Abstract

The question that we are addressing concerns the possibility of creating a zeroth-order Bessel-like beam that spirals around the axis of propagation. The analytical features of the beam propagation are studied theoretically. Approximations to such a light field can be experimentally realized by using an axicon and a hologram. The beam potentially can attract interest in microfabrication applications.

© 2009 Optical Society of America

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References

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  1. Y. Y. Schechner, R. Piestun, and J. Shamir, Phys. Rev. E 54, R50 (1996).
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  4. J. Rosen, B. Salik, and A. Yariv, J. Opt. Soc. Am. A 12, 2446 (1995).
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    [Crossref]
  6. S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
    [Crossref]
  7. R. Piestun, B. Spector, and J. Shamir, J. Mod. Opt. 43, 1495 (1996).
    [Crossref]
  8. C. A. Alonzo, P. J. Rodrigo, and J. Glückstad, Opt. Express 13, 1749 (2005).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  12. J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
    [Crossref]

2009 (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[Crossref] [PubMed]

2005 (1)

2002 (1)

R. Piestun and J. Shamir, Proc. IEEE 90, 222 (2002).
[Crossref]

2000 (1)

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[Crossref]

1997 (1)

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, J. Mod. Opt. 44, 1409 (1997).
[Crossref]

1996 (5)

C. Paterson and R. Smith, Opt. Commun. 124, 131 (1996).
[Crossref]

R. Piestun, B. Spector, and J. Shamir, J. Opt. Soc. Am. A 13, 1837 (1996).
[Crossref]

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[Crossref]

R. Piestun, B. Spector, and J. Shamir, J. Mod. Opt. 43, 1495 (1996).
[Crossref]

Y. Y. Schechner, R. Piestun, and J. Shamir, Phys. Rev. E 54, R50 (1996).
[Crossref]

1995 (1)

1987 (1)

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

Alonzo, C. A.

Arlt, J.

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[Crossref]

Chávez-Cerda, S.

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[Crossref]

Christodoulides, D. N.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[Crossref] [PubMed]

Dholakia, K.

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[Crossref]

Durnin, J.

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]

Glückstad, J.

Khonina, S. N.

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, J. Mod. Opt. 44, 1409 (1997).
[Crossref]

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[Crossref] [PubMed]

Kotlyar, V. V.

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, J. Mod. Opt. 44, 1409 (1997).
[Crossref]

McDonald, G. S.

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[Crossref]

Miceli, J. J.

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

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[Crossref] [PubMed]

New, G. H. C.

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[Crossref]

Paterson, C.

C. Paterson and R. Smith, Opt. Commun. 124, 131 (1996).
[Crossref]

Piestun, R.

R. Piestun and J. Shamir, Proc. IEEE 90, 222 (2002).
[Crossref]

R. Piestun, B. Spector, and J. Shamir, J. Mod. Opt. 43, 1495 (1996).
[Crossref]

Y. Y. Schechner, R. Piestun, and J. Shamir, Phys. Rev. E 54, R50 (1996).
[Crossref]

R. Piestun, B. Spector, and J. Shamir, J. Opt. Soc. Am. A 13, 1837 (1996).
[Crossref]

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[Crossref] [PubMed]

Rodrigo, P. J.

Rosen, J.

Salik, B.

Schechner, Y. Y.

Y. Y. Schechner, R. Piestun, and J. Shamir, Phys. Rev. E 54, R50 (1996).
[Crossref]

Shamir, J.

R. Piestun and J. Shamir, Proc. IEEE 90, 222 (2002).
[Crossref]

R. Piestun, B. Spector, and J. Shamir, J. Mod. Opt. 43, 1495 (1996).
[Crossref]

Y. Y. Schechner, R. Piestun, and J. Shamir, Phys. Rev. E 54, R50 (1996).
[Crossref]

R. Piestun, B. Spector, and J. Shamir, J. Opt. Soc. Am. A 13, 1837 (1996).
[Crossref]

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[Crossref] [PubMed]

Smith, R.

