Abstract

We study theoretically and experimentally the spatial intensity distribution of the zero-order Bessel beam formed by the axicon which possess a rounded tip. Such a tip generates a refracted beam that interferes with the quasi-Bessel beam created behind the axicon. In turn an undesired intensity modulation occurs that significantly disturbs the unique properties of the quasi-Bessel beam – namely the constant shape of the lateral intensity distribution and the slow variation of the on-axis beam intensity along the beam propagation. We show how the spatial filtration of the beam in the Fourier plane improves this spatial beam distribution and removes the undesired modulation. We use an efficient numerical method based on Hankel transformations to simulate the propagation of the beam behind the axicon and filter. We experimentally measure the intensity distribution of the beam in many lateral planes and subsequently reconstruct the spatial intensity distribution of the beam. Computed and measured beam distributions are compared and the obtained agreement is very good.

© 2008 Optical Society of America

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2008 (1)

Y. Zhang, "Analytical expression for the diffraction field of an axicon using the ray-tracing and interference method," Appl. Phys. B 90, 93-96 (2008).
[CrossRef]

2007 (1)

2006 (7)

C. J. Zapata-Rodriguez and A. Sanchez-Losa, "Three-dimensional field distribution in the focal region of low-Fresnel-number axicons," J. Opt. Soc. Am. A 23, 3016-3026 (2006).
[CrossRef]

T. Cizmár, M. Siler, and P. Zemánek, "An optical nanotrap array movable over a millimeter range," Appl. Phys. B 84, 197-203 (2006).
[CrossRef]

P. Fischer, A. E. Carruthers, K. Volke-Sepulveda, E. M. Wright, C. Brown, W. Sibbett, and K. Dholakia, "Enhanced optical guiding of colloidal particles using a supercontinuum light source," Opt. Express 14, 5793-5802 (2006).
[CrossRef]

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 1-15 (2006).
[CrossRef]

T. Cizmár, V. Kollárová, Z. Bouchal, and P. Zemánek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New. J. Phys. 8, 43 (2006).
[CrossRef]

C. W. Zheng, Y. J. Zhang, and D. M. Zhao, "Calculation of the vectorial field distribution of an axicon illuminated by a linearly polarized Gaussian beam," Optik 117, 118-122 (2006).
[CrossRef]

J. Jezek, T. Cizmár, V. Nedela, and P. Zemánek, "Formation of long and thin polymer fiber using nondiffracting beam," Opt. Express 14, 8506-8515 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (4)

A. E. Martirosyan, C. Altucci, C. de Lisio, A. Porzio, S. Solimeno, and V. Tosa, "Fringe pattern of the field diffracted by axicons," J. Opt. Soc. Am. A 21, 770-776 (2004).
[CrossRef]

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 8, 4001-4003 (2004).
[CrossRef]

S. H. Tao, W. M. Lee, and X. Yuan, "Experimental study of Holographic Generation of Fractional Bessel Beams," Appl. Opt. 43, 123-126 (2004).
[CrossRef]

M. Lei and B. L. Yao, "Characteristics of beam profile of Gaussian beam passing through an axicon," Opt. Commun. 239, 367-372 (2004).
[CrossRef]

2003 (2)

2002 (3)

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

Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, and Z. Chen, "High-resolution optical coherence tomography over a large depth range with an axicon lens," Opt. Lett. 27(4), 243-245 (2002).
[CrossRef]

B. Depret, P. Verkerk, and D. Hennequin, "Characterization and modelling of the hollow beam produced by a real conical lens," Opt. Commun. 211, 31-38 (2002).
[CrossRef]

2001 (1)

2000 (4)

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-556 (2000).
[CrossRef]

A. G. Sedukhin, "Marginal phase correction of truncated Bessel beams," J. Opt. Soc. Am. A 17, 1059-1066 (2000).
[CrossRef]

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

V. Jarutis, R. Paskauskas, and A. Stabinis, "Focusing of Laguerre-Gaussian beams by axicon," Opt. Commun. 1841-4, 105-112 (2000).
[CrossRef]

