Abstract

We compare the performances in terms of confinement and depth of field of spherical and conical optics. It turns out that, if the spherical optics is adapted to the usual parallel imaging, conical optics seems to be the optimized solution for systems based on scanning (sequential imaging). It is shown that the optimized confinement capability of conical optics is due to the ability of conical components to generate a single Bessel beam with high efficiency. The calculations are based on Weyl formulas.

© 2007 Optical Society of America

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  25. I. Leiserson, S. G. Lipson, and V. Sarafis, "Superresolution in far-field imaging," Opt. Lett. 25, 209-211 (2000).
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  33. T. Grosjean and D. Courjon, "Polarization filtering induced by imaging systems: effect on image structure," Phys. Rev. E 67, 46611 (2003).
    [CrossRef]
  34. C. J. R. Sheppard and A. Choudhury, "Annular pupils, radial polarization, and superresolution," Appl. Opt. 43, 4322-4327 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
  37. C. J. R. Sheppard, "The use of lenses with annular aperture in scanning optical microscopy," Optik (Stuttgart) 48, 329-334 (1977).
  38. M. Gu, T. Tannous, and C. J. R. Sheppard, "Effect of an annular pupil on confocal imaging through highly scattering media," Opt. Lett. 21, 312-314 (1996).
    [CrossRef] [PubMed]
  39. S. Lindek, C. Cremer, and E. H. Stelzer, "Confocal theta fluorescence microscopy with annular apertures," Appl. Opt. 35, 126-130 (1996).
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    [CrossRef] [PubMed]
  41. G. Scott and N. McArdle, "Efficient generation of nearly diffraction-free beams using an axicon," Opt. Eng. 31, 2640-2643 (1992).
    [CrossRef]
  42. T. Grosjean, D. Courjon, and D. Van Labeke, "Bessel beams as virtual tips for near-field optics," J. Microsc. (Oxford) 210, 319-323 (2003).
    [CrossRef] [PubMed]
  43. T. Tanaka and S. Yamamoto, "Comparison of abberation between axicon and lens," Opt. Commun. 184, 113-118 (2000).
    [CrossRef]
  44. R. Arimoto, C. Saloma, T. Tanaka, and S. Kawata, "Imaging properties of axicon in a scanning optical system," Appl. Opt. 31, 6653-6657 (1992).
    [CrossRef] [PubMed]

2005 (1)

T. D. Milster, "Horizons for optical data storage," Opt. Photon. News 16(3), 28-33 (2005).
[CrossRef]

2004 (3)

2003 (3)

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]

T. Grosjean, D. Courjon, and D. Van Labeke, "Bessel beams as virtual tips for near-field optics," J. Microsc. (Oxford) 210, 319-323 (2003).
[CrossRef] [PubMed]

T. Grosjean and D. Courjon, "Polarization filtering induced by imaging systems: effect on image structure," Phys. Rev. E 67, 46611 (2003).
[CrossRef]

2002 (1)

M. Will, S. Nolte, B. N. Chichkov, and A. Tünnermann, "Optical properties of waveguides fabricated in fused silica by femtosecond laser pulses," Appl. Opt. 21, 4360-4364 (2002).
[CrossRef]

2001 (2)

2000 (4)

M. A. A. Neil, R. Juskaitis, T. Wilson, and Z. J. Laczik, "Optimized pupil-plane filters for confocal microscope point-spread function engineering," Opt. Lett. 25, 245-247 (2000).
[CrossRef]

I. Leiserson, S. G. Lipson, and V. Sarafis, "Superresolution in far-field imaging," Opt. Lett. 25, 209-211 (2000).
[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]

T. Tanaka and S. Yamamoto, "Comparison of abberation between axicon and lens," Opt. Commun. 184, 113-118 (2000).
[CrossRef]

1999 (3)

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and M. Kowalczyk, "Three-dimensional superresolution by annular binary filters," Opt. Commun. 165, 267-278 (1999).
[CrossRef]

