Abstract

We present a general procedure to analyze the axial-irradiance distribution generated by an unlimited diffractive lens under coherent, Gaussian illumination. The resulting on-axis diffraction pattern, which is evaluated in terms of the power complex spectrum of the Fresnel-zone transmittance, explicitly depends on the truncation parameter that we define, which evaluates the effective number of zones illuminated by the Gaussian beam. Depending on the value of this parameter, different kinds of axial behavior are observed. In particular, for moderate values a multiple-focal-shift phenomenon appears, and a simple formula for its evaluation is presented. Additionally, for low values of the truncation parameter, a focal-merge effect is observed in multifocal zone plates.

© 1999 Optical Society of America

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1998 (3)

1997 (3)

1996 (3)

1995 (2)

1994 (1)

1993 (1)

X. Jiang, S. Wang, E. Bernabeu, J. Alda, “ABCD matrix and focal shift for Fresnel zone plates,” Optik (Stuttgart) 95, 16–18 (1993).

1992 (2)

V. P. Koronkevich, I. G. Pal’chikova, “Modern zone plates,” Optoelectron. Instrum. Data Process. 1, 86–100 (1992).

S. Wang, E. Bernabeu, J. Alda, “Unified and generalized Fresnel numbers,” Opt. Quantum Electron. 24, 1351–1358 (1992).
[CrossRef]

1987 (1)

D. G. Greywall, “A micromechanical optical switch with a zone-plate reflector,” J. Phys. D 30, 2191–2208 (1987).
[CrossRef]

1984 (1)

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Y. I. Yurlov, “Fabrication of kinoform optical elements,” Optik (Stuttgart) 67, 257–266 (1984).

1982 (2)

1981 (1)

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

1977 (1)

M. Novotný, “A new series representation of the Fresnel diffraction field of axially symmetrical filters,” Opt. Acta 24, 551–565 (1977).
[CrossRef]

1964 (1)

1952 (1)

Alda, J.

X. Jiang, S. Wang, E. Bernabeu, J. Alda, “ABCD matrix and focal shift for Fresnel zone plates,” Optik (Stuttgart) 95, 16–18 (1993).

S. Wang, E. Bernabeu, J. Alda, “Unified and generalized Fresnel numbers,” Opt. Quantum Electron. 24, 1351–1358 (1992).
[CrossRef]

Anderson, D.

S. De Nicola, D. Anderson, M. Lisak, “Focal shift effects in diffracted focused beams,” Pure Appl. Opt. 7, 1249–1259 (1998).
[CrossRef]

Andrés, P.

Bernabeu, E.

X. Jiang, S. Wang, E. Bernabeu, J. Alda, “ABCD matrix and focal shift for Fresnel zone plates,” Optik (Stuttgart) 95, 16–18 (1993).

S. Wang, E. Bernabeu, J. Alda, “Unified and generalized Fresnel numbers,” Opt. Quantum Electron. 24, 1351–1358 (1992).
[CrossRef]

Boivin, A.

Carter, W. H.

Chmelik, R.

R. Chmelik, “Analytic description of wave fields in focal regions of diffractive lenses,” J. Mod. Opt. 43, 1463–1471 (1996).
[CrossRef]

Churin, E. G.

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Y. I. Yurlov, “Fabrication of kinoform optical elements,” Optik (Stuttgart) 67, 257–266 (1984).

Climent, V.

De Nicola, S.

S. De Nicola, D. Anderson, M. Lisak, “Focal shift effects in diffracted focused beams,” Pure Appl. Opt. 7, 1249–1259 (1998).
[CrossRef]

Dichensheets, D. L.

Dobson, S. L.

Eberly, J. H.

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), Chap. 11.

Fainman, Y.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1996), Sec. 3.4.2.

Greywall, D. G.

D. G. Greywall, “A micromechanical optical switch with a zone-plate reflector,” J. Phys. D 30, 2191–2208 (1987).
[CrossRef]

Hesser, T.

M. Rossi, T. Hesser, “Interference effects in diffractive beam shaping elements,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper DMD3-1.

Jiang, X.

X. Jiang, S. Wang, E. Bernabeu, J. Alda, “ABCD matrix and focal shift for Fresnel zone plates,” Optik (Stuttgart) 95, 16–18 (1993).

Kino, G. S.

Kiriyanov, V. P.

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Y. I. Yurlov, “Fabrication of kinoform optical elements,” Optik (Stuttgart) 67, 257–266 (1984).

Kokoulin, F. I.

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Y. I. Yurlov, “Fabrication of kinoform optical elements,” Optik (Stuttgart) 67, 257–266 (1984).

Koronkevich, V. P.

V. P. Koronkevich, I. G. Pal’chikova, “Modern zone plates,” Optoelectron. Instrum. Data Process. 1, 86–100 (1992).

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Y. I. Yurlov, “Fabrication of kinoform optical elements,” Optik (Stuttgart) 67, 257–266 (1984).

Li, Y.

