Abstract

Both the reflection inside a hemisphere solid immersion lens (SIL) and the reflection inside the gap between the SIL and the optical recording medium are considered. The near-field SIL imaging theory for high numerical aperture is developed by using the vector diffraction and thin-film optics. Numerical results show that the spot size, Strehl ratio, and sidelobe intensity have an oscillatory behavior with the change of thickness of the air gap, which results from the interference effect of the transmitted field. We find that for smaller spot size, the Strehl ratio is smaller but the sidelobe intensity is larger. A certain thickness of air gap is useful for optical storage, which is less than 63nm for the system in the simulated examples.

© 2006 Optical Society of America

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  1. S. M. Mansfield and G. S. Kino, "Solid immersion microscope," Appl. Phys. Lett. 57, 2615-2616 (1990).
    [CrossRef]
  2. B. D. Terris, H. J. Mamin, and D. Ruger, "Near-field optical data storage using a solid immersion lens," Appl. Phys. Lett. 65, 388-390 (1994).
    [CrossRef]
  3. L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
    [CrossRef]
  4. M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, "Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy," J. Appl. Phys. 92, 862-865 (2002).
    [CrossRef]
  5. S. B. Ippolito, S. A. Thome, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, "High spatial resolution subsurface thermal emission microscopy," Appl. Phys. Lett. 84, 4529-4531 (2004).
    [CrossRef]
  6. S. Moehl, H. Zhao, B. D. Don, S. Wachter, and H. Kalt, "Solid immersion lens-enhanced nano-photoluminescence: principle and applications," J. Appl. Phys. 93, 6265-6272 (2003).
    [CrossRef]
  7. J. Zhang, C. W. See, M. G. Somekh, M. C. Pitter, and S. G. Liu, "Wide-field surface plasmon microscopy with solid immersion excitation," J. Appl. Phys. 85, 5451-5453 (2004).
  8. L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens systems," Opt. Commun. 191, 161-172 (2001).
    [CrossRef]
  9. Y. Zhang, C. Zhang, and Y. Zou, "Focal-field distribution of the solid immersion lens system with an annular filter," Optik (Stuttgart) 115, 277-280 (2004).
    [CrossRef]
  10. Y. Zhang, H. Xiao, and C. Zhang, "Diffractive super-resolution elements applied to near-field optical data storage with solid immersion lens," New J. Phys. 6, 75 (2004).
    [CrossRef]
  11. I. Ichimura, S. Hayashi, and G. S. Kino, "High-density optical recording using a solid immersion lens," Appl. Opt. 36, 4339-4348 (1997).
    [CrossRef] [PubMed]
  12. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
    [CrossRef]
  13. T. Milster, J. Jo, and K. Hirota, "Roles of propagation and evanescent waves in solid immersion lens systems," Appl. Opt. 38, 5046-5057 (1999).
    [CrossRef]
  14. D. Flagello, T. Milster, and A. Rosenbluth, "Theory of high-NA imaging in homogeneous thin films," J. Opt. Soc. Am. A 13, 53-63 (1996).
    [CrossRef]
  15. F. Guo, T. E. Schlesinger, and D. D. Stancil, "Optical field study of near-field optical recording with a solid immersion lens," Appl. Opt. 39, 324-332 (2000).
    [CrossRef]
  16. S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, "Theoretical analysis of numerical aperture increasing lens microscopy," J. Appl. Phys. 97, 053105 (2005).
    [CrossRef]
  17. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), p. 64.
  18. P. Török, C. J. R. Sheppard, and P. Varga, "Study of evanescent waves for transmission near-field optical microscopy," J. Mod. Opt. 43, 1167-1183 (1996).
    [CrossRef]
  19. T. R. M. Sales and G. M. Morris, "Diffractive superresolution elements," J. Opt. Soc. Am. A 14, 1637-1646 (1997).
    [CrossRef]
  20. H. Ando, "Phase-shifting apodizer of three or more portions," Jpn. J. Appl. Phys., Part 1 31, 557-567 (1992).
    [CrossRef]

