Abstract

We formulate and apply an efficient finite-difference time-domain algorithm to the analysis of axially symmetric diffractive optical elements. We discuss aspects relating to minimizing numerical dispersion in the incident field, application of absorbing boundary conditions in the radial direction, convergence to a steady state, and propagation of the steady-state electromagnetic fields from the finite-difference time-domain region to the plane of interest. Incorporation of these aspects into a single finite-difference time-domain algorithm results in an extremely efficient and robust method for diffractive optical element analysis. Application to the analysis of subwavelength and multilevel lenses, both with and without loss, for focusing planar and Gaussian beams is presented.

© 1999 Optical Society of America

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  1. T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
    [CrossRef]
  2. G. Granet, B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996).
    [CrossRef]
  3. P. Lalanne, G. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
    [CrossRef]
  4. P. Lalanne, “Improved formulation of the coupled-wave method for two-dimensional gratings,” J. Opt. Soc. Am. A 14, 1592–1598 (1997).
    [CrossRef]
  5. B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518–3526 (1994).
    [CrossRef]
  6. 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]
  7. M. S. Mirotznik, D. W. Prather, J. N. Mait, “A hybrid finite-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309–1322 (1996).
    [CrossRef]
  8. 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]
  9. 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]
  10. P. D. Maker, D. W. Wilson, R. E. Muller, “Fabrication and performance of optical interconnect analog phase holograms made by electron beam lithography,” in Optoelectronic Interconnects and Packaging, R. T. Chen, P. S. Guilfoyle, eds., Proc. SPIECR 62, 415–430 (1996).
  11. A. Wang, A. Prata, “Lenslet analysis by rigorous vector diffraction theory,” J. Opt. Soc. Am. A 12, 1161–1169 (1995).
    [CrossRef]
  12. D. W. Prather, S. Shi, M. S. Mirotznik, J. N. Mait, “Vector-based analysis of axially symmetric and conductive diffractive lenses,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest (Optical Society of America, Washington, D.C., 1998), pp. 94–96.
  13. D. Davidson, R. Ziolkowski, “Body-of-revolution finite-difference time-domain modeling of space–time focusing by a three-dimensional lens,” J. Opt. Soc. Am. A 11, 1471–1490 (1994).
    [CrossRef]
  14. M. Andreasen, “Scattering from bodies of revolution,” IEEE Trans. Antennas Propag. AP-13, 303–310 (1965).
    [CrossRef]
  15. J. Mautz, R. Harrington, “Radiation and scattering from bodies of revolution,” Appl. Sci. Res. 20, 405–435 (1969).
    [CrossRef]
  16. T. Wu, L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio Sci. 12, 709–718 (1977).
    [CrossRef]
  17. J. Mautz, R. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag. 33, 71–80 (1979).
  18. M. Morgan, K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
    [CrossRef]
  19. A. Kishk, L. Shafai, “On the accuracy limits of different integral-equation formulations for numerical solution of dielectric bodies of revolution,” Can. J. Phys. 63, 1532–1539 (1985).
    [CrossRef]
  20. L. Medgyesi-Mitschang, J. Putnam, “Electromagnetic scattering from axially inhomogeneous bodies of revolution,” IEEE Trans. Antennas Propag. AP-32, 797–806 (1984).
    [CrossRef]
  21. A. Kishk, L. Shafai, “Different formulations for numerical solution of single or multibodies of revolution with mixed boundary conditions,” IEEE Trans. Antennas Propag. AP-34, 666–673 (1986).
    [CrossRef]
  22. S. Gedney, R. Mittra, “The use of the FFT for the efficient solution of the problem of electromagnetic scattering by a body of revolution,” IEEE Trans. Antennas Propag. 38, 313–322 (1990).
    [CrossRef]
  23. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).
  24. C. L. Britt, “Solution of electromagnetic scattering problems using time domain techniques,” IEEE Trans. Antennas Propag. 37, 1181–1192 (1989).
    [CrossRef]
  25. A. Taflove, Computational Electromagnetics: The Finite-Difference Time Domain Method (Artech House, Boston, Mass., 1995).
  26. Y. Chen, R. Mittra, P. Harms, “Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,” IEEE Trans. Microwave Theory Tech. 44, 832–839 (1996).
    [CrossRef]
  27. D. Ge, S. Shi, Z. Zhu, “A new FDTD scheme for introducing incident fields,” Microwave J. 11, 187–190 (1995).
  28. F. Teixeira, W. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett. 7, 371–373 (1997).
    [CrossRef]
  29. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]
  30. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  31. G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
    [CrossRef]
  32. K. Umashankar, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. EMC-24, 397–405 (1982).
    [CrossRef]
  33. A. Taflove, K. R. Umashankar, “The finite-difference time-domain (FD-TD) method for numerical modeling of electromagnetic scattering,” IEEE Trans. Magn. 25, 3086–3091 (1989).
    [CrossRef]
  34. D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guided Lett. 4, 268–270 (1994).
    [CrossRef]
  35. W. C. Chew, W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microwave Opt. Technol. Lett. 7, 599–604 (1994).
    [CrossRef]
  36. E. A. Navarro, C. Wu, P. Y. Chung, J. Litva, “Application of PML superabsorbing boundary condition to non-orthogonal FDTD method,” Electron. Lett. 30, 1654–1656 (1994).
    [CrossRef]
  37. Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
    [CrossRef]
  38. W. V. Andrew, C. A. Balanis, P. A. Tirkas, “A comparison of the Berenger perfectly matched layer and the Lindman high-order ABC’s for the FDTD method,” IEEE Microwave Guided Wave Lett. 5, 192–194 (1995).
    [CrossRef]
  39. B. Stupfel, R. Mittra, “A theoretical study of numerical absorbing boundary conditions,” IEEE Trans. Antennas Propag. 43, 478–486 (1995).
    [CrossRef]
  40. C. M. Rappaport, “Interpreting and improving the PML absorbing boundary condition using anisotropic lossy mapping of space,” IEEE Trans. Magn. 32, 968–974 (1996).
    [CrossRef]
  41. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
    [CrossRef]
  42. J. A. Roden, S. D. Gedney, “Efficient implementation of the uniaxial-based PML media in three-dimensional nonorthogonal coordinates with the use of the FDTD technique,” Microwave Opt. Technol. Lett. 14, 71–75 (1997).
    [CrossRef]
  43. F. L. Teixeira, W. C. Chew, “PML-FDTD in cylindrical and spherical grids,” IEEE Microwave Guided Wave Lett. 7, 285–287 (1997).
    [CrossRef]
  44. A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. MTT-23, 623–630 (1975).
    [CrossRef]
  45. A. Taflove, “Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic-penetration problems,” IEEE Trans. Electromagn. Compat. EMC-22, 191–202 (1980).
    [CrossRef]
  46. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  47. A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991).
  48. G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multi-level diffractive optical elements,” (MIT, Cambridge, Mass., 1991).
  49. D. W. Prather, J. N. Mait, M. S. Mirotznik, J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A 15, 1599–1607 (1998).
    [CrossRef]
  50. J. N. Mait, D. W. Prather, M. S. Mirotznik, “Binary subwavelength diffractive-lens design,” Opt. Lett. 23, 1343–1345 (1998).
    [CrossRef]

