Abstract

Using a general focal-length function, two-dimensional long-focal-depth (LFD) metallic cylindrical focusing micromirrors (MCFMs) are designed and the focal performance is systematically investigated based on rigorous electromagnetic theory and the boundary element method. For a positive preset focal depth, simulation results reveal that the designed MCFMs still possess an LFD property and high lateral resolution even when the f-number is reduced to f/0.3. On the other hand, through setting the preset focal depth to be negative, increased lateral resolution is obtained, compared with the conventional MCFM. In addition, under multiwavelength illumination, a large common LFD region is demonstrated for the designed LFD MCFMs, which is due to the intrinsic achromatic property of reflective systems.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

2010 (1)

J. S. Ye and Y. Zhang, “Rigorous electromagnetic analysis of metallic cylindrical focusing micromirrors with high diffraction efficiency, achromatic aberration and long focal depth,” Opt. Commun. 283, 1661–1667 (2010).
[CrossRef]

2009 (1)

2008 (2)

J. L. Liu, J. Lin, H. F. Zhao, and S. T. Liu, “Analysis of closed-boundary cylindrical microlenses with long focal depth designed by the general focal length function,” Opt. Commun. 281, 4188–4193 (2008).
[CrossRef]

D. Feng, P. Ou, L. S. Feng, S. L. Hu, and C. X. Zhang, “Binary sub-wavelength diffractive lenses with long focal depth and high transverse resolution,” Opt. Express 16, 20968–20973(2008).
[CrossRef] [PubMed]

2007 (2)

2004 (1)

2003 (1)

2002 (1)

2001 (1)

1999 (1)

1996 (2)

1993 (1)

1992 (1)

1991 (1)

Bará, S.

Bendickson, J. M.

Davidson, N.

Di, S.

Dong, B. Z.

Ersoy, O. K.

Feng, D.

Feng, L. S.

Friesem, A. A.

Gaylord, T. K.

Glytsis, E. N.

Gu, B. Y.

Hane, K.

Hasman, E.

Hirayama, K.

Hu, B.

Hu, S. L.

Jaroszewicz, Z.

Jin, G. F.

Kolodziejczyk, A.

Lin, J.

J. L. Liu, J. Lin, H. F. Zhao, and S. T. Liu, “Analysis of closed-boundary cylindrical microlenses with long focal depth designed by the general focal length function,” Opt. Commun. 281, 4188–4193 (2008).
[CrossRef]

J. Lin, J. L. Liu, J. S. Ye, and S. T. Liu, “Design of microlenses with long focal depth based on the general focal length function,” J. Opt. Soc. Am. A 24, 1747–1751 (2007).
[CrossRef]

Liu, J.

Liu, J. L.

J. L. Liu, J. Lin, H. F. Zhao, and S. T. Liu, “Analysis of closed-boundary cylindrical microlenses with long focal depth designed by the general focal length function,” Opt. Commun. 281, 4188–4193 (2008).
[CrossRef]

J. Lin, J. L. Liu, J. S. Ye, and S. T. Liu, “Design of microlenses with long focal depth based on the general focal length function,” J. Opt. Soc. Am. A 24, 1747–1751 (2007).
[CrossRef]

Liu, S. T.

Ou, P.

Sochacki, J.

Staronski, L. R.

Sun, X. D.

Wang, J.

Wang, S. Q.

Wang, Y. Q.

Ward, L.

L. Ward, “Optical constants of eight rare-earth elements,” in Handbook of Optical Constants of Solids, E.D.Palik ed. (Academic, 1985), Vol.  3, pp. 294.

Wilson, D. W.

Wu, M. X.

Yan, Y. B.

Yang, G. Z.

Ye, J. S.

Zhang, C. X.

Zhang, Y.

J. S. Ye and Y. Zhang, “Rigorous electromagnetic analysis of metallic cylindrical focusing micromirrors with high diffraction efficiency, achromatic aberration and long focal depth,” Opt. Commun. 283, 1661–1667 (2010).
[CrossRef]

J. S. Ye, Y. Zhang, and K. Hane, “Improved first Rayleigh-Sommerfeld method applied to metallic cylindrical focusing micro mirrors,” Opt. Express 17, 7348–7360 (2009).
[CrossRef] [PubMed]

Zhao, H. F.