2005

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, "Theoretical analysis of numerical aperture increasing lens microscopy," J. Appl. Phys. 97, 053105 (2005).
[CrossRef]

2004

Y. Zhang, C. Zhang, and Y. Zou, "Focal-field distribution of the solid immersion lens system with an annular filter," Optik (Stuttgart) 115, 277-280 (2004).
[CrossRef]

Y. Zhang, H. Xiao, and C. Zhang, "Diffractive super-resolution elements applied to near-field optical data storage with solid immersion lens," New J. Phys. 6, 75 (2004).
[CrossRef]

S. B. Ippolito, S. A. Thome, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, "High spatial resolution subsurface thermal emission microscopy," Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

J. Zhang, C. W. See, M. G. Somekh, M. C. Pitter, and S. G. Liu, "Wide-field surface plasmon microscopy with solid immersion excitation," J. Appl. Phys. 85, 5451-5453 (2004).

2003

S. Moehl, H. Zhao, B. D. Don, S. Wachter, and H. Kalt, "Solid immersion lens-enhanced nano-photoluminescence: principle and applications," J. Appl. Phys. 93, 6265-6272 (2003).
[CrossRef]

2002

M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, "Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy," J. Appl. Phys. 92, 862-865 (2002).
[CrossRef]

2001

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

2000

1999

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), p. 64.

T. Milster, J. Jo, and K. Hirota, "Roles of propagation and evanescent waves in solid immersion lens systems," Appl. Opt. 38, 5046-5057 (1999).
[CrossRef]

1997

1996

D. Flagello, T. Milster, and A. Rosenbluth, "Theory of high-NA imaging in homogeneous thin films," J. Opt. Soc. Am. A 13, 53-63 (1996).
[CrossRef]

P. Török, C. J. R. Sheppard, and P. Varga, "Study of evanescent waves for transmission near-field optical microscopy," J. Mod. Opt. 43, 1167-1183 (1996).
[CrossRef]

1994

B. D. Terris, H. J. Mamin, and D. Ruger, "Near-field optical data storage using a solid immersion lens," Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

1992

H. Ando, "Phase-shifting apodizer of three or more portions," Jpn. J. Appl. Phys., Part 1 31, 557-567 (1992).
[CrossRef]

1990

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

1959

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
[CrossRef]

Akiyama, H.

M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, "Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy," J. Appl. Phys. 92, 862-865 (2002).
[CrossRef]

Ando, H.

H. Ando, "Phase-shifting apodizer of three or more portions," Jpn. J. Appl. Phys., Part 1 31, 557-567 (1992).
[CrossRef]

Baba, M.

M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, "Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy," J. Appl. Phys. 92, 862-865 (2002).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), p. 64.

Crozier, K. B.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Don, B. D.

S. Moehl, H. Zhao, B. D. Don, S. Wachter, and H. Kalt, "Solid immersion lens-enhanced nano-photoluminescence: principle and applications," J. Appl. Phys. 93, 6265-6272 (2003).
[CrossRef]

Elings, V. B.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Eraslan, M. G.

S. B. Ippolito, S. A. Thome, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, "High spatial resolution subsurface thermal emission microscopy," Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

Flagello, D.

Ghislain, L. P.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Goldberg, B. B.

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, "Theoretical analysis of numerical aperture increasing lens microscopy," J. Appl. Phys. 97, 053105 (2005).
[CrossRef]

S. B. Ippolito, S. A. Thome, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, "High spatial resolution subsurface thermal emission microscopy," Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

Guo, F.

Hayashi, S.

Helseth, L. E.

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

Hirota, K.

Ichimura, I.

Ippolito, S. B.

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, "Theoretical analysis of numerical aperture increasing lens microscopy," J. Appl. Phys. 97, 053105 (2005).
[CrossRef]

S. B. Ippolito, S. A. Thome, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, "High spatial resolution subsurface thermal emission microscopy," Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

Jo, J.

Kalt, H.