1998

1997

J. A. Roden, S. D. Gedney, “Efficient implementation of the uniaxial-based PML media in three-dimensional nonorthogonal coordinates with the use of the FDTD technique,” Microwave Opt. Technol. Lett. 14, 71–75 (1997).
[CrossRef]

F. L. Teixeira, W. C. Chew, “PML-FDTD in cylindrical and spherical grids,” IEEE Microwave Guided Wave Lett. 7, 285–287 (1997).
[CrossRef]

P. Lalanne, “Improved formulation of the coupled-wave method for two-dimensional gratings,” J. Opt. Soc. Am. A 14, 1592–1598 (1997).
[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]

F. Teixeira, W. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett. 7, 371–373 (1997).
[CrossRef]

1996

Y. Chen, R. Mittra, P. Harms, “Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,” IEEE Trans. Microwave Theory Tech. 44, 832–839 (1996).
[CrossRef]

C. M. Rappaport, “Interpreting and improving the PML absorbing boundary condition using anisotropic lossy mapping of space,” IEEE Trans. Magn. 32, 968–974 (1996).
[CrossRef]

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

G. Granet, B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996).
[CrossRef]

P. Lalanne, G. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
[CrossRef]

M. S. Mirotznik, D. W. Prather, J. N. Mait, “A hybrid finite-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309–1322 (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]

1995

A. Wang, A. Prata, “Lenslet analysis by rigorous vector diffraction theory,” J. Opt. Soc. Am. A 12, 1161–1169 (1995).
[CrossRef]

Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

W. V. Andrew, C. A. Balanis, P. A. Tirkas, “A comparison of the Berenger perfectly matched layer and the Lindman high-order ABC’s for the FDTD method,” IEEE Microwave Guided Wave Lett. 5, 192–194 (1995).
[CrossRef]

B. Stupfel, R. Mittra, “A theoretical study of numerical absorbing boundary conditions,” IEEE Trans. Antennas Propag. 43, 478–486 (1995).
[CrossRef]

D. Ge, S. Shi, Z. Zhu, “A new FDTD scheme for introducing incident fields,” Microwave J. 11, 187–190 (1995).

1994

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guided Lett. 4, 268–270 (1994).
[CrossRef]

W. C. Chew, W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microwave Opt. Technol. Lett. 7, 599–604 (1994).
[CrossRef]

E. A. Navarro, C. Wu, P. Y. Chung, J. Litva, “Application of PML superabsorbing boundary condition to non-orthogonal FDTD method,” Electron. Lett. 30, 1654–1656 (1994).
[CrossRef]

D. Davidson, R. Ziolkowski, “Body-of-revolution finite-difference time-domain modeling of space–time focusing by a three-dimensional lens,” J. Opt. Soc. Am. A 11, 1471–1490 (1994).
[CrossRef]

B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518–3526 (1994).
[CrossRef]

1990

S. Gedney, R. Mittra, “The use of the FFT for the efficient solution of the problem of electromagnetic scattering by a body of revolution,” IEEE Trans. Antennas Propag. 38, 313–322 (1990).
[CrossRef]

