Abstract

Metallic surface-relief diffractive cylindrical mirrors are designed for on-axis and off-axis focusing and incidence configurations. These diffractive structures are analyzed by both rigorous and scalar integral methods. Two design methods, based on initial assumptions of zero-thickness and finite-thickness structures, are presented for determining the zone-boundary locations and the surface-relief mirror profiles for the general case of an off-axis incident plane wave and off-axis focusing. With the use of these methods, continuous diffractive, multilevel diffractive, and continuous nondiffractive mirrors were designed. Rigorous analysis is performed for both TE and TM polarizations by using an open-region formulation of the boundary element method (BEM) suitable for regions of complex refractive index such as finite-conductivity metals. Three scalar integral methods corresponding to Dirichlet, Neumann, and Kirchhoff boundary conditions are also used to analyze the diffractive mirrors. The diffracted fields from both the rigorous BEM and the scalar methods of analysis are used to calculate a number of performance metrics including diffraction efficiency, sidelobe power, total reflected power, and focal spot size. The performance of the mirrors is evaluated, and the accuracy of the various scalar methods is determined.

© 1999 Optical Society of America

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  1. Feature issue on diffractive optics applications, Appl. Opt. 34, 2399–2559 (1995).
  2. V. P. Koronkevich, I. G. Pal’chikova, “Modern zone plates,” Avtometriya (No. 1), 85–100 (1992).
  3. V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
    [CrossRef]
  4. Y. Hori, H. Asakura, F. Sogawa, M. Kato, H. Serizawa, “External-cavity semiconductor laser with focusing grating mirror,” IEEE J. Quantum Electron. 26, 1747–1755 (1990).
    [CrossRef]
  5. J. W. Goodman, F. J. Leonberger, S.-Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
    [CrossRef]
  6. W. H. Wu, L. A. Bergman, A. R. Johnston, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron Devices ED-34, 706–714 (1987).
    [CrossRef]
  7. J. Jahns, A. Huang, “Planar integration of free-space optical components,” Appl. Opt. 28, 1602–1605 (1989).
    [CrossRef] [PubMed]
  8. Y. H. Lee, J. L. Jewell, J. Jahns, “Microlasers for photonic switching and interconnection,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. SPIE1319, 683–684 (1990).
    [CrossRef]
  9. A. K. Ghosh, “Compact joint transform correlators in planar integrated packages,” in Optical Information Processing Systems and Architectures III, B. Javidi, ed., Proc. SPIE1564, 231–235 (1991).
    [CrossRef]
  10. J. Jahns, “Integrated microoptics for computing and switching applications,” in Miniature and Micro-Optics: Fabrication and System Applications, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. SPIE1544, 246–262 (1991).
    [CrossRef]
  11. B. Acklin, J. Jahns, “Packaging considerations for planar optical interconnection systems,” Appl. Opt. 33, 1391–1397 (1994).
    [CrossRef] [PubMed]
  12. M. J. O’Callaghan, S. H. Perlmutter, R. TeKolste, “Compact optical processing systems using off-axis diffractive optics and FLC-VLSI spatial light modulators,” in Materials, Devices, and Systems for Optoelectronic Processing, J. A. Neff, B. Javidi, eds., Proc. SPIE2848, 72–80 (1996).
    [CrossRef]
  13. S. H. Song, E-H. Lee, S. T. Park, P. S. Kim, “Optical imaging and transforming by using planar integrated optics,” in Optics for Science and New Technology, J.-S. Chang, J. Lee, S. Lee, C. Nam, eds., Proc. SPIE2778, 25–30 (1996).
  14. G. J. Swanson, W. B. Veldkamp, “Binary lenses for use at 10.6 micrometers,” Opt. Eng. (Bellingham) 24, 791–795 (1985).
    [CrossRef]
  15. G. A. Lenkova, “Deflecting focusing kinoform,” Avtometriya (No. 6), 7–12 (1985).
  16. A. Dubik, M. Zajonc, E. Novak, “Focusing kinoform mirror,” Avtometriya (No. 2), 85–88 (1990).
  17. H. Haidner, S. Schröter, H. Bartelt, “The optimization of diffractive binary mirrors with low focal length: diameter ratios,” J. Phys. D 30, 1314–1325 (1997).
    [CrossRef]
  18. E. Hasman, N. Davidson, Y. Danziger, A. A. Friesem, “Diffractive optics: design, realization, and applications,” Fiber Integr. Opt. 16, 1–25 (1997).
    [CrossRef]
  19. Y-L. Kok, “Design of a binary chirped grating for near-field operation,” Opt. Eng. (Bellingham) 33, 3604–3609 (1994).
    [CrossRef]
  20. P. Kipfer, M. Collischon, H. Haidner, J. Schwider, “Diffractive surface relief elements for the use in the infrared: waveguide structures as reflection holograms,” in Non-conventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 100–107 (1994).
    [CrossRef]
  21. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chaps. 3 and 4.
  22. E. Yamashita, Analysis Methods for Electromagnetic Wave Problems (Artech House, Boston, 1990), Chap. 2.
  23. M. Koshiba, Optical Waveguide Theory by the Finite Element Method (KTK Scientific, Tokyo, 1992), pp. 43–47.
  24. K. Miyata, I. Fukai, “Radiation pattern analysis of an offset cylindrical reflector antenna by boundary element method,” Trans. IEICE E70, 761–767 (1987).
  25. Y. Funabiki, T. Kojima, “Analysis of light-beam scattering and the sum and differential signal output by arbitrarily shaped pits and bosses,” Electron. Commun. Jpn., Part 2: Electron. 72, 37–46 (1989).
    [CrossRef]
  26. K. Manabe, Y. Miyazaki, T. Tanaka, “An analysis of scattered near field and induced current of a beam wave by pits on optical disk using boundary element method,” Electron. Commun. Jpn., Part 2: Electron. 72, 1–8 (1989).
    [CrossRef]
  27. T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).
    [CrossRef]
  28. D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary element method for vector modeling diffractive optical elements,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 28–39 (1995).
    [CrossRef]
  29. K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffraction by finite-number-of-periods gratings,” J. Opt. Soc. Am. A 14, 907–917 (1997).
    [CrossRef]
  30. 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]
  31. Y. Nakata, 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]
  32. K. Hirayama, E. N. Glytsis, T. K. Gaylord, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13, 2219–2231 (1996).
    [CrossRef]
  33. 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]
  34. 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]
  35. J. B. Judkins, 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]
  36. J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, “Kinoform lenses,” Appl. Opt. 9, 1883–1887 (1970).
    [PubMed]
  37. E. Noponen, J. Turunen, A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
    [CrossRef]
  38. D. A. Buralli, G. M. Morris, J. R. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 28, 976–983 (1989).
    [CrossRef] [PubMed]
  39. M. Abramowitz, I. E. Stegun, eds., Handbook of Mathematical Functions, Applied Mathematics Series 55 (National Bureau of Standards, Washington, D.C., 1964), p. 364.
  40. J. J. Stamnes, Waves in Focal Regions (Hilger, Boston, 1986), Chaps. 4, 5.
  41. A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991), Chap. 6.
  42. S. Solimeno, B. Crosignani, P. Di Porto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 4.
  43. G. S. Smith, An Introduction to Classical Electromagnetic Radiation (Cambridge U. Press, Port Chester, N.Y., 1997), Chap. 3.
  44. G. Hass, L. Hadley, “Optical properties of metals,” in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 6–119.
  45. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, New York, 1980), Chap. 6.

