Abstract

We have successfully generated vector beams with higher-order polarization states using photonic-crystal lasers. We have analyzed and designed lattice structures that provide cavity modes with different symmetries. Fabricated devices based on these lattice structures produced doughnut-shaped vector beams, with symmetries corresponding to the cavity modes. Our study enables the systematic analysis of vector beams, which we expect will lead to applications such as high-resolution microscopy, laser processing, and optical trapping.

© 2011 OSA

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  1. K. Sakai and S. Noda, “Optical trapping of metal particles in doughnut-shaped beam emitted by photonic-crystal laser,” Electron. Lett. 43(2), 107–108 (2007).
    [CrossRef]
  2. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004).
    [CrossRef] [PubMed]
  3. Y. Kozawa and S. Sato, “Focusing property of a double-ring-shaped radially polarized beam,” Opt. Lett. 31(6), 820–822 (2006).
    [CrossRef] [PubMed]
  4. 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]
  5. H. F. Wang, L. P. Shi, B. Luk’yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
    [CrossRef]
  6. Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24(6), 1793–1798 (2007).
    [CrossRef]
  7. V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32(13), 1455–1461 (1999).
    [CrossRef]
  8. Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering phtonic-crystal lasers,” Nat. Photonics 4(7), 447–450 (2010).
    [CrossRef]
  9. S. C. Tidwell, G. H. Kim, and W. D. Kimura, “Efficient radially polarized laser beam generation with a double interferometer,” Appl. Opt. 32(27), 5222–5229 (1993).
    [CrossRef] [PubMed]
  10. R. Oron, S. Blit, N. Davidson, A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
    [CrossRef]
  11. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27(5), 285–287 (2002).
    [CrossRef]
  12. G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre-Gaussian beams,” Opt. Commun. 237(1–3), 89–95 (2004).
    [CrossRef]
  13. Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera, and S. Kawakami, “Cylindrical vector laser beam generated by the use of a photonic crystal mirror,” Appl. Phys. Express 1(2), 022008 (2008).
    [CrossRef]
  14. H. Kawauchi, Y. Kozawa, S. Sato, T. Sato, and S. Kawakami, “Simultaneous generation of helical beams with linear and radial polarization by use of a segmented half-wave plate,” Opt. Lett. 33(4), 399–401 (2008).
    [CrossRef] [PubMed]
  15. 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]
  16. 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), 316–318 (1999).
    [CrossRef]
  17. 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]
  18. 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]
  19. K. Sakai, E. Miyai, and S. Noda, “Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode,” Appl. Phys. Lett. 89(2), 021101 (2006).
    [CrossRef]
  20. M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express 13(8), 2869–2880 (2005).
    [CrossRef] [PubMed]
  21. W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupling coefficients for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. 11(11), 867–873 (1975).
    [CrossRef]

2010

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]

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering phtonic-crystal lasers,” Nat. Photonics 4(7), 447–450 (2010).
[CrossRef]

2008

H. F. Wang, L. P. Shi, B. Luk’yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[CrossRef]

Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera, and S. Kawakami, “Cylindrical vector laser beam generated by the use of a photonic crystal mirror,” Appl. Phys. Express 1(2), 022008 (2008).
[CrossRef]

H. Kawauchi, Y. Kozawa, S. Sato, T. Sato, and S. Kawakami, “Simultaneous generation of helical beams with linear and radial polarization by use of a segmented half-wave plate,” Opt. Lett. 33(4), 399–401 (2008).
[CrossRef] [PubMed]

2007

Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24(6), 1793–1798 (2007).
[CrossRef]

K. Sakai and S. Noda, “Optical trapping of metal particles in doughnut-shaped beam emitted by photonic-crystal laser,” Electron. Lett. 43(2), 107–108 (2007).
[CrossRef]

2006

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]

Y. Kozawa and S. Sato, “Focusing property of a double-ring-shaped radially polarized beam,” Opt. Lett. 31(6), 820–822 (2006).
[CrossRef] [PubMed]

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode,” Appl. Phys. Lett. 89(2), 021101 (2006).
[CrossRef]

2005

2004

2002

2001

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

R. Oron, S. Blit, N. Davidson, A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
[CrossRef]

1999

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), 316–318 (1999).
[CrossRef]

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32(13), 1455–1461 (1999).
[CrossRef]

1993

1975

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupling coefficients for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. 11(11), 867–873 (1975).
[CrossRef]

Biener, G.

Blit, S.

R. Oron, S. Blit, N. Davidson, A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
[CrossRef]

Bomzon, Z.

