Abstract

A solid immersion lens can be applied for high-resolution subsurface analysis of integrated circuits and other physical systems. We present a thorough analysis of the focal field distribution of a solid immersion lens system of arbitrary thickness. Cases of linearly and radially polarized illumination are examined and accurate expressions derived for the electric field in the image space. The effect of the spherical interface on both transverse and axial intensity profiles is analyzed. The performance and practicality of configurations deviating from the hemispherical and aplanatic cases are studied. The results show that optimal resolution is obtained at focal positions between the hemispherical and aplanatic points when radially polarized illumination is applied.

© 2011 Optical Society of America

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References

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  1. W. Qiang, L. P. Ghislan, and V. B. Elings, “Imaging with solid immersion lenses, spatial resolution, and applications,” Proc. IEEE 88, 1398–1491 (2000).
    [CrossRef]
  2. Y. Zhang, C. Zheng, and Y. Zou, “Focal-field distribution of the solid immersion lens system with an annular filter,” Int. J. Light Electron. Opt. 115, 277–280 (2004).
    [CrossRef]
  3. Y. Zhang, “Theoretical study of near-field optical storage with a solid immersion lens,” J. Opt. Soc. Am. A 23, 2132–2136 (2006).
    [CrossRef]
  4. L. E. Helseth, “Roles of polarization, phase and amplitude in solid immersion lens systems,” Opt. Commun. 191, 161–172(2001).
    [CrossRef]
  5. S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
    [CrossRef]
  6. S. H. Goh and C. J. R. Sheppard, “High aperture focusing through a spherical interface: application to refractive solid immersion lens (RSIL) for subsurface imaging,” Opt. Commun. 282, 1036–1041 (2009).
    [CrossRef]
  7. 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]
  8. L. Novotny and B. Hecht, Principles of Nano-Optics, 1st ed. (Cambridge University Press, 2006).
  9. A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Unlu, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
    [CrossRef]
  10. P. Torok, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12, 325–332 (1995).
    [CrossRef]
  11. E. Wolf, “Electromagnetic diffraction in optical systems. I. an integral representation of the image field,” Proc. R. Soc. London 253, 349–357 (1959).
    [CrossRef]
  12. L. E. Helseth, “Electromagnetic focusing through a tilted dielectric surface,” Opt. Commun. 215, 247–250 (2003).
    [CrossRef]
  13. G. M. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16, 4567–4581 (2008).
    [CrossRef] [PubMed]
  14. 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]
  15. C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43, 4322–4327(2004).
    [CrossRef] [PubMed]
  16. C. J. R. Sheppard and E. Y. S. Yew, “Performance parameters for focusing of radial polarization,” Opt. Lett. 33, 497–499 (2008).
    [CrossRef] [PubMed]
  17. W. H. Steel, “Axicons with spherical surfaces,” in Colloquia of the International Commission for Optics: Optics in Metrology, P.Mollet, ed. (Pergamon, 1960), pp. 181–192.

2009 (1)

S. H. Goh and C. J. R. Sheppard, “High aperture focusing through a spherical interface: application to refractive solid immersion lens (RSIL) for subsurface imaging,” Opt. Commun. 282, 1036–1041 (2009).
[CrossRef]

2008 (3)

2007 (1)

2006 (2)

L. Novotny and B. Hecht, Principles of Nano-Optics, 1st ed. (Cambridge University Press, 2006).

Y. Zhang, “Theoretical study of near-field optical storage with a solid immersion lens,” J. Opt. Soc. Am. A 23, 2132–2136 (2006).
[CrossRef]

2004 (2)

Y. Zhang, C. Zheng, and Y. Zou, “Focal-field distribution of the solid immersion lens system with an annular filter,” Int. J. Light Electron. Opt. 115, 277–280 (2004).
[CrossRef]

C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43, 4322–4327(2004).
[CrossRef] [PubMed]

2003 (1)

L. E. Helseth, “Electromagnetic focusing through a tilted dielectric surface,” Opt. Commun. 215, 247–250 (2003).
[CrossRef]

2001 (1)

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

2000 (1)

W. Qiang, L. P. Ghislan, and V. B. Elings, “Imaging with solid immersion lenses, spatial resolution, and applications,” Proc. IEEE 88, 1398–1491 (2000).
[CrossRef]

1995 (1)

1990 (1)

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

1960 (1)

W. H. Steel, “Axicons with spherical surfaces,” in Colloquia of the International Commission for Optics: Optics in Metrology, P.Mollet, ed. (Pergamon, 1960), pp. 181–192.

1959 (2)

E. Wolf, “Electromagnetic diffraction in optical systems. I. an integral representation of the image field,” Proc. R. Soc. London 253, 349–357 (1959).
[CrossRef]

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]

Behringer, E. R.

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Unlu, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

Booker, G. R.

Choudhury, A.

Elings, V. B.

