Abstract

In order to miniaturize and integrate conveniently in THz quasi-optical systems, binary axicons, based on binary optical ideas, are introduced in our paper and designed for generating pseudo-Bessel beams at THz frequencies. The designed binary axicons are easier to fabricate than holographic axicons, more compact and thus less lossy in the material when compared with classical cone axicons. To calculate the electromagnetic fields diffracted by binary axicons precisely, a two-dimension finite-difference time-domain (2-D FDTD) method in conjunction with Stratton-Chu formulas are employed in this paper. Applying this method, the properties of pseudo-Bessel beams produced by binary axicons are analyzed, and a brief summary is given in the end.

© 2009 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. V. Garcés-Chávez,D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
    [CrossRef] [PubMed]
  5. K. Wang, L. Zeng, and Ch. Yin, "Influence of the incident wave-front on intensity distribution of the nondiffracting beam used in large-scale measurement," Opt. Commun. 216, 99-103 (2003).
    [CrossRef]
  6. S. Monk, J. Arlt, D. A. Robertson, J. Courtial, and M. J. Padgett, "The generation of Bessel beams at millimetre-wave frequencies by use of an axicon," Opt. Commun. 170, 213-215 (1999).
    [CrossRef]
  7. N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, and S. Withington, "The quasi-optical analysis of Bessel beams in the far infrared," Infrared Phys. Technol. 46, 233-247 (2005).
    [CrossRef]
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    [CrossRef]
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  12. J. Courtial and G. Whyte, "Iterative algorithms for holographic shaping of non-diffracting and self-imaging light beams," Opt. Express 14, 2108-2116 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  14. D. Feng, Y. B. Yan, G. F. Jin, Q. F. Tan, and H. T. Liu, "Rigorous electromagnetic design of finite-aperture diffractive optical elements by use of an iterative optimization algorithm," J. Opt. Soc. Am. A 20, 1739- 1745 (2003).
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2006 (3)

2005 (1)

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, and S. Withington, "The quasi-optical analysis of Bessel beams in the far infrared," Infrared Phys. Technol. 46, 233-247 (2005).
[CrossRef]

2003 (5)

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

Z. Bouchal, "Nondiffracting optical beams: physical properties, experiments, and applications," Czech. J. Phys. 53, 537-78 (2003).
[CrossRef]

V. Garcés-Chávez,D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

K. Wang, L. Zeng, and Ch. Yin, "Influence of the incident wave-front on intensity distribution of the nondiffracting beam used in large-scale measurement," Opt. Commun. 216, 99-103 (2003).
[CrossRef]

D. Feng, Y. B. Yan, G. F. Jin, Q. F. Tan, and H. T. Liu, "Rigorous electromagnetic design of finite-aperture diffractive optical elements by use of an iterative optimization algorithm," J. Opt. Soc. Am. A 20, 1739- 1745 (2003).
[CrossRef]

2001 (1)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (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]

1999 (1)

S. Monk, J. Arlt, D. A. Robertson, J. Courtial, and M. J. Padgett, "The generation of Bessel beams at millimetre-wave frequencies by use of an axicon," Opt. Commun. 170, 213-215 (1999).
[CrossRef]

1996 (1)

1987 (1)

1954 (1)

J. H. McLeod, "The axicon: a new type of optical element," J. Opt. Soc. Am 44, 592-597 (1954).
[CrossRef]

Ala-Laurinaho, J.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

Andres, P.

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (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]

S. Monk, J. Arlt, D. A. Robertson, J. Courtial, and M. J. Padgett, "The generation of Bessel beams at millimetre-wave frequencies by use of an axicon," Opt. Commun. 170, 213-215 (1999).
[CrossRef]

Bouchal, Z.

Z. Bouchal, "Nondiffracting optical beams: physical properties, experiments, and applications," Czech. J. Phys. 53, 537-78 (2003).
[CrossRef]

Courtial, J.

J. Courtial and G. Whyte, "Iterative algorithms for holographic shaping of non-diffracting and self-imaging light beams," Opt. Express 14, 2108-2116 (2006).
[CrossRef] [PubMed]

S. Monk, J. Arlt, D. A. Robertson, J. Courtial, and M. J. Padgett, "The generation of Bessel beams at millimetre-wave frequencies by use of an axicon," Opt. Commun. 170, 213-215 (1999).
[CrossRef]

Dholakia, K.

V. Garcés-Chávez,D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (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]

Dultz, W.

V. Garcés-Chávez,D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

Durnin, J.

Feng, D.

Furlan, W. D.

Garces-Chavez, V.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Garcés-Chávez,, V.

V. Garcés-Chávez,D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

Gaylord, T. K.

Glytsis, E. N.

Golub, I.

Hakli, J.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

Hirayama, K.

Jin, G. F.

Koskinen, T.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

Lancis, J.

Lanigan, W.

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, and S. Withington, "The quasi-optical analysis of Bessel beams in the far infrared," Infrared Phys. Technol. 46, 233-247 (2005).
[CrossRef]

Liu, H. T.

Lonnqvist, A.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

Mahon, R.

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, and S. Withington, "The quasi-optical analysis of Bessel beams in the far infrared," Infrared Phys. Technol. 46, 233-247 (2005).
[CrossRef]

Mallat, J.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

McGloin, D.

V. Garcés-Chávez,D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

McLeod, J. H.

J. H. McLeod, "The axicon: a new type of optical element," J. Opt. Soc. Am 44, 592-597 (1954).
[CrossRef]

Meltaus, J.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

Monk, S.