1999 (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "Efficiency of second-harmonic generation with Bessel beams," Phys. Rev. A 60, 2438-2441 (1999).
[CrossRef]

1997 (1)

K. Shinozaki, C. Q. Xu, H. Sasaki, and T. Kamijoh, "A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals," Opt. Commun. 133, 300-304 (1997).
[CrossRef]

1992 (1)

M. R. Lapointe, "Review of non-diffracting Bessel beam experiments," Opt. Laser Technol. 24, 315-321 (1992).
[CrossRef]

1991 (1)

1989 (2)

1987 (2)

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

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

1969 (1)

1954 (1)

??izmár, T.

J. Jezek, T. Cizmár, V. Nedela, and P. Zemánek, "Formation of long and thin polymer fiber using nondiffracting beam," Opt. Express 14, 8506-8515 (2006).
[CrossRef] [PubMed]

V. Karásek, T. Cizmár, O. Brzobohaty, P. Zemánek, V. Garces-Chávez, and K. Dholakia, "Long-range one dimensional longitudinal optical binding," submitted to Phys. Rev. Lett.

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "Efficiency of second-harmonic generation with Bessel beams," Phys. Rev. A 60, 2438-2441 (1999).
[CrossRef]

Altucci, C.

Amako, J.

Arlt, J.

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-556 (2000).
[CrossRef]

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

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "Efficiency of second-harmonic generation with Bessel beams," Phys. Rev. A 60, 2438-2441 (1999).
[CrossRef]

Bouchal, Z.

T. Cizmár, V. Kollárová, Z. Bouchal, and P. Zemánek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New. J. Phys. 8, 43 (2006).
[CrossRef]

Brown, C.

P. Fischer, A. E. Carruthers, K. Volke-Sepulveda, E. M. Wright, C. Brown, W. Sibbett, and K. Dholakia, "Enhanced optical guiding of colloidal particles using a supercontinuum light source," Opt. Express 14, 5793-5802 (2006).
[CrossRef]

Brzobohaty, O.

V. Karásek, T. Cizmár, O. Brzobohaty, P. Zemánek, V. Garces-Chávez, and K. Dholakia, "Long-range one dimensional longitudinal optical binding," submitted to Phys. Rev. Lett.

Campbell, J. P.

Carruthers, A. E.

P. Fischer, A. E. Carruthers, K. Volke-Sepulveda, E. M. Wright, C. Brown, W. Sibbett, and K. Dholakia, "Enhanced optical guiding of colloidal particles using a supercontinuum light source," Opt. Express 14, 5793-5802 (2006).
[CrossRef]

Chen, Z.

Cizmár, T.

T. Cizmár, M. Siler, and P. Zemánek, "An optical nanotrap array movable over a millimeter range," Appl. Phys. B 84, 197-203 (2006).
[CrossRef]

T. Cizmár, V. Kollárová, Z. Bouchal, and P. Zemánek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New. J. Phys. 8, 43 (2006).
[CrossRef]

de Lisio, C.

Denschlag, J. H.

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 1-15 (2006).
[CrossRef]

Depret, B.

B. Depret, P. Verkerk, and D. Hennequin, "Characterization and modelling of the hollow beam produced by a real conical lens," Opt. Commun. 211, 31-38 (2002).
[CrossRef]

Dholakia, K.

P. Fischer, A. E. Carruthers, K. Volke-Sepulveda, E. M. Wright, C. Brown, W. Sibbett, and K. Dholakia, "Enhanced optical guiding of colloidal particles using a supercontinuum light source," Opt. Express 14, 5793-5802 (2006).
[CrossRef]

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

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 8, 4001-4003 (2004).
[CrossRef]

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

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

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-556 (2000).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "Efficiency of second-harmonic generation with Bessel beams," Phys. Rev. A 60, 2438-2441 (1999).
[CrossRef]

V. Karásek, T. Cizmár, O. Brzobohaty, P. Zemánek, V. Garces-Chávez, and K. Dholakia, "Long-range one dimensional longitudinal optical binding," submitted to Phys. Rev. Lett.