L. P. Ghislain and V. B. Elings, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Y. Kondo, K. Nouchi, T. Mitsuyu, M. Watanabe, P. G. Kazansky, and K. Hirao, "Fabrication of long-period fiber gratings by focused irradiation of infrared femtosecond laser pulses," Opt. Lett. 24, 646-648 (1999).
[CrossRef]

1997 (1)

1996 (3)

1995 (1)

Z. Bouchal and M. Olivik, "Non-diffractive vector Bessel beams," J. Mod. Opt. 42, 1555-1566 (1995).
[CrossRef]

1992 (3)

1991 (1)

1990 (1)

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

1987 (3)

J. Durnin, "Exact solutions for nondiffracting beams. i. The scalar theory," J. Opt. Soc. Am. A 4, 651-654 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

F. Gori, G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun. 64, 491-495 (1987).
[CrossRef]

1986 (1)

1985 (1)

Z. S. Hegedus, "Annular pupil arrays. Application to confocal scanning," Opt. Acta 32, 815-826 (1985).
[CrossRef]

1977 (2)

C. J. R. Sheppard and A. Choudhury, "Image formation in the scanning microscope," Opt. Acta 24, 1051-1073 (1977).
[CrossRef]

C. J. R. Sheppard, "The use of lenses with annular aperture in scanning optical microscopy," Optik (Stuttgart) 48, 329-334 (1977).

1960 (1)

1959 (1)

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

1952 (1)

G. Toraldo di Francia, "Supergain antennas and optical resolving power," Nuovo Cimento , Suppl. 9, 426-435 (1952).
[CrossRef]

1919 (1)

H. Weyl, "Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter," Ann. Phys. (Leipzig) 60, 481-500 (1919).
[CrossRef]

Andres, P.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and M. Kowalczyk, "Three-dimensional superresolution by annular binary filters," Opt. Commun. 165, 267-278 (1999).
[CrossRef]

Arimoto, R.

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon Press, 1980, reprinted Cambridge U. Press, 1997).

Bouchal, Z.

Z. Bouchal and M. Olivik, "Non-diffractive vector Bessel beams," J. Mod. Opt. 42, 1555-1566 (1995).
[CrossRef]

Burvall, A.

Chichkov, B. N.

M. Will, S. Nolte, B. N. Chichkov, and A. Tünnermann, "Optical properties of waveguides fabricated in fused silica by femtosecond laser pulses," Appl. Opt. 21, 4360-4364 (2002).
[CrossRef]

Choudhury, A.

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

C. J. R. Sheppard and A. Choudhury, "Image formation in the scanning microscope," Opt. Acta 24, 1051-1073 (1977).
[CrossRef]

Courjon, D.

T. Grosjean and D. Courjon, "Polarization filtering induced by imaging systems: effect on image structure," Phys. Rev. E 67, 46611 (2003).
[CrossRef]

T. Grosjean, D. Courjon, and D. Van Labeke, "Bessel beams as virtual tips for near-field optics," J. Microsc. (Oxford) 210, 319-323 (2003).
[CrossRef] [PubMed]

T. Grosjean and D. Courjon, "Immaterial tip concept by light confinement," J. Microsc. (Oxford) 202, 273-278 (2001).
[CrossRef] [PubMed]

Cremer, C.

di Francia, G. Toraldo

G. Toraldo di Francia, "Supergain antennas and optical resolving power," Nuovo Cimento , Suppl. 9, 426-435 (1952).
[CrossRef]

Dorn, R.

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

Durnin, J.

J. Durnin, "Exact solutions for nondiffracting beams. i. The scalar theory," J. Opt. Soc. Am. A 4, 651-654 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

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]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Echlin, P.

M. Staniforth, J. Goldstein, D. E. Newbury, C. E. Lyman, P. Echlin, E. Lifshin, L. C. Sawyer, J. R. Michael, and D. C. Joy, Scanning Electron Microscopy and X-Ray Microanalysis (Springer, 2002).

Elings, V. B.