S. Moehl, H. Zhao, B. D. Don, S. Wachter, and H. Kalt, "Solid immersion lens-enhanced nano-photoluminescence: principle and applications," J. Appl. Phys. 93, 6265-6272 (2003).
[CrossRef]

Kino, G. S.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

I. Ichimura, S. Hayashi, and G. S. Kino, "High-density optical recording using a solid immersion lens," Appl. Opt. 36, 4339-4348 (1997).
[CrossRef] [PubMed]

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

Koyama, K.

M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, "Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy," J. Appl. Phys. 92, 862-865 (2002).
[CrossRef]

Leblebici, Y.

S. B. Ippolito, S. A. Thome, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, "High spatial resolution subsurface thermal emission microscopy," Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

Liu, S. G.

J. Zhang, C. W. See, M. G. Somekh, M. C. Pitter, and S. G. Liu, "Wide-field surface plasmon microscopy with solid immersion excitation," J. Appl. Phys. 85, 5451-5453 (2004).

Mamin, H. J.

B. D. Terris, H. J. Mamin, and D. Ruger, "Near-field optical data storage using a solid immersion lens," Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

Manalis, S. R.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Mansfield, S. M.

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

Milster, T.

Minne, S. C.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Moehl, S.

S. Moehl, H. Zhao, B. D. Don, S. Wachter, and H. Kalt, "Solid immersion lens-enhanced nano-photoluminescence: principle and applications," J. Appl. Phys. 93, 6265-6272 (2003).
[CrossRef]

Morris, G. M.

Pitter, M. G. Somekh, M. C.

J. Zhang, C. W. See, M. G. Somekh, M. C. Pitter, and S. G. Liu, "Wide-field surface plasmon microscopy with solid immersion excitation," J. Appl. Phys. 85, 5451-5453 (2004).

Quate, C. F.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
[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, Ser. A 253, 358-379 (1959).
[CrossRef]

Rosenbluth, A.

Ruger, D.

B. D. Terris, H. J. Mamin, and D. Ruger, "Near-field optical data storage using a solid immersion lens," Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

Sales, T. R. M.

Schlesinger, T. E.

See, C. W.

J. Zhang, C. W. See, M. G. Somekh, M. C. Pitter, and S. G. Liu, "Wide-field surface plasmon microscopy with solid immersion excitation," J. Appl. Phys. 85, 5451-5453 (2004).

Sheppard, C. J. R.

P. Török, C. J. R. Sheppard, and P. Varga, "Study of evanescent waves for transmission near-field optical microscopy," J. Mod. Opt. 43, 1167-1183 (1996).
[CrossRef]

Stancil, D. D.

Terris, B. D.

B. D. Terris, H. J. Mamin, and D. Ruger, "Near-field optical data storage using a solid immersion lens," Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

Thome, S. A.

S. B. Ippolito, S. A. Thome, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, "High spatial resolution subsurface thermal emission microscopy," Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

Török, P.

P. Török, C. J. R. Sheppard, and P. Varga, "Study of evanescent waves for transmission near-field optical microscopy," J. Mod. Opt. 43, 1167-1183 (1996).
[CrossRef]

Ünlü, M. S.

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, "Theoretical analysis of numerical aperture increasing lens microscopy," J. Appl. Phys. 97, 053105 (2005).
[CrossRef]

S. B. Ippolito, S. A. Thome, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, "High spatial resolution subsurface thermal emission microscopy," Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

Varga, P.

P. Török, C. J. R. Sheppard, and P. Varga, "Study of evanescent waves for transmission near-field optical microscopy," J. Mod. Opt. 43, 1167-1183 (1996).
[CrossRef]

Wachter, S.

S. Moehl, H. Zhao, B. D. Don, S. Wachter, and H. Kalt, "Solid immersion lens-enhanced nano-photoluminescence: principle and applications," J. Appl. Phys. 93, 6265-6272 (2003).
[CrossRef]

Wilder, K.

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), p. 64.

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
[CrossRef]

Xiao, H.