Ding, Z.

Dsehiazer, L. G.

Durnin, J.

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

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

Eberly, J.

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

Fischer, P.

P. Fischer, A. E. Carruthers, K. Volke-Sepulveda, E. M. Wright, C. Brown, W. Sibbett, and K. Dholakia, "Enhanced optical guiding of colloidal particles using a supercontinuum light source," Opt. Express 14, 5793-5802 (2006).
[CrossRef]

Fujii, E.

Garces-Chavez, V.

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 8, 4001-4003 (2004).
[CrossRef]

Garces-Chávez, V.

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

V. Karásek, T. Cizmár, O. Brzobohaty, P. Zemánek, V. Garces-Chávez, and K. Dholakia, "Long-range one dimensional longitudinal optical binding," submitted to Phys. Rev. Lett.

Hennequin, D.

B. Depret, P. Verkerk, and D. Hennequin, "Characterization and modelling of the hollow beam produced by a real conical lens," Opt. Commun. 211, 31-38 (2002).
[CrossRef]

Herman, R. M.

Hitomi, T.

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-556 (2000).
[CrossRef]

Indebetouw, G.

Jarutis, V.

V. Jarutis, R. Paskauskas, and A. Stabinis, "Focusing of Laguerre-Gaussian beams by axicon," Opt. Commun. 1841-4, 105-112 (2000).
[CrossRef]

Jezek, J.

Kamijoh, T.

K. Shinozaki, C. Q. Xu, H. Sasaki, and T. Kamijoh, "A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals," Opt. Commun. 133, 300-304 (1997).
[CrossRef]

Karásek, V.

V. Karásek, T. Cizmár, O. Brzobohaty, P. Zemánek, V. Garces-Chávez, and K. Dholakia, "Long-range one dimensional longitudinal optical binding," submitted to Phys. Rev. Lett.

Kollárová, V.

T. Cizmár, V. Kollárová, Z. Bouchal, and P. Zemánek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New. J. Phys. 8, 43 (2006).
[CrossRef]

Lang, F.

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 1-15 (2006).
[CrossRef]

Lapointe, M. R.

M. R. Lapointe, "Review of non-diffracting Bessel beam experiments," Opt. Laser Technol. 24, 315-321 (1992).
[CrossRef]

Lee, W. M.

Lei, M.

M. Lei and B. L. Yao, "Characteristics of beam profile of Gaussian beam passing through an axicon," Opt. Commun. 239, 367-372 (2004).
[CrossRef]

Martirosyan, A. E.

McGloin, D.

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

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 8, 4001-4003 (2004).
[CrossRef]

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

McLeod, J. H.

Melville, H.

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 8, 4001-4003 (2004).
[CrossRef]

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

Miceli, J. J.

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

Ned??la, V.

Nelson, J. S.

Nourrit, V.

Padgett, M. J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "Efficiency of second-harmonic generation with Bessel beams," Phys. Rev. A 60, 2438-2441 (1999).
[CrossRef]

Paskauskas, R.

V. Jarutis, R. Paskauskas, and A. Stabinis, "Focusing of Laguerre-Gaussian beams by axicon," Opt. Commun. 1841-4, 105-112 (2000).
[CrossRef]

Porzio, A.

Ren, H.

Roskey, D.

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 8, 4001-4003 (2004).
[CrossRef]

Sanchez-Losa, A.

Sasaki, H.

K. Shinozaki, C. Q. Xu, H. Sasaki, and T. Kamijoh, "A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals," Opt. Commun. 133, 300-304 (1997).
[CrossRef]

Sawaki, D.

Schmid, S.

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 1-15 (2006).
[CrossRef]

Sedukhin, A. G.

Shinozaki, K.

K. Shinozaki, C. Q. Xu, H. Sasaki, and T. Kamijoh, "A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals," Opt. Commun. 133, 300-304 (1997).
[CrossRef]

Sibbett, W.