1989

C. L. Britt, “Solution of electromagnetic scattering problems using time domain techniques,” IEEE Trans. Antennas Propag. 37, 1181–1192 (1989).
[CrossRef]

A. Taflove, K. R. Umashankar, “The finite-difference time-domain (FD-TD) method for numerical modeling of electromagnetic scattering,” IEEE Trans. Magn. 25, 3086–3091 (1989).
[CrossRef]

1986

A. Kishk, L. Shafai, “Different formulations for numerical solution of single or multibodies of revolution with mixed boundary conditions,” IEEE Trans. Antennas Propag. AP-34, 666–673 (1986).
[CrossRef]

1985

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

A. Kishk, L. Shafai, “On the accuracy limits of different integral-equation formulations for numerical solution of dielectric bodies of revolution,” Can. J. Phys. 63, 1532–1539 (1985).
[CrossRef]

1984

L. Medgyesi-Mitschang, J. Putnam, “Electromagnetic scattering from axially inhomogeneous bodies of revolution,” IEEE Trans. Antennas Propag. AP-32, 797–806 (1984).
[CrossRef]

1982

K. Umashankar, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. EMC-24, 397–405 (1982).
[CrossRef]

1981

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

1980

A. Taflove, “Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic-penetration problems,” IEEE Trans. Electromagn. Compat. EMC-22, 191–202 (1980).
[CrossRef]

1979

J. Mautz, R. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag. 33, 71–80 (1979).

M. Morgan, K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
[CrossRef]

1977

T. Wu, L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio Sci. 12, 709–718 (1977).
[CrossRef]

1975

A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. MTT-23, 623–630 (1975).
[CrossRef]

1969

J. Mautz, R. Harrington, “Radiation and scattering from bodies of revolution,” Appl. Sci. Res. 20, 405–435 (1969).
[CrossRef]

1966

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

1965

M. Andreasen, “Scattering from bodies of revolution,” IEEE Trans. Antennas Propag. AP-13, 303–310 (1965).
[CrossRef]

Andreasen, M.

M. Andreasen, “Scattering from bodies of revolution,” IEEE Trans. Antennas Propag. AP-13, 303–310 (1965).
[CrossRef]

Andrew, W. V.

W. V. Andrew, C. A. Balanis, P. A. Tirkas, “A comparison of the Berenger perfectly matched layer and the Lindman high-order ABC’s for the FDTD method,” IEEE Microwave Guided Wave Lett. 5, 192–194 (1995).
[CrossRef]

Balanis, C. A.

W. V. Andrew, C. A. Balanis, P. A. Tirkas, “A comparison of the Berenger perfectly matched layer and the Lindman high-order ABC’s for the FDTD method,” IEEE Microwave Guided Wave Lett. 5, 192–194 (1995).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Britt, C. L.

C. L. Britt, “Solution of electromagnetic scattering problems using time domain techniques,” IEEE Trans. Antennas Propag. 37, 1181–1192 (1989).
[CrossRef]

Brodwin, M. E.

A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. MTT-23, 623–630 (1975).
[CrossRef]

Chen, Y.

Y. Chen, R. Mittra, P. Harms, “Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,” IEEE Trans. Microwave Theory Tech. 44, 832–839 (1996).
[CrossRef]

Chew, W.

F. Teixeira, W. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett. 7, 371–373 (1997).
[CrossRef]

Chew, W. C.

F. L. Teixeira, W. C. Chew, “PML-FDTD in cylindrical and spherical grids,” IEEE Microwave Guided Wave Lett. 7, 285–287 (1997).
[CrossRef]

W. C. Chew, W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microwave Opt. Technol. Lett. 7, 599–604 (1994).
[CrossRef]

Chung, P. Y.

E. A. Navarro, C. Wu, P. Y. Chung, J. Litva, “Application of PML superabsorbing boundary condition to non-orthogonal FDTD method,” Electron. Lett. 30, 1654–1656 (1994).
[CrossRef]

Collins, J. P.

Davidson, D.

Gallagher, N. C.

B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518–3526 (1994).
[CrossRef]

Gaylord, T. K.

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]

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Ge, D.

D. Ge, S. Shi, Z. Zhu, “A new FDTD scheme for introducing incident fields,” Microwave J. 11, 187–190 (1995).

Gedney, S.

S. Gedney, R. Mittra, “The use of the FFT for the efficient solution of the problem of electromagnetic scattering by a body of revolution,” IEEE Trans. Antennas Propag. 38, 313–322 (1990).
[CrossRef]

Gedney, S. D.

J. A. Roden, S. D. Gedney, “Efficient implementation of the uniaxial-based PML media in three-dimensional nonorthogonal coordinates with the use of the FDTD technique,” Microwave Opt. Technol. Lett. 14, 71–75 (1997).
[CrossRef]

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

Glytsis, E. N.

Granet, G.

Guizal, B.

Harms, P.

Y. Chen, R. Mittra, P. Harms, “Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,” IEEE Trans. Microwave Theory Tech. 44, 832–839 (1996).
[CrossRef]

Harrington, R.