Y. Li, “Focal shift and focal switch in dual-focus systems,” J. Opt. Soc. Am. A 14, 1297–1304 (1997).
[CrossRef]

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

Lin, P. C.

Lisak, M.

S. De Nicola, D. Anderson, M. Lisak, “Focal shift effects in diffracted focused beams,” Pure Appl. Opt. 7, 1249–1259 (1998).
[CrossRef]

Marti´nez-Corral, M.

McCutchen, C. W.

Milonni, P. W.

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), Chap. 11.

Moreno, V.

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Nishida, N.

Novotný, M.

M. Novotný, “A new series representation of the Fresnel diffraction field of axially symmetrical filters,” Opt. Acta 24, 551–565 (1977).
[CrossRef]

Ojeda-Castañeda, J.

Ono, Y.

Pal’chikova, I. G.

V. P. Koronkevich, I. G. Pal’chikova, “Modern zone plates,” Optoelectron. Instrum. Data Process. 1, 86–100 (1992).

Palchikova, I. G.

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Y. I. Yurlov, “Fabrication of kinoform optical elements,” Optik (Stuttgart) 67, 257–266 (1984).

Poleshchuk, A. G.

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Y. I. Yurlov, “Fabrication of kinoform optical elements,” Optik (Stuttgart) 67, 257–266 (1984).

Román, J. F.

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Rossi, M.

M. Rossi, T. Hesser, “Interference effects in diffractive beam shaping elements,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper DMD3-1.

Salgueiro, J. R.

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Sedukhin, A. G.

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Y. I. Yurlov, “Fabrication of kinoform optical elements,” Optik (Stuttgart) 67, 257–266 (1984).

Shcherbachenko, A. M.

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Y. I. Yurlov, “Fabrication of kinoform optical elements,” Optik (Stuttgart) 67, 257–266 (1984).

Shulman, A. R.

A. R. Shulman, Optical Data Processing (Wiley, New York, 1970), Chap. 9.

Silvestre, E.

Sommargren, G. E.

Sun, P.-C.

Sweeney, D. W.

Wang, S.

X. Jiang, S. Wang, E. Bernabeu, J. Alda, “ABCD matrix and focal shift for Fresnel zone plates,” Optik (Stuttgart) 95, 16–18 (1993).

S. Wang, E. Bernabeu, J. Alda, “Unified and generalized Fresnel numbers,” Opt. Quantum Electron. 24, 1351–1358 (1992).
[CrossRef]

Wolf, E.

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

Yurlov, Y. I.

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Y. I. Yurlov, “Fabrication of kinoform optical elements,” Optik (Stuttgart) 67, 257–266 (1984).

Zapata-Rodri´guez, C. J.

Zhu, L.

Am. J. Phys. (1)

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Appl. Opt. (8)

J. Mod. Opt. (1)

R. Chmelik, “Analytic description of wave fields in focal regions of diffractive lenses,” J. Mod. Opt. 43, 1463–1471 (1996).
[CrossRef]

J. Opt. Soc. Am. (2)

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

J. Phys. D (1)

D. G. Greywall, “A micromechanical optical switch with a zone-plate reflector,” J. Phys. D 30, 2191–2208 (1987).
[CrossRef]

Opt. Acta (1)

M. Novotný, “A new series representation of the Fresnel diffraction field of axially symmetrical filters,” Opt. Acta 24, 551–565 (1977).
[CrossRef]

Opt. Commun. (1)

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

S. Wang, E. Bernabeu, J. Alda, “Unified and generalized Fresnel numbers,” Opt. Quantum Electron. 24, 1351–1358 (1992).
[CrossRef]

Optik (Stuttgart) (2)

V. P. Koronkevich, V. P. Kiriyanov, F. I. Kokoulin, I. G. Palchikova, A. G. Poleshchuk, A. G. Sedukhin, E. G. Churin, A. M. Shcherbachenko, Y. I. Yurlov, “Fabrication of kinoform optical elements,” Optik (Stuttgart) 67, 257–266 (1984).

X. Jiang, S. Wang, E. Bernabeu, J. Alda, “ABCD matrix and focal shift for Fresnel zone plates,” Optik (Stuttgart) 95, 16–18 (1993).

Optoelectron. Instrum. Data Process. (1)

V. P. Koronkevich, I. G. Pal’chikova, “Modern zone plates,” Optoelectron. Instrum. Data Process. 1, 86–100 (1992).

Pure Appl. Opt. (1)

S. De Nicola, D. Anderson, M. Lisak, “Focal shift effects in diffracted focused beams,” Pure Appl. Opt. 7, 1249–1259 (1998).
[CrossRef]

Other (5)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1996), Sec. 3.4.2.

Hint: |sin(x+iy)|2=sin2(x)+sinh2(y).

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), Chap. 11.

A. R. Shulman, Optical Data Processing (Wiley, New York, 1970), Chap. 9.

M. Rossi, T. Hesser, “Interference effects in diffractive beam shaping elements,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper DMD3-1.

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