Abstract

Electromagnetic beams are subject to spatial spreading as they propagate. I have investigated the light propagation passing through a finite-aperture, which is obtained by two-dimensional square-lattice photonic crystals (PCs). It is found that the beam that is coupled to the free-space by exiting the axicon-shape PC resists considerably against the diffraction. The inspection of the beam profile in the transverse to the propagation direction reveals the appearance of the side-lobes, and I have attributed the limited-diffraction beam propagation to these artificially created lobes. I optimize the length of the aperture while keeping the width constant and show that an order of magnitude improvement for beating the diffraction length is achievable. The advantages of the presented PC-based axicon over the bulk refractive axicons are the compactness and integrated nature of the former one, in addition to the flexibility of engineering individual unit cells of PC structure.

© 2009 Optical Society of America

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2008

H. Kurt, “Theoretical study of directional emission enhancement from photonic crystal waveguides with tapered exits,” IEEE Photon. Technol. Lett. 20, 1682-1684 (2008).
[CrossRef]

2007

2006

2005

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

2004

N. Al-Ababneh and M. Testorf, “Analysis of free space optical interconnects based on non-diffracting beams,” Opt. Commun. 242, 393-400 (2004).
[CrossRef]

E. E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

M. Fortin, M. Piché, and E. F. Borra, “Optical tests with Bessel beam interferometry,” Opt. Express 12, 5887-5895 (2004).
[CrossRef] [PubMed]

2003

2002

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, 243-245 (2002).
[CrossRef]

V. Garces-Chavez, 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]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 269, 1101-1103 (2002).
[CrossRef]

2001

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]

G. Gadonas, V. Jarutis, R. Paskauskas, V. Smilgevicius, A. Stabinis, and V. Vaicaitis, “Self-action of Bessel beam in nonlinear medium,” Opt. Commun. 196, 309-316 (2001).
[CrossRef]

2000

V. Magni, “Optimum beams for efficient frequency mixing in crystals with second order nonlinearity,” Opt. Commun. 184, 245-255 (2000).
[CrossRef]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239-245 (2000).
[CrossRef]

R. Grunwald, U. Grieber, F. Tschirschwitz, E. T. J. Nibbering, T. Elsaesser, V. Kebbel, H.-J. Hartmann, and W. Jueptner, “Generation of femtosecond Bessel beams with microaxicon arrays,” Opt. Lett. 25, 981-983 (2000).
[CrossRef]

1997

L. Niggel, T. Lanz, and M. Maier, “Properties of Bessel beams generated by periodic grating of circular symmetry,” J. Opt. Soc. Am. A 14, 27-33 (1997).
[CrossRef]

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287-292 (1997).
[CrossRef]

1995

1994

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

1993

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401-1404 (1993).
[CrossRef] [PubMed]

1991

1989

K. Uehara and H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125-129 (1989).
[CrossRef]

A. Vasara, J. Turunen, and A. T. Friberg, “Realization of general nondiffracting beams with computer generated holograms,” J. Opt. Soc. Am. A 6, 1748-1754 (1989).
[CrossRef] [PubMed]

M. Florjanczyk and R. Tremblay, “Guiding of atoms in a travelling-wave laser trap formed by the axicon,” Opt. Commun. 73, 448-451 (1989).
[CrossRef]

1988

1987

J. E. Durnin, J. J. Miceli, and J. H. 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]

1980

D. M. Greenberger, “Comment on nonspreading wave packets,” Am. J. Phys. 48, 256 (1980).
[CrossRef]

1979

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264-267 (1979).
[CrossRef]

1962

1954

Agio, M.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Al-Ababneh, N.

N. Al-Ababneh and M. Testorf, “Analysis of free space optical interconnects based on non-diffracting beams,” Opt. Commun. 242, 393-400 (2004).
[CrossRef]

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 269, 1101-1103 (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, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239-245 (2000).
[CrossRef]

Baida, F.

Bainier, C.

Balazs, N. L.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264-267 (1979).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Berry, M. V.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264-267 (1979).
[CrossRef]

Birner, A.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Bor, Zs.

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287-292 (1997).
[CrossRef]

Borra, E. F.

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Cavallaro, J. R.

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287-292 (1997).
[CrossRef]

Chen, Z.

Christodoulides, D. N.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979-981 (2007).
[CrossRef] [PubMed]

Courjon, D.

Desyatnikov, A. S.

Dholakia, K.

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

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

V. Garces-Chavez, 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]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 269, 1101-1103 (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, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239-245 (2000).
[CrossRef]

Ding, Z.

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Durnin, J.

Durnin, J. E.

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

Eberly, J. H.

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

Elsaesser, T.

Erdelyi, M.

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287-292 (1997).
[CrossRef]

Fischer, R.

Florjanczyk, M.

M. Florjanczyk and R. Tremblay, “Guiding of atoms in a travelling-wave laser trap formed by the axicon,” Opt. Commun. 73, 448-451 (1989).
[CrossRef]

Fortin, M.

Friberg, A. T.

Fujiwara, S.

Gadonas, G.