L. P. Ghislain and V. B. Elings, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

Friberg, A. T.

Ghislain, L. P.

L. P. Ghislain and V. B. Elings, "Near-field photolithography with a solid immersion lens," Appl. Phys. Lett. 74, 501-503 (1999).
[CrossRef]

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]

Goldstein, J.

M. Staniforth, J. Goldstein, D. E. Newbury, C. E. Lyman, P. Echlin, E. Lifshin, L. C. Sawyer, J. R. Michael, and D. C. Joy, Scanning Electron Microscopy and X-Ray Microanalysis (Springer, 2002).

Gori, F.

F. Gori, G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun. 64, 491-495 (1987).
[CrossRef]

Grosjean, T.

T. Grosjean and D. Courjon, "Polarization filtering induced by imaging systems: effect on image structure," Phys. Rev. E 67, 46611 (2003).
[CrossRef]

T. Grosjean, D. Courjon, and D. Van Labeke, "Bessel beams as virtual tips for near-field optics," J. Microsc. (Oxford) 210, 319-323 (2003).
[CrossRef] [PubMed]

T. Grosjean and D. Courjon, "Immaterial tip concept by light confinement," J. Microsc. (Oxford) 202, 273-278 (2001).
[CrossRef] [PubMed]

Gu, M.

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun. 64, 491-495 (1987).
[CrossRef]

Hegedus, Z. S.

Z. S. Hegedus, "Superresolving filters in confocally scanned imaging systems," J. Opt. Soc. Am. A 3, 1892-1896 (1986).
[CrossRef]

Z. S. Hegedus, "Annular pupil arrays. Application to confocal scanning," Opt. Acta 32, 815-826 (1985).
[CrossRef]

Herman, R. M.

Hirao, K.

Jaroszewicz, Z.

Jiang, Z.

Joy, D. C.

M. Staniforth, J. Goldstein, D. E. Newbury, C. E. Lyman, P. Echlin, E. Lifshin, L. C. Sawyer, J. R. Michael, and D. C. Joy, Scanning Electron Microscopy and X-Ray Microanalysis (Springer, 2002).

Juodkazis, S.

Juskaitis, R.

Kawata, S.

Kazansky, P. G.

Kenney, C. S.

Kettunen, V.

Kino, G. S.

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

Kolacz, K.

Kondo, Y.

Kowalczyk, M.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and M. Kowalczyk, "Three-dimensional superresolution by annular binary filters," Opt. Commun. 165, 267-278 (1999).
[CrossRef]

Kuittinen, M.

Laczik, Z. J.

Leiserson, I.

Leuchs, G.

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

Lifshin, E.

M. Staniforth, J. Goldstein, D. E. Newbury, C. E. Lyman, P. Echlin, E. Lifshin, L. C. Sawyer, J. R. Michael, and D. C. Joy, Scanning Electron Microscopy and X-Ray Microanalysis (Springer, 2002).

Lindek, S.

Lipson, S. G.

Liu, C.-K.

Liu, Z.

Lu, Q.

Lyman, C. E.

M. Staniforth, J. Goldstein, D. E. Newbury, C. E. Lyman, P. Echlin, E. Lifshin, L. C. Sawyer, J. R. Michael, and D. C. Joy, Scanning Electron Microscopy and X-Ray Microanalysis (Springer, 2002).

Mansfield, S. M.

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

Martinez-Corral, M.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and M. Kowalczyk, "Three-dimensional superresolution by annular binary filters," Opt. Commun. 165, 267-278 (1999).
[CrossRef]

Matsuo, S.

McArdle, N.

G. Scott and N. McArdle, "Efficient generation of nearly diffraction-free beams using an axicon," Opt. Eng. 31, 2640-2643 (1992).
[CrossRef]

McLeod, J. H.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Michael, J. R.

M. Staniforth, J. Goldstein, D. E. Newbury, C. E. Lyman, P. Echlin, E. Lifshin, L. C. Sawyer, J. R. Michael, and D. C. Joy, Scanning Electron Microscopy and X-Ray Microanalysis (Springer, 2002).

