Abstract

We demonstrate the formation of a sub-wavelength focal spot with a long depth of focus using a radially polarized, narrow-width annular beam. Theoretical analysis predicts that a tighter focal spot (approximately 0.4λ) and longer depth of focus (more than 4λ) can be formed by a longitudinal electric field when the width of the annular part of the beam is decreased. Experimental measurements using a radially polarized beam from a photonic crystal laser agree well with these predictions. Tight focal spots with long depths of focus have great potential for use in high-tolerance, high-resolution applications in optical systems.

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  1. 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]
  2. K. Yoshiki, K. Ryosuke, M. Hashimoto, T. Araki, and N. Hashimoto, “Second-harmonic-generation microscope using eight-segment polarization-mode converter to observe three-dimensional molecular orientation,” Opt. Lett. 32(12), 1680–1682 (2007).
    [CrossRef] [PubMed]
  3. 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]
  4. M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
    [CrossRef]
  5. S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29(15), 2234 (1990).
    [CrossRef] [PubMed]
  6. 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]
  7. 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]
  8. G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, “Intense longitudinal electric fields generated from transverse electromagnetic waves,” Appl. Phys. Lett. 84(19), 3855 (2004).
    [CrossRef]
  9. S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81(5), 597–600 (2005).
    [CrossRef]
  10. 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]
  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. 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]
  13. 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 (2004).
    [CrossRef] [PubMed]
  14. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
    [CrossRef] [PubMed]
  15. 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. Photonics 1, 1 (2008).
  16. D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007).
    [CrossRef]
  17. 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]
  18. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London, Ser. A 253(1274), 358–379 (1959).
    [CrossRef]
  19. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
    [CrossRef] [PubMed]
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    [CrossRef]
  21. R. Dorn, S. Quabis, and G. Leuchs, “The focus of light−linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917 (2003).
  22. B. Hao and J. Leger, “Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam,” Opt. Express 15(6), 3550–3556 (2007).
    [CrossRef] [PubMed]
  23. M. Born, and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, New York, 1999), chap. 4.

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. Photonics 1, 1 (2008).

2007 (5)

D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007).
[CrossRef]

K. Yoshiki, K. Ryosuke, M. Hashimoto, T. Araki, and N. Hashimoto, “Second-harmonic-generation microscope using eight-segment polarization-mode converter to observe three-dimensional molecular orientation,” Opt. Lett. 32(12), 1680–1682 (2007).
[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]

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
[CrossRef]

B. Hao and J. Leger, “Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam,” Opt. Express 15(6), 3550–3556 (2007).
[CrossRef] [PubMed]

2006 (2)

2005 (1)

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81(5), 597–600 (2005).
[CrossRef]

2004 (3)

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, “Intense longitudinal electric fields generated from transverse electromagnetic waves,” Appl. Phys. Lett. 84(19), 3855 (2004).
[CrossRef]

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 (2004).
[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]

2003 (2)

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

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light−linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917 (2003).

2001 (2)

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]

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]

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]

1990 (1)

1987 (1)

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. R. Soc. London, Ser. 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]

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. Photonics 1, 1 (2008).

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]

Dorn, R.

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81(5), 597–600 (2005).
[CrossRef]

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

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light−linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917 (2003).

Durnin, J.

Feurer, T.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
[CrossRef]

Ford, D. H.

Gupta, D. N.

D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007).
[CrossRef]

Hao, B.

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 (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]

Kant, N.

D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007).
[CrossRef]

Kawata, S.

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]

Kim, D. E.

D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007).
[CrossRef]

Kimura, W. D.

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]

Leger, J.

Leuchs, G.

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81(5), 597–600 (2005).
[CrossRef]

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

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light−linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917 (2003).

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. Photonics 1, 1 (2008).

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]

Meier, M.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
[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]

Miyaji, G.

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, “Intense longitudinal electric fields generated from transverse electromagnetic waves,” Appl. Phys. Lett. 84(19), 3855 (2004).
[CrossRef]

Miyanaga, N.

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, “Intense longitudinal electric fields generated from transverse electromagnetic waves,” Appl. Phys. Lett. 84(19), 3855 (2004).
[CrossRef]

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. 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]

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 (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]

Ohbayashi, K.

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, “Intense longitudinal electric fields generated from transverse electromagnetic waves,” Appl. Phys. Lett. 84(19), 3855 (2004).
[CrossRef]

Ohnishi, D.

Okano, T.

Quabis, S.

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81(5), 597–600 (2005).
[CrossRef]

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

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light−linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917 (2003).

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. London, Ser. A 253(1274), 358–379 (1959).
[CrossRef]

Romano, V.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
[CrossRef]

Ryosuke, K.

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. 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.

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. Photonics 1, 1 (2008).

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. Photonics 1, 1 (2008).

Sueda, K.

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, “Intense longitudinal electric fields generated from transverse electromagnetic waves,” Appl. Phys. Lett. 84(19), 3855 (2004).
[CrossRef]

Suk, H.

D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007).
[CrossRef]

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]

Tsubakimoto, K.