J. Mautz, R. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag. 33, 71–80 (1979).

J. Mautz, R. Harrington, “Radiation and scattering from bodies of revolution,” Appl. Sci. Res. 20, 405–435 (1969).
[CrossRef]

Hirayama, K.

Ishimaru, A.

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

Katz, D. S.

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guided Lett. 4, 268–270 (1994).
[CrossRef]

Kingsland, D. M.

Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

Kishk, A.

A. Kishk, L. Shafai, “Different formulations for numerical solution of single or multibodies of revolution with mixed boundary conditions,” IEEE Trans. Antennas Propag. AP-34, 666–673 (1986).
[CrossRef]

A. Kishk, L. Shafai, “On the accuracy limits of different integral-equation formulations for numerical solution of dielectric bodies of revolution,” Can. J. Phys. 63, 1532–1539 (1985).
[CrossRef]

Lalanne, P.

Lee, J.

Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

Lee, R.

Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

Lichtenberg, B.

B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518–3526 (1994).
[CrossRef]

Litva, J.

E. A. Navarro, C. Wu, P. Y. Chung, J. Litva, “Application of PML superabsorbing boundary condition to non-orthogonal FDTD method,” Electron. Lett. 30, 1654–1656 (1994).
[CrossRef]

Mait, J. N.

D. W. Prather, J. N. Mait, M. S. Mirotznik, J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A 15, 1599–1607 (1998).
[CrossRef]

J. N. Mait, D. W. Prather, M. S. Mirotznik, “Binary subwavelength diffractive-lens design,” Opt. Lett. 23, 1343–1345 (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]

M. S. Mirotznik, D. W. Prather, J. N. Mait, “A hybrid finite-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309–1322 (1996).
[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]

D. W. Prather, S. Shi, M. S. Mirotznik, J. N. Mait, “Vector-based analysis of axially symmetric and conductive diffractive lenses,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest (Optical Society of America, Washington, D.C., 1998), pp. 94–96.

Maker, P. D.

P. D. Maker, D. W. Wilson, R. E. Muller, “Fabrication and performance of optical interconnect analog phase holograms made by electron beam lithography,” in Optoelectronic Interconnects and Packaging, R. T. Chen, P. S. Guilfoyle, eds., Proc. SPIECR 62, 415–430 (1996).

Mautz, J.

J. Mautz, R. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag. 33, 71–80 (1979).

J. Mautz, R. Harrington, “Radiation and scattering from bodies of revolution,” Appl. Sci. Res. 20, 405–435 (1969).
[CrossRef]

Medgyesi-Mitschang, L.

L. Medgyesi-Mitschang, J. Putnam, “Electromagnetic scattering from axially inhomogeneous bodies of revolution,” IEEE Trans. Antennas Propag. AP-32, 797–806 (1984).
[CrossRef]

Mei, K.

M. Morgan, K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
[CrossRef]

Mirotznik, M. S.

J. N. Mait, D. W. Prather, M. S. Mirotznik, “Binary subwavelength diffractive-lens design,” Opt. Lett. 23, 1343–1345 (1998).
[CrossRef]

D. W. Prather, J. N. Mait, M. S. Mirotznik, J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A 15, 1599–1607 (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]

M. S. Mirotznik, D. W. Prather, J. N. Mait, “A hybrid finite-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309–1322 (1996).
[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]

D. W. Prather, S. Shi, M. S. Mirotznik, J. N. Mait, “Vector-based analysis of axially symmetric and conductive diffractive lenses,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest (Optical Society of America, Washington, D.C., 1998), pp. 94–96.

Mittra, R.

Y. Chen, R. Mittra, P. Harms, “Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,” IEEE Trans. Microwave Theory Tech. 44, 832–839 (1996).
[CrossRef]

B. Stupfel, R. Mittra, “A theoretical study of numerical absorbing boundary conditions,” IEEE Trans. Antennas Propag. 43, 478–486 (1995).
[CrossRef]

S. Gedney, R. Mittra, “The use of the FFT for the efficient solution of the problem of electromagnetic scattering by a body of revolution,” IEEE Trans. Antennas Propag. 38, 313–322 (1990).
[CrossRef]

Moharam, M. G.

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Morgan, M.

M. Morgan, K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
[CrossRef]

Morris, G.

Muller, R. E.

P. D. Maker, D. W. Wilson, R. E. Muller, “Fabrication and performance of optical interconnect analog phase holograms made by electron beam lithography,” in Optoelectronic Interconnects and Packaging, R. T. Chen, P. S. Guilfoyle, eds., Proc. SPIECR 62, 415–430 (1996).

Mur, G.

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

Navarro, E. A.

E. A. Navarro, C. Wu, P. Y. Chung, J. Litva, “Application of PML superabsorbing boundary condition to non-orthogonal FDTD method,” Electron. Lett. 30, 1654–1656 (1994).
[CrossRef]

Prata, A.

Prather, D. W.

D. W. Prather, J. N. Mait, M. S. Mirotznik, J. P. Collins, “Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements,” J. Opt. Soc. Am. A 15, 1599–1607 (1998).
[CrossRef]

J. N. Mait, D. W. Prather, M. S. Mirotznik, “Binary subwavelength diffractive-lens design,” Opt. Lett. 23, 1343–1345 (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]

M. S. Mirotznik, D. W. Prather, J. N. Mait, “A hybrid finite-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309–1322 (1996).
[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]

D. W. Prather, S. Shi, M. S. Mirotznik, J. N. Mait, “Vector-based analysis of axially symmetric and conductive diffractive lenses,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest (Optical Society of America, Washington, D.C., 1998), pp. 94–96.

