Abstract

We study the effect of polarization and aperture geometry on the focal spot size of a high numerical aperture (NA) aplanatic lens. We show that for a clear aperture geometry, illuminating the lens by linear or circular polarization is preferable over radial polarization for spot size reduction applications. For annular aperture and objective lenses of 0.85 NA and above we give the sizes of the inner annulus which constitute the transition points to a state where the radial polarization illumination gives smaller spot size. We analyze the evolution, the profile and the effect of transverse and longitudinal field components in the focal plane, and show that they play an opposite role on the spot size in the cases of circular and radial polarization illumination. We show that in the limit of a very thin annulus the radial polarization approaches the prediction of the scalar theory at high NA, whereas the linear and circular polarizations deviate from it. We verify that the longitudinal component generated by radially polarized illumination produces the narrowest spot size for wide range of geometries. Finally, we discuss the effects of tight focusing on a dielectric interface and provide some ideas for circumventing the effects of the interface and even utilize them for spot size reduction.

© 2008 Optical Society of America

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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. R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  3. Q. Zhan and J. R. Leger, "Focus shaping using cylindrical vector beams," Opt. Express 10, 324-331 (2002).
    [PubMed]
  4. G. M. Lerman and U. Levy "Tight focusing of space variant vector optical fields with no cylindrical symmetry of polarization," Opt. Lett. 32, 2194-2196 (2007).
    [CrossRef] [PubMed]
  5. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman," Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings," Opt. Lett. 27, 285 (2002).
    [CrossRef]
  6. U. Levy, C. H. Tsai, L. Pang, and Y. Fainman, "Engineering space-variant inhomogeneous media for polarization control," Opt. Lett. 29, 1718-1720 (2004).
    [CrossRef] [PubMed]
  7. Y. Kozawa and S. Sato, "Focusing property of a double-ring-shaped radially polarized beam," Opt. Lett. 31, 820-822 (2006).
    [CrossRef] [PubMed]
  8. B. Hao and J. Leger, "Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam," Opt. Express 15, 3550-3556 (2007).
    [CrossRef] [PubMed]
  9. A. Shoham, R. Vander, and S. G. Lipson, "Production of radially and azimuthally polarized polychromatic beams," Opt. Lett. 31, 3405-3407 (2006).
    [CrossRef] [PubMed]
  10. E. Descrovi, L. Vaccaro, L. Aeschimann, W. Nakagawa, U. Staufer, and H. -P. Herzig, "Optical properties of microfabricated fully-metal-coated near-field probes in collection mode," J. Opt. Soc. Am. A 22, 1432-1441 (2005).
    [CrossRef]
  11. C. -C. Sun and C. -K. Liu, "Ultrasmall focusing spot with a long depth of focus based on polarization and phase modulation," Opt. Lett. 28, 99-101 (2003).
    [CrossRef] [PubMed]
  12. N. Hayazawa, Y. Saito, and S. Kawata, "Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy," Appl. Phys. Lett. 85, 6239 (2004).
    [CrossRef]
  13. Q. Zhan, "Trapping metallic Rayleigh particles with radial polarization," Opt. Express 12, 3377-3382 (2004).
    [CrossRef] [PubMed]
  14. V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D: Appl. Phys. 32, 1455-1461 (1999).
    [CrossRef]
  15. M. R. Beversluis, L. Novotny, and S. J. Stranick, "Programmable vector point-spread function engineering," Opt. Express 14, 2650-2656 (2006).
    [CrossRef] [PubMed]
  16. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system," Proc. R. Soc. A 253, 358-379 (1959).
    [CrossRef]
  17. K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical vector beams," Opt. Express 7, 77-87 (2000).
    [CrossRef] [PubMed]
  18. N. Davidson and N. Bokor, "High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens," Opt. Lett. 29, 1318-1320 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
  20. E. Y. S. Yew and C. J. R. Sheppard, "Tight focusing of radially polarized Gaussian and Bessel-Gauss beams," Opt. Lett. 32, 3417-3419 (2007).
    [CrossRef] [PubMed]
  21. V. P. Kalosha and I. Golub, "Toward the subdiffraction focusing limit of optical superresolution," Opt. Lett. 32, 3540-3542 (2007).
    [CrossRef] [PubMed]
  22. L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645 (1997).
    [CrossRef]
  23. W. Chen and Q. Zhan, "Numerical study of an apertureless near field scanning optical microscope probe under radial polarization illumination," Opt. Express 15, 4106-4111 (2007).
    [CrossRef] [PubMed]
  24. P. Török, P. Varga, and G. R. Booker, "Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: structure of the electromagnetic field.I," J. Opt. Soc. Am. A 12, 2136-2144 (1995).
    [CrossRef]
  25. L. E. Helseth, "Roles of polarization,phase,and amplitude in solid immersion lens systems," Opt. Commun. 191, 161-172 (2001).
    [CrossRef]
  26. D. Biss and T. Brown, "Cylindrical vector beam focusing through a dielectric interface," Opt. Express 9, 490-497 (2001).
    [CrossRef] [PubMed]
  27. D. Biss and T. Brown, "Polarization vortex driven second harmonic generation," Opt. Lett. 28, 923-925 (2003).
    [CrossRef] [PubMed]
  28. D. P. Biss, K. S. Youngworth, and T. G. Brown, "Longitudinal field imaging," in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing X, J. A. Conchello, C. J. Cogswell, and T. Wilson, eds., Proc. SPIE 4964, 73-87 (2003).
    [CrossRef]
  29. G. M. Lerman, A. Israel, and A. Lewis, "Applying Solid Immersion Near-field Optics to Raman Analysis of Strained Silicon Thin Films," Appl. Phys. Lett. 89, 223122 (2006).
    [CrossRef]