S. Monk, J. Arlt, D. A. Robertson, J. Courtial, and M. J. Padgett, "The generation of Bessel beams at millimetre-wave frequencies by use of an axicon," Opt. Commun. 170, 213-215 (1999).
[CrossRef]

Monsoriu, J. A.

Murphy, J. A.

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, and S. Withington, "The quasi-optical analysis of Bessel beams in the far infrared," Infrared Phys. Technol. 46, 233-247 (2005).
[CrossRef]

Noponen, E.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

Padgett, M. J.

V. Garcés-Chávez,D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

S. Monk, J. Arlt, D. A. Robertson, J. Courtial, and M. J. Padgett, "The generation of Bessel beams at millimetre-wave frequencies by use of an axicon," Opt. Commun. 170, 213-215 (1999).
[CrossRef]

Raisanen, A. V.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

Robertson, D. A.

S. Monk, J. Arlt, D. A. Robertson, J. Courtial, and M. J. Padgett, "The generation of Bessel beams at millimetre-wave frequencies by use of an axicon," Opt. Commun. 170, 213-215 (1999).
[CrossRef]

Saily, J.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

Salo, J.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

Salomaa, M. M.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

Schmitzer, H.

V. Garcés-Chávez,D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

Sibbett, W.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

Tan, Q. F.

Trappe, N.

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, and S. Withington, "The quasi-optical analysis of Bessel beams in the far infrared," Infrared Phys. Technol. 46, 233-247 (2005).
[CrossRef]

Viikari, V.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

Wang, K.

K. Wang, L. Zeng, and Ch. Yin, "Influence of the incident wave-front on intensity distribution of the nondiffracting beam used in large-scale measurement," Opt. Commun. 216, 99-103 (2003).
[CrossRef]

Whyte, G.

Withington, S.

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, and S. Withington, "The quasi-optical analysis of Bessel beams in the far infrared," Infrared Phys. Technol. 46, 233-247 (2005).
[CrossRef]

Yan, Y. B.

Yin, Ch.

K. Wang, L. Zeng, and Ch. Yin, "Influence of the incident wave-front on intensity distribution of the nondiffracting beam used in large-scale measurement," Opt. Commun. 216, 99-103 (2003).
[CrossRef]

Zeng, L.

K. Wang, L. Zeng, and Ch. Yin, "Influence of the incident wave-front on intensity distribution of the nondiffracting beam used in large-scale measurement," Opt. Commun. 216, 99-103 (2003).
[CrossRef]

Czech. J. Phys. (1)

Z. Bouchal, "Nondiffracting optical beams: physical properties, experiments, and applications," Czech. J. Phys. 53, 537-78 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lonnqvist, T. Koskinen, J. Saily, J. Hakli, J. Ala-Laurinaho, J. Mallat, and A. V. Raisanen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1279 (2003).
[CrossRef]

Infrared Phys. Technol. (1)

N. Trappe, R. Mahon, W. Lanigan, J. A. Murphy, and S. Withington, "The quasi-optical analysis of Bessel beams in the far infrared," Infrared Phys. Technol. 46, 233-247 (2005).
[CrossRef]

J. Opt. Soc. Am (1)

J. H. McLeod, "The axicon: a new type of optical element," J. Opt. Soc. Am 44, 592-597 (1954).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (4)

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, V. Garces-Chavez, W. Sibbett, and K. Dholakia, "Optical micromanipulation using a Bessel light beam," Opt. Commun. 197, 239-245 (2001).
[CrossRef]

K. Wang, L. Zeng, and Ch. Yin, "Influence of the incident wave-front on intensity distribution of the nondiffracting beam used in large-scale measurement," Opt. Commun. 216, 99-103 (2003).
[CrossRef]

S. Monk, J. Arlt, D. A. Robertson, J. Courtial, and M. J. Padgett, "The generation of Bessel beams at millimetre-wave frequencies by use of an axicon," Opt. Commun. 170, 213-215 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

V. Garcés-Chávez,D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef] [PubMed]

Other (1)

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, NewYork, 1941).

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Figures (5)

Fig. 1.
Fig. 1.

The design process of a binary axicon. (a) A bulk axicon. (b) An axicon removed the unwanted material (red part). (c) An equivalent binary axicon with continuous profile. (d) An equivalent binary axicon quantized into four levels.

Fig. 2.
Fig. 2.

Schematic diagram of 2-D FDTD computational model, where the 8-level binary axicon is embedded into FDTD grid.

Fig. 3.
Fig. 3.

The axial intensity distributions for the designed binary axicon and the bulk one.

Fig. 4.
Fig. 4.

Electric-field amplitude patterns plotted in a pseudo-color representation. (a) For the bulk axicon. (b) For our designed binary axicon.

Fig. 5.
Fig. 5.

The axial and transverse intensity distributions for the designed binary axicon. (a) The on-axial intensity versus propagation distance z. (b) The transverse intensity distribution at z = 0.8Zmax plane. (c) z = 1.0Zmax . (d) z = 1.2Zmax.

Equations (6)

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

E(ρ,z,t)=J0 (kρ) exp (i(kzzωt))
h(ρ)=φ(ρ)/[(n1n0)k]
h(ρ)=[φ(ρ)mod2π] / [(n1n0)k]
hq(ρ)=int[h(ρ)/Δ] Δ
E(r)=L {jωμ[n×H(r)]G0(r,r)[n×E(r)]×G0(r,r)[nE(r)]G0(r,r)}dL
H(r)=L{jωℰ[n×E(r)]G0(r,r)[n×H(r)]×G0(r,r)[nH(r)]G0(r,r)}dL

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