Abstract

The fractional Talbot effect is demonstrated inside a standard 0.25-pitch Selfoc gradient-index lens under uniform illumination. Comparisons with theoretical expressions of positions and magnification of fractional Talbot images are given.

© 2002 Optical Society of America

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References

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  1. K. Patorski, Prog. Opt. 27, 3 (1989).
  2. J. R. Leger, M. L. Scott, and W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
    [CrossRef]
  3. R. Ulrich, Opt. Commun. 13, 259 (1975).
    [CrossRef]
  4. L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
    [CrossRef]
  5. C. Gómez-Reino, M. V. Pérez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer-Verlag, Berlin, 2002), Chap. 7.
    [CrossRef]
  6. M. T. Flores-Arias, C. Bao, M. V. Pérez, and C. Gómez-Reino, J. Opt. Soc. Am. A 16, 2439 (1999).
    [CrossRef]
  7. M. T. Flores-Arias, M. V. Pérez, C. Gómez-Reino, C. Bao, and C. R. Fernández-Pousa, J. Opt. Soc. Am. A 17, 1007 (2000).
    [CrossRef]
  8. Nippon Sheet Glass Europe N.V./S.A., Selfoc Product Guide (Temse, Belgium, 2001).
  9. T. Alieva and F. Agulló-López, J. Opt. Soc. A 13, 2375 (1996).
    [CrossRef]

2000 (1)

1999 (1)

1996 (1)

T. Alieva and F. Agulló-López, J. Opt. Soc. A 13, 2375 (1996).
[CrossRef]

1995 (1)

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

1989 (1)

K. Patorski, Prog. Opt. 27, 3 (1989).

1988 (1)

J. R. Leger, M. L. Scott, and W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

1975 (1)

R. Ulrich, Opt. Commun. 13, 259 (1975).
[CrossRef]

Agulló-López, F.

T. Alieva and F. Agulló-López, J. Opt. Soc. A 13, 2375 (1996).
[CrossRef]

Alieva, T.

T. Alieva and F. Agulló-López, J. Opt. Soc. A 13, 2375 (1996).
[CrossRef]

Bao, C.

Fernández-Pousa, C. R.

Flores-Arias, M. T.

Gómez-Reino, C.

Leger, J. R.

J. R. Leger, M. L. Scott, and W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

Patorski, K.

K. Patorski, Prog. Opt. 27, 3 (1989).

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

Pérez, M. V.

Scott, M. L.

J. R. Leger, M. L. Scott, and W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

Ulrich, R.

R. Ulrich, Opt. Commun. 13, 259 (1975).
[CrossRef]

Veldkamp, W. B.

J. R. Leger, M. L. Scott, and W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

Appl. Phys. Lett. (1)

J. R. Leger, M. L. Scott, and W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

J. Lightwave Technol. (1)

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

J. Opt. Soc. A (1)

T. Alieva and F. Agulló-López, J. Opt. Soc. A 13, 2375 (1996).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

R. Ulrich, Opt. Commun. 13, 259 (1975).
[CrossRef]

Prog. Opt. (1)

K. Patorski, Prog. Opt. 27, 3 (1989).

Other (2)

Nippon Sheet Glass Europe N.V./S.A., Selfoc Product Guide (Temse, Belgium, 2001).

C. Gómez-Reino, M. V. Pérez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer-Verlag, Berlin, 2002), Chap. 7.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Geometry of the input and readout system: M1, entrance objective; π0, object plane; πE, exit plane of the microlens; πI, image plane; L, distance from π0 to πE; d, distance from πE to the microscope objective; M2, exit objective of focal length f; d, length from the exit objective to πI.

Fig. 2
Fig. 2

(a) Periodic object; (b), (c), (d) fractional Talbot planes z1/2,z1/3, and z1/4, respectively, in air; (e)–(g) the same planes inside the Selfoc GRIN lens.

Fig. 3
Fig. 3

Measured positions versus the fractional Talbot index. Positions as predicted from Eq. (6) are also given. Fractions besides the points indicate the exact fractional Talbot indices.

Fig. 4
Fig. 4

Equivalent system under uniform illumination: d0, distance from the point source to the plane where the image of the grating is formed; LG, length of the lens after the image of the grating; dT, distance after the microlens where the first integer Talbot image is formed.

Fig. 5
Fig. 5

Measured transverse magnification versus fractional Talbot index. Magnifications as predicted from Eq. (7) are also given. The fractions beside the points indicate the exact fractional Talbot indices.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

n2x,y=n021-g2x2+y2.
ABCD=1d0110-1/f11d01×100n0cosgLsingL/g-g singLcosgL,
tangL=n0gfd-fd-d.
tangL=n0gΔ.
MtSΔ=M01+n0gΔ21/2,
tangzβ/α=βp2n0gd0αλ0d0-βp2,
Mt=cosgzβ/α+singzβ/α/n0d0g.
BA=βαp2λ0.
ABCD=1dT01100n0×cosgLsingL/g-g singLcosgL×1001/n0101/d01,
1d0=λ0p2+n0g2dTΔG-1dT+ΔG.

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