1998 (2)

1997 (5)

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]

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

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

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

E. Hasman, N. Davidson, Y. Danziger, A. A. Friesem, “Diffractive optics: design, realization, and applications,” Fiber Integr. Opt. 16, 1–25 (1997).
[CrossRef]

1996 (1)

1995 (2)

1994 (2)

B. Acklin, J. Jahns, “Packaging considerations for planar optical interconnection systems,” Appl. Opt. 33, 1391–1397 (1994).
[CrossRef] [PubMed]

Y-L. Kok, “Design of a binary chirped grating for near-field operation,” Opt. Eng. (Bellingham) 33, 3604–3609 (1994).
[CrossRef]

1993 (1)

1992 (1)

V. P. Koronkevich, I. G. Pal’chikova, “Modern zone plates,” Avtometriya (No. 1), 85–100 (1992).

1991 (1)

T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).
[CrossRef]

1990 (3)

A. Dubik, M. Zajonc, E. Novak, “Focusing kinoform mirror,” Avtometriya (No. 2), 85–88 (1990).

Y. Hori, H. Asakura, F. Sogawa, M. Kato, H. Serizawa, “External-cavity semiconductor laser with focusing grating mirror,” IEEE J. Quantum Electron. 26, 1747–1755 (1990).
[CrossRef]

Y. Nakata, 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]

1989 (4)

D. A. Buralli, G. M. Morris, J. R. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 28, 976–983 (1989).
[CrossRef] [PubMed]

J. Jahns, A. Huang, “Planar integration of free-space optical components,” Appl. Opt. 28, 1602–1605 (1989).
[CrossRef] [PubMed]

Y. Funabiki, T. Kojima, “Analysis of light-beam scattering and the sum and differential signal output by arbitrarily shaped pits and bosses,” Electron. Commun. Jpn., Part 2: Electron. 72, 37–46 (1989).
[CrossRef]

K. Manabe, Y. Miyazaki, T. Tanaka, “An analysis of scattered near field and induced current of a beam wave by pits on optical disk using boundary element method,” Electron. Commun. Jpn., Part 2: Electron. 72, 1–8 (1989).
[CrossRef]

1987 (2)

K. Miyata, I. Fukai, “Radiation pattern analysis of an offset cylindrical reflector antenna by boundary element method,” Trans. IEICE E70, 761–767 (1987).

