Abstract

Measurements of the diffraction characteristics of one-dimensional surface-relief gratings of locally varying profile are compared with rigorous diffraction theory. These gratings result from the superposition of two linear sinusoidal gratings of uniform depth for which the relative phase between the two gratings varies slowly with position. The resultant surface profile exhibits a relatively large-period variation in profile form. The periodic variation in diffraction efficiency that results yields a visual moiré pattern that has interesting asymmetry and polarization properties that alter as the viewing conditions are changed; the gratings can be exploited by diffractive optically variable devices for document security.

© 1999 Optical Society of America

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References

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  1. R. Staub, W. R. Tompkin, and J.-F. Moser, Proc. SPIE 2689, 292 (1996).
    [CrossRef]
  2. E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), pp. 531–554.
  3. S. Johansson and K. Biedermann, Proc. SPIE 240, 44 (1980).
    [CrossRef]
  4. J.-F. Moser, in Optical Document Security, R. van Renesse, ed. (Artech House, London, 1998), pp. 247–266.
  5. J. Turunen, in Micro-Optics, Elements, Systems and Applications, H.-P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 31–52.
  6. M. G. Moharam and T. K. Gaylord, J. Opt. Soc. Am. 72, 1385 (1982).
    [CrossRef]
  7. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A 12, 1077 (1995).
    [CrossRef]
  8. P. Lalanne and G. M. Morris, J. Opt. Soc. Am. A 13, 779 (1996).
    [CrossRef]
  9. K. Hirayama, E. N. Glytsis, and T. K. Gaylord, J. Opt. Soc. Am. A 14, 907 (1997).
    [CrossRef]
  10. W. R. Tompkin and R. Staub, Proc. SPIE 3291, 1 (1998).

1998 (1)

W. R. Tompkin and R. Staub, Proc. SPIE 3291, 1 (1998).

1997 (1)

1996 (2)

P. Lalanne and G. M. Morris, J. Opt. Soc. Am. A 13, 779 (1996).
[CrossRef]

R. Staub, W. R. Tompkin, and J.-F. Moser, Proc. SPIE 2689, 292 (1996).
[CrossRef]

1995 (1)

1982 (1)

1980 (1)

S. Johansson and K. Biedermann, Proc. SPIE 240, 44 (1980).
[CrossRef]

Biedermann, K.

S. Johansson and K. Biedermann, Proc. SPIE 240, 44 (1980).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Grann, E. B.

Hirayama, K.

Johansson, S.

S. Johansson and K. Biedermann, Proc. SPIE 240, 44 (1980).
[CrossRef]

Lalanne, P.

Loewen, E. G.

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), pp. 531–554.

Moharam, M. G.

Morris, G. M.

Moser, J.-F.

R. Staub, W. R. Tompkin, and J.-F. Moser, Proc. SPIE 2689, 292 (1996).
[CrossRef]

J.-F. Moser, in Optical Document Security, R. van Renesse, ed. (Artech House, London, 1998), pp. 247–266.

Pommet, D. A.

Popov, E.

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), pp. 531–554.

Staub, R.

W. R. Tompkin and R. Staub, Proc. SPIE 3291, 1 (1998).

R. Staub, W. R. Tompkin, and J.-F. Moser, Proc. SPIE 2689, 292 (1996).
[CrossRef]

Tompkin, W. R.

W. R. Tompkin and R. Staub, Proc. SPIE 3291, 1 (1998).

R. Staub, W. R. Tompkin, and J.-F. Moser, Proc. SPIE 2689, 292 (1996).
[CrossRef]

Turunen, J.

J. Turunen, in Micro-Optics, Elements, Systems and Applications, H.-P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 31–52.

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Proc. SPIE (3)

W. R. Tompkin and R. Staub, Proc. SPIE 3291, 1 (1998).

R. Staub, W. R. Tompkin, and J.-F. Moser, Proc. SPIE 2689, 292 (1996).
[CrossRef]

S. Johansson and K. Biedermann, Proc. SPIE 240, 44 (1980).
[CrossRef]

Other (3)

J.-F. Moser, in Optical Document Security, R. van Renesse, ed. (Artech House, London, 1998), pp. 247–266.

J. Turunen, in Micro-Optics, Elements, Systems and Applications, H.-P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 31–52.

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), pp. 531–554.

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental setup used to write the gratings. Spherical waves emanate from two pinholes, Pi and Pi, which are separated by a distance 2xi. These waves interfere at the photoresist plate a distance zi from the line connecting the two points.

Fig. 2
Fig. 2

Typical surface-relief measured profiles for values of β of (a) 0°, (b) 90°, (c) 180°, and (d) 270°. The peak-to-peak profile heights of the measured profiles are (a) 145, (b) 115, (c) 140, and (d) 170  nm.

Fig. 3
Fig. 3

Relative phase shift between the two basis functions versus position x, as determined from AFM measurements.

Fig. 4
Fig. 4

Measured and calculated diffraction efficiency (in percent) as a function of the relative phase β in degrees for the +1 and -1 orders for (a) TM and (b) TE illumination. The measured diffraction efficiencies are shown as filled squares for the +1 order and as filled diamonds for the -1 order; the calculated values are shown as solid and dashed curves for the +1 and -1 orders, respectively.

Equations (2)

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f1x=b1sin2Kx+βx,f2x=b2sinKx,
Iix=4Ii0cos2πλOPDix,OPDix2xsinθi1-12cos2θixri2di-1x=1λOPDiχ2sinθiλ×1-32cos2θixri2OPDiχ

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