Abstract

A radially polarized beam possesses peculiar focusing properties compared with a linearly polarized beam, for example, the generation of a strong longitudinal field and zero intensity of the Poynting vector on the beam axis. In order to exploit these focusing properties, here we consider a system in which gold metal cubes are arranged along the propagation direction of the beam. An electric field enhancement of more than 20-times can be generated between two gold cubes separated by a distance λ/10 on the optical axis. This is because the energy of a radially polarized beam can propagate even if a metal cube is located on the beam axis, and a longitudinal field generated between the cubes can induce a surface plasmon mode. We show that these results are peculiar properties that cannot be produced with an incident linearly polarized beam. We also show that the beam can generate multiple regions of electrical field enhancement in the propagating direction when multiple metal cubes are arranged on the beam axis.

© 2013 Optical Society of America

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References

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  1. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express7(2), 77–87 (2000).
    [CrossRef] [PubMed]
  2. K. Kitamura, K. Sakai, and S. Noda, “Sub-wavelength focal spot with long depth of focus generated by radially polarized, narrow-width annular beam,” Opt. Express18(5), 4518–4525 (2010).
    [CrossRef] [PubMed]
  3. H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
    [CrossRef]
  4. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express12(15), 3377–3382 (2004).
    [CrossRef] [PubMed]
  5. K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett.31(14), 2151–2153 (2006).
    [CrossRef] [PubMed]
  6. D. N. Schimpf, W. P. Putnam, M. D. Grogan, S. Ramachandran, and F. X. Kartner, “Radially polarized Bessel-Gauss beams in ABCD optical systems and fiber-based generation,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2013), paper JTh2A.67.
    [CrossRef]
  7. K. Kitamura, M. Nishimoto, K. Sakai, and S. Noda, “Needle-like focus generation by radially polarized halo beams emitted by photonic-crystal ring-cavity laser,” Appl. Phys. Lett.101(22), 221103 (2012).
    [CrossRef]
  8. E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
    [CrossRef] [PubMed]
  9. D. Ohnishi, T. Okano, M. Imada, and S. Noda, “Room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser,” Opt. Express12(8), 1562–1568 (2004).
    [CrossRef] [PubMed]
  10. S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science293(5532), 1123–1125 (2001).
    [CrossRef] [PubMed]
  11. M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett.75(3), 316 (1999).
    [CrossRef]
  12. K. Kitamura, K. Sakai, and S. Noda, “Finite-difference time-domain (FDTD) analysis on the interaction between a metal block and a radially polarized focused beam,” Opt. Express19(15), 13750–13756 (2011).
    [CrossRef] [PubMed]
  13. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A253(1274), 358–379 (1959).
    [CrossRef]
  14. H. Landolt and R. Börnstein, Landolt-Börnstein-Tabellenwerk Zahlenwerte und Funktionen aus Physik, Chemie, Astronomie, Geophysik und Technik, 6th ed. (Springer, 1962), Chap. 28.
  15. J. R. Wait, “Exact surface impedance for a cylindrical conductor,” Electron. Lett.15(20), 659–660 (1979).
    [CrossRef]
  16. S. Kellali, B. Jecko, and A. Reineix, “Implementation of a surface impedance formalism at oblique incidence in FDTD method,” IEEE Trans. Electromagn. Compat.35, 347–356 (1993).

2012 (1)

K. Kitamura, M. Nishimoto, K. Sakai, and S. Noda, “Needle-like focus generation by radially polarized halo beams emitted by photonic-crystal ring-cavity laser,” Appl. Phys. Lett.101(22), 221103 (2012).
[CrossRef]

2011 (1)

2010 (1)

2008 (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

2006 (2)

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[CrossRef] [PubMed]

K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett.31(14), 2151–2153 (2006).
[CrossRef] [PubMed]

2004 (2)

2001 (1)

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science293(5532), 1123–1125 (2001).
[CrossRef] [PubMed]

2000 (1)

1999 (1)

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett.75(3), 316 (1999).
[CrossRef]

1993 (1)

S. Kellali, B. Jecko, and A. Reineix, “Implementation of a surface impedance formalism at oblique incidence in FDTD method,” IEEE Trans. Electromagn. Compat.35, 347–356 (1993).