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27(5), 285–287 (2002).
[CrossRef]

R. Oron, S. Blit, N. Davidson, A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
[CrossRef]

Burnham, R. D.

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupling coefficients for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. 11(11), 867–873 (1975).
[CrossRef]

Chong, C. T.

H. F. Wang, L. P. Shi, B. Luk’yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(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,” 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), 316–318 (1999).
[CrossRef]

Davidson, N.

R. Oron, S. Blit, N. Davidson, A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
[CrossRef]

Friesem, A.

R. Oron, S. Blit, N. Davidson, A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
[CrossRef]

Hasman, E.

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27(5), 285–287 (2002).
[CrossRef]

R. Oron, S. Blit, N. Davidson, A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
[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), 316–318 (1999).
[CrossRef]

Inoue, Y.

Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera, and S. Kawakami, “Cylindrical vector laser beam generated by the use of a photonic crystal mirror,” Appl. Phys. Express 1(2), 022008 (2008).
[CrossRef]

Iwahashi, S.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering phtonic-crystal lasers,” Nat. Photonics 4(7), 447–450 (2010).
[CrossRef]

Kawakami, S.

Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera, and S. Kawakami, “Cylindrical vector laser beam generated by the use of a photonic crystal mirror,” Appl. Phys. Express 1(2), 022008 (2008).
[CrossRef]

H. Kawauchi, Y. Kozawa, S. Sato, T. Sato, and S. Kawakami, “Simultaneous generation of helical beams with linear and radial polarization by use of a segmented half-wave plate,” Opt. Lett. 33(4), 399–401 (2008).
[CrossRef] [PubMed]

Kawauchi, H.

Kim, G. H.

Kimura, W. D.

Kitamura, K.

Kleiner, V.

Kozawa, Y.

Kunishi, W.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering phtonic-crystal lasers,” Nat. Photonics 4(7), 447–450 (2010).
[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]

Kurosaka, Y.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering phtonic-crystal lasers,” Nat. Photonics 4(7), 447–450 (2010).
[CrossRef]

Liang, Y.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering phtonic-crystal lasers,” Nat. Photonics 4(7), 447–450 (2010).
[CrossRef]

Luk’yanchuk, B.

H. F. Wang, L. P. Shi, B. Luk’yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[CrossRef]

Miyai, E.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering phtonic-crystal lasers,” Nat. Photonics 4(7), 447–450 (2010).
[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]

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode,” Appl. Phys. Lett. 89(2), 021101 (2006).
[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), 316–318 (1999).
[CrossRef]

Nesterov, A. V.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32(13), 1455–1461 (1999).
[CrossRef]

Niziev, V. G.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32(13), 1455–1461 (1999).
[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]

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering phtonic-crystal lasers,” Nat. Photonics 4(7), 447–450 (2010).
[CrossRef]

K. Sakai and S. Noda, “Optical trapping of metal particles in doughnut-shaped beam emitted by photonic-crystal laser,” Electron. Lett. 43(2), 107–108 (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]

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode,” Appl. Phys. Lett. 89(2), 021101 (2006).
[CrossRef]

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express 13(8), 2869–2880 (2005).
[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), 1562–1568 (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), 316–318 (1999).
[CrossRef]

Ohnishi, D.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering phtonic-crystal lasers,” Nat. Photonics 4(7), 447–450 (2010).
[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), 1562–1568 (2004).
[CrossRef] [PubMed]

Ohtera, Y.

Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera, and S. Kawakami, “Cylindrical vector laser beam generated by the use of a photonic crystal mirror,” Appl. Phys. Express 1(2), 022008 (2008).
[CrossRef]

Okano, T.

Oron, R.

R. Oron, S. Blit, N. Davidson, A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
[CrossRef]

Petrov, D.

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre-Gaussian beams,” Opt. Commun. 237(1–3), 89–95 (2004).
[CrossRef]

Sakai, K.

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering phtonic-crystal lasers,” Nat. Photonics 4(7), 447–450 (2010).
[CrossRef]

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), 107–108 (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]

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode,” Appl. Phys. Lett. 89(2), 021101 (2006).
[CrossRef]

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), 316–318 (1999).
[CrossRef]

Sato, S.

Sato, T.

Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera, and S. Kawakami, “Cylindrical vector laser beam generated by the use of a photonic crystal mirror,” Appl. Phys. Express 1(2), 022008 (2008).
[CrossRef]

H. Kawauchi, Y. Kozawa, S. Sato, T. Sato, and S. Kawakami, “Simultaneous generation of helical beams with linear and radial polarization by use of a segmented half-wave plate,” Opt. Lett. 33(4), 399–401 (2008).
[CrossRef] [PubMed]

Scifres, D. R.