W. Qiang, L. P. Ghislan, and V. B. Elings, “Imaging with solid immersion lenses, spatial resolution, and applications,” Proc. IEEE 88, 1398–1491 (2000).
[CrossRef]

Ghislan, L. P.

W. Qiang, L. P. Ghislan, and V. B. Elings, “Imaging with solid immersion lenses, spatial resolution, and applications,” Proc. IEEE 88, 1398–1491 (2000).
[CrossRef]

Goh, S. H.

S. H. Goh and C. J. R. Sheppard, “High aperture focusing through a spherical interface: application to refractive solid immersion lens (RSIL) for subsurface imaging,” Opt. Commun. 282, 1036–1041 (2009).
[CrossRef]

Goldberg, B. B.

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Unlu, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics, 1st ed. (Cambridge University Press, 2006).

Helseth, L. E.

L. E. Helseth, “Electromagnetic focusing through a tilted dielectric surface,” Opt. Commun. 215, 247–250 (2003).
[CrossRef]

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

Ippolito, S. B.

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Unlu, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

Kino, G. S.

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

Kozawa, Y.

Laczik, Z.

Lerman, G. M.

Levy, U.

Mansfield, S. M.

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics, 1st ed. (Cambridge University Press, 2006).

Qiang, W.

W. Qiang, L. P. Ghislan, and V. B. Elings, “Imaging with solid immersion lenses, spatial resolution, and applications,” Proc. IEEE 88, 1398–1491 (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. London 253, 358–379 (1959).
[CrossRef]

Sato, S.

Sheppard, C. J. R.

S. H. Goh and C. J. R. Sheppard, “High aperture focusing through a spherical interface: application to refractive solid immersion lens (RSIL) for subsurface imaging,” Opt. Commun. 282, 1036–1041 (2009).
[CrossRef]

C. J. R. Sheppard and E. Y. S. Yew, “Performance parameters for focusing of radial polarization,” Opt. Lett. 33, 497–499 (2008).
[CrossRef] [PubMed]

C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43, 4322–4327(2004).
[CrossRef] [PubMed]

Steel, W. H.

W. H. Steel, “Axicons with spherical surfaces,” in Colloquia of the International Commission for Optics: Optics in Metrology, P.Mollet, ed. (Pergamon, 1960), pp. 181–192.

Swan, A. K.

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Unlu, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

Torok, P.

Unlu, M. S.

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Unlu, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

Vamivakas, A. N.

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Unlu, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

Varga, P.

Wolf, E.

E. Wolf, “Electromagnetic diffraction in optical systems. I. an integral representation of the image field,” Proc. R. Soc. London 253, 349–357 (1959).
[CrossRef]

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]

Yew, E. Y. S.

Younger, R. D.

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Unlu, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

Zhang, Y.

Y. Zhang, “Theoretical study of near-field optical storage with a solid immersion lens,” J. Opt. Soc. Am. A 23, 2132–2136 (2006).
[CrossRef]

Y. Zhang, C. Zheng, and Y. Zou, “Focal-field distribution of the solid immersion lens system with an annular filter,” Int. J. Light Electron. Opt. 115, 277–280 (2004).
[CrossRef]

Zheng, C.

Y. Zhang, C. Zheng, and Y. Zou, “Focal-field distribution of the solid immersion lens system with an annular filter,” Int. J. Light Electron. Opt. 115, 277–280 (2004).
[CrossRef]

Zou, Y.

Y. Zhang, C. Zheng, and Y. Zou, “Focal-field distribution of the solid immersion lens system with an annular filter,” Int. J. Light Electron. Opt. 115, 277–280 (2004).
[CrossRef]

Am. J. Phys. (1)

A. N. Vamivakas, R. D. Younger, B. B. Goldberg, A. K. Swan, M. S. Unlu, E. R. Behringer, and S. B. Ippolito, “A case study for optics: the solid immersion microscope,” Am. J. Phys. 76, 758–768 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57, 2615–2616 (1990).
[CrossRef]

Int. J. Light Electron. Opt. (1)

Y. Zhang, C. Zheng, and Y. Zou, “Focal-field distribution of the solid immersion lens system with an annular filter,” Int. J. Light Electron. Opt. 115, 277–280 (2004).
[CrossRef]

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

Opt. Commun. (3)

L. E. Helseth, “Electromagnetic focusing through a tilted dielectric surface,” Opt. Commun. 215, 247–250 (2003).
[CrossRef]

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

S. H. Goh and C. J. R. Sheppard, “High aperture focusing through a spherical interface: application to refractive solid immersion lens (RSIL) for subsurface imaging,” Opt. Commun. 282, 1036–1041 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. IEEE (1)

W. Qiang, L. P. Ghislan, and V. B. Elings, “Imaging with solid immersion lenses, spatial resolution, and applications,” Proc. IEEE 88, 1398–1491 (2000).
[CrossRef]

Proc. R. Soc. London (2)

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]

E. Wolf, “Electromagnetic diffraction in optical systems. I. an integral representation of the image field,” Proc. R. Soc. London 253, 349–357 (1959).
[CrossRef]

Other (2)

L. Novotny and B. Hecht, Principles of Nano-Optics, 1st ed. (Cambridge University Press, 2006).

W. H. Steel, “Axicons with spherical surfaces,” in Colloquia of the International Commission for Optics: Optics in Metrology, P.Mollet, ed. (Pergamon, 1960), pp. 181–192.

