Abstract

In this Letter, we experimentally demonstrate structured light carrying multiple values of orbital angular momentum (OAM) in the farfield scattering region of Vogel spiral arrays of metallic nanoparticles. Using Fourier–Hankel mode decomposition analysis and interferometric reconstruction of the complex amplitude of scattered waves, we show the ability to encode well-defined numerical sequences, determined by the aperiodic spiral geometry, into azimuthal OAM values, in excellent agreement with analytical scattering theory. The generation of azimuthal sequences of OAM values by light scattering from engineered aperiodic surfaces is relevant to a number of device applications for secure optical communication, classical cryptography, and quantum cryptography.

© 2012 Optical Society of America

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References

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  1. M. Padgett, J. Courtial, and L. Allen, Phys. Today 57, 35 (2004).
    [CrossRef]
  2. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. 45, 8185 (1992).
    [CrossRef]
  3. D. G. Grier, Nature 424, 810 (2003).
    [CrossRef]
  4. A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 5 (2002).
    [CrossRef]
  5. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
    [CrossRef]
  6. D. S. Simon, N. Lawrence, J. Trevino, L. Dal Negro, and A. V. Sergienko are preparing a manuscript to be called “Quantum key distribution with Fibonacci orbital angular momentum states.”
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    [CrossRef]
  8. J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. N. Lawrence, J. Trevino, and L. Dal Negro, J. Appl. Phys. 111, 113101 (2012).
    [CrossRef]
  19. L. Dal Negro and S. V. Boriskina, Laser Photon. Rev. 6, 178 (2012).
    [CrossRef]
  20. J. Trevino, S. F. Liew, H. Noh, H. Cao, and L. Dal Negro, Opt. Express 20, 3015 (2012).
    [CrossRef]
  21. H. Vogel, Math. Biosci. 44, 179 (1979).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012 (4)

J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

N. Lawrence, J. Trevino, and L. Dal Negro, J. Appl. Phys. 111, 113101 (2012).
[CrossRef]

L. Dal Negro and S. V. Boriskina, Laser Photon. Rev. 6, 178 (2012).
[CrossRef]

J. Trevino, S. F. Liew, H. Noh, H. Cao, and L. Dal Negro, Opt. Express 20, 3015 (2012).
[CrossRef]

2011 (3)

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

J. Trevino, H. Cao, and L. Dal Negro, Nano Lett. 11, 2008 (2011).
[CrossRef]

S. F. Liew, H. Noh, J. Trevino, L. D. Negro, and H. Cao, Opt. Express 19, 23631 (2011).
[CrossRef]

2010 (1)

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, Phys. Rev. Lett. 105, 8 (2010).
[CrossRef]

2009 (1)

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

2007 (1)

2004 (2)

2003 (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

2002 (3)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 5 (2002).
[CrossRef]

I. Yamaguchi, T. Matsumura, and J.-I. Kato, Opt. Lett. 27, 1108 (2002).
[CrossRef]

S. Chavez-Cerda, M. Padgett, I. Allison, G. New, J. Gutierrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

1992 (2)

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. 45, 8185 (1992).
[CrossRef]

1979 (1)

H. Vogel, Math. Biosci. 44, 179 (1979).
[CrossRef]

1977 (1)

G. J. Mitchison, Science 196, 270 (1977).
[CrossRef]

Ahmed, N.

J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Aieta, F.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Allen, L.

M. Padgett, J. Courtial, and L. Allen, Phys. Today 57, 35 (2004).
[CrossRef]

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 5 (2002).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. 45, 8185 (1992).
[CrossRef]

Allison, I.

S. Chavez-Cerda, M. Padgett, I. Allison, G. New, J. Gutierrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

Barnett, S.

Barsi, C.

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

Beijersbergen, M.

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, Phys. Rev. Lett. 105, 8 (2010).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. 45, 8185 (1992).
[CrossRef]

Berkhout, G.

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, Phys. Rev. Lett. 105, 8 (2010).
[CrossRef]

Boriskina, S. V.

L. Dal Negro and S. V. Boriskina, Laser Photon. Rev. 6, 178 (2012).
[CrossRef]

Cao, H.

Capasso, F.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Chavez-Cerda, S.

S. Chavez-Cerda, M. Padgett, I. Allison, G. New, J. Gutierrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

Courtial, J.

