Abstract

We study the diffraction fields in a hybrid diffractive–gradient-index element composed of an amplitude zone plate and a quarter-pitch Selfoc gradient-index lens under uniform illumination. Focal positions of the diffractive orders and zone-plate diffraction efficiencies are measured, thereby validating the existing theoretical results.

© 2003 Optical Society of America

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References

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  1. H. P. Herzig, ed., Micro-Optics: Elements, Systems and Applications (Taylor & Francis, London, 1998).
  2. J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Akademie-Verlag, Berlin, 1997), Chap. 1.
  3. J. Ojeda-Castañeda and C. Gómez-Reino, eds., Selected Papers on Zone Plates, Vol. MS 128 of SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1996), and references therein.
  4. J. M. Rivas-Moscoso, C. Gómez-Reino, C. Bao, and M. V. Pérez, J. Mod. Opt. 47, 1549 (2000).
    [CrossRef]
  5. J. M. Rivas-Moscoso, C. Gómez-Reino, M. V. Pérez, and C. Bao, J. Mod. Opt. 48, 915 (2001).
    [CrossRef]
  6. M. T. Flores-Arias, C. Bao, M. V. Pérez, and C. R. Fernández-Pousa, Opt. Lett. 27, 2064 (2002).
    [CrossRef]
  7. Nippon Sheet Glass, Selfoc Product Guide (Nippon Sheet Glass Europe N.V./S.A., Temse, Belgium, 2001).
  8. C. Gómez-Reino, M. V. Pérez, and C. Bao, GRIN Optics: Fundamentals and Applications (Springer-Verlag, Berlin, 2002), Chap. 3.
  9. J. W. Goodman, Introduction to Fourier Optics, 2nd. ed. (McGraw-Hill, New York, 1996), Chap. 5.

2002 (2)

M. T. Flores-Arias, C. Bao, M. V. Pérez, and C. R. Fernández-Pousa, Opt. Lett. 27, 2064 (2002).
[CrossRef]

C. Gómez-Reino, M. V. Pérez, and C. Bao, GRIN Optics: Fundamentals and Applications (Springer-Verlag, Berlin, 2002), Chap. 3.

2001 (2)

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

J. M. Rivas-Moscoso, C. Gómez-Reino, M. V. Pérez, and C. Bao, J. Mod. Opt. 48, 915 (2001).
[CrossRef]

2000 (1)

J. M. Rivas-Moscoso, C. Gómez-Reino, C. Bao, and M. V. Pérez, J. Mod. Opt. 47, 1549 (2000).
[CrossRef]

1998 (1)

H. P. Herzig, ed., Micro-Optics: Elements, Systems and Applications (Taylor & Francis, London, 1998).

1997 (1)

J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Akademie-Verlag, Berlin, 1997), Chap. 1.

1996 (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd. ed. (McGraw-Hill, New York, 1996), Chap. 5.

Bao, C.

M. T. Flores-Arias, C. Bao, M. V. Pérez, and C. R. Fernández-Pousa, Opt. Lett. 27, 2064 (2002).
[CrossRef]

C. Gómez-Reino, M. V. Pérez, and C. Bao, GRIN Optics: Fundamentals and Applications (Springer-Verlag, Berlin, 2002), Chap. 3.

J. M. Rivas-Moscoso, C. Gómez-Reino, M. V. Pérez, and C. Bao, J. Mod. Opt. 48, 915 (2001).
[CrossRef]

J. M. Rivas-Moscoso, C. Gómez-Reino, C. Bao, and M. V. Pérez, J. Mod. Opt. 47, 1549 (2000).
[CrossRef]

Fernández-Pousa, C. R.

Flores-Arias, M. T.

Gómez-Reino, C.

C. Gómez-Reino, M. V. Pérez, and C. Bao, GRIN Optics: Fundamentals and Applications (Springer-Verlag, Berlin, 2002), Chap. 3.

J. M. Rivas-Moscoso, C. Gómez-Reino, M. V. Pérez, and C. Bao, J. Mod. Opt. 48, 915 (2001).
[CrossRef]

J. M. Rivas-Moscoso, C. Gómez-Reino, C. Bao, and M. V. Pérez, J. Mod. Opt. 47, 1549 (2000).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd. ed. (McGraw-Hill, New York, 1996), Chap. 5.

