Abstract

We demonstrate experimentally that deviations of a nearly sinusoidal grating from the exact sine profile strongly influence the shape of the surface plasmon resonance anomalies in higher diffraction orders, especially in the first order. It is shown that this effect can be applied to an accurate determination of the actual surface corrugation of nearly sinusoidal gratings.

© 1977 Optical Society of America

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References

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  1. R. W. Wood, Lond. Edinb. Dublin Phil. Mag. 4, 396 (1902).
  2. R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
    [CrossRef]
  3. I. Pockrand, H. Raether, Opt. Commun. 17, 353 (1976).
    [CrossRef]
  4. I. Pockrand, J. Phys. D: Appl. Phys. 9, 2423 (1976).
    [CrossRef]
  5. W. Rothballer, Opt. Commun. 20, 429 (1977).
    [CrossRef]
  6. E. Kröger (to be published).
  7. S. Austin, F. T. Stone, Appl. Opt. 15, 1071 (1976).S. Austin, F. T. Stone, Appl. Opt. 15, 2126 (1976).
    [CrossRef] [PubMed]
  8. E. Kretschmann, Z. Phys. 241, 313 (1971).
    [CrossRef]
  9. R. Petit, Nouv. Rev. Opt. 3, 129 (1975).
    [CrossRef]

1977 (1)

W. Rothballer, Opt. Commun. 20, 429 (1977).
[CrossRef]

1976 (3)

S. Austin, F. T. Stone, Appl. Opt. 15, 1071 (1976).S. Austin, F. T. Stone, Appl. Opt. 15, 2126 (1976).
[CrossRef] [PubMed]

I. Pockrand, H. Raether, Opt. Commun. 17, 353 (1976).
[CrossRef]

I. Pockrand, J. Phys. D: Appl. Phys. 9, 2423 (1976).
[CrossRef]

1975 (1)

R. Petit, Nouv. Rev. Opt. 3, 129 (1975).
[CrossRef]

1971 (1)

E. Kretschmann, Z. Phys. 241, 313 (1971).
[CrossRef]

1968 (1)

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[CrossRef]

1902 (1)

R. W. Wood, Lond. Edinb. Dublin Phil. Mag. 4, 396 (1902).

Arakawa, E. T.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[CrossRef]

Austin, S.

Cowan, J. J.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[CrossRef]

Hamm, R. N.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[CrossRef]

Kretschmann, E.

E. Kretschmann, Z. Phys. 241, 313 (1971).
[CrossRef]

Kröger, E.

E. Kröger (to be published).

Petit, R.

R. Petit, Nouv. Rev. Opt. 3, 129 (1975).
[CrossRef]

Pockrand, I.

I. Pockrand, H. Raether, Opt. Commun. 17, 353 (1976).
[CrossRef]

I. Pockrand, J. Phys. D: Appl. Phys. 9, 2423 (1976).
[CrossRef]

Raether, H.

I. Pockrand, H. Raether, Opt. Commun. 17, 353 (1976).
[CrossRef]

Ritchie, R. H.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[CrossRef]

Rothballer, W.

W. Rothballer, Opt. Commun. 20, 429 (1977).
[CrossRef]

Stone, F. T.

Wood, R. W.

R. W. Wood, Lond. Edinb. Dublin Phil. Mag. 4, 396 (1902).

Appl. Opt. (1)

J. Phys. D: Appl. Phys. (1)

I. Pockrand, J. Phys. D: Appl. Phys. 9, 2423 (1976).
[CrossRef]

Lond. Edinb. Dublin Phil. Mag. (1)

R. W. Wood, Lond. Edinb. Dublin Phil. Mag. 4, 396 (1902).

Nouv. Rev. Opt. (1)

R. Petit, Nouv. Rev. Opt. 3, 129 (1975).
[CrossRef]

Opt. Commun. (2)

I. Pockrand, H. Raether, Opt. Commun. 17, 353 (1976).
[CrossRef]

W. Rothballer, Opt. Commun. 20, 429 (1977).
[CrossRef]

Phys. Rev. Lett. (1)

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1968).
[CrossRef]

Z. Phys. (1)

E. Kretschmann, Z. Phys. 241, 313 (1971).
[CrossRef]

Other (1)

E. Kröger (to be published).

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Figures (3)

Fig. 1
Fig. 1

Calculated relative first-order intensity (Rp(−1) = Ip(−1)/Ip(0)) as a function of incidence angle θ0 for nearly sinusoidal silver gratings. Grating constant a = 6000 Å, wavelength of the light λ = 5682 Å, H(1) = 147 Å, and H(2) = −0.0 H(1)(1), −0.16 H(1) (2), −0.25 H(1) (3), and +0.16 H(1) (2a). The dielectric function of silver was assumed to be εAg = −13.2 + j 0.48 for the curves 1, 2, and 3 and εAg = −12.2 + j 0.48 for curve 3a. (Inset: Ag is silver; Ph is the photoresist; Q is fused silica.)

Fig. 2
Fig. 2

Measured relative first-order intensity as a function of θ0 for nearly sinusoidal silver gratings (full lines). The different pre-exposure energy in grating fabrication for curves 1–4 can be deduced from Fig. 3. The dashed lines are calculated with H(1) = 150 Å; H(2) = −0.05 H(1) (1), −0.11 H(1) (2), −0.16 H(1) (3), and −0.26 H(1) (4). (a = 6000 Å; λ = 5145 Å.)

Fig. 3
Fig. 3

Dependence of relative second-harmonic amplitude H(2)/H(1) on pre-exposure energy I in holographic grating fabrication. The energies of interference exposure are 28.5 mJ/cm2 (1), 35.9 mJ/cm2 (2), 54.7 mJ/cm2 (3), and 79.8 mJ/cm2 (4). The photoresist used is Shipley AZ 1350 (a = 6000 Å; H(1) = 150 Å).

Equations (1)

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s ( x ) = H ( 1 ) cos ( 2 π x / a ) + H ( 2 ) cos ( 4 π x / a ) + .

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