P. Fischer, A. E. Carruthers, K. Volke-Sepulveda, E. M. Wright, C. Brown, W. Sibbett, and K. Dholakia, "Enhanced optical guiding of colloidal particles using a supercontinuum light source," Opt. Express 14, 5793-5802 (2006).
[CrossRef]

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

Siler, M.

T. Cizmár, M. Siler, and P. Zemánek, "An optical nanotrap array movable over a millimeter range," Appl. Phys. B 84, 197-203 (2006).
[CrossRef]

Solimeno, S.

Stabinis, A.

V. Jarutis, R. Paskauskas, and A. Stabinis, "Focusing of Laguerre-Gaussian beams by axicon," Opt. Commun. 1841-4, 105-112 (2000).
[CrossRef]

Summers, M. D.

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 8, 4001-4003 (2004).
[CrossRef]

Tao, S. H.

Thalhammer, G.

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 1-15 (2006).
[CrossRef]

Tosa, V.

Verkerk, P.

B. Depret, P. Verkerk, and D. Hennequin, "Characterization and modelling of the hollow beam produced by a real conical lens," Opt. Commun. 211, 31-38 (2002).
[CrossRef]

Volke-Sepulveda, K.

P. Fischer, A. E. Carruthers, K. Volke-Sepulveda, E. M. Wright, C. Brown, W. Sibbett, and K. Dholakia, "Enhanced optical guiding of colloidal particles using a supercontinuum light source," Opt. Express 14, 5793-5802 (2006).
[CrossRef]

Wang, L.

Wiggins, T. A.

Winkler, K.

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 1-15 (2006).
[CrossRef]

Wright, E. M.

P. Fischer, A. E. Carruthers, K. Volke-Sepulveda, E. M. Wright, C. Brown, W. Sibbett, and K. Dholakia, "Enhanced optical guiding of colloidal particles using a supercontinuum light source," Opt. Express 14, 5793-5802 (2006).
[CrossRef]

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 8, 4001-4003 (2004).
[CrossRef]

Xu, C. Q.

K. Shinozaki, C. Q. Xu, H. Sasaki, and T. Kamijoh, "A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals," Opt. Commun. 133, 300-304 (1997).
[CrossRef]

Yao, B. L.

M. Lei and B. L. Yao, "Characteristics of beam profile of Gaussian beam passing through an axicon," Opt. Commun. 239, 367-372 (2004).
[CrossRef]

Yuan, X.-C.

Zapata-Rodriguez, C. J.

Zemánek, P.

T. Cizmár, M. Siler, and P. Zemánek, "An optical nanotrap array movable over a millimeter range," Appl. Phys. B 84, 197-203 (2006).
[CrossRef]

T. Cizmár, V. Kollárová, Z. Bouchal, and P. Zemánek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New. J. Phys. 8, 43 (2006).
[CrossRef]

J. Jezek, T. Cizmár, V. Nedela, and P. Zemánek, "Formation of long and thin polymer fiber using nondiffracting beam," Opt. Express 14, 8506-8515 (2006).
[CrossRef] [PubMed]

V. Karásek, T. Cizmár, O. Brzobohaty, P. Zemánek, V. Garces-Chávez, and K. Dholakia, "Long-range one dimensional longitudinal optical binding," submitted to Phys. Rev. Lett.

Zhang, Y.

Zhang, Y. J.

C. W. Zheng, Y. J. Zhang, and D. M. Zhao, "Calculation of the vectorial field distribution of an axicon illuminated by a linearly polarized Gaussian beam," Optik 117, 118-122 (2006).
[CrossRef]

Zhao, D. M.

C. W. Zheng, Y. J. Zhang, and D. M. Zhao, "Calculation of the vectorial field distribution of an axicon illuminated by a linearly polarized Gaussian beam," Optik 117, 118-122 (2006).
[CrossRef]

Zhao, Y.

Zheng, C.

Zheng, C. W.