Pérez, M. V.

C. Gómez-Reino, M. V. Pérez, and C. Bao, GRIN Optics: Fundamentals and Applications (Springer-Verlag, Berlin, 2002), Chap. 3.

M. T. Flores-Arias, C. Bao, M. V. Pérez, and C. R. Fernández-Pousa, Opt. Lett. 27, 2064 (2002).
[CrossRef]

J. M. Rivas-Moscoso, C. Gómez-Reino, M. V. Pérez, and C. Bao, J. Mod. Opt. 48, 915 (2001).
[CrossRef]

J. M. Rivas-Moscoso, C. Gómez-Reino, C. Bao, and M. V. Pérez, J. Mod. Opt. 47, 1549 (2000).
[CrossRef]

Rivas-Moscoso, J. M.

J. M. Rivas-Moscoso, C. Gómez-Reino, M. V. Pérez, and C. Bao, J. Mod. Opt. 48, 915 (2001).
[CrossRef]

J. M. Rivas-Moscoso, C. Gómez-Reino, C. Bao, and M. V. Pérez, J. Mod. Opt. 47, 1549 (2000).
[CrossRef]

J. Mod. Opt. (2)

J. M. Rivas-Moscoso, C. Gómez-Reino, C. Bao, and M. V. Pérez, J. Mod. Opt. 47, 1549 (2000).
[CrossRef]

J. M. Rivas-Moscoso, C. Gómez-Reino, M. V. Pérez, and C. Bao, J. Mod. Opt. 48, 915 (2001).
[CrossRef]

Opt. Lett. (1)

SPIE Milestone Series (1)

J. Ojeda-Castañeda and C. Gómez-Reino, eds., Selected Papers on Zone Plates, Vol. MS 128 of SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1996), and references therein.

Other (5)

H. P. Herzig, ed., Micro-Optics: Elements, Systems and Applications (Taylor & Francis, London, 1998).

J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Akademie-Verlag, Berlin, 1997), Chap. 1.

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

C. Gómez-Reino, M. V. Pérez, and C. Bao, GRIN Optics: Fundamentals and Applications (Springer-Verlag, Berlin, 2002), Chap. 3.

J. W. Goodman, Introduction to Fourier Optics, 2nd. ed. (McGraw-Hill, New York, 1996), Chap. 5.

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Figures (5)

Fig. 1
Fig. 1

Geometry of the input and readout systems: M1, focusing objective; π0, πE, and πI, object plane, exit plane of the microlens, and image plane, respectively; M2, observation objective.

Fig. 2
Fig. 2

Photographs of (a) the ZP, (b) the plane where diffractive order m=7 is focused, and (c) a plane halfway between the planes, where orders m=6 and m=7 focus inside a Selfoc GRIN lens.

Fig. 3
Fig. 3

Equivalent system under uniform illumination: l, distance from the point source to the image plane of the ZP inside the microlens; LZP, lens length from the image of the ZP to the exit face; dm, image of the point source corresponding to the mth diffractive order.

Fig. 4
Fig. 4

Focal positions z inside a Selfoc GRIN lens as a function of diffractive order m. Measured (experimental) positions and positions given by Eq. (8) are shown.

Fig. 5
Fig. 5

ZP diffraction efficiency ratios Rm versus diffractive order m in a Selfoc GRIN lens for foci inside and outside the lens. Measured ratios and ratios given by Eq. (10) are shown. The shaded area represents the 95% confidence interval on parameter estimate /p. Inset, an enlargement for the higher orders.

Equations (10)

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n2x,y=n021-g2x2+y2,
ABCD=1s0110-1/f1×1s01100n0×cosgLsingL/g-g singLcosgL,
tangL=n0gΔ,
MtSΔ=M01+n0gΔ21/2,
ABCD=1dm01100n0×cosgLZPsingLZP/g-g singLZPcosgLZP×1001/n010-2mλ0/p11l01,
dm=-1UmLZP=p-2mλlΔZP+lpn02g2lpΔZP-p-2mλ0l,
l=singLZP+n0gd0 cosgLZPn02g2d0 singLZP-n0g cosgLZP.
zm=1/gtan-1n0glp/2mλ0l-p.
r=0.610λ0singLn0ga+cosgLdma,
Rm=Im/I0=sinc2m/p,

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