Abstract

We discuss a computer generated hologram whose transmittance is defined in terms of the Jacobi-Anger identity. If the hologram is implemented with a continuous phase spatial light modulator it generates integer-order non-diffracting Bessel beams, with a common asymptotic radial frequency, at separated propagation axes. On the other hand, when the hologram is implemented with a low-resolution pixelated phase modulator, it is possible to generate multiple Bessel beams with a common propagation axis. We employ this superposition of multiple Bessel beams to generate non-diffracting periodic and quasi-periodic wave fields.

© 2007 Optical Society of America

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    [CrossRef]
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2007 (2)

2005 (2)

S. H. Tao, X-C Yuan, B. S. Ahluwalia, "The generation of an array of nondiffracting beams by a single composite computer generated hologram," J. Opt. A: Pure Appl. Opt. 7,40-46 (2005).
[CrossRef]

Z. Chen, H. Martin, A. Bezryadina, D. Neshev, Y. S. Kivshar, D. N. Christodoulides, "Experiments on Gaussian beams and vortices in optically induced photonic lattices," J. Opt. Soc. Am. B 22, 1395-1405 (2005).
[CrossRef]

2004 (2)

2003 (1)

2002 (1)

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

2000 (1)

1999 (2)

R. M. Herman and T. A. Wiggins, "Productions and uses of diffraction less beams," J. Opt. Soc. Am. A 8, 932- 942 (1999).

S. Chavez-Cerda. "A new approach to Bessel beams," J. Mod. Opt.,  46, 923-930 (1999).

1998 (1)

V. V. Kotlyar, S. N. Khonina, V. A. Soifer, "Light fields decomposition in angular harmonics by means of diffractive optics," J. Mod. Opt. 45, 1495-1506 (1998).

1996 (1)

R. P. Macdonal, S. A. Boothroyd, T. Okamoto, J. Chrostowoski, B. A. Syrett, "Interboard optical data distribution by Bessel beam shadowing," Opt. Commun. 122, 169-177 (1996).

1992 (1)

J. Lu and J. F. Greenleaf, "Diffraction-limited beams and their applications for ultrasonic imaging and tissue characterization," Proc. SPIE 1733, 92-119 (1992).

1989 (1)

1987 (1)

J. Durnin, J. J. Miceli, Jr., J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef]

1986 (1)

1954 (1)

Ahluwalia, B. S.

S. H. Tao, X-C Yuan, B. S. Ahluwalia, "The generation of an array of nondiffracting beams by a single composite computer generated hologram," J. Opt. A: Pure Appl. Opt. 7,40-46 (2005).
[CrossRef]

Arrizón, V.

Barnett, S.

Bezryadina, A.

Boothroyd, S. A.

R. P. Macdonal, S. A. Boothroyd, T. Okamoto, J. Chrostowoski, B. A. Syrett, "Interboard optical data distribution by Bessel beam shadowing," Opt. Commun. 122, 169-177 (1996).

Bouchal, Z.

Z. Bouchal, J. Courtial, "The connection of singular and nondiffracting optics" J. Opt. A: Pure Appl. Opt. 6, S184-8, 2004.
[CrossRef]

Carrada, R.

Cavalcanti, S. B.

Chavez-Cerda, S.

S. Chavez-Cerda. "A new approach to Bessel beams," J. Mod. Opt.,  46, 923-930 (1999).

Chen, Z.

Christodoulides, D. N.

Chrostowoski, J.

R. P. Macdonal, S. A. Boothroyd, T. Okamoto, J. Chrostowoski, B. A. Syrett, "Interboard optical data distribution by Bessel beam shadowing," Opt. Commun. 122, 169-177 (1996).

Courtial, J.

Desyatnikov, A. S.

Dholakia, K.

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

Durnin, J.

J. Durnin, J. J. Miceli, Jr., J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef]

J. Durnin, " Exact solutions for nondiffracting beams. I. The scalar theory," J. Opt. Soc. Am. A 4, 651-654 (1986).

Eberly, J. H.

J. Durnin, J. J. Miceli, Jr., J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef]

Elsaesser, T.

Franke-Arnold, S.

Friberg, A. T.

Garcés-Chávez, V.

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

Gibson, G.

González, L. A.

Greenleaf, J. F.

J. Lu and J. F. Greenleaf, "Diffraction-limited beams and their applications for ultrasonic imaging and tissue characterization," Proc. SPIE 1733, 92-119 (1992).