W. H. Wu, L. A. Bergman, A. R. Johnston, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron Devices ED-34, 706–714 (1987).
[CrossRef]

1985 (2)

G. J. Swanson, W. B. Veldkamp, “Binary lenses for use at 10.6 micrometers,” Opt. Eng. (Bellingham) 24, 791–795 (1985).
[CrossRef]

G. A. Lenkova, “Deflecting focusing kinoform,” Avtometriya (No. 6), 7–12 (1985).

1984 (1)

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

1970 (1)

Acklin, B.

Asakura, H.

Y. Hori, H. Asakura, F. Sogawa, M. Kato, H. Serizawa, “External-cavity semiconductor laser with focusing grating mirror,” IEEE J. Quantum Electron. 26, 1747–1755 (1990).
[CrossRef]

Athale, R. A.

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Bartelt, H.

H. Haidner, S. Schröter, 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.

Bergman, L. A.

W. H. Wu, L. A. Bergman, A. R. Johnston, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron Devices ED-34, 706–714 (1987).
[CrossRef]

Buralli, D. A.

Collischon, M.

P. Kipfer, M. Collischon, H. Haidner, J. Schwider, “Diffractive surface relief elements for the use in the infrared: waveguide structures as reflection holograms,” in Non-conventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 100–107 (1994).
[CrossRef]

Crosignani, B.

S. Solimeno, B. Crosignani, P. Di Porto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 4.

Danziger, Y.

E. Hasman, N. Davidson, Y. Danziger, A. A. Friesem, “Diffractive optics: design, realization, and applications,” Fiber Integr. Opt. 16, 1–25 (1997).
[CrossRef]

Davidson, N.

E. Hasman, N. Davidson, Y. Danziger, A. A. Friesem, “Diffractive optics: design, realization, and applications,” Fiber Integr. Opt. 16, 1–25 (1997).
[CrossRef]

Di Porto, P.

S. Solimeno, B. Crosignani, P. Di Porto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 4.

Dubik, A.

A. Dubik, M. Zajonc, E. Novak, “Focusing kinoform mirror,” Avtometriya (No. 2), 85–88 (1990).

Esener, S. C.

W. H. Wu, L. A. Bergman, A. R. Johnston, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron Devices ED-34, 706–714 (1987).
[CrossRef]

Feldman, M. R.

W. H. Wu, L. A. Bergman, A. R. Johnston, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron Devices ED-34, 706–714 (1987).
[CrossRef]

Friesem, A. A.

E. Hasman, N. Davidson, Y. Danziger, A. A. Friesem, “Diffractive optics: design, realization, and applications,” Fiber Integr. Opt. 16, 1–25 (1997).
[CrossRef]

Fukai, I.

K. Miyata, I. Fukai, “Radiation pattern analysis of an offset cylindrical reflector antenna by boundary element method,” Trans. IEICE E70, 761–767 (1987).

Funabiki, Y.

Y. Funabiki, T. Kojima, “Analysis of light-beam scattering and the sum and differential signal output by arbitrarily shaped pits and bosses,” Electron. Commun. Jpn., Part 2: Electron. 72, 37–46 (1989).
[CrossRef]

Gaylord, T. K.

Ghosh, A. K.

A. K. Ghosh, “Compact joint transform correlators in planar integrated packages,” in Optical Information Processing Systems and Architectures III, B. Javidi, ed., Proc. SPIE1564, 231–235 (1991).
[CrossRef]

Glytsis, E. N.

Goodman, J. W.

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

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

Guest, C. C.

W. H. Wu, L. A. Bergman, A. R. Johnston, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron Devices ED-34, 706–714 (1987).
[CrossRef]

Hadley, L.

G. Hass, L. Hadley, “Optical properties of metals,” in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 6–119.

Haidner, H.

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

P. Kipfer, M. Collischon, H. Haidner, J. Schwider, “Diffractive surface relief elements for the use in the infrared: waveguide structures as reflection holograms,” in Non-conventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 100–107 (1994).
[CrossRef]

Harrigan, M. E.

Hasman, E.

E. Hasman, N. Davidson, Y. Danziger, A. A. Friesem, “Diffractive optics: design, realization, and applications,” Fiber Integr. Opt. 16, 1–25 (1997).
[CrossRef]

Hass, G.

G. Hass, L. Hadley, “Optical properties of metals,” in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 6–119.

Hirayama, K.

Hirsch, P. M.

Hori, Y.

Y. Hori, H. Asakura, F. Sogawa, M. Kato, H. Serizawa, “External-cavity semiconductor laser with focusing grating mirror,” IEEE J. Quantum Electron. 26, 1747–1755 (1990).
[CrossRef]

Huang, A.

