Abstract

Radially polarized focused beams have attracted a great deal of attention because of their unique properties characterized by the longitudinal field. Although this longitudinal field is strongly confined to the beam axis, the energy flow, i.e., the Poynting vector, has null intensity on the axis. Hence, the interaction of the focused beam and matter has thus far been unclear. We analyzed the interactions between the focused beam and a subwavelength metal block placed at the center of the focus using three-dimensional finite-difference time-domain (FDTD) calculation. We found that most of the Poynting energy propagates through to the far-field, and that a strong enhancement of the electric field appeared on the metal surface. This enhancement is attributed to the constructive interference of the symmetric electric field and the coupling to the surface plasmon mode.

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2010 (1)

2009 (2)

2007 (2)

2006 (2)

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature 441(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]

2005 (1)

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95(26), 267407 (2005).
[CrossRef] [PubMed]

2004 (4)

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239 (2004).
[CrossRef]

M. Yokoyama and S. Noda, “Finite-Difference Time-Domain Simulation of Two-Dimensional Photonic Crystal Surface-Emitting Laser Having a Square-Lattice Slab Structure,” IEICE Trans. Electron . 87-C, 386 (2004).

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. Express 12(8), 1562–1568 (2004).
[CrossRef] [PubMed]

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004).
[CrossRef] [PubMed]

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

2001 (2)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[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,” Science 293(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. 35, 347 (1993).

1990 (1)

1979 (1)

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

1972 (1)

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60(9), 1107–1109 (1972).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253(1274), 358–379 (1959).
[CrossRef]

Araki, T.

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[CrossRef] [PubMed]

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[CrossRef] [PubMed]

Chen, J.

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,” Science 293(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]

Ding, J.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

Fan, Y.-X.

Ford, D. H.

Hashimoto, M.

Hashimoto, N.

Hayazawa, N.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239 (2004).
[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. Express 12(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,” Science 293(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. 35, 347 (1993).

Jia, D.

Kato, J.

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95(26), 267407 (2005).
[CrossRef] [PubMed]

Kawata, S.

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95(26), 267407 (2005).
[CrossRef] [PubMed]

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239 (2004).
[CrossRef]

Kellali, S.

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

Kimura, W. D.

Kitamura, K.

Kozawa, Y.

Kunishi, W.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature 441(7096), 946 (2006).
[CrossRef] [PubMed]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

Matsumura, K.

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60(9), 1107–1109 (1972).
[CrossRef]

Miyai, E.

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature 441(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,” Science 293(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]

Mushiake, Y.

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60(9), 1107–1109 (1972).
[CrossRef]

Nakajima, N.

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60(9), 1107–1109 (1972).
[CrossRef]

Noda, S.

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. Express 18(5), 4518–4525 (2010).
[CrossRef] [PubMed]

K. Sakai and S. Noda, “Optical trapping of metal particles in doughnut-shaped beam emitted by photonic-crystal laser,” Electron. Lett. 43(2), 107 (2007).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature 441(7096), 946 (2006).
[CrossRef] [PubMed]

M. Yokoyama and S. Noda, “Finite-Difference Time-Domain Simulation of Two-Dimensional Photonic Crystal Surface-Emitting Laser Having a Square-Lattice Slab Structure,” IEICE Trans. Electron . 87-C, 386 (2004).

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. Express 12(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,” Science 293(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]

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[CrossRef] [PubMed]

Ohnishi, D.

Okano, T.

Ono, A.

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95(26), 267407 (2005).
[CrossRef] [PubMed]

Qin, J.-Q.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

Reineix, A.

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

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253(1274), 358–379 (1959).
[CrossRef]

Ryosuke, K.

Sahinöz, A.

Saito, Y.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239 (2004).
[CrossRef]

Sakai, K.

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. Express 18(5), 4518–4525 (2010).
[CrossRef] [PubMed]

K. Sakai and S. Noda, “Optical trapping of metal particles in doughnut-shaped beam emitted by photonic-crystal laser,” Electron. Lett. 43(2), 107 (2007).
[CrossRef]

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature 441(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.

Sendur, K.

Tidwell, S. C.

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 (1979).
[CrossRef]

Wang, H.-T.

Wang, X.-L.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253(1274), 358–379 (1959).
[CrossRef]

Yokoyama, M.

M. Yokoyama and S. Noda, “Finite-Difference Time-Domain Simulation of Two-Dimensional Photonic Crystal Surface-Emitting Laser Having a Square-Lattice Slab Structure,” IEICE Trans. Electron . 87-C, 386 (2004).

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,” Science 293(5532), 1123–1125 (2001).
[CrossRef] [PubMed]

Yonezawa, K.

Yoshiki, K.

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[CrossRef] [PubMed]

Zhan, Q.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85(25), 6239 (2004).
[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. (2)

K. Sakai and S. Noda, “Optical trapping of metal particles in doughnut-shaped beam emitted by photonic-crystal laser,” Electron. Lett. 43(2), 107 (2007).
[CrossRef]

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

IEEE Trans. (1)

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

IEICE Trans. Electron (1)

M. Yokoyama and S. Noda, “Finite-Difference Time-Domain Simulation of Two-Dimensional Photonic Crystal Surface-Emitting Laser Having a Square-Lattice Slab Structure,” IEICE Trans. Electron . 87-C, 386 (2004).

Nature (1)

E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Photonics: lasers producing tailored beams,” Nature 441(7096), 946 (2006).
[CrossRef] [PubMed]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. Lett. (3)

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95(26), 267407 (2005).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[CrossRef] [PubMed]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[CrossRef] [PubMed]

Proc. IEEE (1)

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60(9), 1107–1109 (1972).
[CrossRef]

Proc. Roy. Soc. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. A 253(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,” Science 293(5532), 1123–1125 (2001).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Calculation model of three-dimensional FDTD analysis.(a) 3D model, (b) x-z plane

Fig. 2
Fig. 2

Time-averaged distributions of the electric field intensity (Ei: i = total, x, y, z) and the Poynting vector (Sz) calculated by the FDTD method: (a) for a linearly (x) polarized Gaussian beam, and (b) for a radially polarized beam.

Fig. 3
Fig. 3

Total electric field intensity profiles when interacting with a gold block placed at the center of the focus (at x/λ = 0.0, y/λ = 0.0, z/λ = 0.0) calculated by the FDTD method: (a) and (c) for a linearly (x) polarized Gaussian beam and (b) and (d) for a radially polarized beam. Gold cubes half a wavelength on a side produce a significant difference in the intensity distribution between the two beams in (a) and (b). When the size of the gold block increased in the x and y direction, the transmitted energy decreased for both focused beams. The size of the block in the x and y direction is one wavelength in (c) and (d).

Fig. 4
Fig. 4

Time dependence of total electrical intensity profiles and electrical vectors interacting with a gold block at the focal spot (the center at x/λ = 0.0, y/λ = 0.0, z/λ = 0.0) by the FDTD method. (a) is for a linearly (x) polarized Gaussian beam and (b) is for a radially polarized beam.

Fig. 5
Fig. 5

Calculated total electrical intensity profiles interacted with half-wavelength-sized perfect conductivity at a focal spot (the center at x/λ = 0.0, y/λ = 0.0, z/λ = 0.0) by the FDTD method. (a) is the time-averaged intensity profile and (b) is the intensity profile and electrical vectors with time.

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