C. Paterson and R. Smith, Opt. Commun. 124, 131 (1996).
[Crossref]

Soifer, V. A.

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, J. Mod. Opt. 44, 1409 (1997).
[Crossref]

Spector, B.

R. Piestun, B. Spector, and J. Shamir, J. Mod. Opt. 43, 1495 (1996).
[Crossref]

R. Piestun, B. Spector, and J. Shamir, J. Opt. Soc. Am. A 13, 1837 (1996).
[Crossref]

Yariv, A.

J. Mod. Opt. (2)

V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, J. Mod. Opt. 44, 1409 (1997).
[Crossref]

R. Piestun, B. Spector, and J. Shamir, J. Mod. Opt. 43, 1495 (1996).
[Crossref]

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

Opt. Commun. (3)

S. Chávez-Cerda, G. S. McDonald, and G. H. C. New, Opt. Commun. 123, 225 (1996).
[Crossref]

C. Paterson and R. Smith, Opt. Commun. 124, 131 (1996).
[Crossref]

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[Crossref]

Opt. Express (1)

Phys. Rev. E (1)

Y. Y. Schechner, R. Piestun, and J. Shamir, Phys. Rev. E 54, R50 (1996).
[Crossref]

Phys. Rev. Lett. (1)

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

Proc. IEEE (1)

R. Piestun and J. Shamir, Proc. IEEE 90, 222 (2002).
[Crossref]

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[Crossref] [PubMed]

Cited By

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Figures (3)

Fig. 1
Fig. 1

Particular oriented segments of an axicon (a) can be effectively replaced by the proper hologram and a conventional axicon (b).

Fig. 2
Fig. 2

DOE with the period P and the track of the zero-order Bessel beam peak behind the DOE.

Fig. 3
Fig. 3

(a) Dependence of the maximum allowable displacement Δ m of the zeroth-order Bessel beam with respect to propagation distance or number of beam revolutions. (b) Intensity distribution of the beam at different distances z beyond the DOE. Parameters are Δ = 10 μ m , P = 0.5 mm , α = 4 ° , n a = 1.5 , λ = 1.064 μ m .

Equations (16)

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F ( ρ ) = e i β ρ ,
F Δ , ψ ( ρ , φ ) = e i β ρ + i β Δ cos ( φ ψ ) .
F Δ , Γ ( ρ , φ ) = e i β ρ + i β Δ cos ( φ Γ ρ ) .
A ( x , y ) = d ξ d η A 0 ( ξ , η ) G ( x ξ , y η ) ,
A 0 ( ξ , η ) = A 0 ( ρ cos φ , ρ sin φ ) = a 0 e ρ 2 w 2 F Δ , Γ ( ρ , φ ) .
A ( r , ψ ) = a 0 k 2 π i z 0 e ρ 2 w 2 i β ρ + i k 2 z ( r 2 + ρ 2 ) Φ ( ρ ) ρ d ρ ,
Φ ( ρ ) 0 2 π d φ e i ( β Δ cos ( φ Γ ρ ) k r ρ z cos ( φ ψ ) )
s ( ρ ) = [ ( β Δ ) 2 + ( k r ρ z ) 2 2 β Δ k r ρ z cos ( ψ Γ ρ ) ] 1 2 .
A a 0 β ( 2 π z i k ) 1 2 J 0 ( s c ) e i ( k r 2 2 z β 2 z 2 k ) ( z β w k ) 2 ,
I z J 0 2 ( s c ) exp [ 2 ( z γ w ) 2 ] .
δ ψ δ z = Γ γ = 2 π γ P .
l = 2 π γ Γ = P γ .
δ s = ( s ξ ) ξ = 0 ξ max 1 .
r 2 z λ 4 1 1 + ( z Γ γ ) 2 .
Δ m = μ [ z λ 1 + ( z γ Γ ) 2 ] 1 2 ,
L A = z 2 z 1 = l π [ ( μ 2 4 π λ l Δ 2 ) 2 1 ] 1 2 ,

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