Ido, J.

T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991), Chap. 6.

Jahns, J.

B. Acklin, J. Jahns, “Packaging considerations for planar optical interconnection systems,” Appl. Opt. 33, 1391–1397 (1994).
[CrossRef] [PubMed]

J. Jahns, A. Huang, “Planar integration of free-space optical components,” Appl. Opt. 28, 1602–1605 (1989).
[CrossRef] [PubMed]

J. Jahns, “Integrated microoptics for computing and switching applications,” in Miniature and Micro-Optics: Fabrication and System Applications, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. SPIE1544, 246–262 (1991).
[CrossRef]

Y. H. Lee, J. L. Jewell, J. Jahns, “Microlasers for photonic switching and interconnection,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. SPIE1319, 683–684 (1990).
[CrossRef]

Jewell, J. L.

Y. H. Lee, J. L. Jewell, J. Jahns, “Microlasers for photonic switching and interconnection,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. SPIE1319, 683–684 (1990).
[CrossRef]

Johnston, A. R.

W. H. Wu, L. A. Bergman, A. R. Johnston, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron Devices ED-34, 706–714 (1987).
[CrossRef]

Jordan, J. A.

Judkins, J. B.

Kato, M.

Y. Hori, H. Asakura, F. Sogawa, M. Kato, H. Serizawa, “External-cavity semiconductor laser with focusing grating mirror,” IEEE J. Quantum Electron. 26, 1747–1755 (1990).
[CrossRef]

Kim, P. S.

S. H. Song, E-H. Lee, S. T. Park, P. S. Kim, “Optical imaging and transforming by using planar integrated optics,” in Optics for Science and New Technology, J.-S. Chang, J. Lee, S. Lee, C. Nam, eds., Proc. SPIE2778, 25–30 (1996).

Kipfer, P.

P. Kipfer, M. Collischon, H. Haidner, J. Schwider, “Diffractive surface relief elements for the use in the infrared: waveguide structures as reflection holograms,” in Non-conventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 100–107 (1994).
[CrossRef]

Kojima, T.

T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).
[CrossRef]

Y. Funabiki, T. Kojima, “Analysis of light-beam scattering and the sum and differential signal output by arbitrarily shaped pits and bosses,” Electron. Commun. Jpn., Part 2: Electron. 72, 37–46 (1989).
[CrossRef]

Kok, Y-L.

Y-L. Kok, “Design of a binary chirped grating for near-field operation,” Opt. Eng. (Bellingham) 33, 3604–3609 (1994).
[CrossRef]

Koronkevich, V. P.

V. P. Koronkevich, I. G. Pal’chikova, “Modern zone plates,” Avtometriya (No. 1), 85–100 (1992).

Koshiba, M.

Kung, S.-Y.

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Lee, E-H.

S. H. Song, E-H. Lee, S. T. Park, P. S. Kim, “Optical imaging and transforming by using planar integrated optics,” in Optics for Science and New Technology, J.-S. Chang, J. Lee, S. Lee, C. Nam, eds., Proc. SPIE2778, 25–30 (1996).

Lee, S. H.

W. H. Wu, L. A. Bergman, A. R. Johnston, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron Devices ED-34, 706–714 (1987).
[CrossRef]

Lee, Y. H.

Y. H. Lee, J. L. Jewell, J. Jahns, “Microlasers for photonic switching and interconnection,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. SPIE1319, 683–684 (1990).
[CrossRef]

Lenkova, G. A.

G. A. Lenkova, “Deflecting focusing kinoform,” Avtometriya (No. 6), 7–12 (1985).

Leonberger, F. J.

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Lesem, L. B.

Mait, J. N.

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]

D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary element method for vector modeling diffractive optical elements,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 28–39 (1995).
[CrossRef]

Manabe, K.

K. Manabe, Y. Miyazaki, T. Tanaka, “An analysis of scattered near field and induced current of a beam wave by pits on optical disk using boundary element method,” Electron. Commun. Jpn., Part 2: Electron. 72, 1–8 (1989).
[CrossRef]

Mirotznik, M. S.

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]

D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary element method for vector modeling diffractive optical elements,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 28–39 (1995).
[CrossRef]

Miyata, K.

K. Miyata, I. Fukai, “Radiation pattern analysis of an offset cylindrical reflector antenna by boundary element method,” Trans. IEICE E70, 761–767 (1987).

Miyazaki, Y.

K. Manabe, Y. Miyazaki, T. Tanaka, “An analysis of scattered near field and induced current of a beam wave by pits on optical disk using boundary element method,” Electron. Commun. Jpn., Part 2: Electron. 72, 1–8 (1989).
[CrossRef]

Moreno, V.

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Morris, G. M.