2007 (6)

2006 (4)

2005 (1)

2004 (4)

2003 (3)

2002 (2)

2001 (2)

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

D. Biss and T. Brown, "Cylindrical vector beam focusing through a dielectric interface," Opt. Express 9, 490-497 (2001).
[CrossRef] [PubMed]

2000 (2)

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

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

1999 (1)

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D: Appl. Phys. 32, 1455-1461 (1999).
[CrossRef]

1997 (1)

L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645 (1997).
[CrossRef]

1995 (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. A 253, 358-379 (1959).
[CrossRef]

Aeschimann, L.

Beversluis, M. R.

Bian, R. X.

L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645 (1997).
[CrossRef]

Biener, G.

Biss, D.

Bokor, N.

Bomzon, Z.

Booker, G. R.

Brown, T.

Brown, T. G.

Chen, W.

Davidson, N.

Descrovi, E.

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]

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]

Fainman, Y.

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]

Golub, I.

Hao, B.

Hasman, E.

Hayazawa, N.

N. Hayazawa, Y. Saito, and S. Kawata, "Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy," Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

Helseth, L. E.

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

Herzig, H. -P.

Israel, A.

G. M. Lerman, A. Israel, and A. Lewis, "Applying Solid Immersion Near-field Optics to Raman Analysis of Strained Silicon Thin Films," Appl. Phys. Lett. 89, 223122 (2006).
[CrossRef]

Kalosha, V. P.

Kawata, S.

N. Hayazawa, Y. Saito, and S. Kawata, "Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy," Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

Kleiner, V.

Kozawa, Y.

Leger, J.

Leger, J. R.

Lerman, G. M.

G. M. Lerman and U. Levy "Tight focusing of space variant vector optical fields with no cylindrical symmetry of polarization," Opt. Lett. 32, 2194-2196 (2007).
[CrossRef] [PubMed]

G. M. Lerman, A. Israel, and A. Lewis, "Applying Solid Immersion Near-field Optics to Raman Analysis of Strained Silicon Thin Films," Appl. Phys. Lett. 89, 223122 (2006).
[CrossRef]

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]

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

Levy, U.