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, Phys. Rev. Lett. 105, 8 (2010).
[CrossRef]

M. Padgett, J. Courtial, and L. Allen, Phys. Today 57, 35 (2004).
[CrossRef]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
[CrossRef]

S. Chavez-Cerda, M. Padgett, I. Allison, G. New, J. Gutierrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

Dal Negro, L.

N. Lawrence, J. Trevino, and L. Dal Negro, J. Appl. Phys. 111, 113101 (2012).
[CrossRef]

L. Dal Negro and S. V. Boriskina, Laser Photon. Rev. 6, 178 (2012).
[CrossRef]

J. Trevino, S. F. Liew, H. Noh, H. Cao, and L. Dal Negro, Opt. Express 20, 3015 (2012).
[CrossRef]

J. Trevino, H. Cao, and L. Dal Negro, Nano Lett. 11, 2008 (2011).
[CrossRef]

L. Dal Negro, N. Lawrence, and J. Trevino, Opt. Express20, 18209 (2012).
[CrossRef]

D. S. Simon, N. Lawrence, J. Trevino, L. Dal Negro, and A. V. Sergienko are preparing a manuscript to be called “Quantum key distribution with Fibonacci orbital angular momentum states.”

Dolinar, S.

J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Fazal, I. M.

J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Fleischer, J. W.

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

Franke-Arnold, S.

Gaburro, Z.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Genevet, P.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Gibson, G.

Grier, D. G.

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

Gutierrez-Vega, J.

S. Chavez-Cerda, M. Padgett, I. Allison, G. New, J. Gutierrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

Heckenberg, N. R.

Houdre, R.

Huang, H.

J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Kato, J.-I.

Kats, M.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Kotlyar, M.

Krauss, T. F.

Lavery, M.

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, Phys. Rev. Lett. 105, 8 (2010).
[CrossRef]

Lawrence, N.

N. Lawrence, J. Trevino, and L. Dal Negro, J. Appl. Phys. 111, 113101 (2012).
[CrossRef]

L. Dal Negro, N. Lawrence, and J. Trevino, Opt. Express20, 18209 (2012).
[CrossRef]

D. S. Simon, N. Lawrence, J. Trevino, L. Dal Negro, and A. V. Sergienko are preparing a manuscript to be called “Quantum key distribution with Fibonacci orbital angular momentum states.”

Le Thomas, N.

Liew, S. F.

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 5 (2002).
[CrossRef]

S. Chavez-Cerda, M. Padgett, I. Allison, G. New, J. Gutierrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Matsumura, T.

McDuff, R.

Mitchison, G. J.

G. J. Mitchison, Science 196, 270 (1977).
[CrossRef]

Negro, L. D.

New, G.

S. Chavez-Cerda, M. Padgett, I. Allison, G. New, J. Gutierrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

Noh, H.

O’Brien, D.

O’Neil, A.

S. Chavez-Cerda, M. Padgett, I. Allison, G. New, J. Gutierrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 5 (2002).
[CrossRef]

Padgett, M.

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, Phys. Rev. Lett. 105, 8 (2010).
[CrossRef]

M. Padgett, J. Courtial, and L. Allen, Phys. Today 57, 35 (2004).
[CrossRef]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
[CrossRef]

S. Chavez-Cerda, M. Padgett, I. Allison, G. New, J. Gutierrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

Padgett, M. J.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 5 (2002).
[CrossRef]

Pas’ko, V.

Ren, Y.

J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Sergienko, A. V.

D. S. Simon, N. Lawrence, J. Trevino, L. Dal Negro, and A. V. Sergienko are preparing a manuscript to be called “Quantum key distribution with Fibonacci orbital angular momentum states.”

Simon, D. S.

D. S. Simon, N. Lawrence, J. Trevino, L. Dal Negro, and A. V. Sergienko are preparing a manuscript to be called “Quantum key distribution with Fibonacci orbital angular momentum states.”

Smith, C. P.

Spreeuw, R.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. 45, 8185 (1992).
[CrossRef]

Tetienne, J.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Trevino, J.

