Abstract

A particular class of Montgomery’s self-imaging objects that we call continuously self-imaging gratings (CSIG’s) is introduced. When they are illuminated by a plane wave, these objects produce a field whose intensity profile is a propagation- and wavelength-invariant biperiodic array of bright spots. The mathematical construction of these objects and their intrinsic properties are described. On a practical level, CSIG’s are compact and achromatic nondiffracting array generators. We show that a good CSIG approximation can be realized by a two-level phase grating that is experimentally tested.

© 2001 Optical Society of America

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References

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2000 (3)

N. Guérineau, B. Harchaoui, and J. Primot, Opt. Commun. 180, 199 (2000).
[CrossRef]

R. Grunwald, U. Griebner, F. Tschirschwitz, E. T. Nibbering, T. Elsaesser, V. Kebbel, H.-J. Hartmann, and W. Jüptner, Opt. Lett. 25, 981 (2000).
[CrossRef]

C. Yu, M. R. Wang, A. J. Varela, and B. Chen, Opt. Commun. 177, 369 (2000).
[CrossRef]

1999 (2)

N. Guérineau and J. Primot, J. Opt. Soc. Am. A 16, 293 (1999).
[CrossRef]

E. Tajahuerce, P. Andrés, J. Lancis, M. Fernadez-Alonso, and V. Climent, J. Mod. Opt. 46, 49 (1999).
[CrossRef]

1998 (1)

1995 (1)

1994 (1)

E. Bonet, P. Andrés, J. C. Barreiro, and A. Pons, Opt. Commun. 106, 39 (1994).
[CrossRef]

1993 (1)

1990 (2)

1987 (1)

1985 (1)

J. Durnin, J. Opt. Soc. Am. A 2, P110 (1985).

1984 (1)

B. Packross, R. Eschbach, and O. Bryngdahl, Opt. Commun. 50, 205 (1984).
[CrossRef]

1976 (1)

Andrés, P.

E. Tajahuerce, P. Andrés, J. Lancis, M. Fernadez-Alonso, and V. Climent, J. Mod. Opt. 46, 49 (1999).
[CrossRef]

E. Bonet, P. Andrés, J. C. Barreiro, and A. Pons, Opt. Commun. 106, 39 (1994).
[CrossRef]

Arrizon, V.

Barreiro, J. C.

E. Bonet, P. Andrés, J. C. Barreiro, and A. Pons, Opt. Commun. 106, 39 (1994).
[CrossRef]

Bonet, E.

E. Bonet, P. Andrés, J. C. Barreiro, and A. Pons, Opt. Commun. 106, 39 (1994).
[CrossRef]

Bryngdahl, O.

B. Packross, R. Eschbach, and O. Bryngdahl, Opt. Commun. 50, 205 (1984).
[CrossRef]

Chen, B.

C. Yu, M. R. Wang, A. J. Varela, and B. Chen, Opt. Commun. 177, 369 (2000).
[CrossRef]

Climent, V.

E. Tajahuerce, P. Andrés, J. Lancis, M. Fernadez-Alonso, and V. Climent, J. Mod. Opt. 46, 49 (1999).
[CrossRef]

Durnin, J.

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. Durnin, J. Opt. Soc. Am. A 2, P110 (1985).

Elsaesser, T.

Eschbach, R.

B. Packross, R. Eschbach, and O. Bryngdahl, Opt. Commun. 50, 205 (1984).
[CrossRef]

Fernadez-Alonso, M.

E. Tajahuerce, P. Andrés, J. Lancis, M. Fernadez-Alonso, and V. Climent, J. Mod. Opt. 46, 49 (1999).
[CrossRef]

Griebner, U.

Grunwald, R.

Guérineau, N.

N. Guérineau, B. Harchaoui, and J. Primot, Opt. Commun. 180, 199 (2000).
[CrossRef]

N. Guérineau and J. Primot, J. Opt. Soc. Am. A 16, 293 (1999).
[CrossRef]

Harchaoui, B.

N. Guérineau, B. Harchaoui, and J. Primot, Opt. Commun. 180, 199 (2000).
[CrossRef]

Hartmann, H.-J.

Jüptner, W.

Kebbel, V.

Kettunen, V.

Lancis, J.

E. Tajahuerce, P. Andrés, J. Lancis, M. Fernadez-Alonso, and V. Climent, J. Mod. Opt. 46, 49 (1999).
[CrossRef]

Leger, J. R.

Lohmann, A. W.

Montgomery, W. D.

Nibbering, E. T.

Packross, B.

B. Packross, R. Eschbach, and O. Bryngdahl, Opt. Commun. 50, 205 (1984).
[CrossRef]

Patorski, K.

K. Patorski, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 1–108.
[CrossRef]

Pons, A.

E. Bonet, P. Andrés, J. C. Barreiro, and A. Pons, Opt. Commun. 106, 39 (1994).
[CrossRef]

Primot, J.

Sogno, L.

Swanson, G. J.

Szwaykowski, P.

Tajahuerce, E.

E. Tajahuerce, P. Andrés, J. Lancis, M. Fernadez-Alonso, and V. Climent, J. Mod. Opt. 46, 49 (1999).
[CrossRef]

Thomas, J. A.

Tschirschwitz, F.

Turunen, J.

Varela, A. J.

C. Yu, M. R. Wang, A. J. Varela, and B. Chen, Opt. Commun. 177, 369 (2000).
[CrossRef]

Wang, M. R.

C. Yu, M. R. Wang, A. J. Varela, and B. Chen, Opt. Commun. 177, 369 (2000).
[CrossRef]

Yu, C.

C. Yu, M. R. Wang, A. J. Varela, and B. Chen, Opt. Commun. 177, 369 (2000).
[CrossRef]

Appl. Opt. (2)

J. Mod. Opt. (1)

E. Tajahuerce, P. Andrés, J. Lancis, M. Fernadez-Alonso, and V. Climent, J. Mod. Opt. 46, 49 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Commun. (4)

N. Guérineau, B. Harchaoui, and J. Primot, Opt. Commun. 180, 199 (2000).
[CrossRef]

E. Bonet, P. Andrés, J. C. Barreiro, and A. Pons, Opt. Commun. 106, 39 (1994).
[CrossRef]

B. Packross, R. Eschbach, and O. Bryngdahl, Opt. Commun. 50, 205 (1984).
[CrossRef]

C. Yu, M. R. Wang, A. J. Varela, and B. Chen, Opt. Commun. 177, 369 (2000).
[CrossRef]

Opt. Lett. (3)

Other (1)

K. Patorski, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 1–108.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Construction in the Fourier plane of three CSIG’s by selection of orders from a Cartesian grid with rings of different radii (three rings are represented that select, from innermost to outermost, 8, 12, and 24  orders of the grid).

Fig. 2
Fig. 2

Representation of the transmittance, tCSIG, of a 24-order CSIG by its (a) absolute value (gray scale) and (b) sign (two levels).

Fig. 3
Fig. 3

Experimental intensity profiles recorded at different distances z from the approximated CSIG from z=0 to z=20 mm.

Equations (11)

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

Z=2a02/Δλ.
Tk=AΦringρ-α,
Er,z=E0R2Tkexp2iπλz1-λ2k24π21/2×expik · rdk.
Er,z=E0exp2iπλz1-λ2α24π21/2tr.
Er,z2=E02tr2.
TCSIGk=grid1/a0kringρ-α.
rad=α/2π=η/a0,
tCSIGr=grida0r*J0αr,
tCSIGr=tCSIGrsigntCSIGr,
signtr={+1if tr0-1if tr<0.
Z=2a02/η2Δλ,

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