Milster, T. D.

T. D. Milster, "Horizons for optical data storage," Opt. Photon. News 16(3), 28-33 (2005).
[CrossRef]

Misawa, H.

Mitsuyu, T.

Neil, M. A. A.

Newbury, D. E.

M. Staniforth, J. Goldstein, D. E. Newbury, C. E. Lyman, P. Echlin, E. Lifshin, L. C. Sawyer, J. R. Michael, and D. C. Joy, Scanning Electron Microscopy and X-Ray Microanalysis (Springer, 2002).

Nishii, J.

Nolte, S.

M. Will, S. Nolte, B. N. Chichkov, and A. Tünnermann, "Optical properties of waveguides fabricated in fused silica by femtosecond laser pulses," Appl. Opt. 21, 4360-4364 (2002).
[CrossRef]

Nouchi, K.

Olivik, M.

Z. Bouchal and M. Olivik, "Non-diffractive vector Bessel beams," J. Mod. Opt. 42, 1555-1566 (1995).
[CrossRef]

Overfelt, P. L.

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun. 64, 491-495 (1987).
[CrossRef]

Pluta, M.

M. Pluta, Advanced Light Microscopy Vol. I: Principles and Basic Properties (Elsevier, 1988).

Powell, J.

J. Powell, CO2 Laser Cutting (Springer, 1998).
[PubMed]

Quabis, S.

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

Recami, E.

Richards, B.

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

Saloma, C.

Sarafis, V.

Sawyer, L. C.

M. Staniforth, J. Goldstein, D. E. Newbury, C. E. Lyman, P. Echlin, E. Lifshin, L. C. Sawyer, J. R. Michael, and D. C. Joy, Scanning Electron Microscopy and X-Ray Microanalysis (Springer, 2002).

Scott, G.

G. Scott and N. McArdle, "Efficient generation of nearly diffraction-free beams using an axicon," Opt. Eng. 31, 2640-2643 (1992).
[CrossRef]

Shaarawi, A. M.

Sheppard, C. J. R.

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

M. Gu, T. Tannous, and C. J. R. Sheppard, "Effect of an annular pupil on confocal imaging through highly scattering media," Opt. Lett. 21, 312-314 (1996).
[CrossRef] [PubMed]

C. J. R. Sheppard, "The use of lenses with annular aperture in scanning optical microscopy," Optik (Stuttgart) 48, 329-334 (1977).

C. J. R. Sheppard and A. Choudhury, "Image formation in the scanning microscope," Opt. Acta 24, 1051-1073 (1977).
[CrossRef]

Stammes, J. J.

J. J. Stammes, Waves in Focal Regions (Adam Hilger, 1986).

Staniforth, M.

M. Staniforth, J. Goldstein, D. E. Newbury, C. E. Lyman, P. Echlin, E. Lifshin, L. C. Sawyer, J. R. Michael, and D. C. Joy, Scanning Electron Microscopy and X-Ray Microanalysis (Springer, 2002).

Stelzer, E. H.

Sun, C.-C.

Sun, H.-B.

Sun, K.

Tanaka, T.

Tannous, T.

Tünnermann, A.

M. Will, S. Nolte, B. N. Chichkov, and A. Tünnermann, "Optical properties of waveguides fabricated in fused silica by femtosecond laser pulses," Appl. Opt. 21, 4360-4364 (2002).
[CrossRef]

Turunen, J.

Vahimaa, P.

Van Labeke, D.

T. Grosjean, D. Courjon, and D. Van Labeke, "Bessel beams as virtual tips for near-field optics," J. Microsc. (Oxford) 210, 319-323 (2003).
[CrossRef] [PubMed]

Watanabe, M.

Weyl, H.

H. Weyl, "Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter," Ann. Phys. (Leipzig) 60, 481-500 (1919).
[CrossRef]

Wiggins, T. A.

Will, M.