Nakata, Y.

Noponen, E.

Novak, E.

A. Dubik, M. Zajonc, E. Novak, “Focusing kinoform mirror,” Avtometriya (No. 2), 85–88 (1990).

O’Callaghan, M. J.

M. J. O’Callaghan, S. H. Perlmutter, R. TeKolste, “Compact optical processing systems using off-axis diffractive optics and FLC-VLSI spatial light modulators,” in Materials, Devices, and Systems for Optoelectronic Processing, J. A. Neff, B. Javidi, eds., Proc. SPIE2848, 72–80 (1996).
[CrossRef]

Pal’chikova, I. G.

V. P. Koronkevich, I. G. Pal’chikova, “Modern zone plates,” Avtometriya (No. 1), 85–100 (1992).

Park, S. T.

S. H. Song, E-H. Lee, S. T. Park, P. S. Kim, “Optical imaging and transforming by using planar integrated optics,” in Optics for Science and New Technology, J.-S. Chang, J. Lee, S. Lee, C. Nam, eds., Proc. SPIE2778, 25–30 (1996).

Perlmutter, S. H.

M. J. O’Callaghan, S. H. Perlmutter, R. TeKolste, “Compact optical processing systems using off-axis diffractive optics and FLC-VLSI spatial light modulators,” in Materials, Devices, and Systems for Optoelectronic Processing, J. A. Neff, B. Javidi, eds., Proc. SPIE2848, 72–80 (1996).
[CrossRef]

Prather, D. W.

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]

D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary element method for vector modeling diffractive optical elements,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 28–39 (1995).
[CrossRef]

Rogers, J. R.

Román, J. F.

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Salgueiro, J. R.

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Schröter, S.

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

Schwider, J.

P. Kipfer, M. Collischon, H. Haidner, J. Schwider, “Diffractive surface relief elements for the use in the infrared: waveguide structures as reflection holograms,” in Non-conventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 100–107 (1994).
[CrossRef]

Serizawa, H.

Y. Hori, H. Asakura, F. Sogawa, M. Kato, H. Serizawa, “External-cavity semiconductor laser with focusing grating mirror,” IEEE J. Quantum Electron. 26, 1747–1755 (1990).
[CrossRef]

Smith, G. S.

G. S. Smith, An Introduction to Classical Electromagnetic Radiation (Cambridge U. Press, Port Chester, N.Y., 1997), Chap. 3.

Sogawa, F.

Y. Hori, H. Asakura, F. Sogawa, M. Kato, H. Serizawa, “External-cavity semiconductor laser with focusing grating mirror,” IEEE J. Quantum Electron. 26, 1747–1755 (1990).
[CrossRef]

Solimeno, S.

S. Solimeno, B. Crosignani, P. Di Porto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 4.

Song, S. H.

S. H. Song, E-H. Lee, S. T. Park, P. S. Kim, “Optical imaging and transforming by using planar integrated optics,” in Optics for Science and New Technology, J.-S. Chang, J. Lee, S. Lee, C. Nam, eds., Proc. SPIE2778, 25–30 (1996).

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Hilger, Boston, 1986), Chaps. 4, 5.

Swanson, G. J.

G. J. Swanson, W. B. Veldkamp, “Binary lenses for use at 10.6 micrometers,” Opt. Eng. (Bellingham) 24, 791–795 (1985).
[CrossRef]

Tanaka, T.

K. Manabe, Y. Miyazaki, T. Tanaka, “An analysis of scattered near field and induced current of a beam wave by pits on optical disk using boundary element method,” Electron. Commun. Jpn., Part 2: Electron. 72, 1–8 (1989).
[CrossRef]

TeKolste, R.

M. J. O’Callaghan, S. H. Perlmutter, R. TeKolste, “Compact optical processing systems using off-axis diffractive optics and FLC-VLSI spatial light modulators,” in Materials, Devices, and Systems for Optoelectronic Processing, J. A. Neff, B. Javidi, eds., Proc. SPIE2848, 72–80 (1996).
[CrossRef]

Turunen, J.

Van Rooy, D. L.

Vasara, A.

Veldkamp, W. B.

G. J. Swanson, W. B. Veldkamp, “Binary lenses for use at 10.6 micrometers,” Opt. Eng. (Bellingham) 24, 791–795 (1985).
[CrossRef]

Wu, W. H.

W. H. Wu, L. A. Bergman, A. R. Johnston, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron Devices ED-34, 706–714 (1987).
[CrossRef]

Yamashita, E.

E. Yamashita, Analysis Methods for Electromagnetic Wave Problems (Artech House, Boston, 1990), Chap. 2.

Yu, P. K. L.

W. H. Wu, L. A. Bergman, A. R. Johnston, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron Devices ED-34, 706–714 (1987).
[CrossRef]

Zajonc, M.

