Abstract

An improved first Rayleigh-Sommerfeld method (IRSM1) is intensively applied to analyzing the focal properties of metallic cylindrical focusing micro mirrors. A variety of metallic cylindrical focusing mirrors with different f-numbers, different polarization of incidence, or different types of profiles are investigated. The focal properties include the focal spot size, the diffraction efficiency, the real focal length, the total reflected power, and the normalized sidelobe power. Numerical results calculated by the IRSM1, the original first Rayleigh-Sommerfeld method (ORSM1), and the rigorous boundary element method (BEM) are presented for quantitative comparison. It is found that the IRSM1 is much more accurate than the ORSM1 in performance analysis of metallic cylindrical focusing mirrors, especially for cylindrical refractive focusing mirrors with small f-numbers. Moreover, the IRSM1 saves great amounts of computational time and computer memory in calculations, in comparison with the vectorial BEM.

© 2009 Optical Society of America

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  1. Feature issue on "Diffractive optics appliations,"Appl. Opt. 34, 2399-2559 (1995).
    [CrossRef]
  2. D. A. Pommet, M. G. Moharam, and E. B. Grann, "Limits of scalar diffraction theory for diffractive phase elements," J. Opt. Soc. Am. A 11, 1827-1834 (1994).
    [CrossRef]
  3. J. N. Mait, "Understanding diffractive optic design in the scalar domain," J. Opt. Soc. Am. A 12, 2145-2158 (1995).
    [CrossRef]
  4. J. M. Bendickson, E. N. Glytsis, and 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]
  5. 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]
  6. 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]
  7. D. W. Prather, M. S. Mirotznik, and J. N. Mait, "Boundary integral methods applied to the analysis of diffractive optical elements," J. Opt. Soc. Am. A 14, 34-43 (1997).
    [CrossRef]
  8. K. Hirayama, E. N. Glytsis, and T. K. Gaylord, "Rigorous electromagnetic analysis of diffraction by finite number-of-periods gratings," J. Opt. Soc. Am. A 14, 907-917 (1997).
    [CrossRef]
  9. H. Haidner, S. Schröter, and H. Bartelt, "The optimization of diffractive binary mirrors with low focal length: diameter ratios," J. Phys. D 30, 1314-1325 (1997).
    [CrossRef]
  10. J. B. Judkins and R.W. Ziolkowski, "Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings," J. Opt. Soc. Am. A 12, 1974-1983 (1995).
    [CrossRef]
  11. Y. Nakata and M. Koshiba, "Boundary-element analysis of plane-wave diffraction from groove-type dielectric and metallic gratings," J. Opt. Soc. Am. A 7, 1494-1502 (1990).
    [CrossRef]
  12. 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]
  13. E. Noponen, J. Turunen, and A. Vasara, "Electromagnetic theory and design of diffractive-lens arrays," J. Opt. Soc. Am. A 10, 434-443 (1993).
    [CrossRef]
  14. D. M. Mackie, D.W. Prather, and S. Y. Shi, "Preoptimization improvements to subwavelength diffractive lenses," Appl. Opt. 41, 6168-6175 (2002).
    [CrossRef]
  15. J. S. Ye, B. Y. Gu, B. Z. Dong, and S. T. Liu, "Improved first Rayleigh-Sommerfeld method for analysis of cylindrical microlenses with small f-numbers," Opt. Lett. 29, 2345-2347 (2004).
    [CrossRef]
  16. J. S. Ye, B. Y. Gu, B. Z. Dong, and S. T. Liu, "Applications of improved first Rayleigh-Sommerfeld method to analyze the performance of cylindrical microlenses with different f-numbers," J. Opt. Soc. Am. A 22, 862-869 (2005).
    [CrossRef]
  17. C. Rydberg, B. Y. Gu, and G. Z. Yang, "Design method for small-f-number microlenses based on a finite thickness model in combination with the Yang-Gu phase-retrieval algorithm," J. Opt. Soc. Am. A 24, 517-521 (2007).
    [CrossRef]
  18. M. Koshiba, OpticalWaveguide Theory by the Finite Element Method (KTK Scientific, Tokyo, 1992), pp. 43-47.
  19. 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]
  20. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999), Chap. 1.
  21. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chaps. 3 and 4.
  22. E. D. Palik ed., Handbook of Optical Constants of Solids (Academic Press, INC., Orlando, Florida, 1985), pp. 356.

