Abstract

We analyze the far field and near field diffraction pattern produced by an amplitude grating whose strips present rough edges. Due to the stochastic nature of the edges a statistical approach is performed. The grating with rough edges is not purely periodic, although it still divides the incident beam in diffracted orders. The intensity of each diffraction order is modified by the statistical properties of the irregular edges and it strongly decreases when roughness increases except for the zero-th diffraction order. This decreasing firstly affects to the higher orders. Then, it is possible to obtain an amplitude binary grating with only diffraction orders -1, 0 and +1. On the other hand, numerical simulations based on Rayleigh-Sommerfeld approach have been used for the case of near field. They show that the edges of the self-images are smoother than the edges of the grating. Finally, we fabricate gratings with rough edges and an experimental verification of the results is performed.

© 2008 Optical Society of America

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    [CrossRef]
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2008 (1)

2007 (2)

F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, "Talbot effect with rough reflection gratings," Appl. Opt. 46, 3668- 3673 (2007)
[CrossRef]

L.M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, "Talbot effect in metallic gratings under Gaussian illumination," Opt. Commun. 278, 23-27 (2007).
[CrossRef]

2006 (2)

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, "One-way diffraction grating," Phys. Rev. E 74, 056611 (2006).
[CrossRef]

F. Shen and A. Wang, "Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula," Appl. Opt. 45, 1102-1110 (2006)
[CrossRef]

2005 (2)

Y. Lu, C. Zhou, and H. Luo, "Talbot effect of a grating with different kind of flaws," J. Opt. Soc. Am. A 22, 2662-2667 (2005)
[CrossRef]

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, and B. F. Whiting, "Phase effect in the diffraction of light: beyond the grating equation," Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

2003 (1)

2002 (1)

V. A. Doroshenko, "Singular integral equations in the problem of wave diffraction by a grating of imperfect flat irregular strips," Telecommunications and Radio Engineering 57, 65-72 (2002)

2001 (1)

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, "Far field of beams generated by quasi-homogeneous sources passing through polarization gratings," Opt. Commun. 195, 339-350 (2001)
[CrossRef]

2000 (1)

N. Guérineau, B. Harchaoui, and J. Primot, "Talbot effect re-examined: demonstration of an achromatic and continuous self-imaging regime," Opt. Commun. 180, 199-203 (2000).
[CrossRef]

1999 (2)

1998 (1)

M. V. Glazov., and S. N. Rashkeev, "Light scattering from rough surfaces with superimposed periodic structures," Appl. Phys. B 66, 217-223 (1998)
[CrossRef]

1994 (1)

1989 (1)

K. Patorski, "The self-imaging phenomenon and its applications," Prog. Opt. 27, 1-108 (1989).

1836 (1)

W. H. F. Talbot, "Facts relating to optical science," Philos. Mag. 9, 401-407 (1836).

Bernabeu, E.

Borghi, R.

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, "Far field of beams generated by quasi-homogeneous sources passing through polarization gratings," Opt. Commun. 195, 339-350 (2001)
[CrossRef]

Deshpande, A. J.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, and B. F. Whiting, "Phase effect in the diffraction of light: beyond the grating equation," Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Doroshenko, V. A.

V. A. Doroshenko, "Singular integral equations in the problem of wave diffraction by a grating of imperfect flat irregular strips," Telecommunications and Radio Engineering 57, 65-72 (2002)

Gallatin, G. M.

Glazov, M. V.

M. V. Glazov., and S. N. Rashkeev, "Light scattering from rough surfaces with superimposed periodic structures," Appl. Phys. B 66, 217-223 (1998)
[CrossRef]

Gori, F.

Guérineau, N.

N. Guérineau, B. Harchaoui, and J. Primot, "Talbot effect re-examined: demonstration of an achromatic and continuous self-imaging regime," Opt. Commun. 180, 199-203 (2000).
[CrossRef]

Harchaoui, B.

N. Guérineau, B. Harchaoui, and J. Primot, "Talbot effect re-examined: demonstration of an achromatic and continuous self-imaging regime," Opt. Commun. 180, 199-203 (2000).
[CrossRef]

Hibbins, A. P.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, "One-way diffraction grating," Phys. Rev. E 74, 056611 (2006).
[CrossRef]

Lockyear, M. J.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, "One-way diffraction grating," Phys. Rev. E 74, 056611 (2006).
[CrossRef]

Lu, Y.

Luo, H.

Michel, T. R.

