Abstract

An optimization method for diffractive superresolution elements (DSEs) for radially polarized light is proposed. Only the longitudinal component of the focused field of radially polarized light is considered for optimization, and the results are 0, π two-phase distributed DSEs. A series of such DSEs are designed, and the corresponding superresolution performances are calculated with both longitudinal and transverse components of the focused field of radially polarized light. Simulation results show that good superresolution performance can be obtained by the optimization method considering only the longitudinal component of the focused field of radially polarized light. Simulation results also show that such DSEs realize better superresolution performance with radially polarized light than with linearly polarized light.

© 2010 Optical Society of America

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. J. Kim, D. C. Kim, and S. H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Tech. 72, 441–446 (2009).
    [Crossref] [PubMed]
  3. N. M. Mojarad and M. Agio, “Tailoring the excitation of localized surface plasmon-polariton resonances by focusing radially-polarized beams,” Opt. Express 17, 117–122 (2009).
    [Crossref] [PubMed]
  4. 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. Express 17, 3698–3706 (2009).
    [Crossref] [PubMed]
  5. Y. I. Salamin, “Acceleration in vacuum of bare nuclei by tightly focused radially polarized laser light,” Opt. Lett. 32, 3462–3464 (2007).
    [Crossref] [PubMed]
  6. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87 (2000).
    [Crossref] [PubMed]
  7. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901/1–4 (2003).
    [Crossref]
  8. Y. Kozawa and S. Sato, “Focusing property of a double-ring-shaped radially polarized beam,” Opt. Lett. 31, 820–822 (2006).
    [Crossref] [PubMed]
  9. M. T. Caballero, C. Ibanez-Lopez, and M. Martinez-Corral, “Shaded-mask filtering: novel strategy for improvement of resolution in radial-polarization scanning microscopy,” Opt. Eng. 45, 098003 (2006).
    [Crossref]
  10. H. F. Wang, L. P. Shi, B. Luκyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
    [Crossref]
  11. Y. Yoon, W. Kim, N. Park, K. Park, and Y. Park, “Feasibility study of the application of radially polarized illumination to solid immersion lens-based near-field optics,” Opt. Lett. 34, 1961–1963 (2009).
    [Crossref] [PubMed]
  12. Y. Zhao, Q. Zhan, Y. Zhang, and Y. Li, “Creation of a three-dimensional optical chain for controllable particle delivery,” Opt. Lett. 30, 848–850 (2005).
    [Crossref] [PubMed]
  13. I. J. Cox, C. J. R. Sheppard, and T. Wilson, “Reappraisal of arrays of concentric annuli as super-resolving filters,” J. Opt. Soc. Am. 72, 1287–1291 (1982).
    [Crossref]
  14. M. Martinez-Corral, M. T. Caballero, E. H. K. Stelzer, and J. Swoger, “Tailoring the axial shape of the point spread function using the Toraldo concept,” Opt. Express 10, 98–103 (2002).
    [PubMed]
  15. J. K. Strayer, Linear Programming and Its Applications (Springer-Verlag, 1989), Chap. 2.
    [Crossref]
  16. H. Liu, Y. Yan, Q. Tan, and G. Jin, “Theories for the design of diffractive superresolution elements and limits of optical superresolution,” J. Opt. Soc. Am. A 19, 2185–2193 (2002).
    [Crossref]
  17. H. Liu, Y. Yan, D. Yi, and G. Jin, “Theories for the design of a hybrid refractive-diffractive superresolution lens with high numerical aperture,” J. Opt. Soc. Am. A 20, 913–924 (2003).
    [Crossref]
  18. H. Liu, Y. Yan, and G. Jin, “Design theories and performance limits of diffractive superresolution elements with the highest sidelobe suppressed,” J. Opt. Soc. Am. A 22, 828–838 (2005).
    [Crossref]
  19. G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1)* LG beam,” Opt. Commun. 271, 190–196 (2007).
    [Crossref]
  20. R. H. Jordan and D. G. Hall, “Free-space azimuthal paraxial wave equation: the azimuthal Bessel-Gauss beam solution.” Opt. Lett. 19, 427–429 (1994).
    [Crossref] [PubMed]
  21. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London 253, 358–379 (1959).
    [Crossref]

2009 (4)

2008 (1)

H. F. Wang, L. P. Shi, B. Luκyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[Crossref]

2007 (2)

Y. I. Salamin, “Acceleration in vacuum of bare nuclei by tightly focused radially polarized laser light,” Opt. Lett. 32, 3462–3464 (2007).
[Crossref] [PubMed]

G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1)* LG beam,” Opt. Commun. 271, 190–196 (2007).
[Crossref]

2006 (2)

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

M. T. Caballero, C. Ibanez-Lopez, and M. Martinez-Corral, “Shaded-mask filtering: novel strategy for improvement of resolution in radial-polarization scanning microscopy,” Opt. Eng. 45, 098003 (2006).
[Crossref]

2005 (2)

2004 (1)

2003 (2)

2002 (2)

2000 (1)

1994 (1)

1989 (1)

J. K. Strayer, Linear Programming and Its Applications (Springer-Verlag, 1989), Chap. 2.
[Crossref]

1982 (1)

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 253, 358–379 (1959).
[Crossref]

Agio, M.

