Abstract

We analyze theoretically the diffraction of phase gratings in the deep Fresnel field on the basis of the theory of scalar diffraction and Green's theorem and present the general formula for the diffraction intensity of a one-dimensional sinusoidal phase grating. The numerical calculations show that in the deep Fresnel region the diffraction distribution can be described by designating three characteristic regions that are influenced by the parameters of the grating. The microlensing effect of the interface of the phase grating provides the corresponding explanation. Moreover, according to the viewpoint that the diffraction intensity distribution is the result of the interference of the diffraction orders of the grating, we find that the diffraction patterns, depending on the carved depth of the phase grating, are determined by the contributing diffraction orders, their relative power, and the quasi-Talbot effect of the phase grating, which results from the second meeting of the diffraction orders carrying most of the power of the total field, as in the case of the amplitude grating.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2007 (1)

2006 (1)

2005 (2)

Y. L. Sheng and L. Sun, "Near-field diffraction of irregular phase gratings with multiple phase-shifts," Opt. Express 13, 6111-6115 (2005).
[CrossRef]

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot effect in waveguide arrays," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef]

2004 (1)

2003 (2)

2001 (1)

2000 (1)

1999 (1)

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Temporal matter-wave-dispersion Talbot effect," Phys. Rev. Lett. 83, 5407-5411 (1999).
[CrossRef]

1995 (1)

C. Zhou and L. Liu, "Simple equations for the calculation of a multilevel phase grating for Talbot array illuminator," Opt. Commun. 115, 40-44 (1995).
[CrossRef]

1994 (2)

L. Li, "Bremmer series, R-matrix propagation algorithm, and numerical modeling of diffraction gratings," J. Opt. Soc. Am. A 11, 2829-2835 (1994).

J. F. Clauser and S. F. Li, "Talbot-vonLau atom interferometry with cold slow potassium," Phys. Rev. A 49, R2213-R2216 (1994).
[CrossRef]

1992 (1)

1989 (1)

Appl. Opt. (3)

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

Opt. Commun. (1)

C. Zhou and L. Liu, "Simple equations for the calculation of a multilevel phase grating for Talbot array illuminator," Opt. Commun. 115, 40-44 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

J. F. Clauser and S. F. Li, "Talbot-vonLau atom interferometry with cold slow potassium," Phys. Rev. A 49, R2213-R2216 (1994).
[CrossRef]

Phys. Rev. Lett. (2)

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Temporal matter-wave-dispersion Talbot effect," Phys. Rev. Lett. 83, 5407-5411 (1999).
[CrossRef]

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, "Discrete Talbot effect in waveguide arrays," Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef]

Other (4)

X. P. Wu and F. P. Chiang, "Coherent chromatic speckle," in Proceedings Of the International Conference on Advanced Experimental Mechanics (Peiyang S. & T. Development Co., 1988), pp. C19-C24.

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

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, 2001).

M. Abramowitz and I. A. Stegum, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 4th ed. (National Bureau of Standards, 1965).

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