Y. Zhang, H. Xiao, and C. Zhang, "Diffractive super-resolution elements applied to near-field optical data storage with solid immersion lens," New J. Phys. 6, 75 (2004).
[CrossRef]

Yoshita, M.

M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, "Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy," J. Appl. Phys. 92, 862-865 (2002).
[CrossRef]

Zhang, C.

Y. Zhang, C. Zhang, and Y. Zou, "Focal-field distribution of the solid immersion lens system with an annular filter," Optik (Stuttgart) 115, 277-280 (2004).
[CrossRef]

Y. Zhang, H. Xiao, and C. Zhang, "Diffractive super-resolution elements applied to near-field optical data storage with solid immersion lens," New J. Phys. 6, 75 (2004).
[CrossRef]

Zhang, J.

J. Zhang, C. W. See, M. G. Somekh, M. C. Pitter, and S. G. Liu, "Wide-field surface plasmon microscopy with solid immersion excitation," J. Appl. Phys. 85, 5451-5453 (2004).

Zhang, Y.

Y. Zhang, C. Zhang, and Y. Zou, "Focal-field distribution of the solid immersion lens system with an annular filter," Optik (Stuttgart) 115, 277-280 (2004).
[CrossRef]

Y. Zhang, H. Xiao, and C. Zhang, "Diffractive super-resolution elements applied to near-field optical data storage with solid immersion lens," New J. Phys. 6, 75 (2004).
[CrossRef]

Zhao, H.

S. Moehl, H. Zhao, B. D. Don, S. Wachter, and H. Kalt, "Solid immersion lens-enhanced nano-photoluminescence: principle and applications," J. Appl. Phys. 93, 6265-6272 (2003).
[CrossRef]

Zou, Y.

Y. Zhang, C. Zhang, and Y. Zou, "Focal-field distribution of the solid immersion lens system with an annular filter," Optik (Stuttgart) 115, 277-280 (2004).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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

B. D. Terris, H. J. Mamin, and D. Ruger, "Near-field optical data storage using a solid immersion lens," Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

S. B. Ippolito, S. A. Thome, M. G. Eraslan, B. B. Goldberg, M. S. Ünlü, and Y. Leblebici, "High spatial resolution subsurface thermal emission microscopy," Appl. Phys. Lett. 84, 4529-4531 (2004).
[CrossRef]

J. Appl. Phys.

S. Moehl, H. Zhao, B. D. Don, S. Wachter, and H. Kalt, "Solid immersion lens-enhanced nano-photoluminescence: principle and applications," J. Appl. Phys. 93, 6265-6272 (2003).
[CrossRef]

J. Zhang, C. W. See, M. G. Somekh, M. C. Pitter, and S. G. Liu, "Wide-field surface plasmon microscopy with solid immersion excitation," J. Appl. Phys. 85, 5451-5453 (2004).

M. Yoshita, K. Koyama, M. Baba, and H. Akiyama, "Fourier imaging study of efficient near-field optical coupling in solid immersion fluorescence microscopy," J. Appl. Phys. 92, 862-865 (2002).
[CrossRef]

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, "Theoretical analysis of numerical aperture increasing lens microscopy," J. Appl. Phys. 97, 053105 (2005).
[CrossRef]

J. Mod. Opt.

P. Török, C. J. R. Sheppard, and P. Varga, "Study of evanescent waves for transmission near-field optical microscopy," J. Mod. Opt. 43, 1167-1183 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys., Part 1

H. Ando, "Phase-shifting apodizer of three or more portions," Jpn. J. Appl. Phys., Part 1 31, 557-567 (1992).
[CrossRef]

New J. Phys.

Y. Zhang, H. Xiao, and C. Zhang, "Diffractive super-resolution elements applied to near-field optical data storage with solid immersion lens," New J. Phys. 6, 75 (2004).
[CrossRef]

Opt. Commun.