A. Dubik, M. Zajonc, E. Novak, “Focusing kinoform mirror,” Avtometriya (No. 2), 85–88 (1990).

Ziolkowski, R. W.

Am. J. Phys. (1)

V. Moreno, J. F. Román, J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Appl. Opt. (6)

Avtometriya (3)

G. A. Lenkova, “Deflecting focusing kinoform,” Avtometriya (No. 6), 7–12 (1985).

A. Dubik, M. Zajonc, E. Novak, “Focusing kinoform mirror,” Avtometriya (No. 2), 85–88 (1990).

V. P. Koronkevich, I. G. Pal’chikova, “Modern zone plates,” Avtometriya (No. 1), 85–100 (1992).

Electron. Commun. Jpn., Part 2: Electron. (3)

Y. Funabiki, T. Kojima, “Analysis of light-beam scattering and the sum and differential signal output by arbitrarily shaped pits and bosses,” Electron. Commun. Jpn., Part 2: Electron. 72, 37–46 (1989).
[CrossRef]

K. Manabe, Y. Miyazaki, T. Tanaka, “An analysis of scattered near field and induced current of a beam wave by pits on optical disk using boundary element method,” Electron. Commun. Jpn., Part 2: Electron. 72, 1–8 (1989).
[CrossRef]

T. Kojima, J. Ido, “Boundary-element method analysis of light-beam scattering and the sum and differential signal output by DRAW-type optical disk models,” Electron. Commun. Jpn., Part 2: Electron. 74, 11–20 (1991).
[CrossRef]

Fiber Integr. Opt. (1)

E. Hasman, N. Davidson, Y. Danziger, A. A. Friesem, “Diffractive optics: design, realization, and applications,” Fiber Integr. Opt. 16, 1–25 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. Hori, H. Asakura, F. Sogawa, M. Kato, H. Serizawa, “External-cavity semiconductor laser with focusing grating mirror,” IEEE J. Quantum Electron. 26, 1747–1755 (1990).
[CrossRef]

IEEE Trans. Electron Devices (1)

W. H. Wu, L. A. Bergman, A. R. Johnston, C. C. Guest, S. C. Esener, P. K. L. Yu, M. R. Feldman, S. H. Lee, “Implementation of optical interconnections for VLSI,” IEEE Trans. Electron Devices ED-34, 706–714 (1987).
[CrossRef]

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

J. Phys. D (1)

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

Opt. Eng. (Bellingham) (2)

G. J. Swanson, W. B. Veldkamp, “Binary lenses for use at 10.6 micrometers,” Opt. Eng. (Bellingham) 24, 791–795 (1985).
[CrossRef]

Y-L. Kok, “Design of a binary chirped grating for near-field operation,” Opt. Eng. (Bellingham) 33, 3604–3609 (1994).
[CrossRef]

Proc. IEEE (1)

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Trans. IEICE (1)

K. Miyata, I. Fukai, “Radiation pattern analysis of an offset cylindrical reflector antenna by boundary element method,” Trans. IEICE E70, 761–767 (1987).

Other (17)

D. W. Prather, M. S. Mirotznik, J. N. Mait, “Boundary element method for vector modeling diffractive optical elements,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 28–39 (1995).
[CrossRef]

M. Abramowitz, I. E. Stegun, eds., Handbook of Mathematical Functions, Applied Mathematics Series 55 (National Bureau of Standards, Washington, D.C., 1964), p. 364.

J. J. Stamnes, Waves in Focal Regions (Hilger, Boston, 1986), Chaps. 4, 5.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991), Chap. 6.

S. Solimeno, B. Crosignani, P. Di Porto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla., 1986), Chap. 4.

G. S. Smith, An Introduction to Classical Electromagnetic Radiation (Cambridge U. Press, Port Chester, N.Y., 1997), Chap. 3.

G. Hass, L. Hadley, “Optical properties of metals,” in American Institute of Physics Handbook, D. E. Gray, ed. (McGraw-Hill, New York, 1972), pp. 6–119.

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

Y. H. Lee, J. L. Jewell, J. Jahns, “Microlasers for photonic switching and interconnection,” in Optics in Complex Systems, F. Lanzl, H. Preuss, G. Weigelt, eds., Proc. SPIE1319, 683–684 (1990).
[CrossRef]

A. K. Ghosh, “Compact joint transform correlators in planar integrated packages,” in Optical Information Processing Systems and Architectures III, B. Javidi, ed., Proc. SPIE1564, 231–235 (1991).
[CrossRef]

J. Jahns, “Integrated microoptics for computing and switching applications,” in Miniature and Micro-Optics: Fabrication and System Applications, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. SPIE1544, 246–262 (1991).
[CrossRef]

