Abstract

We report the experimental implementation of pseudo-nondiffracting beams by use of diffractive phase elements (DPE’s). Based on the conjugate-gradient method presented in J. Opt. Soc. Am. A 15, 144–151 (1998), these DPE’s are designed and fabricated on a flat quartz substrate. The experimental results show that the performance of the fabricated DPE’s is in good agreement with the theoretical prediction.

© 1998 Optical Society of America

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References

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  1. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffractive-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  2. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  3. J. Rosen, B. Salik, A. Yariv, “Pseudo-nondiffracting beams generated by radial harmonic functions,” J. Opt. Soc. Am. A 12, 2446–2457 (1995).
    [CrossRef]
  4. N. Davidson, A. A. Friesem, E. Hasman, “Holographic axilens: high resolution and long focal depth,” Opt. Lett. 16, 523–525 (1991).
    [CrossRef] [PubMed]
  5. J. Sochacki, S. Bará, J. Jaroszewicz, A. Kolodziejczyk, “Phase retardation of the uniform-intensity axilens,” Opt. Lett. 17, 7–9 (1992).
    [CrossRef] [PubMed]
  6. A. T. Friberg, “Stationary-phase analysis of generalized axicons,” J. Opt. Soc. Am. A 13, 743–750 (1996).
    [CrossRef]
  7. S. N. Khonina, V. V. Kotlyar, V. A. Soifer, “Calculation of the focusators into a longitudinal line-segment and study of a focal area,” J. Mod. Opt. 40, 761–769 (1993).
    [CrossRef]
  8. R. Piestun, J. Shamir, “Control of wave-front propagation with diffractive elements,” Opt. Lett. 19, 771–773 (1994).
    [CrossRef] [PubMed]
  9. B.-Z. Dong, G.-Z. Yang, B.-Y. Gu, O. K. Ersoy, “Iterative optimization approach for designing an axicon with long focal depth and high transverse resolution,” J. Opt. Soc. Am. A 13, 97–103 (1996).
    [CrossRef]
  10. J. Rosen, “Synthesis of nondiffracting beams in free space,” Opt. Lett. 19, 369–371 (1994).
    [PubMed]
  11. J. Rosen, A. Yariv, “Synthesis of an arbitrary axial field profile by computer-generated holograms,” Opt. Lett. 19, 843–845 (1994).
    [CrossRef] [PubMed]
  12. B. Salik, J. Rosen, A. Yariv, “One-dimensional beam shaping,” J. Opt. Soc. Am. A 12, 1702–1706 (1995).
    [CrossRef]
  13. R. Liu, B.-Z. Dong, G.-Z. Yang, B.-Y. Gu, “Generation of pseudo-nondiffracting beams with use of diffractive phase elements designed by the conjugate-gradient method,” J. Opt. Soc. Am. A 15, 144–151 (1998).
    [CrossRef]
  14. R. Liu, B.-Y. Gu, B.-Z. Dong, G.-Z. Yang, “Diffractive phase elements that synthesize color pseudonondiffracting beams,” Opt. Lett. 23, 633–635 (1998).
    [CrossRef]
  15. M. Avriel, Nonlinear Programming: Analysis and Methods (Englewood Cliffs, N.J., 1976), Chap. 10, pp. 288–321.
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chap 2, pp. 4–29.
  17. R. Piestun, B. Specktor, J. Shamir, “Wave fields in three dimensions: analysis and synthesis,” J. Opt. Soc. Am. A 13, 1837–1848 (1996).
    [CrossRef]

1998

1996

1995

1994

1993

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, “Calculation of the focusators into a longitudinal line-segment and study of a focal area,” J. Mod. Opt. 40, 761–769 (1993).
[CrossRef]

1992

1991

1987

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

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

Avriel, M.

M. Avriel, Nonlinear Programming: Analysis and Methods (Englewood Cliffs, N.J., 1976), Chap. 10, pp. 288–321.

Bará, S.

Davidson, N.

Dong, B.-Z.

Durnin, J.

J. Durnin, “Exact solutions 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, “Diffractive-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

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

Ersoy, O. K.

Friberg, A. T.

Friesem, A. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chap 2, pp. 4–29.

Gu, B.-Y.

Hasman, E.

Jaroszewicz, J.

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, “Calculation of the focusators into a longitudinal line-segment and study of a focal area,” J. Mod. Opt. 40, 761–769 (1993).
[CrossRef]

Kolodziejczyk, A.

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, “Calculation of the focusators into a longitudinal line-segment and study of a focal area,” J. Mod. Opt. 40, 761–769 (1993).
[CrossRef]

Liu, R.

Miceli, J. J.

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

Piestun, R.

Rosen, J.

Salik, B.

Shamir, J.

Sochacki, J.

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, “Calculation of the focusators into a longitudinal line-segment and study of a focal area,” J. Mod. Opt. 40, 761–769 (1993).
[CrossRef]

Specktor, B.

Yang, G.-Z.

Yariv, A.

J. Mod. Opt.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, “Calculation of the focusators into a longitudinal line-segment and study of a focal area,” J. Mod. Opt. 40, 761–769 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Phys. Rev. Lett.

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

Other

M. Avriel, Nonlinear Programming: Analysis and Methods (Englewood Cliffs, N.J., 1976), Chap. 10, pp. 288–321.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chap 2, pp. 4–29.

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Figures (8)

Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

Distribution of the surface-relief depth of the designed eight-level DPE.

Fig. 3
Fig. 3

Photographic masks for the eight-level DPE: (a) mask 1, (b) mask 2, (c) mask 3.

Fig. 4
Fig. 4

Section profile of the surface-relief trace of the eight-level DPE, obtained by scanning with a Sloan Dektak profilemeter.

Fig. 5
Fig. 5

Experimental setup of the optical system for measuring the performance of the designed DPE.

Fig. 6
Fig. 6

(a) Measured axial intensity distribution generated by the DPE fabricated to produce a double-segment PNDB. (b) Theoretical design result.

Fig. 7
Fig. 7

Output intensity distribution on the transverse plane at (a) z = 0.6 m, (b) z = 0.8 m, (c) z = 1.0 m, (d) z = 1.2 m, (e) z = 1.4 m.

Fig. 8
Fig. 8

(a) Measured axial intensity distribution generated by the DPE fabricated to produce a single-segment PNDB. (b) Theoretical design result.

Equations (3)

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E = α = 1 N z   W α m = 1 N 2 α ρ ˆ 2 m α - n = 1 N 1   G mn z α ρ 1 n   exp i ϕ 1 n 2 ,
G mn z α = 2 π i λ z α exp i 2 π z α λ exp i π r 2 m α 2 + r 1 n 2 λ z α × J 0 2 π r 2 m α r 1 n λ z α r 1 n .
W α = 0.98 N p in   the   signal   region 0.02 N z - N p in   other   region ,

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