Abstract

We first present nonparaxial designs for a microcylindrical axilens with different long focal depths and rigorously analyze electromagnetic field distributions of the axilens using integral equations and the boundary-element method. Numerical results show that the designed axilenses indeed have the special feature of attaining a long focal depth while keeping high transverse resolution for numerical apertures of 2.4, 2.0, and 1.0. The ratio between the extended focal depth of the designed axilens and the focal depth of the conventional focal lens is 1.41, the corresponding maximal extended focal depth of the axilens can reach 28 μm, and the spot size of the focal beam is ∼10 μm over the focal range.

© 2001 Optical Society of America

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References

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  1. N. Davidson, A. A. Friesem, E. Hasman, “Holographic axilens: high resolution and long focal depth,” Opt. Lett. 16, 523–525 (1991).
    [CrossRef] [PubMed]
  2. J. Sochacki, S. Bará, Z. Jaroszewicz, A. Kołodziejczyk, “Phase retardation of the uniform-intensity axilens,” Opt. Lett. 17, 7–9 (1992).
    [CrossRef] [PubMed]
  3. J. Sochacki, A. Kołodziejczyk, Z. Jaroszewicz, S. Bará, “Nonparaxial design of generalized axicons,” Appl. Opt. 31, 5326–5330 (1992).
    [CrossRef] [PubMed]
  4. L. F. Staroński, J. Sochacki, Z. Jaroszewicz, A. Kołodziejczyk, “Lateral distribution and flow of energy in uniform-intensity axicons,” J. Opt. Soc. Am. A 9, 2091–2094 (1992).
    [CrossRef]
  5. J. Sochacki, Z. Jaroszewicz, L. R. Staroński, A. Kołodziejczyk, “Annular-aperture logarithmic axicon,” J. Opt. Soc. Am. A 10, 1765–1768 (1993).
    [CrossRef]
  6. Z. Jaroszewicz, J. Sochacki, A. Kołodziejczyk, L. R. Staroński, “Apodized annular-aperture logarithmic axicon: smoothness and uniformity of intensity distributions,” Opt. Lett. 18, 1893–1895 (1993).
    [CrossRef] [PubMed]
  7. B.-Z. Dong, G.-Z. Yang, B.-Y. Gu, “Iterative optimization approach for designing an axicon with long focal depth and high transverse resolution,” J. Opt. Soc. Am. A 13, 97–103 (1996).
    [CrossRef]
  8. R. Kant, “Superresolution and increase depth of focus: an inverse problem of vector diffraction,” J. Mod. Opt. 47, 905–916 (2000).
    [CrossRef]
  9. K. Yashiro, S. Ohkawa, “Boundary element method for electromagnetic field problems,” IEEE Trans. Antennas Propag. AP-33, 383–389 (1985).
    [CrossRef]
  10. K. Hirayama, E. N. Glytsis, T. K. Gaylord, D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).
    [CrossRef]
  11. J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary-element method with application to diffractive cylindrical lenses,” J. Opt. Soc. Am. A 15, 1822–1837 (1998).
    [CrossRef]
  12. K. Hirayama, K. Igarashi, Y. Hayashi, E. N. Glytsis, T. K. Gaylord, “Finite-substrate-thickness cylindrical diffractive lenses: exact and approximate boundary-element methods,” J. Opt. Soc. Am. A 16, 1294–1302 (1999).
    [CrossRef]
  13. E. N. Glytsis, M. E. Harrigan, T. K. Gaylord, K. Hirayama, “Effects of fabrication errors on the performance of cylindrical diffractive lenses: rigorous boundary-element method and scalar approximation,” Appl. Opt. 37, 6591–6602 (1998).
    [CrossRef]
  14. E. N. Glytsis, M. E. Harrigan, K. Hirayama, T. K. Gaylord, “Collimating cylindrical diffractive lenses: rigorous electromagnetic analysis and scalar approximation,” Appl. Opt. 37, 34–43 (1998).
    [CrossRef]
  15. M. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK Scientific, Tokyo, 1992), pp.43–47.
  16. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980), Chap. 6.
  17. S. Kagami, I. Fukai, “Application of boundary-element method to electro-magnetic field problems,” IEEE Trans. Microwave Theory Tech. MTT-32, 455–461 (1984).
    [CrossRef]
  18. D. A. Buralli, G. M. Morris, J. R. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 28, 976–983 (1989).
    [CrossRef] [PubMed]

2000 (1)

R. Kant, “Superresolution and increase depth of focus: an inverse problem of vector diffraction,” J. Mod. Opt. 47, 905–916 (2000).
[CrossRef]

1999 (1)

1998 (3)

1996 (2)

1993 (2)

1992 (3)

1991 (1)

1989 (1)

1985 (1)

K. Yashiro, S. Ohkawa, “Boundary element method for electromagnetic field problems,” IEEE Trans. Antennas Propag. AP-33, 383–389 (1985).
[CrossRef]

1984 (1)

S. Kagami, I. Fukai, “Application of boundary-element method to electro-magnetic field problems,” IEEE Trans. Microwave Theory Tech. MTT-32, 455–461 (1984).
[CrossRef]

Bará, S.

Bendickson, J. M.

Buralli, D. A.

Davidson, N.

Dong, B.-Z.

Friesem, A. A.

Fukai, I.

S. Kagami, I. Fukai, “Application of boundary-element method to electro-magnetic field problems,” IEEE Trans. Microwave Theory Tech. MTT-32, 455–461 (1984).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Gu, B.-Y.

Harrigan, M. E.