C. W. Zheng, Y. J. Zhang, and D. M. Zhao, "Calculation of the vectorial field distribution of an axicon illuminated by a linearly polarized Gaussian beam," Optik 117, 118-122 (2006).
[CrossRef]

Appl. Opt. (2)

S. H. Tao, W. M. Lee, and X. Yuan, "Experimental study of Holographic Generation of Fractional Bessel Beams," Appl. Opt. 43, 123-126 (2004).
[CrossRef]

Y. Zhang, "Simple and rigorous analytical expression of the propagating field behind an axicon illuminated by an azimuthally polarized beam," Appl. Opt. 46, 7252-7257 (2007).
[CrossRef] [PubMed]

Appl. Phys. B (3)

Y. Zhang, "Analytical expression for the diffraction field of an axicon using the ray-tracing and interference method," Appl. Phys. B 90, 93-96 (2008).
[CrossRef]

T. Cizmár, M. Siler, and P. Zemánek, "An optical nanotrap array movable over a millimeter range," Appl. Phys. B 84, 197-203 (2006).
[CrossRef]

J. Arlt, T. Hitomi, and K. Dholakia, "Atom guiding along Laguerre-Gaussian and Bessel light beams," Appl. Phys. B 71, 549-556 (2000).
[CrossRef]

Appl. Phys. Lett. (1)

V. Garces-Chavez, D. Roskey, M. D. Summers, H. Melville, D. McGloin, E. M. Wright, and K. Dholakia, "Optical levitation in a Bessel light beam," Appl. Phys. Lett. 8, 4001-4003 (2004).
[CrossRef]

Contemp. Phys. (1)

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

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (9)

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

Nature (1)

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

New J. Phys. (1)

S. Schmid, G. Thalhammer, K. Winkler, F. Lang, and J. H. Denschlag, "Long distance transport of ultracold atoms using a 1D optical lattice," New J. Phys. 8, 1-15 (2006).
[CrossRef]

New. J. Phys. (1)

T. Cizmár, V. Kollárová, Z. Bouchal, and P. Zemánek, "Sub-micron particle organization by self-imaging of non-diffracting beams," New. J. Phys. 8, 43 (2006).
[CrossRef]

Opt. Commun. (5)

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

V. Jarutis, R. Paskauskas, and A. Stabinis, "Focusing of Laguerre-Gaussian beams by axicon," Opt. Commun. 1841-4, 105-112 (2000).
[CrossRef]

M. Lei and B. L. Yao, "Characteristics of beam profile of Gaussian beam passing through an axicon," Opt. Commun. 239, 367-372 (2004).
[CrossRef]

K. Shinozaki, C. Q. Xu, H. Sasaki, and T. Kamijoh, "A comparison of optical second-harmonic generation efficiency using Bessel and Gaussian beams in bulk crystals," Opt. Commun. 133, 300-304 (1997).
[CrossRef]

B. Depret, P. Verkerk, and D. Hennequin, "Characterization and modelling of the hollow beam produced by a real conical lens," Opt. Commun. 211, 31-38 (2002).
[CrossRef]

Opt. Express (2)

P. Fischer, A. E. Carruthers, K. Volke-Sepulveda, E. M. Wright, C. Brown, W. Sibbett, and K. Dholakia, "Enhanced optical guiding of colloidal particles using a supercontinuum light source," Opt. Express 14, 5793-5802 (2006).
[CrossRef]

J. Jezek, T. Cizmár, V. Nedela, and P. Zemánek, "Formation of long and thin polymer fiber using nondiffracting beam," Opt. Express 14, 8506-8515 (2006).
[CrossRef] [PubMed]

Opt. Laser Technol. (1)

M. R. Lapointe, "Review of non-diffracting Bessel beam experiments," Opt. Laser Technol. 24, 315-321 (1992).
[CrossRef]

Opt. Lett. (2)

Optik (1)

C. W. Zheng, Y. J. Zhang, and D. M. Zhao, "Calculation of the vectorial field distribution of an axicon illuminated by a linearly polarized Gaussian beam," Optik 117, 118-122 (2006).
[CrossRef]

Phys. Rev. A (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, "Efficiency of second-harmonic generation with Bessel beams," Phys. Rev. A 60, 2438-2441 (1999).
[CrossRef]

Phys. Rev. Lett (1)

V. Karásek, T. Cizmár, O. Brzobohaty, P. Zemánek, V. Garces-Chávez, and K. Dholakia, "Long-range one dimensional longitudinal optical binding," submitted to Phys. Rev. Lett.