Putnam, J.

L. Medgyesi-Mitschang, J. Putnam, “Electromagnetic scattering from axially inhomogeneous bodies of revolution,” IEEE Trans. Antennas Propag. AP-32, 797–806 (1984).
[CrossRef]

Rappaport, C. M.

C. M. Rappaport, “Interpreting and improving the PML absorbing boundary condition using anisotropic lossy mapping of space,” IEEE Trans. Magn. 32, 968–974 (1996).
[CrossRef]

Roden, J. A.

J. A. Roden, S. D. Gedney, “Efficient implementation of the uniaxial-based PML media in three-dimensional nonorthogonal coordinates with the use of the FDTD technique,” Microwave Opt. Technol. Lett. 14, 71–75 (1997).
[CrossRef]

Sacks, Z. S.

Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

Shafai, L.

A. Kishk, L. Shafai, “Different formulations for numerical solution of single or multibodies of revolution with mixed boundary conditions,” IEEE Trans. Antennas Propag. AP-34, 666–673 (1986).
[CrossRef]

A. Kishk, L. Shafai, “On the accuracy limits of different integral-equation formulations for numerical solution of dielectric bodies of revolution,” Can. J. Phys. 63, 1532–1539 (1985).
[CrossRef]

Shi, S.

D. Ge, S. Shi, Z. Zhu, “A new FDTD scheme for introducing incident fields,” Microwave J. 11, 187–190 (1995).

D. W. Prather, S. Shi, M. S. Mirotznik, J. N. Mait, “Vector-based analysis of axially symmetric and conductive diffractive lenses,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest (Optical Society of America, Washington, D.C., 1998), pp. 94–96.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Stupfel, B.

B. Stupfel, R. Mittra, “A theoretical study of numerical absorbing boundary conditions,” IEEE Trans. Antennas Propag. 43, 478–486 (1995).
[CrossRef]

Swanson, G. J.

G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multi-level diffractive optical elements,” (MIT, Cambridge, Mass., 1991).

Taflove, A.

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guided Lett. 4, 268–270 (1994).
[CrossRef]

A. Taflove, K. R. Umashankar, “The finite-difference time-domain (FD-TD) method for numerical modeling of electromagnetic scattering,” IEEE Trans. Magn. 25, 3086–3091 (1989).
[CrossRef]

K. Umashankar, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. EMC-24, 397–405 (1982).
[CrossRef]

A. Taflove, “Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic-penetration problems,” IEEE Trans. Electromagn. Compat. EMC-22, 191–202 (1980).
[CrossRef]

A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. MTT-23, 623–630 (1975).
[CrossRef]

A. Taflove, Computational Electromagnetics: The Finite-Difference Time Domain Method (Artech House, Boston, Mass., 1995).

Teixeira, F.

F. Teixeira, W. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett. 7, 371–373 (1997).
[CrossRef]

Teixeira, F. L.

F. L. Teixeira, W. C. Chew, “PML-FDTD in cylindrical and spherical grids,” IEEE Microwave Guided Wave Lett. 7, 285–287 (1997).
[CrossRef]

Thiele, E. T.

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guided Lett. 4, 268–270 (1994).
[CrossRef]

Tirkas, P. A.

W. V. Andrew, C. A. Balanis, P. A. Tirkas, “A comparison of the Berenger perfectly matched layer and the Lindman high-order ABC’s for the FDTD method,” IEEE Microwave Guided Wave Lett. 5, 192–194 (1995).
[CrossRef]

Tsai, L.

T. Wu, L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio Sci. 12, 709–718 (1977).
[CrossRef]

Umashankar, K.

K. Umashankar, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. EMC-24, 397–405 (1982).
[CrossRef]

Umashankar, K. R.

A. Taflove, K. R. Umashankar, “The finite-difference time-domain (FD-TD) method for numerical modeling of electromagnetic scattering,” IEEE Trans. Magn. 25, 3086–3091 (1989).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Wang, A.

Weedon, W. H.

W. C. Chew, W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microwave Opt. Technol. Lett. 7, 599–604 (1994).
[CrossRef]

Wilson, D. W.

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]

P. D. Maker, D. W. Wilson, R. E. Muller, “Fabrication and performance of optical interconnect analog phase holograms made by electron beam lithography,” in Optoelectronic Interconnects and Packaging, R. T. Chen, P. S. Guilfoyle, eds., Proc. SPIECR 62, 415–430 (1996).

Wu, C.

E. A. Navarro, C. Wu, P. Y. Chung, J. Litva, “Application of PML superabsorbing boundary condition to non-orthogonal FDTD method,” Electron. Lett. 30, 1654–1656 (1994).
[CrossRef]

Wu, T.

T. Wu, L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio Sci. 12, 709–718 (1977).
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

Zhu, Z.

