Abstract

We report the first experimental generation of the superposition of higher-order Bessel beams, by means of a spatial light modulator (SLM) and a ring slit aperture. We present illuminating a ring slit aperture with light which has an azimuthal phase dependence, such that the field produced is a superposition of two or more higher-order Bessel beams. The experimentally produced fields are in good agreement with those calculated theoretically. The significance of these fields is that even though one is able to generate fields which carry zero orbital angular momentum, a rotation in the field’s intensity profile as it propagates is observed.

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  12. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44(8), 592–597 (1954).
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  14. D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28(8), 657–659 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
  16. V. V. Kotlyar, S. N. Khonina, R. V. Skidanov, and V. A. Soifer, “Rotation of laser beams with zero of the orbital angular momentum,” Opt. Commun. 274(1), 8–14 (2007).
    [CrossRef]
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2008

2007

V. V. Kotlyar, S. N. Khonina, R. V. Skidanov, and V. A. Soifer, “Rotation of laser beams with zero of the orbital angular momentum,” Opt. Commun. 274(1), 8–14 (2007).
[CrossRef]

2003

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Three-dimensional arrays of optical bottles,” Opt. Commun. 225(4-6), 215–222 (2003).
[CrossRef]

D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28(8), 657–659 (2003).
[CrossRef] [PubMed]

2001

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

2000

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[CrossRef]

1996

1994

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).
[CrossRef] [PubMed]

1991

1989

1988

1987

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

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

1954

Arlt, J.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[CrossRef]

Burger, L.

Carcole, E.

Choi, K.

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).
[CrossRef] [PubMed]

Cottrell, D. M.

Davis, J. A.

Dholakia, K.

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Three-dimensional arrays of optical bottles,” Opt. Commun. 225(4-6), 215–222 (2003).
[CrossRef]

D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28(8), 657–659 (2003).
[CrossRef] [PubMed]

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

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

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Fenichel, H.

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).
[CrossRef] [PubMed]

Forbes, A.

Friberg, A. T.

Garcés-Chávez, V.

Herman, R. M.

Hogervorst, W.

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

Indebetouw, G.

Kazak, N. S.

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

Khilo, N. A.

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

Khonina, S. N.

V. V. Kotlyar, S. N. Khonina, R. V. Skidanov, and V. A. Soifer, “Rotation of laser beams with zero of the orbital angular momentum,” Opt. Commun. 274(1), 8–14 (2007).
[CrossRef]

King, T. A.

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

Kotlyar, V. V.

V. V. Kotlyar, S. N. Khonina, R. V. Skidanov, and V. A. Soifer, “Rotation of laser beams with zero of the orbital angular momentum,” Opt. Commun. 274(1), 8–14 (2007).
[CrossRef]

Lee, H. S.

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).
[CrossRef] [PubMed]

McGloin, D.

D. McGloin, V. Garcés-Chávez, and K. Dholakia, “Interfering Bessel beams for optical micromanipulation,” Opt. Lett. 28(8), 657–659 (2003).
[CrossRef] [PubMed]

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Three-dimensional arrays of optical bottles,” Opt. Commun. 225(4-6), 215–222 (2003).
[CrossRef]

McLeod, J. H.

Melville, H.

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Three-dimensional arrays of optical bottles,” Opt. Commun. 225(4-6), 215–222 (2003).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Paterson, C.

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124(1-2), 121–130 (1996).
[CrossRef]

Ryzhevich, A. A.

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

Sibbett, W.

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Three-dimensional arrays of optical bottles,” Opt. Commun. 225(4-6), 215–222 (2003).
[CrossRef]

Skidanov, R. V.

V. V. Kotlyar, S. N. Khonina, R. V. Skidanov, and V. A. Soifer, “Rotation of laser beams with zero of the orbital angular momentum,” Opt. Commun. 274(1), 8–14 (2007).
[CrossRef]

Smith, R.

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124(1-2), 121–130 (1996).
[CrossRef]

Soifer, V. A.

V. V. Kotlyar, S. N. Khonina, R. V. Skidanov, and V. A. Soifer, “Rotation of laser beams with zero of the orbital angular momentum,” Opt. Commun. 274(1), 8–14 (2007).
[CrossRef]

Spalding, G. C.

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Three-dimensional arrays of optical bottles,” Opt. Commun. 225(4-6), 215–222 (2003).
[CrossRef]

Stewart, B. W.

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).
[CrossRef] [PubMed]

Turunen, J.

Vasara, A.