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

Optik (Stuttgart)

Y. Zhang, C. Zhang, and Y. Zou, "Focal-field distribution of the solid immersion lens system with an annular filter," Optik (Stuttgart) 115, 277-280 (2004).
[CrossRef]

Proc. R. Soc. London, Ser. A

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London, Ser. A 253, 358-379 (1959).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), p. 64.

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Figures (8)

Fig. 1
Fig. 1

Geometry of the SIL above an air gap. (b) and (c) The propagation of light through a SIL and an air gap, respectively.

Fig. 2
Fig. 2

Intensity distribution along the x direction. The solid and dashed curves are the cases without and with the air gap of h = 5 nm .

Fig. 3
Fig. 3

Aberration functions of the transmitted field for the s and p polarizations. The dotted and dashed curves are the cases with a gap of h = 5 nm . The dashed–dotted and solid curves are the cases without a gap. The dotted and dashed–dotted curves denote the phase for the s polarization, and the dashed and solid curves denote the phase for the p polarization.

Fig. 4
Fig. 4

Intensity distribution of a system with a gap of h = 5 nm for several different refractive indices of n 2 .

Fig. 5
Fig. 5

FWHM in the x direction as a function of the thickness h of the air gap.

Fig. 6
Fig. 6

Strehl ratio as a function of the thickness h of the air gap.

Fig. 7
Fig. 7

Sidelobe intensity in the x direction as a function of the thickness h of the air gap.

Fig. 8
Fig. 8

Intensity distribution along the x direction for h = 50 nm at the longitudinal displacements from the surface of the sample of d = 0 , 20, 50, and 100 nm .

Tables (1)

Tables Icon

Table 1 Parameters for Field Simulation

Equations (13)

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

δ SIL = 4 π λ n 2 R ,
r 12 j , t 12 j t 21 j r 23 j exp ( i δ SIL ) , t 12 j t 21 j ( r 23 j ) 2 r 21 j exp ( 2 i δ SIL ) , t 12 j t 21 j ( r 23 j ) 3 ( r 21 j ) 2 exp ( 3 i δ SIL ) , .
t 12 j t 23 j , t 12 j t 23 j r 21 j r 23 j exp ( 2 i δ SIL ) , t 12 j t 23 j ( r 21 j r 23 j ) 2 exp ( 3 i δ SIL ) ,
r ̃ SIL j = r 12 j + r 23 j exp ( i δ SIL ) 1 + r 12 j r 23 j exp ( i δ SIL ) .
t ̃ SIL j = t 12 j t 23 j exp ( i δ SIL 2 ) 1 + r 12 j r 23 j exp ( i δ SIL ) .
t sys s = t ̃ SIL s t 34 s exp ( i δ gap 2 ) 1 + r ̃ SIL s r 34 s exp ( i δ gap ) ,
t sys p = t ̃ SIL p t 34 p exp ( i δ gap 2 ) 1 + r ̃ SIL p r 34 p exp ( i δ gap ) ,
δ gap = 4 π λ n 3 h cos θ 2 .
E ( ρ c , θ c , z c ) = ( i ( I 0 + I 2 cos 2 ϕ c ) i I 2 sin 2 ϕ c 2 I 1 cos ϕ c ) ,
I 0 = 0 α ( t sys s + t sys p cos θ 4 ) cos θ 1 sin θ 1 J 0 ( k 2 ρ 2 sin θ 2 ) exp ( i k 4 z c cos θ 4 ) exp ( i k 0 Ψ ) d θ 1 ,
I 1 = 0 α t sys p sin θ 4 cos θ 1 sin θ 1 J 1 ( k 2 ρ c sin θ 2 ) exp ( i k 4 z c cos θ 4 ) exp ( i k 0 Ψ ) d θ 1 ,
I 2 = 0 α ( t sys s t sys p cos θ 4 ) cos θ 1 sin θ 1 J 2 ( k 2 ρ c sin θ 2 ) exp ( i k 4 z c cos θ 4 ) exp ( i k 0 Ψ ) d θ 1 ,
ψ = h ( n 4 cos θ 4 n 1 cos θ 1 ) .

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