Abstract

We consider the focusing performance of a radially polarized sinh-Gaussian beam. The sinh-Gaussian beam can be considered as superposition of a series of eccentric Gaussian beam. Based on the Richards-Wolf formulas, high beam quality and subwavelength focusing are achieved for the radially polarized incident sinh-Gaussian beam. Therefore, sinh-Gaussian beam can be applied in the focusing system with high numerical aperture to achieve focusing with superresolution.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt.43, 4322–4327 (2004).
    [CrossRef] [PubMed]
  2. T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun.272, 314–319 (2007).
    [CrossRef]
  3. V. V. Kotlyar, S. S. Stafeev, L. O’Faolain, and V. A. Soifer, “Tight focusing with a binary microaxicon,” Opt. Lett.36, 3100–3102 (2011).
    [CrossRef] [PubMed]
  4. X. P. Li, Y. Y. Cao, and M. Gu, “Superresolution-focal-volume induced 3.0 Tbytes/disk capacity by focusing a radially polarized beam,” Opt. Lett.36, 2510–2512 (2011).
    [CrossRef] [PubMed]
  5. M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett.22, 1905–1907 (1997).
    [CrossRef]
  6. H. Wang, L. Shi, B. Luḱyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2, 501–505 (2008).
    [CrossRef]
  7. Y. J. Zhang and J. P. Bai, “Improving the recording ability of a near-field optical storage system by higher-order radially polarized beams,” Opt. Express17, 3698–3706 (2009).
    [CrossRef] [PubMed]
  8. K. G. Makris and D. Psaltis, “Superoscillatory diffraction-free beams,” Opt. Lett.36, 4335–4337 (2011).
    [CrossRef] [PubMed]
  9. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical vector beams,” Opt. Express7, 77–87 (2000).
    [CrossRef] [PubMed]
  10. L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun.191, 161–172 (2001).
    [CrossRef]
  11. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91, 233901 (2003).
    [CrossRef] [PubMed]
  12. G. M. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express16, 4567–4581 (2008).
    [CrossRef] [PubMed]
  13. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon.1, 1–57 (2009).
    [CrossRef]
  14. Q.F. Tan, K. Cheng, Z.H. Zhou, and G.F. Jin, “Diffractive superresolution elements for radially polarized light,” J. Opt. Soc. Am. A27, 1355–1360 (2010).
    [CrossRef]
  15. Y. Kozawa and S. Sato, “Sharper focal spot formed by higher-order radially polarized laser beams,” J. Opt. Soc. Am. A24, 1793–1798 (2007).
    [CrossRef]
  16. S. Vyas, M. Niwa, Y. Kozawa, and S. Sato, “Diffractive properties of obstructed vector Laguerre-Gaussian beam under tight focusing condition,” J. Opt. Soc. Am. A28, 1387–1394 (2011).
    [CrossRef]
  17. Y. Kozawa and S. Sato, “Focusing of higher-order radially polarized Laguerre-Gaussian beam,” J. Opt. Soc. Am. A29, 2439–2443 (2012).
    [CrossRef]
  18. K. Huang, P. Shi, G. W. Cao, X. Ke Li, B. Zhang, and Y. P. Li, “Vector-vortex Bessel-Gauss beams and their tightly focusing properties,” Opt. Lett.36, 888–890 (2011).
    [CrossRef] [PubMed]
  19. Q.G. Sun, K.Y. Zhou, G.Y. Fang, G.Q. Zhang, Z.J. Liu, and S.T. Liu, “Hollow sinh-Gaussian beams and their paraxial properties,” Opt. Express20, 9682–9691 (2012).
    [CrossRef] [PubMed]
  20. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. structure of the image field in an aplanatic system,” Proc. R. Soc. A253, 358–379 (1959).
    [CrossRef]
  21. 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, 4518–4525 (2010).
    [CrossRef] [PubMed]

2012

2011

2010

2009

2008

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

G. M. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express16, 4567–4581 (2008).
[CrossRef] [PubMed]

2007

2004

2003

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

2001

L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun.191, 161–172 (2001).
[CrossRef]

2000

1997

1959

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

Bai, J. P.