Back, S. H.

J. Kim, D. C. Kim, and S. H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Tech. 72, 441–446 (2009).
[Crossref] [PubMed]

Bai, J. P.

Brown, T. G.

Caballero, M. T.

M. T. Caballero, C. Ibanez-Lopez, and M. Martinez-Corral, “Shaded-mask filtering: novel strategy for improvement of resolution in radial-polarization scanning microscopy,” Opt. Eng. 45, 098003 (2006).
[Crossref]

M. Martinez-Corral, M. T. Caballero, E. H. K. Stelzer, and J. Swoger, “Tailoring the axial shape of the point spread function using the Toraldo concept,” Opt. Express 10, 98–103 (2002).
[PubMed]

Chong, C. T.

H. F. Wang, L. P. Shi, B. Luκyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[Crossref]

Choudhury, A.

Cox, I. J.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901/1–4 (2003).
[Crossref]

Hall, D. G.

Ibanez-Lopez, C.

M. T. Caballero, C. Ibanez-Lopez, and M. Martinez-Corral, “Shaded-mask filtering: novel strategy for improvement of resolution in radial-polarization scanning microscopy,” Opt. Eng. 45, 098003 (2006).
[Crossref]

Jackel, S.

G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1)* LG beam,” Opt. Commun. 271, 190–196 (2007).
[Crossref]

Jin, G.

Jordan, R. H.

Kim, D. C.

J. Kim, D. C. Kim, and S. H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Tech. 72, 441–446 (2009).
[Crossref] [PubMed]

Kim, J.

J. Kim, D. C. Kim, and S. H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Tech. 72, 441–446 (2009).
[Crossref] [PubMed]

Kim, W.

Kozawa, Y.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901/1–4 (2003).
[Crossref]

Li, Y.

Liu, H.

Lu?yanchuk, B.

H. F. Wang, L. P. Shi, B. Luκyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[Crossref]

Lumer, Y.

G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1)* LG beam,” Opt. Commun. 271, 190–196 (2007).
[Crossref]

Machavariani, G.

G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1)* LG beam,” Opt. Commun. 271, 190–196 (2007).
[Crossref]

Martinez-Corral, M.

M. T. Caballero, C. Ibanez-Lopez, and M. Martinez-Corral, “Shaded-mask filtering: novel strategy for improvement of resolution in radial-polarization scanning microscopy,” Opt. Eng. 45, 098003 (2006).
[Crossref]

M. Martinez-Corral, M. T. Caballero, E. H. K. Stelzer, and J. Swoger, “Tailoring the axial shape of the point spread function using the Toraldo concept,” Opt. Express 10, 98–103 (2002).
[PubMed]

Mojarad, N. M.

Moshe, I.

G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1)* LG beam,” Opt. Commun. 271, 190–196 (2007).
[Crossref]

Park, K.

Park, N.

Park, Y.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901/1–4 (2003).
[Crossref]

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 253, 358–379 (1959).
[Crossref]

Salamin, Y. I.

Sato, S.

Sheppard, C.

H. F. Wang, L. P. Shi, B. Luκyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[Crossref]

Sheppard, C. J. R.

Shi, L. P.

H. F. Wang, L. P. Shi, B. Luκyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[Crossref]

Stelzer, E. H. K.

Strayer, J. K.

J. K. Strayer, Linear Programming and Its Applications (Springer-Verlag, 1989), Chap. 2.
[Crossref]

Swoger, J.

Tan, Q.

Wang, H. F.

H. F. Wang, L. P. Shi, B. Luκyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 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. London 253, 358–379 (1959).
[Crossref]

Yan, Y.

Yi, D.

Yoon, Y.

Youngworth, K. S.

Zhan, Q.

Zhang, Y.

Zhang, Y. J.

Zhao, Y.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Microsc. Res. Tech. (1)

J. Kim, D. C. Kim, and S. H. Back, “Demonstration of high lateral resolution in laser confocal microscopy using annular and radially polarized light,” Microsc. Res. Tech. 72, 441–446 (2009).
[Crossref] [PubMed]

Nat. Photonics (1)

H. F. Wang, L. P. Shi, B. Luκyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[Crossref]

Opt. Commun. (1)

G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1)* LG beam,” Opt. Commun. 271, 190–196 (2007).
[Crossref]

Opt. Eng. (1)

M. T. Caballero, C. Ibanez-Lopez, and M. Martinez-Corral, “Shaded-mask filtering: novel strategy for improvement of resolution in radial-polarization scanning microscopy,” Opt. Eng. 45, 098003 (2006).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901/1–4 (2003).
[Crossref]

Proc. R. Soc. London (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 253, 358–379 (1959).
[Crossref]

Other (1)

J. K. Strayer, Linear Programming and Its Applications (Springer-Verlag, 1989), Chap. 2.
[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 (7)

Fig. 1
Fig. 1

System layout.