D. Ge, S. Shi, Z. Zhu, “A new FDTD scheme for introducing incident fields,” Microwave J. 11, 187–190 (1995).

Ziolkowski, R.

Appl. Sci. Res.

J. Mautz, R. Harrington, “Radiation and scattering from bodies of revolution,” Appl. Sci. Res. 20, 405–435 (1969).
[CrossRef]

Arch. Elektr. Uebertrag.

J. Mautz, R. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag. 33, 71–80 (1979).

Can. J. Phys.

A. Kishk, L. Shafai, “On the accuracy limits of different integral-equation formulations for numerical solution of dielectric bodies of revolution,” Can. J. Phys. 63, 1532–1539 (1985).
[CrossRef]

Electron. Lett.

E. A. Navarro, C. Wu, P. Y. Chung, J. Litva, “Application of PML superabsorbing boundary condition to non-orthogonal FDTD method,” Electron. Lett. 30, 1654–1656 (1994).
[CrossRef]

IEEE Microwave Guided Lett.

D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guided Lett. 4, 268–270 (1994).
[CrossRef]

IEEE Microwave Guided Wave Lett.

W. V. Andrew, C. A. Balanis, P. A. Tirkas, “A comparison of the Berenger perfectly matched layer and the Lindman high-order ABC’s for the FDTD method,” IEEE Microwave Guided Wave Lett. 5, 192–194 (1995).
[CrossRef]

F. Teixeira, W. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett. 7, 371–373 (1997).
[CrossRef]

F. L. Teixeira, W. C. Chew, “PML-FDTD in cylindrical and spherical grids,” IEEE Microwave Guided Wave Lett. 7, 285–287 (1997).
[CrossRef]

IEEE Trans. Antennas Propag.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

M. Andreasen, “Scattering from bodies of revolution,” IEEE Trans. Antennas Propag. AP-13, 303–310 (1965).
[CrossRef]

L. Medgyesi-Mitschang, J. Putnam, “Electromagnetic scattering from axially inhomogeneous bodies of revolution,” IEEE Trans. Antennas Propag. AP-32, 797–806 (1984).
[CrossRef]

A. Kishk, L. Shafai, “Different formulations for numerical solution of single or multibodies of revolution with mixed boundary conditions,” IEEE Trans. Antennas Propag. AP-34, 666–673 (1986).
[CrossRef]

S. Gedney, R. Mittra, “The use of the FFT for the efficient solution of the problem of electromagnetic scattering by a body of revolution,” IEEE Trans. Antennas Propag. 38, 313–322 (1990).
[CrossRef]

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

C. L. Britt, “Solution of electromagnetic scattering problems using time domain techniques,” IEEE Trans. Antennas Propag. 37, 1181–1192 (1989).
[CrossRef]

B. Stupfel, R. Mittra, “A theoretical study of numerical absorbing boundary conditions,” IEEE Trans. Antennas Propag. 43, 478–486 (1995).
[CrossRef]

Z. S. Sacks, D. M. Kingsland, R. Lee, J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995).
[CrossRef]

M. Morgan, K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
[CrossRef]

IEEE Trans. Electromagn. Compat.

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

K. Umashankar, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. EMC-24, 397–405 (1982).
[CrossRef]

A. Taflove, “Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic-penetration problems,” IEEE Trans. Electromagn. Compat. EMC-22, 191–202 (1980).
[CrossRef]

IEEE Trans. Magn.

A. Taflove, K. R. Umashankar, “The finite-difference time-domain (FD-TD) method for numerical modeling of electromagnetic scattering,” IEEE Trans. Magn. 25, 3086–3091 (1989).
[CrossRef]

C. M. Rappaport, “Interpreting and improving the PML absorbing boundary condition using anisotropic lossy mapping of space,” IEEE Trans. Magn. 32, 968–974 (1996).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

Y. Chen, R. Mittra, P. Harms, “Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,” IEEE Trans. Microwave Theory Tech. 44, 832–839 (1996).
[CrossRef]

A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. MTT-23, 623–630 (1975).
[CrossRef]

J. Comput. Phys.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

J. Mod. Opt.

M. S. Mirotznik, D. W. Prather, J. N. Mait, “A hybrid finite-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309–1322 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Microwave J.

D. Ge, S. Shi, Z. Zhu, “A new FDTD scheme for introducing incident fields,” Microwave J. 11, 187–190 (1995).

Microwave Opt. Technol. Lett.

W. C. Chew, W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microwave Opt. Technol. Lett. 7, 599–604 (1994).
[CrossRef]

J. A. Roden, S. D. Gedney, “Efficient implementation of the uniaxial-based PML media in three-dimensional nonorthogonal coordinates with the use of the FDTD technique,” Microwave Opt. Technol. Lett. 14, 71–75 (1997).
[CrossRef]

Opt. Eng.

B. Lichtenberg, N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518–3526 (1994).
[CrossRef]

Opt. Lett.

Proc. IEEE

T. K. Gaylord, M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Radio Sci.

T. Wu, L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio Sci. 12, 709–718 (1977).
[CrossRef]

Other

D. W. Prather, S. Shi, M. S. Mirotznik, J. N. Mait, “Vector-based analysis of axially symmetric and conductive diffractive lenses,” in Diffractive Optics and Micro-Optics, Vol. 10 of 1998 OSA Technical Digest (Optical Society of America, Washington, D.C., 1998), pp. 94–96.