Wiggins, T. A.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177(1-6), 297–301 (2000).
[CrossRef]

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124(1-2), 121–130 (1996).
[CrossRef]

D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Three-dimensional arrays of optical bottles,” Opt. Commun. 225(4-6), 215–222 (2003).
[CrossRef]

T. A. King, W. Hogervorst, N. S. Kazak, N. A. Khilo, and A. A. Ryzhevich, “Formation of higher-order Bessel light beams in biaxial crystals,” Opt. Commun. 187(4-6), 407–414 (2001).
[CrossRef]

V. V. Kotlyar, S. N. Khonina, R. V. Skidanov, and V. A. Soifer, “Rotation of laser beams with zero of the orbital angular momentum,” Opt. Commun. 274(1), 8–14 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

H. S. Lee, B. W. Stewart, K. Choi, and H. Fenichel, “Holographic nondiverging hollow beam,” Phys. Rev. A 49(6), 4922–4927 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Supplementary Material (4)

» Media 1: AVI (355 KB)     
» Media 2: AVI (416 KB)     
» Media 3: AVI (857 KB)     
» Media 4: AVI (1135 KB)     

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Figures (7)

Fig. 1
Fig. 1

Extension of Durnin’s ring slit experiment [2]. (b) and (c): Illuminating the ring slit aperture with a beam whose angular spectrum carries an azimuthally varying phase generates higher-order and superpositions of higher-order Bessel beams.

Fig. 2
Fig. 2

The experimental design for generating a superposition of two higher-order Bessel beams. The interferometer used to interfere the field produced at the Fourier plane with a plane wave is denoted in the shaded overlay. (M: mirror; BS: beam-splitter; L: lens and D: diaphragm). Note the distances and angles are not to scale.

Fig. 3
Fig. 3

The columns from left to right represent the phase patterns applied to the liquid crystal display of the SLM, the observed intensity distribution of the superposition, the theoretical prediction, and interference pattern of the superposition field and a plane wave, respectively. Data is shown for (a) – (d): A0, (e) – (h): A3, (i) – (l): A4,-4, (m) – (p): A2,-4, and (q) – (t): A4,-2. The illuminated ring slit is shown as a shaded overlay on the phase pattern.

Fig. 4
Fig. 4

(a) Phase pattern applied to the liquid crystal display. The shaded overlay denotes the section of the phase pattern which is illuminated by the ring field. (b) The experimental beam cross-section of the field produced at the Fourier plane. (c) It is in good agreement with the calculated field.

Fig. 5
Fig. 5

Images of the intensity profile of the experimentally produced field A 3,-3 captured at intervals along its propagation. The grey area denotes the region in which the Bessel field exists.

Fig. 6
Fig. 6

Video clips containing experimental images for fields (left): A 3,-3 (media 1) and (right): A 4,-4 (media 2) which were captured at intervals along the beam’s propagation.

Fig. 7
Fig. 7

Video clips containing theoretically calculated images for the rotation of fields (left): A 3,-3 (media 3) and (right): A 4,-4 (media 4).

Equations (11)

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E ( r , ϕ , z ) = a 0 J m ( k r r ) exp [ i ( k z z + m ϕ ) ] ,
A m , n ( r , ϕ , z ) = i λ z 0 2 π R Δ R + Δ τ ( r , ϕ ) exp [ i k 0 2 f ( 1 z f ) r 1 2 ] exp [ i k 0 r r 1 f cos ( ϕ 1 ϕ ) ] r 1 d r 1 d ϕ 1
τ ( r , ϕ ) = { exp ( i m ϕ ) , exp ( i n ϕ ) , R r ( R Δ ) R r ( R + Δ ) .
A m ( r , ϕ , z ) = i k 0 f R Δ R i m exp ( i m ϕ ) J m ( k 0 r r 1 f ) exp [ r 1 2 w 2 + i k 0 r 1 2 2 f ( 1 z f ) ] r 1 d r 1 ,
A n ( r , ϕ , z ) = i k 0 f R R + Δ i n exp ( i n ϕ ) J n ( k 0 r r 1 f ) exp [ r 1 2 w 2 + i k 0 r 1 2 2 f ( 1 z f ) ] r 1 d r 1 ,
A m , n ( r , ϕ , z ) = A m ( r , ϕ , z ) + A n ( r , ϕ , z ) .
A m , m ( r , ϕ , z ) = J m ( k r r ) sin ( m ϕ ) exp ( i k z z ) .
A m , m ( r , ϕ , z ) = J m ( k 1 r r ) exp ( i ( k 1 z z + m ϕ ) ) + J m ( k 2 r r ) exp ( i ( k 2 z z m ϕ ) )
A m , m ( r , ϕ , z ) ~ J m ( k r r ) exp ( i k 1 z z + m ϕ ) ( 1 + exp [ i ( Δ k z 2 m ϕ ) ] ) ,
I m , m ( r , ϕ , z ) J m 2 ( k r r ) ( 1 + cos ( Δ k z 2 m ϕ ) ) .
d ϕ d z = Δ k 2 m .

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