J. L. Liu, J. Lin, H. F. Zhao, and S. T. Liu, “Analysis of closed-boundary cylindrical microlenses with long focal depth designed by the general focal length function,” Opt. Commun. 281, 4188–4193 (2008).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. A (7)

S. Q. Wang, J. Liu, B. Y. Gu, Y. Q. Wang, B. Hu, X. D. Sun, and S. Di, “Rigorous electromagnetic analysis of the common focusing characteristics of a cylindrical microlens with long focal depth and under multiwavelength illumination,” J. Opt. Soc. Am. A 24, 512–516 (2007).
[CrossRef]

J. Lin, J. L. Liu, J. S. Ye, and S. T. Liu, “Design of microlenses with long focal depth based on the general focal length function,” J. Opt. Soc. Am. A 24, 1747–1751 (2007).
[CrossRef]

J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, “Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors,” J. Opt. Soc. Am. A 16, 113–130 (1999).
[CrossRef]

B. Z. Dong, G. Z. Yang, B. Y. Gu, and 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, and D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).
[CrossRef]

B. Z. Dong, J. Liu, B. Y. Gu, G. Z. Yang, and 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]

J. S. Ye, B. Z. Dong, B. Y. Gu, G. Z. Yang, and S. T. Liu, “Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on rigorous electromagnetic theory,” J. Opt. Soc. Am. A 19, 2030–2035 (2002).
[CrossRef]

Opt. Commun. (2)

J. L. Liu, J. Lin, H. F. Zhao, and S. T. Liu, “Analysis of closed-boundary cylindrical microlenses with long focal depth designed by the general focal length function,” Opt. Commun. 281, 4188–4193 (2008).
[CrossRef]

J. S. Ye and Y. Zhang, “Rigorous electromagnetic analysis of metallic cylindrical focusing micromirrors with high diffraction efficiency, achromatic aberration and long focal depth,” Opt. Commun. 283, 1661–1667 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Other (1)

L. Ward, “Optical constants of eight rare-earth elements,” in Handbook of Optical Constants of Solids, E.D.Palik ed. (Academic, 1985), Vol.  3, pp. 294.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the 2D open-boundary LFD MCFM.

Fig. 2
Fig. 2

Scattered electric field intensity distributions in region S 1 for the f / 1.0 LFD MCFMs with preset focal depths of (a)  δ f = 0 μm , (b)  δ f = 10 μm , and (c)  δ f = 20 μm . The diameters and beginning focal lengths are all 10 μm . The FLEMF is chosen to be 2.0. The incident light is TE polarized with a free-space wavelength of 0.6888 μm . The red (blue) districts indicate the regions with high (low) field intensities, respectively.

Fig. 3
Fig. 3

(a) Blue (top), green (middle), and red (bottom) curves represent the normalized axial intensity distributions of the f / 1.0 LFD MCFMs with preset focal depths of 0, 10, and 20 μm , respectively. Parameters are the same as those in Fig. 2. (b) Scattered electric field intensity distributions on three lateral planes within the LFD region for the f / 1.0 LFD MCFM with a preset focal depth of 10 μm . Solid curve illustrates the intensity profile on the real focal plane with y = 16.36 μm , the magenta dashed and black dashed curves correspond to the two transverse planes ( y = 13.10 and 21.09 μm ) with 80% of the maximum axial intensity.

Fig. 4
Fig. 4

(a) Relative focal depth versus the FLEMF for the f / 1.0 LFD MCFMs with different preset focal depths. Other pa rameters are the same as above. The blue (bottom) and red (top) curves correspond to preset focal depths of 10 and 20 μm , respectively. (b) Normalized axial intensity distributions for the f / 1.0 LFD MCFM with a preset focal depth of 20 μm . The black and the red (gray in print) curves correspond to FLEMFs of 3.5 and 2.0, respectively. The dashed lines identify the LFD regions.

Fig. 5
Fig. 5

Focal performance of the f / 0.5 LFD MCFMs with negative preset focal depths. The beginning focal lengths are 5 μm , the diameters are 10 μm , and the FLEMF is 2.0. The incident wavelength is 0.6888 μm . The incident polarization is TE polarization. The blue (spikey) and the red curves respectively represent the focal spot size and the diffraction efficiency, corresponding to the left and right vertical axes.

Fig. 6
Fig. 6

Normalized axial intensity distributions of the f / 1.0 LFD MCFMs under multiwavelength illumination for preset focal depths of (a)  10 μm and (b)  20 μm . The diameters and beginning focal lengths are 10 μm . The FLEMF is 2.0. The incident polarization is TE polarization. The blue (top), green (middle), and red (bottom) curves denote incident wavelengths of 0.6888, 0.8266, and 0.9537 μm , respectively. The beginning and ending positions of the common LFD regions are marked by the two arrows.

Tables (4)

Tables Icon

Table 1 Focal Performance of the LFD MCFMs with Different f-Numbers

Tables Icon

Table 2 Focal Performance of the f / 1.0 LFD MCFMs with Negative Preset Focal Depths

Tables Icon

Table 3 Common LFD Properties of the f / 1.0 MCFMs under Multiwavelength Illumination

Tables Icon

Table 4 Common LFD Properties of the f / 0.5 MCFMs under Multiwavelength Illumination

Equations (2)

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h ( x ) = x 2 4 f ,
f ( x ) = f 0 + δ f | x R | a ,

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