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]

P. D. Maker, D. W. Wilson, R. E. Muller, “Fabrication and performance of optical interconnect analog phase holograms made by electron beam lithography,” in Optoelectronic Interconnects and Packaging, R. T. Chen, P. S. Guilfoyle, eds., Proc. SPIECR 62, 415–430 (1996).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

A. Taflove, Computational Electromagnetics: The Finite-Difference Time Domain Method (Artech House, Boston, Mass., 1995).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

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

G. J. Swanson, “Binary optics technology: theoretical limits on the diffraction efficiency of multi-level diffractive optical elements,” (MIT, Cambridge, Mass., 1991).

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Figures (10)

Fig. 1
Fig. 1

Geometry used in the axially symmetric formulation of the FDTD algorithm. EM, electromagnetic.

Fig. 2
Fig. 2

2D FDTD mesh used to represent the 3D field components in the axially symmetric formulation.

Fig. 3
Fig. 3

Geometry used to solve for the singular Ez component along the axis of propagation.

Fig. 4
Fig. 4

Comparison between the 1D FDTD and the analytic propagation of the incident field through a homogeneous free space for the field components (a) Eρ, (b) Eϕ, and (c) Ez.

Fig. 5
Fig. 5

Illustration of the PML absorbing regions in cylindrical coordinates.

Fig. 6
Fig. 6

Example used to determine the number of time steps needed to obtain a steady-state condition: (a) eight-level diffractive lens with 102.47-µm diameter and 80-µm focal length; (b) time-dependent field values at Imax, Jmax in the FDTD mesh; (c) overlay of the electric-field magnitude in the focal plane for T=1500, 2T=3000, and 4T=6000 number of time steps.

Fig. 7
Fig. 7

Comparison between the FDTD and the analytic solutions for the magnitudes of the total electric field for the scattering from (a) a dielectric sphere with radius 2λ and relative permittivity 2.25 at axial locations of (b) 5λ and (c) 10λ.

Fig. 8
Fig. 8

(a) Binary and (b) eight-level diffractive lenses used in the comparison study of lossy and lossless material with planar and Gaussian incident fields.

Fig. 9
Fig. 9

Illustration of (a) the analysis of an electrically large lens of 150-µm diameter and 100-µm focal length and of (b) a line scan of the total electric-field magnitude in the focal plane of the lens. This problem took 2.5 h on a 300-MHz PC and required 20.7 Mbytes of memory.

Fig. 10
Fig. 10

Analysis of a subwavelength diffractive lens: (a) lens profile, (b) line scan of the total electric-field magnitude in the focal plane of (a), and (c) regional plot of the electric-field magnitude in the focal plane.

Tables (1)

Tables Icon

Table 1 Summary of Results for the Binary and Eight-Level Lens Comparison Studya

Equations (68)