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupling coefficients for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. 11(11), 867–873 (1975).
[CrossRef]

Sheppard, C.

H. F. Wang, L. P. Shi, B. Luk’yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[CrossRef]

Shi, L. P.

H. F. Wang, L. P. Shi, B. Luk’yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[CrossRef]

Streifer, W.

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupling coefficients for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. 11(11), 867–873 (1975).
[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), 316–318 (1999).
[CrossRef]

Volpe, G.

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre-Gaussian beams,” Opt. Commun. 237(1–3), 89–95 (2004).
[CrossRef]

Wang, H. F.

H. F. Wang, L. P. Shi, B. Luk’yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[CrossRef]

Yokoyama, M.

M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express 13(8), 2869–2880 (2005).
[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]

Zhan, Q.

Appl. Opt.

Appl. Phys. Express

Y. Kozawa, S. Sato, T. Sato, Y. Inoue, Y. Ohtera, and S. Kawakami, “Cylindrical vector laser beam generated by the use of a photonic crystal mirror,” Appl. Phys. Express 1(2), 022008 (2008).
[CrossRef]

Appl. Phys. Lett.

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), 316–318 (1999).
[CrossRef]

K. Sakai, E. Miyai, and S. Noda, “Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode,” Appl. Phys. Lett. 89(2), 021101 (2006).
[CrossRef]

R. Oron, S. Blit, N. Davidson, A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000).
[CrossRef]

Electron. Lett.

K. Sakai and S. Noda, “Optical trapping of metal particles in doughnut-shaped beam emitted by photonic-crystal laser,” Electron. Lett. 43(2), 107–108 (2007).
[CrossRef]

IEEE J. Quantum Electron.

W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupling coefficients for distributed feedback single- and double-heterostructure diode lasers,” IEEE J. Quantum Electron. 11(11), 867–873 (1975).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. D

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32(13), 1455–1461 (1999).
[CrossRef]

Nat. Photonics

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering phtonic-crystal lasers,” Nat. Photonics 4(7), 447–450 (2010).
[CrossRef]

H. F. Wang, L. P. Shi, B. Luk’yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[CrossRef]

Nature

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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).
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Figures (7)

Fig. 1
Fig. 1

Schematic structure of photonic crystal laser.

Fig. 2
Fig. 2

Three types of photonic crystal structure considered in this paper. (a) Square lattice, where the lattice constant (a) is equal to the wavelength in the medium (λ d ). (b) Triangular lattice and (c) square lattice with larger lattice constant.

Fig. 3
Fig. 3

Reciprocal space representations of (a) square lattice with 4 fundamental waves at lowest-order Γ(2) points, (b) triangular lattice with 6 fundamental waves at lowest-order Γ(2) points, and (c) square lattice with 8 fundamental waves at higher-order Γ(5) points.

Fig. 4
Fig. 4

Photonic band structures corresponding to the lattice structures in Figs. 2(a)2(c). The enlarged band structure in the region enclosed by the red square is the band edge where Γ-point oscillation with the fundamental waves shown in Fig. 3 is produced. The mode numbers, denoted by superscripts, correspond to the number of fundamental waves. Corresponding electromagnetic field distributions of the unit cell in the PC plane are shown for the modes of lowest frequency, indicated by red arrows in the enlarged band diagrams. The color scale represents magnetic field and the black arrows indicate electric field. A white circle indicates the lattice hole of a PC.

Fig. 5
Fig. 5

Scanning electron microscope images of fabricated photonic crystals. (a) Square lattice with a = 296nm, (b) triangular lattice with a = 341nm, (c) square lattice with a = 660nm.

Fig. 6
Fig. 6

Beam patterns obtained from fabricated devices with the PC structures shown in Figs. 5(a)5(c). Yellow arrows indicate the electric field direction. For each device, the two panels on the right-hand side show the intensity pattern after passing through a polarizer. According to the multiple-lobe patterns, the polarization direction along the circumference of the doughnut beam rotates once for (a), twice for (b), and three times for (c).

Fig. 7
Fig. 7

Photonic band structures and electromagnetic field distributions of the TM mode for the PC structures shown in Figs. 2(a)2(c). In the electromagnetic field distributions, the color scale represents electric field and the black arrows indicate magnetic field.

Equations (4)

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2 π λ d = b = 4 π 3 a ,
2 π λ d = 5 b = 5 2 π a ,
a = 2 3 λ d ,
a = 5 λ d ,

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