P. Kipfer, M. Collischon, H. Haidner, J. Schwider, “Diffractive surface relief elements for the use in the infrared: waveguide structures as reflection holograms,” in Non-conventional Optical Imaging Elements, J. Nowak, M. Zajac, eds., Proc. SPIE2169, 100–107 (1994).
[CrossRef]

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

E. Yamashita, Analysis Methods for Electromagnetic Wave Problems (Artech House, Boston, 1990), Chap. 2.

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

M. J. O’Callaghan, S. H. Perlmutter, R. TeKolste, “Compact optical processing systems using off-axis diffractive optics and FLC-VLSI spatial light modulators,” in Materials, Devices, and Systems for Optoelectronic Processing, J. A. Neff, B. Javidi, eds., Proc. SPIE2848, 72–80 (1996).
[CrossRef]

S. H. Song, E-H. Lee, S. T. Park, P. S. Kim, “Optical imaging and transforming by using planar integrated optics,” in Optics for Science and New Technology, J.-S. Chang, J. Lee, S. Lee, C. Nam, eds., Proc. SPIE2778, 25–30 (1996).

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Figures (7)

Fig. 1
Fig. 1

Geometry for the open-region integral equation formulation and various parameters related to diffractive mirror designs. The boundary Γ divides all space into the open, semi-infinite regions S1 with real refractive index n1 and S2 with complex refractive index n˜2. The linear boundary Γr is used in the scalar methods to determine the reflected fields. A wave is incident at an arbitrary angle α from region S1 and is to be focused by the metallic diffractive mirror to the point (xf, f), which makes an angle β with the positive y axis. The surface-relief profile of the metallic diffractive mirror is given by h(x), which can be a stepwise function as shown, or a continuous or piecewise-continuous function depending on the mirror type. The quantity x0 gives the location of the center of the central Fresnel zone, xm- and xm+1- are Fresnel zone boundaries, and xm,i- is the location of a step transition within the mth zone of a multilevel mirror.

Fig. 2
Fig. 2

(a) Geometry used to determine the center point of the central Fresnel zone x0 of a diffractive mirror for arbitrary incidence and focusing angles. The ray that is incident at x0 is specularly reflected to the focal point (xf, f) according to the optical law of reflection. (b) Geometry used to determine the surface-relief profile hft(x) for the finite-thickness mirror design. The dashed lines indicate planes of constant phase. The distance between them, δ(x), indicates the path difference between a ray incident at an arbitrary point within a particular Fresnel zone of the mirror and a ray incident at the inner zone boundary of the same zone.

Fig. 3
Fig. 3

Diffracted field intensity for two-level, four-level, and eight-level diffractive mirrors and a continuous nondiffractive mirror, all designed for normal incidence and on-axis focusing. All mirrors are designed with D=500 µm, f=375 µm, and n˜2=11.5-j67.5 corresponding to gold for λ0=10 µm. The diffracted fields are determined by using the BEM for TE incidence. Dark regions indicate areas of high field intensity.

Fig. 4
Fig. 4

(a) Diffraction efficiency, (b) normalized sidelobe power, (c) normalized reflected power, and (d) normalized spot size versus f-number for eight-level diffractive mirrors designed for normal incidence and on-axis focusing. All mirrors are designed with D=500 µm and n˜2=11.5-j67.5. The mirrors have been analyzed by the rigorous BEM for both TE and TM incidence and by the Dirichlet, Neumann, and Kirchhoff scalar integral methods.

Fig. 5
Fig. 5

Diffracted field intensity as determined by the BEM for TE and TM incidence on an eight-level diffractive mirror designed for normal incidence and 45° off-axis focusing. The mirror is designed with D=500 µm, f=375 µm, and n˜2=11.5-j67.5.

Fig. 6
Fig. 6

Same as Fig. 5, but for 45° off-axis incidence and on-axis focusing.

Fig. 7
Fig. 7

Diffracted field intensity as determined by the BEM for TE incidence on an eight-level diffractive mirror designed for (a) 5° off-axis incidence and 5° off-axis focusing, (b) 25° off-axis incidence and 25° off-axis focusing, and (c) 45° off-axis incidence and 45° off-axis focusing. All mirrors are designed with D=500 µm, f=375 µm, and n˜2=11.5-j67.5.

