Abstract

We report a highly efficient method for generation of any high-order nondiffracting Bessel beam employing a phase hologram whose transmittance coincides with the phase modulation of such a beam. It is remarkable that the Bessel beam generated by this hologram, at the plane of this device, has peak amplitude higher than the amplitude of the beam employed to illuminate it.

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References

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1987

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

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

1979

Chen, N.-X.

Cong, W.-X.

Cottrell, D. M.

Cox, A. J.

Davis, J. A.

Dibble, D. C.

Durnin, J.

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

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Friberg, A. T.

Gu, B.-Y.

Guérineau, N.

Guertin, J.

Harchaoui, B.

Heggarty, K.

Kettunen, V.

Lanzi, T.

Maier, M.

Miceli, J. J.

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Niggi, L.

Primot, J.

Stark, H.

Turunen, J.

Vasara, A.

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Figures (8)

Fig. 1
Fig. 1

Coefficients b m for several values of index m. The order q of the codified Bessel beams are equal to 0 (triangles), 2 (circles), and 4 (squares).

Fig. 2
Fig. 2

Efficiencies η q m of the PHs that encode the Bessel beams J q ( λ m ξ ) exp ( i q θ ) , for beams orders q = 0 (triangles), q = 2 (squares), and q = 4 (circles).

Fig. 3
Fig. 3

Phases of the holograms that encode the beams (a) B 1 ( ξ , θ ) = J 1 ( λ 10 ξ ) exp ( i θ ) and (b) B 2 ( ξ , θ ) = J 2 ( λ 10 ξ ) exp ( i 2 θ ) .

Fig. 4
Fig. 4

Fourier transform amplitudes of the PHs shown in (a) Fig. 3a and (b) Fig. 3b.

Fig. 5
Fig. 5

Amplitudes of the reconstructed fields obtained by filtering the most brilliant rings in the Fourier spectra of (a) Fig. 4a and (b) Fig. 4b.

Fig. 6
Fig. 6

Experimental setup employed for the generation of nondiffracting Bessel beams.

Fig. 7
Fig. 7

Experimental Fourier transform amplitudes of the PHs that encode the beams (a) B 1 ( ξ , θ ) = J 1 ( λ 10 ξ ) exp ( i θ ) and (b) B 2 ( ξ , θ ) = J 2 ( λ 10 ξ ) exp ( i 2 θ ) .

Fig. 8
Fig. 8

Amplitudes of the experimentally generated fields (a) B 1 ( ξ , θ ) = J 1 ( λ 10 ξ ) exp ( i θ ) , and (b) B 2 ( ξ , θ ) = J 2 ( λ 10 ξ ) exp ( i 2 θ ) .

Equations (6)

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B q ( ξ , θ ) = J q ( 2 π α R ξ ) exp ( i q θ )
h q ( ξ , θ ) = sgn [ J q ( 2 π α R ξ ) ] exp ( i q θ ) ,
b n = 2 J q + 1 2 ( λ n ) 0 1 x f ( x ) J q ( λ n x ) d x .
h q ( ξ , θ ) = n = 1 b n J q ( λ n ξ ) exp ( i q θ ) .
2 π α R = λ m
η q m = P h 1 0 2 π 0 1 ξ b m 2 J q 2 ( λ m ξ ) d ξ d θ = 2 b m 2 0 1 ξ J q 2 ( λ m ξ ) d ξ .

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