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, “Intense longitudinal electric fields generated from transverse electromagnetic waves,” Appl. Phys. Lett. 84(19), 3855 (2004).
[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. Photonics 1, 1 (2008).

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. London, Ser. A 253(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,” 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]

Appl. Opt. (1)

Appl. Phys. B (1)

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81(5), 597–600 (2005).
[CrossRef]

Appl. Phys. Lett. (3)

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]

G. Miyaji, N. Miyanaga, K. Tsubakimoto, K. Sueda, and K. Ohbayashi, “Intense longitudinal electric fields generated from transverse electromagnetic waves,” Appl. Phys. Lett. 84(19), 3855 (2004).
[CrossRef]

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]

Appl. Phys., A Mater. Sci. Process. (1)

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007).
[CrossRef]

Electron. Lett. (1)

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. Mod. Opt. (1)

R. Dorn, S. Quabis, and G. Leuchs, “The focus of light−linear polarization breaks the rotational symmetry of the focal spot,” J. Mod. Opt. 50, 1917 (2003).

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

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. Photonics 1, 1 (2008).

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 (3)

Opt. Lett. (2)

Phys. Lett. A (1)

D. N. Gupta, N. Kant, D. E. Kim, and H. Suk, “Electron acceleration to GeV energy by a radially polarized laser,” Phys. Lett. A 368(5), 402–407 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

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. R. Soc. London, Ser. 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. London, Ser. 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]

Other (1)

M. Born, and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, New York, 1999), chap. 4.

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic sketch of the focusing of a radially polarized beam with δ=0.0. The red and blue arrows indicate the longitudinal and radial electric fields, respectively. (b) Cross-sectional intensity profiles of the electric field components at the focus. The sum of the radial (blue line) and longitudinal (red line) components gives the total intensity profile (black line).

Fig. 2
Fig. 2

(a) Schematic sketch of the focusing of a radially polarized, narrow-width annular beam with δ=0.8. (b) Cross-sectional intensity profiles of the electric field components at the focus. The central peak of the total intensity (black line) is dominated by the longitudinal component (red line); the contribution of the radial component (blue line) has been decreased.

Fig. 3
Fig. 3

Intensity profiles of the electric fields through the focus (a) for δ=0.0 (the original doughnut beam) and (b) for δ=0.8 (a narrow-width annular beam). A long, sharp focal spot is formed for δ=0.8. The cross-sectional intensity profiles for δ=0.8 show that the longitudinal component (red line) dominates the total intensity (black line), with a much smaller contribution from the radial component (blue line). The focal plane lies at z/λ=0.0. (c) Focal spot size and depth of focus as a function of the ratio of inner and outer focusing angles δ.

Fig. 4
Fig. 4

Schematic sketch of the interference of optical rays near the focal point. The blue and red arrows indicate rays originating from the outermost and innermost parts of the input beam, respectively. The dotted lines indicate the wave fronts of these rays. For the original beam (a), the rays are only in phase at the focal plane (z=0), whereas for the narrow-width annular beam (b), the rays are in phase on the beam axis even away from the focal plane.

Fig. 5
Fig. 5

(a) Cross-sectional structure of the detector. We used the edge of a metallic (Ti/Au) film of thickness 200 nm on top of a GaAs-based photo-diode as a knife-edge. The distance between the top of the detection area and the depletion (photo-absorption) layer was 200 nm. (b) Top view of the fabricated detector. The detection area was formed next to the knife-edge; the rest of the surface was covered by an insulator. (c) Experimental set-up. The beam emitted by the photonic-crystal laser was focused by an objective lens with 0.9 NA. The detector was placed at the focal plane and scanned using a high-resolution xyz stage. The cross-sectional beam profile was modified by placing a shading mask just before the objective lens. (d) In order to obtain the two-dimensional profile, several scans at different angles (ψ) are required.

Fig. 6
Fig. 6

Normalized cross-sectional intensity profiles at the focal plane (z=0) and its vicinity. (a) Intensity profiles for the original beam (δ=0.0) show significant changes from a single peak to a double peak for a deviation of ±1 μm from the focal plane. The intensity profile at z=2 μm could not be measured due to the small signal intensity. (b) Intensity profiles for the narrower-width annular beam (δ=0.8), show a central peak for all observation planes from −2 μm to 2 μm.

Equations (4)

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e = [ e ρ e ϕ e z ] = [ A 0 α cos 1 2 θ sin ( 2 θ ) l 0 ( θ ) J 1 ( k ρ sin θ ) e i k z cos θ d θ 0 2 i A 0 α cos 1 2 θ sin 2 θ l 0 ( θ ) J 0 ( k ρ sin θ ) e i k z cos θ d θ ] .
l 0 ( θ ) = exp [ β 0 2 ( sin θ sin α ) 2 ] J 1 ( 2 β 0 sin θ sin α ) .
l ( θ ) = T ( θ )     l 0 ( θ ) ,
T ( θ ) = { 0 ( 0 θ δ α ) 1 ( δ α < θ α ) .

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