Phys. Rev. Lett. (1)

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

Other (5)

T. Cizmar, V. Garces-Chávez, K. Dholakia, and P. Zemánek, "Optical conveyor belt for delivery of submicron objects," Appl. Phys. Lett.  86, 174,101:1-3 (2005).

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, J. Bu, H. Wang, X. Peng, and H. B. Niu, "Microfabricated-composite hologram-enabled multiple channel longitudinal optical guiding of microparticles in nondiffracting core of a Bessel beam array," Appl. Phys. Lett.  87, 084104 (2005).
[CrossRef]

X. Tsampoula, V. Garcés-Chávez, M. Comrie, D. J. Stevenson, B. Agate, C. T. A. Brown, F. Gunn-Moore, and K. Dholakia, "Femtosecond cellular transfection using a nondiffracting light beam," Appl. Phys. Lett.  91, 053,902:1-3 (2007).
[CrossRef]

T. Cizmár, "Optical traps generated by non-traditional beams," Ph.D. thesis, Masaryk University in Brno (2006). URL http://www.isibrno.cz/omitec/download.php?Cizmar PhD thesis.pdf.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

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Figures (12)

Fig. 1.
Fig. 1.

A: Formation of a quasi-Bessel beam (QBB) by a perfect axicon illuminated by a Gaussian beam with a beam waist placed on the axicon front surface. The planar wavefronts of the Gaussian beam near the beam waist are denoted by straight red lines. Wavevectors k of the plane waves forming the QBB lie on the surface of a cone with semi-apex angle α 0. The intensity profile along the propagation axis is shown together with invariant shape of the radial profile at two axial positions z 1 and z 2. zmax is the maximum propagation distance where the QBB exists and τ is the apex angle of the axicon. B: Influence of the round axicon tip. New wave refracted by the round tip propagates behind the axicon and interferes with the QBB. This results in axial modulation of the optical intensity with a period λ/(1-cosα 0), where λ is the wave wavelength in the medium. Due to the interference the radial intensity distribution is no longer invariant (see examples at z 1 and z 2). Inset: Approximation of the round tip of the axicon by a hyperboloid of revolution of two sheets and the meaning of its parameters a and b.

Fig. 2.
Fig. 2.

Calculated axial optical intensity distribution behind the axicon with different values of axicon tip parameter a illustrated in the inset. The intensity distribution for the perfect axicon (a=0 µm) is plotted as a full line. With increasing a the spatial distribution of the optical intensity is significantly disturbed. The presented results were calculated for the Gaussian beam waist w 0=2140 µm, wavelength λ vac=1064 nm, apex angle of the axicon τ=170°, and axicon refractive index n=1.50669.

Fig. 3.
Fig. 3.

A free-space propagation method was used to calculate the spatial optical intensity distribution of the field behind the perfect axicon illuminated by a Gaussian beam (beam waist w 0=2140 µm) at the wavelength λ=1064 nm. The telescope is formed from lenses L 1 and L 2 of focal lengths f 1=50 mm and f 2=11 mm, respectively. The white curves show the numerically calculated axial intensity profiles.

Fig. 4.
Fig. 4.

The spatial-frequency spectrum |S(R)|2 of the field behind the perfect axicon and axicon with round tip calculated for the Gaussian beam waist w 0=2140 µm, the wavelength λ vac=1064 nm and the apex angle of the axicon τ=170°, and axicon refractive index n=1.50669. The hyperbolic shape of the axicon tip (see the inset) creates low frequency components in the spatial-frequency spectrum.

Fig. 5.
Fig. 5.

Measured shape of the axicon and its contour plot.

Fig. 6.
Fig. 6.