Mondello, A.

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, "Far field of beams generated by quasi-homogeneous sources passing through polarization gratings," Opt. Commun. 195, 339-350 (2001)
[CrossRef]

Mueller, G.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, and B. F. Whiting, "Phase effect in the diffraction of light: beyond the grating equation," Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Naulleau, P. P.

Patorski, K.

K. Patorski, "The self-imaging phenomenon and its applications," Prog. Opt. 27, 1-108 (1989).

Piquero, G.

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, "Far field of beams generated by quasi-homogeneous sources passing through polarization gratings," Opt. Commun. 195, 339-350 (2001)
[CrossRef]

Primot, J.

N. Guérineau, B. Harchaoui, and J. Primot, "Talbot effect re-examined: demonstration of an achromatic and continuous self-imaging regime," Opt. Commun. 180, 199-203 (2000).
[CrossRef]

Quetschke, V.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, and B. F. Whiting, "Phase effect in the diffraction of light: beyond the grating equation," Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Rashkeev, S. N.

M. V. Glazov., and S. N. Rashkeev, "Light scattering from rough surfaces with superimposed periodic structures," Appl. Phys. B 66, 217-223 (1998)
[CrossRef]

Reitze, D. H.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, and B. F. Whiting, "Phase effect in the diffraction of light: beyond the grating equation," Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Sambles, J. R.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, "One-way diffraction grating," Phys. Rev. E 74, 056611 (2006).
[CrossRef]

Sanchez-Brea, L. M.

Sanchez-Brea, L.M.

L.M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, "Talbot effect in metallic gratings under Gaussian illumination," Opt. Commun. 278, 23-27 (2007).
[CrossRef]

Santarsiero, M.

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, "Far field of beams generated by quasi-homogeneous sources passing through polarization gratings," Opt. Commun. 195, 339-350 (2001)
[CrossRef]

Shen, F.

Someda, C. G.

Talbot, W. H. F.

W. H. F. Talbot, "Facts relating to optical science," Philos. Mag. 9, 401-407 (1836).

Tanner, D. B.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, and B. F. Whiting, "Phase effect in the diffraction of light: beyond the grating equation," Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Torcal-Milla, F. J.

Wang, A.

White, K. R.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, "One-way diffraction grating," Phys. Rev. E 74, 056611 (2006).
[CrossRef]

Whiting, B. F.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, and B. F. Whiting, "Phase effect in the diffraction of light: beyond the grating equation," Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Wise, S.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, and B. F. Whiting, "Phase effect in the diffraction of light: beyond the grating equation," Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Zhou, C.

Appl. Opt. (3)

Appl. Phys. B (1)

M. V. Glazov., and S. N. Rashkeev, "Light scattering from rough surfaces with superimposed periodic structures," Appl. Phys. B 66, 217-223 (1998)
[CrossRef]

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

Opt. Commun. (3)

N. Guérineau, B. Harchaoui, and J. Primot, "Talbot effect re-examined: demonstration of an achromatic and continuous self-imaging regime," Opt. Commun. 180, 199-203 (2000).
[CrossRef]

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, "Far field of beams generated by quasi-homogeneous sources passing through polarization gratings," Opt. Commun. 195, 339-350 (2001)
[CrossRef]

L.M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, "Talbot effect in metallic gratings under Gaussian illumination," Opt. Commun. 278, 23-27 (2007).
[CrossRef]

Opt. Lett. (2)

Philos. Mag. (1)

W. H. F. Talbot, "Facts relating to optical science," Philos. Mag. 9, 401-407 (1836).

Phys. Rev. E (1)

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles, "One-way diffraction grating," Phys. Rev. E 74, 056611 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, and B. F. Whiting, "Phase effect in the diffraction of light: beyond the grating equation," Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef]

Prog. Opt. (1)

K. Patorski, "The self-imaging phenomenon and its applications," Prog. Opt. 27, 1-108 (1989).

Telecommunications and Radio Engineering (1)

V. A. Doroshenko, "Singular integral equations in the problem of wave diffraction by a grating of imperfect flat irregular strips," Telecommunications and Radio Engineering 57, 65-72 (2002)

Other (6)

M. Born, and E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1980).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

E. G. Loewen and E. Popov, Diffraction gratings and applications (Marcel Dekker, New York, 1997).

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech House Norwood, 1987).

C. Palmer, Diffraction Grating Handbook (Richardson Grating Laboratory, New York, 2000).

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).

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