1979 (1)

J. R. Wait, “Exact surface impedance for a cylindrical conductor,” Electron. Lett.15(20), 659–660 (1979).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A253(1274), 358–379 (1959).
[CrossRef]

Brown, T. G.

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Chutinan, A.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science293(5532), 1123–1125 (2001).
[CrossRef] [PubMed]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett.75(3), 316 (1999).
[CrossRef]

Imada, M.

D. Ohnishi, T. Okano, M. Imada, and S. Noda, “Room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser,” Opt. Express12(8), 1562–1568 (2004).
[CrossRef] [PubMed]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science293(5532), 1123–1125 (2001).
[CrossRef] [PubMed]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett.75(3), 316 (1999).
[CrossRef]

Jecko, B.

S. Kellali, B. Jecko, and A. Reineix, “Implementation of a surface impedance formalism at oblique incidence in FDTD method,” IEEE Trans. Electromagn. Compat.35, 347–356 (1993).

Kellali, S.

S. Kellali, B. Jecko, and A. Reineix, “Implementation of a surface impedance formalism at oblique incidence in FDTD method,” IEEE Trans. Electromagn. Compat.35, 347–356 (1993).

Kitamura, K.

Kozawa, Y.

Kunishi, W.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[CrossRef] [PubMed]

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Miyai, E.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[CrossRef] [PubMed]

Mochizuki, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science293(5532), 1123–1125 (2001).
[CrossRef] [PubMed]

Murata, M.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett.75(3), 316 (1999).
[CrossRef]

Nishimoto, M.

K. Kitamura, M. Nishimoto, K. Sakai, and S. Noda, “Needle-like focus generation by radially polarized halo beams emitted by photonic-crystal ring-cavity laser,” Appl. Phys. Lett.101(22), 221103 (2012).
[CrossRef]

Noda, S.

K. Kitamura, M. Nishimoto, K. Sakai, and S. Noda, “Needle-like focus generation by radially polarized halo beams emitted by photonic-crystal ring-cavity laser,” Appl. Phys. Lett.101(22), 221103 (2012).
[CrossRef]

K. Kitamura, K. Sakai, and S. Noda, “Finite-difference time-domain (FDTD) analysis on the interaction between a metal block and a radially polarized focused beam,” Opt. Express19(15), 13750–13756 (2011).
[CrossRef] [PubMed]

K. Kitamura, K. Sakai, and S. Noda, “Sub-wavelength focal spot with long depth of focus generated by radially polarized, narrow-width annular beam,” Opt. Express18(5), 4518–4525 (2010).
[CrossRef] [PubMed]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[CrossRef] [PubMed]

D. Ohnishi, T. Okano, M. Imada, and S. Noda, “Room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser,” Opt. Express12(8), 1562–1568 (2004).
[CrossRef] [PubMed]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science293(5532), 1123–1125 (2001).
[CrossRef] [PubMed]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett.75(3), 316 (1999).
[CrossRef]

Ohnishi, D.

Okano, T.

Reineix, A.

S. Kellali, B. Jecko, and A. Reineix, “Implementation of a surface impedance formalism at oblique incidence in FDTD method,” IEEE Trans. Electromagn. Compat.35, 347–356 (1993).

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A253(1274), 358–379 (1959).
[CrossRef]

Sakai, K.

K. Kitamura, M. Nishimoto, K. Sakai, and S. Noda, “Needle-like focus generation by radially polarized halo beams emitted by photonic-crystal ring-cavity laser,” Appl. Phys. Lett.101(22), 221103 (2012).
[CrossRef]

K. Kitamura, K. Sakai, and S. Noda, “Finite-difference time-domain (FDTD) analysis on the interaction between a metal block and a radially polarized focused beam,” Opt. Express19(15), 13750–13756 (2011).
[CrossRef] [PubMed]

K. Kitamura, K. Sakai, and S. Noda, “Sub-wavelength focal spot with long depth of focus generated by radially polarized, narrow-width annular beam,” Opt. Express18(5), 4518–4525 (2010).
[CrossRef] [PubMed]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[CrossRef] [PubMed]

Sasaki, G.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett.75(3), 316 (1999).
[CrossRef]

Sato, S.