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Figures (10)

Fig. 1
Fig. 1

Illustrations of the optical system under consideration. In the physical system, a lens focuses incoming plane waves to a spot of finite size. The equivalent system depicts the meridional plane containing incident and refracted rays, in which incoming plane waves encounter a spherical reference surface and are focused to a point.

Fig. 2
Fig. 2

Geometry of plane waves passing through a tilted mismatched interface medium.

Fig. 3
Fig. 3

Geometry describing the focusing of plane waves through a spherical mismatched-media interface, such as a-SIL. In this case, the SIL is of arbitrary thickness. Notations for the system are indicated in the figure.

Fig. 4
Fig. 4

Special cases of focusing through a-SIL, wherein incoming rays are normally incident and focused to a centric point [(a)— hemispherical SIL], or refracted at the interface and focused to an aplanatic point [(b)—aplanatic SIL].

Fig. 5
Fig. 5

Change in spatial resolution with objective NA at different focusing planes for a-SIL under linearly polarized illumination for the azimuthal plane ϕ = 0 °

Fig. 6
Fig. 6

Change in spatial resolution with objective NA at different focusing planes for a-SIL under linearly polarized illumination for the azimuthal plane ϕ = 90 ° .

Fig. 7
Fig. 7

Change in spatial resolution with objective NA at different focusing planes for a-SIL under radially polarized illumination.

Fig. 8
Fig. 8

Normalized transverse intensity plots for optimal configurations of a system under radially polarized illumination.

Fig. 9
Fig. 9

Normalized axial intensity plots for optimal configurations of a system under radially polarized illumination.

Fig. 10
Fig. 10

Normalized axial intensity plots at the focusing plane d = 120 μm for increments of the objective NA.

Equations (19)

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E ( x , y , z ) = k x 2 + k y 2 k 2 E ^ e i ( k x x + k y y + k z z ) d k x d k y ,
E = 2 π i k z E ^ e i k r r .
E ( x , y , z ) = i r e i k r 2 π k x 2 + k y 2 k 2 E e i ( k x x + k y y + k z z ) 1 k z d k x d k y .
Ψ = ( k 1 , z k 2 , z ) z 0 ,
Ψ = ( k 1 , z k 2 , z ) ( z 0 ) ,
z 0 = R + l cos θ 1 ( l sin θ R ) 2 l 2 sin 2 θ R .
Ψ = ( k 1 1 ( l sin θ R ) 2 k SIL 1 ( n 1 l sin θ n SIL R ) 2 ) ( ( R + l cos θ 1 ( l sin θ R ) 2 l 2 sin 2 θ R ) ) ,
θ = θ + sin 1 l sin θ R sin 1 n 1 l sin θ n SIL R .
Ψ = ( k 1 k SIL ) R ,
θ = θ ,
Ψ = k 1 R cos θ ( 1 ( n SIL n 1 ) 2 ) ,
θ = sin 1 ( n SIL n 1 sin θ ) ,
E ( r p , θ p , ϕ p ) = i k 1 f e i k 1 f 2 E 0 n 1 n 2 ( I G , L , 0 + I G , L , 2 cos 2 ϕ p I G , L , 2 sin 2 ϕ p 2 i I G , L , 1 cos ϕ p ) ,
I G , L , 0 = 0 θ max cos 1 2 θ sin θ J 0 ( k SIL r p sin θ p sin θ ) ( t s + t p cos θ ) e i k SIL r p cos θ p cos θ e i Ψ d θ ,
I G , L , 1 = 0 θ max cos 1 2 θ sin θ J 1 ( k SIL r p sin θ p sin θ ) ( t p sin θ ) e i k SIL r p cos θ p cos θ e i Ψ d θ ,
I G , L , 2 = 0 θ max cos 1 2 θ sin θ J 2 ( k SIL r p sin θ p sin θ ) ( t s t p cos θ ) e i k SIL r p cos θ p cos θ e i Ψ d θ ,
E ( r p , θ p , ϕ p ) = i k 1 f e i k 1 f 2 E 0 n 1 n 2 ( 2 i I G , R , 1 cos ϕ p 2 i I G , R , 1 sin ϕ p 2 I G , R , 0 ) ,
I G , R , 0 = 0 θ max cos 1 2 θ sin θ sin θ t p J 0 ( k SIL r p sin θ p sin θ ) e i k SIL r p cos θ p cos θ e i Ψ d θ ,
I G , R , 1 = 0 θ max cos 1 2 θ sin θ cos θ t p J 1 ( k SIL r p sin θ p sin θ ) e i k SIL r p cos θ p cos θ e i Ψ d θ .

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