(0)(α, α) g(α-αi)-ReH3a(0)(αi, αi)*[H3a(2)(αi, αi)-G3a(2)(αi, αi)r(0)(αi)]|G3a(0)(αi, αi)|2.

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