N. Lawrence, J. Trevino, and L. Dal Negro, J. Appl. Phys. 111, 113101 (2012).
[CrossRef]

J. Trevino, S. F. Liew, H. Noh, H. Cao, and L. Dal Negro, Opt. Express 20, 3015 (2012).
[CrossRef]

S. F. Liew, H. Noh, J. Trevino, L. D. Negro, and H. Cao, Opt. Express 19, 23631 (2011).
[CrossRef]

J. Trevino, H. Cao, and L. Dal Negro, Nano Lett. 11, 2008 (2011).
[CrossRef]

L. Dal Negro, N. Lawrence, and J. Trevino, Opt. Express20, 18209 (2012).
[CrossRef]

D. S. Simon, N. Lawrence, J. Trevino, L. Dal Negro, and A. V. Sergienko are preparing a manuscript to be called “Quantum key distribution with Fibonacci orbital angular momentum states.”

Tur, M.

J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Vasnetsov, M.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Vogel, H.

H. Vogel, Math. Biosci. 44, 179 (1979).
[CrossRef]

Wan, W.

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

Wang, J.

J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

White, A. G.

Willner, A. E.

J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Woerdman, J.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. 45, 8185 (1992).
[CrossRef]

Yamaguchi, I.

Yan, Y.

J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yang, J.-yuan

J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yu, N.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Yue, Y.

J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

J. Appl. Phys. (1)

N. Lawrence, J. Trevino, and L. Dal Negro, J. Appl. Phys. 111, 113101 (2012).
[CrossRef]

J. Opt. B (1)

S. Chavez-Cerda, M. Padgett, I. Allison, G. New, J. Gutierrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, J. Opt. B 4, S52 (2002).
[CrossRef]

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

Laser Photon. Rev. (1)

L. Dal Negro and S. V. Boriskina, Laser Photon. Rev. 6, 178 (2012).
[CrossRef]

Math. Biosci. (1)

H. Vogel, Math. Biosci. 44, 179 (1979).
[CrossRef]

Nano Lett. (1)

J. Trevino, H. Cao, and L. Dal Negro, Nano Lett. 11, 2008 (2011).
[CrossRef]

Nat. Photonics (2)

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

J. Wang, J.-yuan Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Nature (2)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. (1)

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. 45, 8185 (1992).
[CrossRef]

Phys. Rev. Lett. (2)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 5 (2002).
[CrossRef]

G. Berkhout, M. Lavery, J. Courtial, M. Beijersbergen, and M. Padgett, Phys. Rev. Lett. 105, 8 (2010).
[CrossRef]

Phys. Today (1)

M. Padgett, J. Courtial, and L. Allen, Phys. Today 57, 35 (2004).
[CrossRef]

Science (2)

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

G. J. Mitchison, Science 196, 270 (1977).
[CrossRef]

Other (2)

L. Dal Negro, N. Lawrence, and J. Trevino, Opt. Express20, 18209 (2012).
[CrossRef]

D. S. Simon, N. Lawrence, J. Trevino, L. Dal Negro, and A. V. Sergienko are preparing a manuscript to be called “Quantum key distribution with Fibonacci orbital angular momentum states.”

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Figures (3)

Fig. 1.
Fig. 1.

(a), (d) SEMs of GA and μ spirals respectively composed of 500 nm diameter gold nanoparticles on fused silica. (b), (e) Analytically calculated far field intensity from the spirals in (a), (d) at 633 nm. (c), (f) Experimentally measured far field radiation pattern from (a), (d), respectively, at 633 nm. White circles denote region where scattered light intensity is dominant.

Fig. 2.
Fig. 2.

(a) Optical set up used for the complex amplitude retrieval. (b), (c) Analytically calculated phase portrait of far field radiation from GA and μ spirals, respectively. (d), (e) Experimentally measured phase portrait from GA and μ spirals, respectively. Shaded area indicates region where scattered field intensity is too low to measure phase accurately. These regions are ignored during FHD.

Fig. 3.
Fig. 3.

(a), (c) FHD, summed over radial wavevector, for GA spirals and (b), (d) μ spirals. In (a), (b) FHD is obtained using analytically calculated far field, while in (c), (d) FHD is obtained using experimentally measured far field.

Tables (1)

Tables Icon

Table 1. Fourier–Hankel Decomposition Peaks

Equations (6)

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

rn=a0n,
θn=nα,
ρ(r,θ)=n=1N1rδ(rna0)δ(θnα).
E(νr,νθ)=E0n=1Nej2πna0νrcos(νθnα).
f(m,kr)=12π002πrdrdθE(r,θ)Jm(krr)eimθ,
f(m,kr)=n=1NAm(kr)einmα,

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