Fig. 2
Fig. 2

Focusing properties of radially polarized light. (a) Field distribution at the focal plane of radially polarized light at NA = 0.95 . The longitudinal component of the focused field (dotted–dashed curve) determines the central intensity. The transverse component of the focused field (dashed curve) affects only the radius of the main lobe and the heights of the side lobes. The overall distribution (solid curve) is the sum of both components. (b) Shows that the ratio of the maximum intensities of the two components (solid curve) exceeds the one at high NA.

Fig. 3
Fig. 3

Definition of superresolution parameters. The solid curve is the distribution of the direct focusing of linearly polarized light at the focal plane in a high-NA focusing system, subscripted L. The dashed curve is the superresolution distribution, subscripted S. r L H and r s H are FWHMs of the two distributions normalized by the direct focusing of linearly polarized light. I L and I s are the maximum intensities normalized by the central intensity of the direct focusing of linearly polarized light

Fig. 4
Fig. 4

Intensity distributions at the focal plane of radially polarized light (solid curves) and linearly polarized light (dashed curves) with DSEs for the same G (a) or S (b).

Fig. 5
Fig. 5

Intensity distributions of the transverse component of DSE-1 (solid curves) and DSE-3 (dashed curves).

Fig. 6
Fig. 6

Comparison of superresolution performance of radially and linearly polarized light. The decrease of G is at the price of decrease of S. The optimal numerical results of DSEs for radially polarized light and considering only the longitudinal component (triangles) and both components (crosses) of the focused field, and linearly polarized light (solid curve).

Fig. 7
Fig. 7

Intensity distributions with Bessel–Gauss (solid curves), ideal plane wave (dashed curves), Bessel (dotted curves), and Gauss (dotted–dashed curve) incident beams with optimized DSEs for the same G = 0.65 .

Tables (2)

Tables Icon

Table 1 Simulation Results of 0, π Two-Phase Distributed DSEs a

Tables Icon

Table 2 Simulation Results with Different Incident Beams a

Equations (21)

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

e r ( ρ ) = C 0 α U ( θ ) cos 1 2 θ sin ( 2 θ ) l 0 ( θ ) J 1 ( k ρ sin θ ) d θ ,
e z ( ρ ) = 2 i C 0 α U ( θ ) cos 1 2 θ sin 2 θ l 0 ( θ ) J 0 ( k ρ sin θ ) d θ ,
I ( ρ ) = | e r 2 ( ρ ) | + | e z 2 ( ρ ) | ,
l 0 ( θ ) = exp ( β 0 2 ( sin θ sin α ) 2 ) J 1 ( 2 β 0 sin θ sin α ) ,
max U ( θ ) I ( 0 ) = | 0 α D 2 ( θ ) U ( θ ) d θ | 2 ,
0 α D 2 ( θ ) U ( θ ) J 0 ( k γ sin θ ) d θ = 0 ,
| U ( θ ) | 1 ,
max U ( θ ) I ( 0 ) = | 0 α D 2 ( θ ) A ( θ ) d θ | 2 + | 0 α D 2 ( θ ) B ( θ ) d θ | 2 .
ϕ = n π + arctan ( 0 α [ A 0 ( θ ) B 0 ( θ ) ] D 2 ( θ ) d θ 0 α [ A 0 ( θ ) + B 0 ( θ ) ] D 2 ( θ ) d θ )
0 α D 2 ( θ ) A ( θ ) d θ = 0 α D 2 ( θ ) B ( θ ) d θ .
max A ( θ ) E ( 0 ) = 0 α D 2 ( θ ) A ( θ ) d θ ,
max A ( θ ) E ( 0 ) = 0 α D 2 ( θ ) A ( θ ) d θ ,
0 α D 2 ( θ ) A ( θ ) J 0 ( k γ sin θ ) d θ = 0 ,
A ( θ ) = B ( θ ) ,
| A ( θ ) | 1 2 .
F [ ϕ ( θ ) , κ ] = 0 α cos ϕ ( θ ) D 2 ( θ ) d θ + κ 0 α cos ϕ ( θ ) D 2 ( θ ) J 0 ( k γ sin θ ) d θ ,
| δ F | ϕ ( θ ) = 0 α [ 1 + κ J 0 ( k γ sin θ ) ] sin ϕ ( θ ) D 2 ( θ ) δ ϕ ( θ ) d θ = 0 ,
A ( θ ) = 1 2 or 1 2 .
max A ( θ ) E ( 0 ) = j = 1 K t j θ j θ j + 1 D 2 ( θ ) d θ ,
j = 1 K t j θ j θ j + 1 D 2 ( θ ) J 0 ( k γ sin θ ) d θ = 0 ,
1 t j 1 .

Metrics