Brown, T. G.

Cao, G. W.

Cao, Y. Y.

Cheng, K.

Chong, C. T.

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

Choudhury, A.

Courjon, D.

T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun.272, 314–319 (2007).
[CrossRef]

Dorn, R.

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

Fang, G.Y.

Grosjean, T.

T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun.272, 314–319 (2007).
[CrossRef]

Gu, M.

Helseth, L. E.

L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun.191, 161–172 (2001).
[CrossRef]

Huang, K.

Jin, G.F.

Juskaitis, R.

Ke Li, X.

Kitamura, K.

Kotlyar, V. V.

Kozawa, Y.

Lerman, G. M.

Leuchs, G.

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

Levy, U.

Li, X. P.

Li, Y. P.

Liu, S.T.

Liu, Z.J.

Luk´yanchuk, B.

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

Makris, K. G.

Neil, M. A. A.

Niwa, M.

Noda, S.

O’Faolain, L.

Psaltis, D.

Quabis, S.

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

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, 358–379 (1959).
[CrossRef]

Sakai, K.

Sato, S.

Sheppard, C.

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

Sheppard, C. J. R.

Shi, L.

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

Shi, P.

Soifer, V. A.

Stafeev, S. S.

Sun, Q.G.

Tan, Q.F.

Vyas, S.

Wang, H.

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

Wilson, T.

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, 358–379 (1959).
[CrossRef]

Youngworth, K. S.

Zhan, Q.

Zhang, B.

Zhang, G.Q.

Zhang, Y. J.

Zhou, K.Y.

Zhou, Z.H.

Adv. Opt. Photon.

Appl. Opt.

J. Opt. Soc. Am. A

Nat. Photonics

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

Opt. Commun.

L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun.191, 161–172 (2001).
[CrossRef]

T. Grosjean and D. Courjon, “Smallest focal spots,” Opt. Commun.272, 314–319 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

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

Proc. R. Soc. A

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Normalized radial electric field distribution at z = 0 for different value of parameter ω0 and m. (a) for ω = 0.25 and (b) for m = 4.

Fig. 2
Fig. 2

Focusing performance of radially polarized sinh-Gaussian beam E m ω 0 with (ω0, m) focused by lens with NA = 0.95. (a1)–(a4) for (0.125, 4), (b1)–(b4) for (0.25, 4) and (c1)–(c4) for (0.25, 8), respectively. (a1), (b1) and (c1) are the density distribution on the focal plane z = 0. The red, green and black curve represents the radial component, longitudinal component and the total electric energy density, respectively. (a2)–(a4), (b2)–(b4), (c2)–(c4), contour of the electrical energy density distribution on the rz plane. Where, (a2), (b2) and (c2) represent the distribution of the radial field component. (a3), (b3) and (c3) represent the distribution of the longitudinal field component. (a4), (b4) and (c4) represent the distribution of the total field component.

Fig. 3
Fig. 3

The density distribution on the focal plane z = 0 for three different radial polarized incident beam. (a) for first order Bessel beam J1, (b) for Bessel-Gaussian beam and (c) for Gaussian beam, respectively.

Tables (1)

Tables Icon

Table 1 Focusing performance of sinh-Gaussian beam with different parameters focused by lens with NA=0.95

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

E m ω 0 ( θ ) = sinh m ( sin θ ω 0 ) exp ( sin 2 θ ω 0 2 ) ,
E r ( r , z ) = A 0 α cos 1 / 2 θ sin ( 2 θ ) E m ( θ ) J 1 ( k r sin θ ) exp ( i k z cos θ ) d θ ,
E z ( r , z ) = 2 i A 0 α cos 1 / 2 θ sin 2 θ E m ( θ ) J 0 ( k r sin θ ) exp ( i k z cos θ ) d θ .

Metrics