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Tokuda, T.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett.75(3), 316 (1999).
[CrossRef]

Wait, J. R.

J. R. Wait, “Exact surface impedance for a cylindrical conductor,” Electron. Lett.15(20), 659–660 (1979).
[CrossRef]

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A253(1274), 358–379 (1959).
[CrossRef]

Yokoyama, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science293(5532), 1123–1125 (2001).
[CrossRef] [PubMed]

Yonezawa, K.

Youngworth, K. S.

Zhan, Q.

Appl. Phys. Lett. (2)

K. Kitamura, M. Nishimoto, K. Sakai, and S. Noda, “Needle-like focus generation by radially polarized halo beams emitted by photonic-crystal ring-cavity laser,” Appl. Phys. Lett.101(22), 221103 (2012).
[CrossRef]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett.75(3), 316 (1999).
[CrossRef]

Electron. Lett. (1)

J. R. Wait, “Exact surface impedance for a cylindrical conductor,” Electron. Lett.15(20), 659–660 (1979).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

S. Kellali, B. Jecko, and A. Reineix, “Implementation of a surface impedance formalism at oblique incidence in FDTD method,” IEEE Trans. Electromagn. Compat.35, 347–356 (1993).

Nat. Photonics (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Nature (1)

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature441(7096), 946 (2006).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (1)

Proc. R. Soc. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. A253(1274), 358–379 (1959).
[CrossRef]

Science (1)

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science293(5532), 1123–1125 (2001).
[CrossRef] [PubMed]

Other (2)

D. N. Schimpf, W. P. Putnam, M. D. Grogan, S. Ramachandran, and F. X. Kartner, “Radially polarized Bessel-Gauss beams in ABCD optical systems and fiber-based generation,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2013), paper JTh2A.67.
[CrossRef]

H. Landolt and R. Börnstein, Landolt-Börnstein-Tabellenwerk Zahlenwerte und Funktionen aus Physik, Chemie, Astronomie, Geophysik und Technik, 6th ed. (Springer, 1962), Chap. 28.

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Figures (5)

Fig. 1
Fig. 1

Calculation model for three-dimensional FDTD analysis. (a) 3D model; (b) time-averaged distributions of the electric field intensity (Ei: i = total, x, z) and the Poynting vector (Sz) calculated by the FDTD method for a focused radially polarized beam.

Fig. 2
Fig. 2

Maximum electric-field intensity as a function of the separation (d) between the gold cubes. The intensity is normalized with respect to the maximum intensity of the focused beam in free space.

Fig. 3
Fig. 3

Calculated intensity profiles of total electrical field interacting with two half-wavelength sized gold cubes. The time-averaged intensity profiles of a linearly polarized beam (a) and a radially polarized beam (b) with a cube separation d/λ = 0.1. Inset images are normalized with respect to the maximum intensity in free space. The intensity profiles and electric field vector of a linearly polarized beam (c) and a radially polarized beam (d) with a cube separation d/λ = 0.1. The intensity profile and electric field vectors of a radially polarized beam with a cube separation d/λ = 0.5 (e). The intensity profile and Poynting vector of a radially polarized beam (f).

Fig. 4
Fig. 4

Calculated electric fields excited by x-polarized plane wave. Two perfect conductors are placed a separation of 0.6λ (a) and 0.1λ (b).

Fig. 5
Fig. 5

The time-averaged intensity profiles of a radially polarized beam with a cube separation d/λ = 0.1. The intensity is normalized with respect to the maximum intensity in free space. Two (a), three (b), four (c), five (d), and six (e) gold cubes were arranged.

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