Abstract

It is shown that a hemispherical-rod microlens can act as a fractional Fourier transform device with a continuously varying degree of fractionality. It is believed to be the first proposed device to perform such a task; its most immediate applications include optical tomography.

© 1998 Optical Society of America

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References

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  1. D. Dragoman, Progr. Opt. 37, 1 (1997).
    [CrossRef]
  2. D. Mendlovic, Y. Bitran, R. G. Dorsch, C. Ferreira, J. Garcia, and H. M. Ozaktas, Appl. Opt. 34, 7451 (1995).
    [CrossRef] [PubMed]
  3. D. Mendlovic, Z. Zalevsky, N. Conforti, R. G. Dorsch, and A. W. Lohmann, Appl. Opt. 34, 7615 (1995).
    [CrossRef] [PubMed]
  4. A. Sahin, H. M. Ozaktas, and D. Mendlovic, Opt. Commun. 120, 134 (1995).
    [CrossRef]
  5. A. W. Lohmann, Opt. Commun. 115, 434 (1995).
    [CrossRef]
  6. M. F. Erden, H. M. Ozaktas, A. Sahin, and D. Mendlovic, Opt. Commun. 136, 52 (1997).
    [CrossRef]
  7. K.-H. Brenner and J. Bähr, in Micro-Optics Conference/Gradient-Index ’97, Technical Digest AP971222 (1997), p. 24.
  8. A. A. Tovar and L. W. Casperson, J. Opt. Soc. Am. A 12, 1522 (1995).
    [CrossRef]
  9. D. F. V. James and G. S. Agarwal, Opt. Commun. 126, 207 (1996).
    [CrossRef]
  10. V. Namias, J. Inst. Math. Its Appl. 25, 241 (1980).
    [CrossRef]
  11. A. W. Lohmann, J. Opt. Soc. Am. A 11, 1798 (1994).
    [CrossRef]

1997 (2)

M. F. Erden, H. M. Ozaktas, A. Sahin, and D. Mendlovic, Opt. Commun. 136, 52 (1997).
[CrossRef]

D. Dragoman, Progr. Opt. 37, 1 (1997).
[CrossRef]

1996 (1)

D. F. V. James and G. S. Agarwal, Opt. Commun. 126, 207 (1996).
[CrossRef]

1995 (5)

1994 (1)

1980 (1)

V. Namias, J. Inst. Math. Its Appl. 25, 241 (1980).
[CrossRef]

Agarwal, G. S.

D. F. V. James and G. S. Agarwal, Opt. Commun. 126, 207 (1996).
[CrossRef]

Bähr, J.

K.-H. Brenner and J. Bähr, in Micro-Optics Conference/Gradient-Index ’97, Technical Digest AP971222 (1997), p. 24.

Bitran, Y.

Brenner, K.-H.

K.-H. Brenner and J. Bähr, in Micro-Optics Conference/Gradient-Index ’97, Technical Digest AP971222 (1997), p. 24.

Casperson, L. W.

Conforti, N.

Dorsch, R. G.

Dragoman, D.

D. Dragoman, Progr. Opt. 37, 1 (1997).
[CrossRef]

Erden, M. F.

M. F. Erden, H. M. Ozaktas, A. Sahin, and D. Mendlovic, Opt. Commun. 136, 52 (1997).
[CrossRef]

Ferreira, C.

Garcia, J.

James, D. F. V.

D. F. V. James and G. S. Agarwal, Opt. Commun. 126, 207 (1996).
[CrossRef]

Lohmann, A. W.

Mendlovic, D.

Namias, V.

V. Namias, J. Inst. Math. Its Appl. 25, 241 (1980).
[CrossRef]

Ozaktas, H. M.

M. F. Erden, H. M. Ozaktas, A. Sahin, and D. Mendlovic, Opt. Commun. 136, 52 (1997).
[CrossRef]

A. Sahin, H. M. Ozaktas, and D. Mendlovic, Opt. Commun. 120, 134 (1995).
[CrossRef]

D. Mendlovic, Y. Bitran, R. G. Dorsch, C. Ferreira, J. Garcia, and H. M. Ozaktas, Appl. Opt. 34, 7451 (1995).
[CrossRef] [PubMed]

Sahin, A.

M. F. Erden, H. M. Ozaktas, A. Sahin, and D. Mendlovic, Opt. Commun. 136, 52 (1997).
[CrossRef]

A. Sahin, H. M. Ozaktas, and D. Mendlovic, Opt. Commun. 120, 134 (1995).
[CrossRef]

Tovar, A. A.

Zalevsky, Z.

Appl. Opt. (2)

J. Inst. Math. Its Appl. (1)

V. Namias, J. Inst. Math. Its Appl. 25, 241 (1980).
[CrossRef]

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

Opt. Commun. (4)

D. F. V. James and G. S. Agarwal, Opt. Commun. 126, 207 (1996).
[CrossRef]

A. Sahin, H. M. Ozaktas, and D. Mendlovic, Opt. Commun. 120, 134 (1995).
[CrossRef]

A. W. Lohmann, Opt. Commun. 115, 434 (1995).
[CrossRef]

M. F. Erden, H. M. Ozaktas, A. Sahin, and D. Mendlovic, Opt. Commun. 136, 52 (1997).
[CrossRef]

Progr. Opt. (1)

D. Dragoman, Progr. Opt. 37, 1 (1997).
[CrossRef]

Other (1)

K.-H. Brenner and J. Bähr, in Micro-Optics Conference/Gradient-Index ’97, Technical Digest AP971222 (1997), p. 24.

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Figures (2)

Fig. 1
Fig. 1

(a) H-rod microlens and the propagation of rays in its meridional and sagittal planes between the input and output planes. (b) Ray propagation in the meridional plane of a H-rod microlens: Rays that are incident under different angles propagate over different z distances.

Fig. 2
Fig. 2

Dependence of the degree of fractionality of the FRFT on the input ray angle for two values of x¯i: -100 µm (solid curve) and -200 µm (dotted curve); n0=1.631, A=6.5×10-4 µm-1.

Equations (11)

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

nx, y=n01-A22x2+y2, x0,
xopo=cosAzsinAzn0A-n0AsinAzcosAzxipi=Mzxipi,
zo=1Aarctanpin0Ax¯i+xi,po=-n0Ax¯i+xi1+pin0Ax¯i+xi21/2+n0A xi.
zopo=01n0A2x¯i-n0A0xipi.
zoAsinAz¯ox¯ipo=cosAz¯osinAz¯on0A-n0AsinAz¯ocosAz¯oxipi,
Mz=AzBzCzDz
fxo, z=fxiexpik2BzAzxi2-2xixo+Dzxo2dxi,
f0, z=fxi+x¯iexpikn0A2cosAzsinAzxi2dxi=fxiexpik2n0AcosAzsinAzxi-x¯i2dxigz, x¯i.
Fαuf=Kfxiexp×ikn0Au2+xi2cosαπ22sinαπ2-uxisinαπ2dxi,
K=expiπ4-iαπ42π sinαπ21/2,
gz, x¯i=1KF2Az/πx¯i×fxexpikn0Ax¯icosAz-1sinAz.

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