Abstract

In the regime of Fresnel diffraction, a novel algorithm is proposed for aperture design for getting expected diffraction patterns. Experiments have verified the feasibility of this method. It may be used in beam transition, optics communication, information encryption, and other related fields.

© 2014 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge University, 1999).
  2. A. Roger and D. Maystre, J. Opt. Soc. Am. 70, 1483 (1980).
    [CrossRef]
  3. J. Fienup, Appl. Opt. 21, 2758 (1982).
    [CrossRef]
  4. J. Li and C. Li, Appl. Opt. 47, A97 (2008).
    [CrossRef]
  5. S. A. Collins, J. Opt. Soc. Am. 60, 1168 (1970).
    [CrossRef]
  6. S. Wang and D. Zhao, Matrix Optics (CHEP-Springer, 2000).

2008 (1)

1982 (1)

1980 (1)

1970 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge University, 1999).

Collins, S. A.

Fienup, J.

Li, C.

Li, J.

Maystre, D.

Roger, A.

Wang, S.

S. Wang and D. Zhao, Matrix Optics (CHEP-Springer, 2000).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge University, 1999).

Zhao, D.

S. Wang and D. Zhao, Matrix Optics (CHEP-Springer, 2000).

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

Other (2)

M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge University, 1999).

S. Wang and D. Zhao, Matrix Optics (CHEP-Springer, 2000).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of the aperture and the expected diffraction pattern.

Fig. 2.
Fig. 2.

Design and experimental demonstration for expected diffraction pattern (English word optics). (a) Expected diffraction pattern, (b) designed aperture, (c) numeric simulation pattern, and (d) experimental pattern.

Fig. 3.
Fig. 3.

Schematic diagram of the experimental apparatus.

Fig. 4.
Fig. 4.

Design and experimental demonstration for geometrical pattern (star). (a) Expected diffraction pattern, (b) designed aperture, (c) numeric simulation pattern, and (d) experimental pattern.

Fig. 5.
Fig. 5.

Design and experimental demonstration for Chinese characters (Zhejiang University). (a) Expected diffraction pattern, (b) designed aperture, (c) numeric simulation pattern, and (d) experimental pattern.

Equations (9)

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E2(x2,y2,z)=ik2πBeikzsE1(x1,y1)exp{ik2B[A(x12+y12)2(x1x2+y1y2)+D(x22+y22)]}dx1dy1,
E2(x2,y2,z)=eikziλzsE1(x1,y1)×exp{ik2z[(x1x2)2+(y1y2)2]}dx1dy1.
E2(x2,y2,z)=4a2zeiπz(x22+y22)sinc(2πax2z)sinc(2πay2z).
E2(x2,y2;x0,y0,z)=4a2zexp{iπz[(x2x0)2+(y2y0)2]}×sinc(2πa(x2x0)z)sinc(2πa(y2y0)z).
(|iπλzx12|,|iπλzy12|)|iπλza2|=9π10,0001,
Iexp(x2,y2)=Iexp(x2,y2)x2,y2Iexp(x2,y2)/N,
I(x2,y2)=|x0,y0E2(x2,y2;x0,y0,z)|2,
I(x2,y2)=I(x2,y2)x2,y2I(x2,y2)/N.
εx2,y2(|I(x2,y2)Iexp(x2,y2)|2).

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