Griebner, U.

Grunwald, R.

Hartmann, H-J

Herman, R. M.

Hickmann, J. M.

Jüptner, W.

Kebbel, V.

Khonina, S. N.

V. V. Kotlyar, S. N. Khonina, V. A. Soifer, "Light fields decomposition in angular harmonics by means of diffractive optics," J. Mod. Opt. 45, 1495-1506 (1998).

Kivshar, Y. S.

Kotlyar, V. V.

V. V. Kotlyar, S. N. Khonina, V. A. Soifer, "Light fields decomposition in angular harmonics by means of diffractive optics," J. Mod. Opt. 45, 1495-1506 (1998).

Lu, J.

J. Lu and J. F. Greenleaf, "Diffraction-limited beams and their applications for ultrasonic imaging and tissue characterization," Proc. SPIE 1733, 92-119 (1992).

Macdonal, R. P.

R. P. Macdonal, S. A. Boothroyd, T. Okamoto, J. Chrostowoski, B. A. Syrett, "Interboard optical data distribution by Bessel beam shadowing," Opt. Commun. 122, 169-177 (1996).

Martin, H.

McGloin, D.

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

McLeod, J. H.

Melville, H.

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

Miceli, J. J.

J. Durnin, J. J. Miceli, Jr., J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef]

Neshev, D.

Nibbering, E. T. J.

Okamoto, T.

R. P. Macdonal, S. A. Boothroyd, T. Okamoto, J. Chrostowoski, B. A. Syrett, "Interboard optical data distribution by Bessel beam shadowing," Opt. Commun. 122, 169-177 (1996).

Padgett, M.

Pas'ko, V.

Ruiz, U.

Shchesnovich, V. S.

Sibbett, W.

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

Soifer, V. A.

V. V. Kotlyar, S. N. Khonina, V. A. Soifer, "Light fields decomposition in angular harmonics by means of diffractive optics," J. Mod. Opt. 45, 1495-1506 (1998).

Syrett, B. A.

R. P. Macdonal, S. A. Boothroyd, T. Okamoto, J. Chrostowoski, B. A. Syrett, "Interboard optical data distribution by Bessel beam shadowing," Opt. Commun. 122, 169-177 (1996).

Tao, S. H.

S. H. Tao, X-C Yuan, B. S. Ahluwalia, "The generation of an array of nondiffracting beams by a single composite computer generated hologram," J. Opt. A: Pure Appl. Opt. 7,40-46 (2005).
[CrossRef]

Tschirschwitz, F.

Turunen, J.

Vasara, A.

Vasnetsov, M.

Wiggins, T. A.

Yuan, X-C

S. H. Tao, X-C Yuan, B. S. Ahluwalia, "The generation of an array of nondiffracting beams by a single composite computer generated hologram," J. Opt. A: Pure Appl. Opt. 7,40-46 (2005).
[CrossRef]

J. Mod. Opt. (2)

S. Chavez-Cerda. "A new approach to Bessel beams," J. Mod. Opt.,  46, 923-930 (1999).

V. V. Kotlyar, S. N. Khonina, V. A. Soifer, "Light fields decomposition in angular harmonics by means of diffractive optics," J. Mod. Opt. 45, 1495-1506 (1998).

J. Opt. A: Pure Appl. Opt. (2)

Z. Bouchal, J. Courtial, "The connection of singular and nondiffracting optics" J. Opt. A: Pure Appl. Opt. 6, S184-8, 2004.
[CrossRef]

S. H. Tao, X-C Yuan, B. S. Ahluwalia, "The generation of an array of nondiffracting beams by a single composite computer generated hologram," J. Opt. A: Pure Appl. Opt. 7,40-46 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (1)

Nature (1)

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

Opt. Commun. (1)

R. P. Macdonal, S. A. Boothroyd, T. Okamoto, J. Chrostowoski, B. A. Syrett, "Interboard optical data distribution by Bessel beam shadowing," Opt. Commun. 122, 169-177 (1996).

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, Jr., J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef]

Proc. SPIE (1)

J. Lu and J. F. Greenleaf, "Diffraction-limited beams and their applications for ultrasonic imaging and tissue characterization," Proc. SPIE 1733, 92-119 (1992).

Other (1)

G. N. Watson, A treatise on the theory of Bessel functions (Cambridge University Press, 1922), p. 22.

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