Hasman, E.

Hayashi, Y.

Hirayama, K.

Igarashi, K.

Jaroszewicz, Z.

Kagami, S.

S. Kagami, I. Fukai, “Application of boundary-element method to electro-magnetic field problems,” IEEE Trans. Microwave Theory Tech. MTT-32, 455–461 (1984).
[CrossRef]

Kant, R.

R. Kant, “Superresolution and increase depth of focus: an inverse problem of vector diffraction,” J. Mod. Opt. 47, 905–916 (2000).
[CrossRef]

Kolodziejczyk, A.

Koshiba, M.

M. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK Scientific, Tokyo, 1992), pp.43–47.

Morris, G. M.

Ohkawa, S.

K. Yashiro, S. Ohkawa, “Boundary element method for electromagnetic field problems,” IEEE Trans. Antennas Propag. AP-33, 383–389 (1985).
[CrossRef]

Rogers, J. R.

Sochacki, J.

Staronski, L. F.

Staronski, L. R.

Wilson, D. W.

Yang, G.-Z.

Yashiro, K.

K. Yashiro, S. Ohkawa, “Boundary element method for electromagnetic field problems,” IEEE Trans. Antennas Propag. AP-33, 383–389 (1985).
[CrossRef]

Appl. Opt. (4)

IEEE Trans. Antennas Propag. (1)

K. Yashiro, S. Ohkawa, “Boundary element method for electromagnetic field problems,” IEEE Trans. Antennas Propag. AP-33, 383–389 (1985).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

S. Kagami, I. Fukai, “Application of boundary-element method to electro-magnetic field problems,” IEEE Trans. Microwave Theory Tech. MTT-32, 455–461 (1984).
[CrossRef]

J. Mod. Opt. (1)

R. Kant, “Superresolution and increase depth of focus: an inverse problem of vector diffraction,” J. Mod. Opt. 47, 905–916 (2000).
[CrossRef]

J. Opt. Soc. Am. A (6)

Opt. Lett. (3)

Other (2)

M. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK Scientific, Tokyo, 1992), pp.43–47.

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980), Chap. 6.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of a two-dimensional scattering problem in a cylindrical system.

Fig. 2
Fig. 2

Diffracted field intensity distribution as a function of the axial distance around the focal region for the axilenses with different designed focal depths, where the size of the aperture of the axilens is D=30 μm. Curves a and b are for axilenses with preset focal depths δy=30 and 60 μm, respectively; curve c is for the conventional focal lens, δy=0.

Fig. 3
Fig. 3

Diffracted intensity distribution on three planes of different distances from the axilens surface: dashed curve, for y=-58 μm; solid curve, for y=-67 μm; dotted curve, for y=-81 μm.

Fig. 4
Fig. 4

Intensity distribution of the electric field plotted in a 256 gray-level representation for axilenses with present focal depths (a) δy=30 μm and (b) δy=60 μm, and for (c) the conventional lens, δy=0 μm. The bright (dark) region indicates the high (low) field intensity areas.

Fig. 5
Fig. 5

Axial intensity distribution around the focal range for axilenses with aperture D=25 μm and with different preset focal depth parameters. Curves a and b are for preset focal depths δy=30 and 60 μm, respectively; curve c is for the conventional focal lens, δy=0.

Fig. 6
Fig. 6

Lateral intensity distribution on three planes of different distances from the axilens surface: dashed curve, y=-54 μm; solid curve, y=-65 μm; dotted curve, y=-82 μm.

Fig. 7
Fig. 7

Same as Fig. 4, except that the aperture of the axilens is 25 μm.

Fig. 8
Fig. 8

Axial intensity distribution around the focal region for an axilens of NA=1.0. Curves a and b are for preset focal depths δy=30 and 60 μm, respectively; curve c is for the conventional focal lens, δy=0 μm.

Tables (1)

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Table 1 Definition of Notation

Equations (21)

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-E1(r1)+Γ[E1(rΓ)nˆ  G1(r1, rΓ)
-G1(r1, rΓ)nˆ  E1(rΓ)]dl=-Einc(r1),
E2(r2)+Γ[E2(rΓ)nˆ  G2(r2, rΓ)
-G2(r2, rΓ)nˆ  E2(rΓ)]dl=0.
θΓ2π-1E1(rΓ)+Γ[E1(rΓ)nˆ  G1(rΓ, rΓ)
-G1(rΓ, rΓ)nˆ  E1(rΓ)]dl=-Einc(rΓ),
θΓ2πE2(rΓ)+Γ[E2(rΓ)nˆ  G2(rΓ, rΓ)
-G2(rΓ, rΓ)  E2(rΓ)]dl=0,
Gi(ri, rΓ)=(-j/4)H0(2)(ki|ri-rΓ|)(i=1, 2)
N1=ξ(ξ-1)/2,
N2=(1-ξ)(1+ξ),
N3=ξ(1+ξ)/2,
E(rΓ)=N1N2N3{EI(rΓ),EII(rΓ),EIII(rΓ)},
E(rΓ)=N1N2N3{EI(rΓ),EII(rΓ),EIII(rΓ)},
w(x)=10|x|D2exp-10|x|-D22D2|x|D2+s0D2+s<|x|<,
ϕ(x)=2πλx22 f,
ϕ(x)=2πλx22 f(x),
f(x)=f0+δy x2R2,
ϕ(x)=n2n1-n2(f2+x2)1/2.
ϕ(x)=n2n1-n2f0+δy x2R22+x21/2.
Einc=w(x)exp[ϕ(x)].

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