Abstract

We find that a microcylindrical axilens with a closed boundary and with an f-number less than 1 still can achieve the properties of long focal depth and high transverse resolution, unlike a microcylindrical axilens with an open boundary, which fails to maintain those properties for low f-numbers. The focusing characteristics of the closed-boundary axilens and the open-boundary axilens are numerically investigated based on the boundary integral method. The numerical results show that the ratio of the extended focal depth of the closed-boundary axilens to the focal depth of the conventional microlens can reach up to 1.26 and 2.12 for the preset focal depths 3 and 5 µm, respectively, even though the f-number is reduced to 1/3.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2001 (1)

2000 (1)

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

1999 (1)

1998 (3)

1997 (1)

1996 (2)

1993 (2)

1992 (3)

1991 (1)

1985 (1)

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

Bará, S.

Bendickson, J. M.

Davidson, N.

Dong, B.-Z.

Ersoy, O. K.

Friesem, A. A.

Gaylord, T. K.

Glytsis, E. N.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, Berlin, 1968), Chap. 3.

Gu, B.-Y.

Harrigan, M. E.

Hasman, E.

Hayashi, Y.

Hirayama, K.

Igarashi, K.

Jaroszewicz, Z.

Kant, R.

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

Kolodziejczyk, A.

Liu, J.

Mait, J. N.

Mirotznik, M. S.

Ohkawa, S.

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

Prather, D. W.

Sochacki, J.

Staronski, L. R.

Wang, J.

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. (3)

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]

J. Mod. Opt. (1)

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

J. Opt. Soc. Am. A (8)

L. R. 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]

B.-Z. Dong, J. Liu, B.-Y. Gu, G.-Z. Yang, J. Wang, “Rigorous electromagnetic analysis of a microcylindrical axilens with long focal depth and high transverse resolution,” J. Opt. Soc. Am. A 18, 1465–1470 (2001).
[CrossRef]

B.-Z. Dong, G.-Z. Yang, B.-Y. Gu, O. K. Ersoy, “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]

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]

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]

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]

D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary integral methods applied to the analysis of diffractive optical elements,” J. Opt. Soc. Am. A 14, 34–43 (1997).
[CrossRef]

J. Sochacki, Z. Jaroszewicz, L. R. Staroński, A. Kołodziejczyk, “Annular-aperture logarithmic axicon,” J. Opt. Soc. Am. A 10, 1765–1768 (1993).
[CrossRef]

Opt. Lett. (3)

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, Berlin, 1968), Chap. 3.

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of a closed-boundary axilens used for the boundary integral method.

Fig. 2
Fig. 2

(a) Variation of the axial intensity of a diffracted field with the axial distance around the focal region for the designed CBAs with different predesigned focal depths. Curves a and b correspond to the preset focal depths δf=3 and 5 µm, respectively, with f/#=1/2; curve c corresponds to δf=0, i.e., the conventional cylindrical lens. (b) Variation of the lateral distribution of the diffracted field intensity on the three observation planes, with f/#=1/2. The dashed curve corresponds to the observation plane at y=-7.25 µm, the solid curve corresponds to the observation plane at y=-8.91 µm, and the dotted–dashed curve corresponds to the observation plane at y=-10.84 µm.

Fig. 3
Fig. 3

Intensity distributions of the electric fields plotted in a gray-level representation, corresponding to Fig. 2; (a) for δf=3 µm, (b) for δf=5 µm, and (c) for the conventional lens, i.e., δf=0 µm. The bright (dark) regions indicate the areas of high (low) field intensity.

Fig. 4
Fig. 4

(a) Same as Fig. 2(a) except for f/#=1/3, (b) same as Fig. 2(b) except for f/#=1/3.

Fig. 5
Fig. 5

Geometry of the axilens with an open boundary used for the boundary integral method.

Tables (3)

Tables Icon

Table 1 Performance of the CBAs for Several f-Numbersa

Tables Icon

Table 2 Performance of the OBAs for Several f-Numbersa

Tables Icon

Table 3 Comparison of Relative Extended Focal Depth for the CBAs and the OBAs

Equations (5)

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

0=EΓsc(rΓ)1-θ2π+ΓEΓsc(rΓ)G1(rΓ, rΓ)nˆ-G1(rΓ, rΓ)EΓsc(rΓ)nˆdl+EΓinc(rΓ)1-θ2π+ΓEΓinc(rΓ)G1(rΓ, rΓ)nˆ-G1(rΓ, rΓ)EΓinc(rΓ)nˆdl,
0=EΓsc(rΓ)θ2π+ΓG2(rΓ, rΓ)EΓsc(rΓ)nˆ-EΓsc(rΓ)G2(rΓ, rΓ)nˆdl,
Eobsinc(r)=-apeEapeinc(r)G2RS1(r, r)ndl=-apeEapeinc(r)jk22cos(γ)H1(2)(k2|r-r|)dl,
ϕ(x)=-122πλn2n1-n2(f2+x2-f)+ϕ0forthefirstboundary122πλn2n1-n2(f2+x2-f)forthesecondboundary,
η=-d/2d/2If(x2, yf)dx2-RRIape(x1, yape)dx1,

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