G. Gadonas, V. Jarutis, R. Paskauskas, V. Smilgevicius, A. Stabinis, and V. Vaicaitis, “Self-action of Bessel beam in nonlinear medium,” Opt. Commun. 196, 309-316 (2001).
[CrossRef]

Garces-Chavez, V.

V. Garces-Chavez, 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, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239-245 (2000).
[CrossRef]

Garcés-Chávez, V.

García-Vidal, F. J.

E. E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Golub, I.

Gösele, U.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Greenberger, D. M.

D. M. Greenberger, “Comment on nonspreading wave packets,” Am. J. Phys. 48, 256 (1980).
[CrossRef]

Grieber, U.

Grosjean, T.

Grunwald, R.

Hartmann, H.-J.

Herman, R. M.

Herminghaus, S.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401-1404 (1993).
[CrossRef] [PubMed]

Horvath, Z. L.

M. Erdelyi, Z. L. Horvath, G. Szabo, Zs. Bor, F. K. Tittel, J. R. Cavallaro, and M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287-292 (1997).
[CrossRef]

Inoue, T.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys. A: Mater. Sci. Process. A84, 423-430 (2006).
[CrossRef]

Jarutis, V.

G. Gadonas, V. Jarutis, R. Paskauskas, V. Smilgevicius, A. Stabinis, and V. Vaicaitis, “Self-action of Bessel beam in nonlinear medium,” Opt. Commun. 196, 309-316 (2001).
[CrossRef]

Jueptner, W.

Kebbel, V.

Kikuchi, H.

K. Uehara and H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125-129 (1989).
[CrossRef]

Kivshar, Y. S.

Kizuka, Y.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys. A: Mater. Sci. Process. A84, 423-430 (2006).
[CrossRef]

Kramper, P.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Krolikowski, W.

Kurt, H.

H. Kurt, “Theoretical study of directional emission enhancement from photonic crystal waveguides with tapered exits,” IEEE Photon. Technol. Lett. 20, 1682-1684 (2008).
[CrossRef]

Lanz, T.

Liu, H.

Lopez-Aguayo, S.

MacDonald, M. P.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 269, 1101-1103 (2002).
[CrossRef]

Magni, V.

V. Magni, “Optimum beams for efficient frequency mixing in crystals with second order nonlinearity,” Opt. Commun. 184, 245-255 (2000).
[CrossRef]

Maier, M.

Martín-Moreno, L.

E. E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Matsuoka, Y.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys. A: Mater. Sci. Process. A84, 423-430 (2006).
[CrossRef]

McGloin, D.

McLeod, J. H.

Melville, H.

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

Moreno, E. E.

E. E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Müller, F.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Nelson, J. S.

Neshev, D. N.

Nibbering, E. T. J.

Niggel, L.

Paskauskas, R.

G. Gadonas, V. Jarutis, R. Paskauskas, V. Smilgevicius, A. Stabinis, and V. Vaicaitis, “Self-action of Bessel beam in nonlinear medium,” Opt. Commun. 196, 309-316 (2001).
[CrossRef]

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 269, 1101-1103 (2002).
[CrossRef]

Piché, M.

Ren, H.

Rosen, J.

Salik, B.

Sandoghar, V.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Sibbett, W.

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M. Florjanczyk and R. Tremblay, “Guiding of atoms in a travelling-wave laser trap formed by the axicon,” Opt. Commun. 73, 448-451 (1989).
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[CrossRef] [PubMed]

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[CrossRef]

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A. Taflove, Computational Electrodynamics--The Finite-Difference Time-Domain Method (Artech House, 2000).

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Figures (6)

Fig. 1
Fig. 1

Geometrical representation of a 2D axicon-shape square-lattice PC structure. The dielectric rods in the air background comprise the periodic structure. The length of the second part L 2 is kept constant at 10 a and the first section’s length L 1 is varied from 0 to 15 a .

Fig. 2
Fig. 2

Steady-state electric field variation of the electromagnetic beam through an axicon-shape PC. The two vertical dotted lines indicate the locations of the detector planes at which the beam widths of the light are obtained. The border of the complete PC geometry is shown by the connecting dotted lines.

Fig. 3
Fig. 3

The beam’s amplitude width variations (FWHM) are recorded at the two detector planes when the length L 1 is varied.

Fig. 4
Fig. 4

Steady-state electric field variation of the electromagnetic beam through an axicon-shape PC for two cases: L 1 = 5 a and L 1 = 8 a . The two dotted vertical lines are the locations where the cross-sectional profiles of the field amplitudes are taken.

Fig. 5
Fig. 5

Transverse-mode amplitude profiles of the beam at the first detector plane for two cases whose steady-state electric field maps are presented in Fig. 4. The Bessel beam of zero-order, first kind is plotted by the solid curve for a reference. The dashed and dotted curves represent the mode profiles for L 1 = 5 a and L 1 = 8 a , respectively.

Fig. 6
Fig. 6

Normalized intensity variations of the limited-diffraction beam and a reference Gaussian beam along the transverse direction to propagation. (a) Initially, the limited-diffraction beam and Gaussian beam have the same FWHM. (b) The intensity profiles after propagating 10 a distance. (c) and (d) correspond to the cases where the beams travel distances of 20 a and 30 a , respectively. The normalization is performed to make easy comparisons of the FWHM values.

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