Abstract

We compare two phase optical elements that are employed to generate approximate Bessel–Gauss beams of arbitrary order. These elements are the helical axicon (HA) and the kinoform of the desired Bessel–Gauss beam. The HA generates a Bessel beam (BB) by free propagation, and the kinoform is employed in a Fourier spatial filtering optical setup. As the main result, it is obtained that the error in the BBs generated with the kinoform is smaller than the error in the beams obtained with the HA. On the other hand, it is obtained that the efficiencies of the methods are approximately 1.0 (HA) and 0.7 (kinoform).

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2013 (1)

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photon. News 24(6), 22–29 (2013).
[CrossRef]

2012 (2)

2011 (2)

2009 (2)

2008 (1)

2007 (1)

2005 (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

2003 (2)

2002 (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

2001 (1)

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A 63, 063602 (2001).
[CrossRef]

2000 (1)

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

1996 (1)

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

1989 (1)

1987 (1)

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

Abram, G.

Agnew, M.

Alieva, T.

Ando, T.

Arlt, J.

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A 63, 063602 (2001).
[CrossRef]

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

Arrizón, V.

Bouchal, Z.

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).
[CrossRef]

Boyd, R. W.

Calvo, M. L.

Cámara, A.

Carrada, R.

Chattrapiban, N.

Cheben, P.

Cizmár, T.

Cofield, D.

Dholakia, K.

T. Cizmár, V. Kllárová, X. Tsampoula, F. Gunn-Moore, W. Sibbett, Z. Bouchal, and K. Dholakia, “Generation of multiple Bessel beams for a biophotonics workstation,” Opt. Express 16, 14024–14035 (2008).
[CrossRef]

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

J. E. Molloy, K. Dholakia, and M. Padgett, “Optical tweezers in a new light,” J. Mod. Opt. 50, 1501–1507 (2003).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A 63, 063602 (2001).
[CrossRef]

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

Dudley, A.

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photon. News 24(6), 22–29 (2013).
[CrossRef]

Durnin, J.

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

Eberly, J. H.

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

Forbes, A.

Friberg, A. T.

Fukuchi, N.

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

González, L. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1966).

Gunn-Moore, F.

Hill, W. T.

Inoue, T.

Kärtner, F. X.

Kllárová, V.

Lavery, M.

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photon. News 24(6), 22–29 (2013).
[CrossRef]

Leach, J.

Martínez-Matos, Ó.

Matsumoto, N.

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

McLaren, M.

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

Méndez, G.

Miceli, J. J.

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

Molloy, J. E.

J. E. Molloy, K. Dholakia, and M. Padgett, “Optical tweezers in a new light,” J. Mod. Opt. 50, 1501–1507 (2003).
[CrossRef]

Ohtake, Y.

Padgett, M.

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photon. News 24(6), 22–29 (2013).
[CrossRef]

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).
[CrossRef]

J. E. Molloy, K. Dholakia, and M. Padgett, “Optical tweezers in a new light,” J. Mod. Opt. 50, 1501–1507 (2003).
[CrossRef]

Padgett, M. J.

Paterson, C.

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

Putnam, W. P.

Rodrigo, J. A.

Rogers, E. A.

Roux, F. S.

Roy, R.

Ruiz, U.

Sánchez-de-la-Llave, D.

Schimpf, D. N.

Sibbett, W.

T. Cizmár, V. Kllárová, X. Tsampoula, F. Gunn-Moore, W. Sibbett, Z. Bouchal, and K. Dholakia, “Generation of multiple Bessel beams for a biophotonics workstation,” Opt. Express 16, 14024–14035 (2008).
[CrossRef]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

Smith, R.

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

Soneson, J.

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A 63, 063602 (2001).
[CrossRef]

Tsampoula, X.

Turunen, J.

Vassara, A.

Wright, E. M.

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A 63, 063602 (2001).
[CrossRef]

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

J. Mod. Opt. (1)

J. E. Molloy, K. Dholakia, and M. Padgett, “Optical tweezers in a new light,” J. Mod. Opt. 50, 1501–1507 (2003).
[CrossRef]

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

Nat. Photonics (1)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).
[CrossRef]

Nature (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef]

Opt. Commun. (2)

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

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

Opt. Express (4)

Opt. Lett. (3)

Opt. Photon. News (1)

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photon. News 24(6), 22–29 (2013).
[CrossRef]

Phys. Rev. A (1)

J. Arlt, K. Dholakia, J. Soneson, and E. M. Wright, “Optical dipole traps and atomic waveguides based on Bessel light beams,” Phys. Rev. A 63, 063602 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

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

Other (2)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1966).

M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of Bessel-Gaussian modes,” http://arxiv.org/abs/1306.2767 .

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Figures (10)

Fig. 1.
Fig. 1.

(a) Phase modulation of the first order BBK, (b) Fourier spectrum modulus of the BBK when it is illuminated by the Gaussian beam exp(r2/R2), (c) BBK Fourier spectrum after the application of the annular SF, and (d) intensity of the numerically generated BGB.

Fig. 2.
Fig. 2.

Interference region (dark gray), where a BGB is approximately generated by a HA and plane z=zc of maximum interference area.

Fig. 3.
Fig. 3.

Efficiencies of BBKs with m=10 and m=20 in generation of BGBs of orders q=0 to 10.

Fig. 4.
Fig. 4.

RMSDs of transverse profiles of BGB of orders q=0 to 10 generated by HAs and BBKs, employing pupils with (a) m=10 and (b) m=20.

Fig. 5.
Fig. 5.

(a) Transverse phase profiles and (b) phases of a theoretical BGB and of the approximate BGBs generated by a HA and a BBK with m=10.

Fig. 6.
Fig. 6.

(a) Transverse intensity profiles and (b) phases of a theoretical BGB and of the approximate BGBs generated by a HA and a BBK with m=20.

Fig. 7.
Fig. 7.

RMSDs of transverse intensity profiles of BGB of orders q=0 to 10 generated by HAs and BBKs, employing a pupil with m=10.

Fig. 8.
Fig. 8.

Optical setup for the experimental generation of a BGB employing a BBK.

Fig. 9.
Fig. 9.

Intensities of the first order BGBs experimentally generated by (a) a BBK and (b) a HA. The limiting pupils covers 10 roots of the radial modulation J1(2πr/r0).

Fig. 10.
Fig. 10.

Transverse intensity profiles of the experimental BGBs displayed in Fig. 9 and of the corresponding theoretic BGB.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

b(r,θ)=Jq(2πr/r0)exp(r2/w2)exp[iqθ],
t(r,θ)=f1(r)exp(iqθ).
t(r,θ)=n=1bnJq(λnr/R)exp(iqθ),
bn=2Jq+12(λn)01xf1(Rx)Jq(λnx)dx.
f1(r)=sgn[Jq(2πr/r0)]circ(r/R),
f1(r)=exp(i2πr/r0)circ(r/R).
g(r,θ)=exp(iqθ)g1(r),
D=[A10R/2|b1(r)αexp(iβ)g1(r)|2dr]1/2,
D=[A10R/2|Ib(r)αIg(r)|2dr]1/2,

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