Experimental set-up. Laser: IPG, YLM-10-1064-LP, wavelength 1064 nm, maximal power 10 W, beam-waist of incident Gaussian beam w 0=2140 µm; axicon: EKSPLA 130-0270, apex angle τ=170°; lenses L 1, L 2: focal lengths f 1=50 mm and f 2=11 mm; objective: Mitutoyo M Plan Apo SL 80X; CCD camera: IDT X Stream VISION XS-3.

Fig. 7.
Fig. 7.

Comparison of measured and calculated axial intensity profile I 0 of the QBB generated by the round-tip axicon measured directly behind the axicon (left – measurement region A in Fig. 6) and behind the demagnifying telescope (right – measurement region B).

Fig. 8.
Fig. 8.

Comparison of measured and calculated radius ρ 0 of the high intensity QBB core generated by the round-tip axicon measured directly behind the axicon (left) and behind the demagnifying telescope (right).

Fig. 9.
Fig. 9.

The measured (left) and calculated (right) spatial intensity distribution of the QBB generated behind the round-tip axicon for the same parameters as in Fig. 7.

Fig. 10.
Fig. 10.

Calculated axial intensity profile for perfect axicon (open circle with full line), and round-tip axicon with a=33.7 µm. Different radii Rf of the spatial filter placed in the Fourier plane were considered: 0 µm (full), 1973 µm (dashed), 2064 µm (dotted), and 2138 µm (dot-dashed) (see the inset for corresponding spatial frequency spectrum cut-off).

Fig. 11.
Fig. 11.

Comparison of measured (full with plus marks) and best fit calculated (full blue) axial intensity profiles I 0 (left) and beam core radii ρ 0 (right) for filtered QBB.

Fig. 12.
Fig. 12.

The measured (left) and calculated (right) 2D spatial intensity profiles of filtered QBB generated behind the round-tip axicon. The parameters were the same as in Fig. 11.

Equations (16)

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

α 0 = arcsin ( n n 0 cos τ 2 ) + τ π 2 n n 0 n 0 π τ 2 .
E ( ρ , z ) = E 0 2 π k z w 0 sin α 0 z max exp ( z 2 z max 2 π i 4 ) J 0 ( k ρ sin α 0 ) exp ( i k z cos α 0 ) ,
I ( ρ , z ) = 4 P k sin α 0 w 0 z z max J 0 2 ( k ρ sin α 0 ) exp ( 2 z 2 z max 2 ) I 0 ( z ) J 0 2 ( 2.4048 ρ ρ 0 ) ,
z 2 a 2 ρ 2 b 2 = 1 giving z = a 2 + ( a ρ b ) 2 .
z = a 2 + ρ 2 tan 2 ( τ 2 ) .
E ( ρ , 0 ) = E 0 exp ( ρ 2 w 0 2 ) exp ( i k n Δ 0 ) exp [ i k ( n 0 n ) a 2 + ρ 2 tan 2 ( τ 2 ) ] ,
S ( R , z ) = S ( R , 0 ) exp ( i k z 1 R 2 ) ,
S ( R , 0 ) = k 0 E ( ρ , 0 ) ρ J 0 ( k R ρ ) d ρ ,
S i 0 = k j = 1 N E ( ρ j , 0 ) ρ j Δ ρ j J 0 ( k R i ρ j ) ,
S i z = S i 0 exp ( i k z 1 R i 2 ) .
E i z = k j = 1 N R j Δ R j S j z J 0 ( k R j ρ i ) ,
N = k ρ max ,
ρ = ρ max · [ 0 , ( 1 N ) 2 , ( 2 N ) 2 , . . . , 1 ] ,
R = [ 0 , ( 1 N ) 2 , ( 2 N ) 2 , . . . , 1 ] ,
E ( ρ , z L i ) = E 0 ( ρ , z L i ) exp ( i k 2 f i ρ 2 ) ,
I ( ρ , z i ) = I 0 ( z i ) J 0 2 { 2.4048 [ x x 0 ( z i ) ] 2 + [ y y 0 ( z i ) ] 2 ρ 0 ( z i ) } + O ( z i ) ,

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