Abstract

The concept and the generation of polarized pseudonondiffracting beams (PNDB’s) from polarization-selective diffractive phase elements (DPE’s) are presented for what we believe is the first time in a monochromatic illuminating system. The polarized PNDB’s behave as segmented almost constant axial-intensity distributions with individual different polarization states in different segments. The pure polarization state in each segment can be arbitrarily preset. The design of polarization-selective DPE’s is achieved with the use of the conjugate-gradient method. The simulation results show that the DPE’s we designed can successfully implement the desired polarization modulation. Furthermore the PNDB’s characteristics of axial-intensity uniformity and beamlike shape are well achieved with the DPE’s we designed.

© 1999 Optical Society of America

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References

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    [CrossRef]
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1998 (2)

1995 (3)

1994 (2)

1987 (2)

J. Durnin, “Exact solution for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Avriel, M.

M. Avriel, Nonlinear Programming: Analysis and Methods, 1st ed. (Prentice-Hall, Englewood Cliffs, N.J., 1976), Chap. 10, p. 299.

Dong, B. Z.

Durnin, J.

J. Durnin, “Exact solution for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, San Francisco, 1968), Chap. 4, p. 60.

Gu, B. Y.

Liu, H. K.

Liu, R.

Miceli, J. J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Piestun, R.

Rosen, J.

Salik, B.

Shamir, J.

Yang, G. Z.

Yariv, A.

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

Opt. Lett. (4)

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Other (2)

J. W. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, San Francisco, 1968), Chap. 4, p. 60.

M. Avriel, Nonlinear Programming: Analysis and Methods, 1st ed. (Prentice-Hall, Englewood Cliffs, N.J., 1976), Chap. 10, p. 299.

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of a diffractive optical system for the polarized PNDB’s.

Fig. 2
Fig. 2

Axial-intensity distribution of the dual-segment PNDB’s with e light polarization (dotted curve) and o light polarization (solid curve), appearing in the designated first and second segments, respectively.

Fig. 3
Fig. 3

Three-dimensional plot of the dual-segment PNDB’s with two polarization states, corresponding to Fig. 2.

Fig. 4
Fig. 4

Axial-intensity distribution of the triple-segment polarized PNDB’s with the e light polarization (dotted curves) located at the first two segments and the o light polarization (solid curve) appearing in the designated third segment.

Fig. 5
Fig. 5

Axial-intensity distribution for the polarized PNDB’s with four segments. The polarization states of the four segments are alternately changed by the o light polarization (solid curves) and e light polarization (dotted curves).

Equations (5)

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U2α, zβ=2πiλzβexpi2πzβ/λ×0R1m ρ1r1,αexpi 2πλnα-1hr1×expiπr12/λzβr1dr1.
E=α=12β=1Nz Wα, zβρ˜2α, zβ-|U2α, zβ|2,
Eyξyξ=-2 Im α=12β=1NzeoWα, zβ×2πλnα-1hm cosyξρ1ξ,α×expi 2πλnα-1hm sinyξ×1-ρ˜2α, zβ|U2α, zβ|×Gzβ, ξU2*α, zβ,
Gzβ, ξ=2πiλzβ expi2πzβ/λexpiπξ2/λzβξ.
PCTeo=β=1Neoz|U2oe, zβ|2β=1Neoz|U2eo, zβ|2,

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