Abstract

Single-transverse higher-order radially polarized beams with multiple rings are selectively generated from a Nd:YAG laser cavity by using a reflectivity-modified and polarization-selective photonic crystal mirror. As predicted by theoretical analysis [ A. A. Tovar, J. Opt. Soc. Am. A 15, 2705 (1998) ], the intensity distribution and propagation characteristics of the higher-order radially polarized beams are expressed by a Laguerre–Gaussian formula.

© 2010 Optical Society of America

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References

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  1. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1-7 (2000).
    [CrossRef]
  2. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1-57 (2009).
    [CrossRef]
  3. A. A. Tovar, “Production and propagation of cylindrically polarized Laguerre-Gaussian laser beams” J. Opt. Soc. Am. A 15, 2705-2711 (1998).
    [CrossRef]
  4. Y. Kozawa and S. Sato, “Focusing property of a double-ring-shaped radially polarized beam,” Opt. Lett. 31, 820-822 (2006).
    [CrossRef] [PubMed]
  5. Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A 24, 1793-1798 (2007).
    [CrossRef]
  6. H. Wang, L. Shi, B. Luk'yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nature Photon. 2, 501-505 (2008).
    [CrossRef]
  7. Y. Kozawa and S. Sato, “Single higher-order transverse mode operation of a radially polarized Nd:YAG laser using an annularly reflectivity-modulated photonic crystal coupler,” Opt. Lett. 33, 2278-2280 (2008).
    [CrossRef] [PubMed]
  8. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8189 (1992).
    [CrossRef] [PubMed]
  9. 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, 022008 (2008).
    [CrossRef]
  10. A. E. Siegman, Lasers (University Science Books, 1986).

2009 (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1-57 (2009).
[CrossRef]

2008 (3)

H. Wang, L. Shi, B. Luk'yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nature Photon. 2, 501-505 (2008).
[CrossRef]

Y. Kozawa and S. Sato, “Single higher-order transverse mode operation of a radially polarized Nd:YAG laser using an annularly reflectivity-modulated photonic crystal coupler,” Opt. Lett. 33, 2278-2280 (2008).
[CrossRef] [PubMed]

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, 022008 (2008).
[CrossRef]

2007 (1)

2006 (1)

2000 (1)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1-7 (2000).
[CrossRef]

1998 (1)

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Chong, C. T.

H. Wang, L. Shi, B. Luk'yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nature Photon. 2, 501-505 (2008).
[CrossRef]

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1-7 (2000).
[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, 022008 (2008).
[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, 022008 (2008).
[CrossRef]

Kozawa, Y.

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Luk'yanchuk, B.

H. Wang, L. Shi, B. Luk'yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nature Photon. 2, 501-505 (2008).
[CrossRef]

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, 022008 (2008).
[CrossRef]

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1-7 (2000).
[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, 022008 (2008).
[CrossRef]

Sheppard, C.

H. Wang, L. Shi, B. Luk'yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nature Photon. 2, 501-505 (2008).
[CrossRef]

Shi, L.

H. Wang, L. Shi, B. Luk'yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nature Photon. 2, 501-505 (2008).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Tovar, A. A.

Wang, H.

H. Wang, L. Shi, B. Luk'yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nature Photon. 2, 501-505 (2008).
[CrossRef]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Zhan, Q.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1-57 (2009).
[CrossRef]

Adv. Opt. Photonics (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1-57 (2009).
[CrossRef]

Appl. Phys. Express (1)

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, 022008 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nature Photon. (1)

H. Wang, L. Shi, B. Luk'yanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nature Photon. 2, 501-505 (2008).
[CrossRef]

Opt. Commun. (1)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8189 (1992).
[CrossRef] [PubMed]

Other (1)

A. E. Siegman, Lasers (University Science Books, 1986).

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Figures (5)

Fig. 1
Fig. 1

Intensity profiles of TM 0 n modes ( n = 1 , 2, 3, and 4) along the radial direction. The horizontal axis is in units of the Gaussian beam width w.

Fig. 2
Fig. 2

(a) Schematic of a substrate pattern for a reflectivity-modified PhCM. The units are micrometers. (b) Cavity configuration.

Fig. 3
Fig. 3

(a) Calculated Gaussian beam diameter 2 w at each element as a function of the distance d between the lens and the PhCM. (b) Node order of a TM 0 n mode that coincides with the annulus of the PhCM as a function of the distance d.

Fig. 4
Fig. 4

Measured intensity profiles along the horizontal axis across the center of the beam (dotted curve) with the result of the curve-fitting (solid curve) for generated (a) TM 02 , (b) TM 03 , (c) TM 04 , and (d) TM 05 mode beams.

Fig. 5
Fig. 5

Polarization distributions of the generated TM 03 [(a)–(d)] and TM 04 mode [(e)–(h)] beams. (a) and (e) Total intensity distributions. (b)–(d) and (f)–(h) Intensity patterns after passage through a linear polarizer. Each arrow indicates the polarizer’s axis.

Equations (1)

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E ( r , z ) = E 0 w 0 w ( 2 r w ) L n 1 1 ( 2 r 2 w 2 ) exp ( r 2 w 2 ) exp ( i k r 2 2 R i k z + i 2 n ψ ) ,

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