Lewis, A.

G. M. Lerman, A. Israel, and A. Lewis, "Applying Solid Immersion Near-field Optics to Raman Analysis of Strained Silicon Thin Films," Appl. Phys. Lett. 89, 223122 (2006).
[CrossRef]

Lipson, S. G.

Liu, C. -K.

Nakagawa, W.

Nesterov, A. V.

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D: Appl. Phys. 32, 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: Appl. Phys. 32, 1455-1461 (1999).
[CrossRef]

Novotny, L.

M. R. Beversluis, L. Novotny, and S. J. Stranick, "Programmable vector point-spread function engineering," Opt. Express 14, 2650-2656 (2006).
[CrossRef] [PubMed]

L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645 (1997).
[CrossRef]

Pang, L.

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]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[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. A 253, 358-379 (1959).
[CrossRef]

Saito, Y.

N. Hayazawa, Y. Saito, and S. Kawata, "Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy," Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

Sato, S.

Sheppard, C. J. R.

Shoham, A.

Staufer, U.

Stranick, S. J.

Sun, C. -C.

Török, P.

Tsai, C. H.

Vaccaro, L.

Vander, R.

Varga, P.

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. A 253, 358-379 (1959).
[CrossRef]

Xie, X. S.

L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645 (1997).
[CrossRef]

Yew, E. Y. S.

Youngworth, K. S.

Zhan, Q.

Appl. Phys. Lett. (2)

N. Hayazawa, Y. Saito, and S. Kawata, "Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy," Appl. Phys. Lett. 85, 6239 (2004).
[CrossRef]

G. M. Lerman, A. Israel, and A. Lewis, "Applying Solid Immersion Near-field Optics to Raman Analysis of Strained Silicon Thin Films," Appl. Phys. Lett. 89, 223122 (2006).
[CrossRef]

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

J. Phys. D: Appl. Phys. (1)

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D: Appl. Phys. 32, 1455-1461 (1999).
[CrossRef]

Opt. Commun. (2)

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

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. Express (7)

Opt. Lett. (10)

A. Shoham, R. Vander, and S. G. Lipson, "Production of radially and azimuthally polarized polychromatic beams," Opt. Lett. 31, 3405-3407 (2006).
[CrossRef] [PubMed]

U. Levy, C. H. Tsai, L. Pang, and Y. Fainman, "Engineering space-variant inhomogeneous media for polarization control," Opt. Lett. 29, 1718-1720 (2004).
[CrossRef] [PubMed]

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

G. M. Lerman and U. Levy "Tight focusing of space variant vector optical fields with no cylindrical symmetry of polarization," Opt. Lett. 32, 2194-2196 (2007).
[CrossRef] [PubMed]

E. Y. S. Yew and C. J. R. Sheppard, "Tight focusing of radially polarized Gaussian and Bessel-Gauss beams," Opt. Lett. 32, 3417-3419 (2007).
[CrossRef] [PubMed]

V. P. Kalosha and I. Golub, "Toward the subdiffraction focusing limit of optical superresolution," Opt. Lett. 32, 3540-3542 (2007).
[CrossRef] [PubMed]

C. -C. Sun and C. -K. Liu, "Ultrasmall focusing spot with a long depth of focus based on polarization and phase modulation," Opt. Lett. 28, 99-101 (2003).
[CrossRef] [PubMed]

D. Biss and T. Brown, "Polarization vortex driven second harmonic generation," Opt. Lett. 28, 923-925 (2003).
[CrossRef] [PubMed]

N. Davidson and N. Bokor, "High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens," Opt. Lett. 29, 1318-1320 (2004).
[CrossRef] [PubMed]

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

Phys. Rev. Lett. (2)

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

L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645 (1997).
[CrossRef]

Proc. R. Soc. 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. A 253, 358-379 (1959).
[CrossRef]

Other (1)

D. P. Biss, K. S. Youngworth, and T. G. Brown, "Longitudinal field imaging," in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing X, J. A. Conchello, C. J. Cogswell, and T. Wilson, eds., Proc. SPIE 4964, 73-87 (2003).
[CrossRef]

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Figures (14)

Fig. 1.
Fig. 1.