Tables (6)

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Table 1 Normalized Total Reflected Power Obtained with the BEM and Scalar Methods for Various Types of Focusing Mirror Profile

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Table 2 Diffraction Efficiency Obtained with the BEM and Scalar Methods for Various Types of Focusing Mirror Profile

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Table 3 Normalized Sidelobe Power Obtained with the BEM and Scalar Methods for Various Types of Focusing Mirror Profile

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Table 4 Diffraction Efficiency Obtained with the BEM and Scalar Methods for Eight-Level f/0.75 Diffractive Mirrors in Various Off-Axis Incidence and/or Off-Axis Focusing Configurations

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Table 5 Normalized Total Reflected Power Obtained with the BEM and Scalar Methods for Eight-Level f/0.75 Diffractive Mirrors in Various Off-Axis Incidence and/or Off-Axis Focusing Configurations

Tables Icon

Table 6 Normalized Average Sidelobe Power Obtained with the BEM and Scalar Methods for Eight-Level f/0.75 Diffractive Mirrors in Various Off-Axis Incidence and/or Off-Axis Focusing Configurations

Equations (37)

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x0=f(tan β-tan α).
(xm±-x0)sin α+[(xm±-xf)2+f2]1/2
-[(x0-xf)2+f2]1/2=mλ1,m=1, 2, ,
xm±=x0+[-mλ1 sin α±(m2λ12+2mλ1f cos α)1/2]sec2 α.
xm+|α=β=0°=-xm-|α=β=0°=(m2λ12+2mλ1f)1/2.
k1(x-x0)sin α+Φmir(x)+k1[(x-xf)2+f2]1/2
-k1[(x0-xf)2+f2]1/2=2πm,
hzt(x)=12{x sin α+[(x-xf)2+f2]1/2-f(cos α+tan β sin α)-mλ1}
forxm+xmin(xm+1+, D/2)ifxx0,formax(xm+1-,-D/2)xxm-ifxx0.
hzt(x)|α=β=0°=12(x2+f2-f-mλ1).
hzt(xm,i±)-i hmaxN=0fori=1, 2, , N-1,
k1δ(x)+k1{(x-xf)2+[f-hft(x)]2}1/2
-k1[(xm±-xf)2+f2]1/2=0
hft(x)=-B-(B2-4AC)1/22A,
A=sin2 α,
B=-2 f(1+cos2 α)-2 cos α(f tan β sin α-x sin α+mλ1),
C=(x-f tan β)2+f2-(f cos α+f tan β sin α-x sin α+mλ1)2.
hft(x)|α=β=0°=x2-2 fmλ1-m2λ124f+2mλ1.
-ϕ1t(r1)+ΓϕΓ(rΓ) G1n(r1, rΓ)-p1G1(r1, rΓ)ψΓ(rΓ)dl=-ϕinc(r1),r1S1,
ϕ2t(r2)+ΓϕΓ(rΓ) G2n(r2, rΓ)-p2G2(r2, rΓ)ψΓ(rΓ)dl=0,r2S2,
Gi(ri, rΓ)=-j4H0(2)(ki|ri-rΓ|)(i=1, 2),
ϕ1t(rΓ)=ϕ2t(rΓ)ϕΓ(rΓ),
1p1ϕ1tn(rΓ)=1p2ϕ2tn(rΓ)ψΓ(rΓ).
θΓ2π-1ϕΓ(rΓ)+ΓϕΓ(rΓ) G1n(rΓ, rΓ)-p1G1(rΓ, rΓ)ψΓ(rΓ)dl=-ϕinc(rΓ),
θΓ2πϕΓ(rΓ)+ΓϕΓ(rΓ) G2n(rΓ, rΓ)-p2G2(rΓ, rΓ)ψΓ(rΓ)dl=0,
ϕinc(r1)=ϕ0w(x)exp(-jk1x sin α)exp(jk1y cos α),r1S1,
ϕΓr(rΓr)=Rϕ0w(x)exp(-jk1x sin α)exp[-jΔ(x)]ϕΓrn(rΓr)=-jk1 cosα Rϕ0w(x)exp(-jk1x sin α)exp[-jΔ(x)]rΓr,
Δ(x)=-2γk1h(x),
ϕ1K(r1)=ϕ1inc(r1)+ΓrϕΓr(rΓr) G1n(r1, rΓr)-G1(r1, rΓr) ϕΓrn(rΓr)dl,r1S1.
ϕ1RS1(r1)=ϕ1inc(r1)+2ΓrϕΓr(rΓr) G1n(r1, rΓr)dl,r1S1.
ϕ1RS2(r1)=ϕ1inc(r1)-2ΓrG1(r1, rΓr) ϕΓrn(rΓr)dl,r1S1.
Φ(kx)=-ϕΓr(rΓr)exp(jkxx)dx,
ϕ1PW1(r1)=ϕ1inc(r1)+12π-Φ(kx)×exp[-j(kxx+kyy)]dkx,
ky=k12-kx2forkx2k12-jkx2-k12forkx2>k12.
A1(ρn, y=y1)=1Mm=-M/2M/2-1Ez1s(mΔx, y1)×exp(jρnmΔx),
Pr=ReL2η1m=-M/2M/2-1 β1m*k1|A1(ρm, y=y1)|2,
Pf=Reb-a2η1m=-M/2M/2-1n=-M/2M/2-1 expj(ρm-ρn)×b+a2 β1m*k1[A1(ρm, y=f)]*×A1(ρn, y=f)sinc(ρm-ρn)b-a2,

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