M. Will, S. Nolte, B. N. Chichkov, and A. Tünnermann, "Optical properties of waveguides fabricated in fused silica by femtosecond laser pulses," Appl. Opt. 21, 4360-4364 (2002).
[CrossRef]

Wilson, T.

Wolf, E.

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

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon Press, 1980, reprinted Cambridge U. Press, 1997).

Xu, Y.

Yamamoto, S.

T. Tanaka and S. Yamamoto, "Comparison of abberation between axicon and lens," Opt. Commun. 184, 113-118 (2000).
[CrossRef]

Zamboni-Rached, M.

Zapata-Rodriguez, C. J.

M. Martinez-Corral, P. Andres, C. J. Zapata-Rodriguez, and M. Kowalczyk, "Three-dimensional superresolution by annular binary filters," Opt. Commun. 165, 267-278 (1999).
[CrossRef]

Ann. Phys. (1)

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Figures (3)

Fig. 1
Fig. 1

Scheme of the considered focusing system consisting of an aplanetic focusing objective and a SIL.

Fig. 2
Fig. 2

Characterization of a radially polarized focused beam (a), (c) without angular frequency filtering and (b), (d) with focusing optimization, when NA = sin ( π / 3 ) = 0.87 . (a), (b) Intensity in the (x, y) transverse plane; (c), (d) intensity in the (x, z) longitudinal plane. (e) Comparison between the normalized profiles of (c) at z = 0 (dashed curve) and z = 5 λ (dotted curve) and the normalized profile of (d) whatever value z.

Fig. 3
Fig. 3

Characterization of a radially polarized focused beam (a), (c) without angular frequency filtering and (b), (d) with focusing optimization, when NA = 1.5   sin ( π / 3 ) = 1.73 . (a), (b) Intensity (I) in the (x, y) transverse plane; (c), (d) I 0.2 in the (x, z) longitudinal plane. (e) Comparison between the normalized profiles of (c) at z = 0 (dashed curve) and z = λ (dotted curve) and the normalized profile of (d) whatever value z.

Equations (14)

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E ( r ) = i 2 π a ( u , v ) w  exp [ i ( u x + v y + w z ) ] d u d v ,
E ( r , ξ ) = i k 2 π 0 π / 2 d θ   sin   θ 0 2 π d ψ A ( θ , ψ ) × exp [ i α r   cos ( ψ ξ ) + i w z ] ,
A ( θ , ψ ) = cos   θ f ( θ ) P ( θ , ψ ) .
f ( θ ) = L G [ R ( θ ) ] × circ [ R ( θ ) 1 ] ,
circ ( R 1 ) = 1   if   R < 1,
= 0   if   R > 1 .
E ( r , ξ ) = i k E 0 T 2 π 0 π / 2 d θ   sin   θ cos   θ f ( θ ) B B ( θ , r , ξ ) ,
B B x = π   exp [ i w z ] [ ( t s + t p r   cos   θ ) cos   ϕ J 0 ( α r ) + ( t s t p r   cos   θ ) ( cos   ϕ   cos   2 ξ + a sin ϕ sin 2 ξ ) J 2 ( α r ) ] ,
B B y = π   exp [ i w z ] [ ( t s + t p r   cos   θ ) a   sin   ϕ J 0 ( α r ) ( t s t p r   cos   θ ) ( a   sin   ϕ   cos   2 ξ cos   ϕ sin 2 ξ ) J 2 ( α r ) ] ,
B B z = 2 i π   exp [ i w z ] sin   θ t p z ( cos   ϕ   cos   ξ + a   sin   ϕ sin ξ ) J 1 ( α r ) ,
B B x = i   exp [ i w z ] t p r   cos   θ   cos   ξ J 1 ( α r ) ,
B B y = i   exp [ i w z ] t p r   cos   θ   sin   ξ J 1 ( α r ) ,
B B z = exp [ i w z ] t p z   sin   θ J 0 ( α r ) ,
F ( θ ) = δ ( R ( θ ) 1 ) .

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