2007 (1)

2005 (1)

2004 (1)

2002 (2)

2001 (1)

1999 (1)

1998 (1)

1997 (3)

1996 (1)

1995 (3)

1994 (1)

1993 (1)

1990 (1)

Bartelt, H.

H. Haidner, S. Schröter, and H. Bartelt, "The optimization of diffractive binary mirrors with low focal length: diameter ratios," J. Phys. D 30, 1314-1325 (1997).
[CrossRef]

Bendickson, J. M.

Dong, B. Z.

Gaylord, T. K.

Glytsis, E. N.

Grann, E. B.

Gu, B. Y.

Haidner, H.

H. Haidner, S. Schröter, and H. Bartelt, "The optimization of diffractive binary mirrors with low focal length: diameter ratios," J. Phys. D 30, 1314-1325 (1997).
[CrossRef]

Hirayama, K.

Judkins, J. B.

Koshiba, M.

Liu, J.

Liu, S. T.

Mackie, D. M.

Mait, J. N.

Mirotznik, M. S.

Moharam, M. G.

Nakata, Y.

Noponen, E.

Pommet, D. A.

Prather, D. W.

Prather, D.W.

Rydberg, C.

Schröter, S.

H. Haidner, S. Schröter, and H. Bartelt, "The optimization of diffractive binary mirrors with low focal length: diameter ratios," J. Phys. D 30, 1314-1325 (1997).
[CrossRef]

Shi, S. Y.

Turunen, J.

Vasara, A.

Wang, J.

Wilson, D. W.

Yang, G. Z.

Ye, J. S.

Ziolkowski, R.W.

Appl. Opt. (2)

J. Opt. Soc. Am. A (14)

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]

D. A. Pommet, M. G. Moharam, and E. B. Grann, "Limits of scalar diffraction theory for diffractive phase elements," J. Opt. Soc. Am. A 11, 1827-1834 (1994).
[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]

J. M. Bendickson, E. N. Glytsis, and 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, and J. N. Mait, "Boundary integral methods applied to the analysis of diffractive optical elements," J. Opt. Soc. Am. A 14, 34-43 (1997).
[CrossRef]

K. Hirayama, E. N. Glytsis, and T. K. Gaylord, "Rigorous electromagnetic analysis of diffraction by finite number-of-periods gratings," J. Opt. Soc. Am. A 14, 907-917 (1997).
[CrossRef]

Y. Nakata and M. Koshiba, "Boundary-element analysis of plane-wave diffraction from groove-type dielectric and metallic gratings," J. Opt. Soc. Am. A 7, 1494-1502 (1990).
[CrossRef]

E. Noponen, J. Turunen, and A. Vasara, "Electromagnetic theory and design of diffractive-lens arrays," J. Opt. Soc. Am. A 10, 434-443 (1993).
[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]

J. B. Judkins and R.W. Ziolkowski, "Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings," J. Opt. Soc. Am. A 12, 1974-1983 (1995).
[CrossRef]

J. N. Mait, "Understanding diffractive optic design in the scalar domain," J. Opt. Soc. Am. A 12, 2145-2158 (1995).
[CrossRef]

J. S. Ye, B. Y. Gu, B. Z. Dong, and S. T. Liu, "Applications of improved first Rayleigh-Sommerfeld method to analyze the performance of cylindrical microlenses with different f-numbers," J. Opt. Soc. Am. A 22, 862-869 (2005).
[CrossRef]

C. Rydberg, B. Y. Gu, and G. Z. Yang, "Design method for small-f-number microlenses based on a finite thickness model in combination with the Yang-Gu phase-retrieval algorithm," J. Opt. Soc. Am. A 24, 517-521 (2007).
[CrossRef]

J. Phys. D (1)

H. Haidner, S. Schröter, and H. Bartelt, "The optimization of diffractive binary mirrors with low focal length: diameter ratios," J. Phys. D 30, 1314-1325 (1997).
[CrossRef]

Opt. Lett. (1)

Other (4)

M. Koshiba, OpticalWaveguide Theory by the Finite Element Method (KTK Scientific, Tokyo, 1992), pp. 43-47.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999), Chap. 1.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chaps. 3 and 4.

E. D. Palik ed., Handbook of Optical Constants of Solids (Academic Press, INC., Orlando, Florida, 1985), pp. 356.

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