Energy density distribution of longitudinal (left) and transverse (center) components, and total energy density (right) for circular polarization illumination and an annular aperture with 0.95 NA objective lens and 0.9 NA of inner annulus. Axes are in wavelength units. Units in color bars are arbitrary.

Fig. 2.
Fig. 2.

Energy density distribution of longitudinal (left) and transverse (center) components, and total energy density (right) for radial polarization illumination and an annular aperture with 0.95 NA objective lens and 0.9 NA of inner annulus. Axes are in wavelength units. Units in color bars are arbitrary.

Fig. 3.
Fig. 3.

Spot size of energy density vs. NA for a clear aperture and radially (triangles) and circularly (circles) input polarized fields. The z component of the radially polarized beam is also shown (rectangles). Inset: zoom in on the high NA section of the graph.

Fig. 4.
Fig. 4.

Spot size of energy density vs. NAmin/NAmax for radially (triangles), linearly (circles) and circularly (rectangles) polarized beams for the case of NAmax of 0.85. The longitudinal component of the radially polarized beam is shown as well (stars).

Fig. 5.
Fig. 5.

Spot size of energy density vs. NAmin/NAmax for radially (triangles), linearly (circles) and circularly (rectangles) polarized beams for the case of NAmax of 0.9. The longitudinal component of the radially polarized beam is shown as well (stars).

Fig. 6.
Fig. 6.

Spot size of energy density vs. NAmin/NAmax for radially (triangles), linearly (circles) and circularly (rectangles) polarized beams for the case of NAmax of 0.95. The longitudinal component of the radially polarized beam is shown as well (stars).

Fig. 7.
Fig. 7.

Spot size vs. NAmin/NAmax for transverse (rectangles) and longitudinal (circles) components and total energy density (triangles) for circularly polarized beam for the case of NAmax of 0.95.

Fig. 8.
Fig. 8.

Spot size vs. NAmin/NAmax for transverse (rectangles) and longitudinal (circles) components and total energy density (triangles) for radially polarized beam for the case of NAmax of 0.7.

Fig. 9.
Fig. 9.

Spot size of energy density vs. NA for radially (triangles), linearly (circles) and circularly (rectangles) polarized beams. The z component of the radial polarization (stars) and results from scalar theory (diamonds) are shown as well. Annulus ratio of 0.99 is used.

Fig. 10.
Fig. 10.

Two point resolution according to Rayleigh criterion for NA of 0.9 and NAmin of 0.45 (left), 0.65 (center) and 0.85 (right) for circular (red) and radial (blue) polarizations.

Fig. 11.
Fig. 11.

Spot size of energy density vs. NAmin/NAmax for radially (triangles) and circularly (circles) polarized beams for the case of NAmax of 0.7. The longitudinal component of the radially polarized beam is shown as well (rectangles).

Fig. 12.
Fig. 12.

Cross section of the energy density before and after the interface for the case of passing from a medium with refractive index of 1 a medium with refractive index of 1.5. We use clear aperture illumination with NA of 0.95.

Fig. 13.
Fig. 13.

Energy density before and after the interface for the case of passing from refractive index of 1.5 to 3.5 media. Clear aperture and NA=0.95 lens is assumed. Scale is in arbitrary units.

Fig. 14.
Fig. 14.

Cross section of the energy density at the focal plane for the case of passing from refractive index of 1.5 to 3.5 media (red). For comparison, we also plot the energy density for a case focusing through a uniform medium having refractive index of 1 (blue).

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