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

-μ Hρt=1ρEzϕ-Eϕz,
ε Eρt+σEρ=1ρHzϕ-Hϕz,
-μ Hϕt=Eρz-Ezρ,
ε Eϕt+σEϕ=Hρz-Hzρ,
-μ Hzt=1ρ(ρEϕ)ρ-1ρEρϕ,
ε Ezt+σEz=1ρ(ρHϕ)ρ-1ρHρϕ,
Eγ(ρ, ϕ, z, t)=k=0E1γ,k(ρ, z, t)cos(kϕ)+k=1E2γ,k(ρ, z, t)sin(kϕ),
Hγ(ρ, ϕ, z, t)=k=0H1γ,k(ρ, z, t)cos(kϕ)+k=1H2γ,k(ρ, z, t)sin(kϕ),
μ H2ρ,kt=kρE1z,k+E2ϕ,kz,
ε E2ρ,kt+σE2ρ,k=-kρH1z,k-H2ϕ,kz,
μ H1ϕ,kt=-E1ρ,kz+E1z,kρ,
ε E1ϕ,kt+σE1ϕ,k=H1ρ,kz-H1z,kρ,
μ H2z,kt=-1ρ(ρE2ϕ,k)ρ-kρE1ρ,k,
ε E2z,kt+σE2z,k=1ρ(ρH2ϕ,k)ρ-kρH1ρ,k,
Hρ,kn(i, j)
=Hρ,kn-1(i, j)+kΔtμρ0(i)Ez,kn-(1/2)(i, j)+ΔtµΔz[Eϕ,kn-(1/2)(i, j+1)-Eϕ,kn-(1/2)(i, j)],
Hϕ,kn(i, j)
=Hϕ,kn-1(i, j)-kΔtµΔz[Eρ,kn-(1/2)(i, j+1)-Eρ,kn-(1/2)(i, j)]+ΔtµΔρ[Ez,kn-(1/2)(i+1, j)-Ez,kn-(1/2)(i, j)],
Hz,kn(i, j)
=Hz,kn-1(i, j)-kΔtμρ(i)Eρ,kn-(1/2)(i, j)-ΔtµΔρρ(i)[ρ0(i+1)Eϕ,kn-(1/2)(i+1, j)-ρ0(i)Eϕ,kn-(1/2)(i, j)],
Eρ,kn+(1/2)(i, j)
=2ε-Δtσ2ε+ΔtσEρ,kn-(1/2)(i, j)+2kΔtρ(i)(2ε+Δtσ)Hz,kn(i, j)-2ΔtΔz(2ε+Δtσ)[Hϕ,kn(i, j)-Hϕ,kn(i, j-1)],
Eϕ,kn+(1/2)(i, j)
=2ε-Δtσ2ε+ΔtσEϕ,kn-(1/2)(i, j)+2ΔtΔz(2ε+Δtσ)×[Hρ,kn(i, j)-Hρ,kn(i, j-1)]-2ΔtΔρ(2ε+Δtσ)[Hz,kn(i, j)-Hz,kn(i-1, j)],
Ez,kn+(1/2)(i, j)
=2ε-Δtσ2ε+ΔtσEz,kn-(1/2)(i, j)-2kΔtρ0(i)(2ε+Δtσ)Hρ,kn(i, j)-2ΔtΔρρ0(i)(2ε+Δtσ)[ρ(i)Hϕ,kn(i, j)-ρ(i-1)Hϕ,kn(i-1, j)],
cΔtmin(Δρ, Δz)s,
s×Hds=sε Et+σEds=cH·dl.
ε Ez,0t+σEz,0=2ρ(1)Hϕ,0.
Ez,kn+(1/2)(1, j)=2ε-Δtσ2ε+ΔtσEz,kn-(1/2)(1, j)+8Δtρ(1)(2ε+Δtσ)Hϕ,kn(1, j),k=0,
Ez,kn+(1/2)(1, j)=0,k1.
Einc=(xˆ cos θi-zˆ sin θi)E0(x, y)f(t, r)=(ρˆ cos θi cos ϕ-ϕˆ cos θi sin ϕ-zˆ sin θi)×E0(ρ, ϕ)f(t, r),
Hinc=yˆ E0(ρ, ϕ)η0f(t, r)=-(ρˆ sin ϕ+ϕˆ cos ϕ) E0(ρ, ϕ)ηf(t, r),
μ0 Hρ,1inct=Eϕ,1incz,μ0 Hϕ,1inct=-Eρ,1incz,
ε0 Eϕ,1inct=Hρ,1incz,ε0 Eρ,1inct=-Hϕ,1incz.
Eϕ,1inc,(n+(1/2))(k)=Eϕ,1inc,(n-(1/2))(k)+Δtε0Δz[Hρ,1inc(n)(k)-Hρ,1inc(n)(k-1)],
Hρ,1inc,(n+1)(k)=Hρ,1inc,(n)(k)+Δtμ0Δz[Eϕ,1inc(n+(1/2))(k+1)-Eϕ,1inc(n+(1/2))(k)],
ρρ˜=0ρsρ(ρ)dρ,zz˜=0zsz(z)dz,
jω sϕszsρμ0Hρ,k=kρEz,k+Eϕ,kz,
jω sρszsϕμ0Hϕ,k=-Eρ,kz+Ez,kρ,
jω sρsϕszμ0Hz,k=-1ρ(ρEϕ,k)ρ-kρEρ,k,
jω sϕszsρε0Eρ,k=-kρHz,k-Hϕ,kz,
jω sρszsϕε0Eϕ,k=Hρ,kz-Hz,kρ,
jω sρsϕszε0Ez,k=1ρ(ρHϕ,k)ρ-kρHρ,k,
sρ=1-j σρωε0,
sϕ=ρ˜ρ=1ρ0ρ1-j σρωε0dρ=1-j γρωε0,
sz=1-j σzωε0.
Bρ,k=μ0 sϕsρHρ,k,
jωBρ,k+σzε0Bρ,k=kρEz,k+Eϕ,kz,
jωμ0Hρ,k+μ0 γρε0Hρ,k=jωBρ,k+σρε0Bρ,k,
Bρn(i, j)=2ε0-Δtσz2ε0+ΔtσzBρn-1(i, j)+2kΔtε0ρ0(i)(2ε0+Δtσz)Ezn-(1/2)(i, j)+2Δtε0Δz(2ε0+Δtσz)[Eϕn-(1/2)(i, j+1)-Eϕn-(1/2)(i, j)],
Hρn(i, j)=2ε0-Δtγρ2ε0+ΔtγρHρn-1(i, j)+1μ02ε0-Δtσρ2ε0+ΔtγρBρn(i, j)+2ε0-Δtσρ2ε0+ΔtγρBρn-1(i, j),
E(r)=-S1{jωμ0G(r, r)[nˆ×H(r)]+[nˆ×E(r)]G(r, r)+[nˆ·E(r)]G(r, r)}ds
Escat(r)=Etscat(r)+Ebscat(r)+Erscat(r),
Etscat(r)=St[jωμ0G(r, r)(zˆ×H)+(zˆ×E)G(r, r)+(zˆ·E)G(r, r)]ds,
Ebscat(r)=-Sb[jωμ0G(r, r)(zˆ×H)+(zˆ×E)G(r, r)+(zˆ·E)G(r, r)]ds,
Erscat(r)=-Sr[jωμ0G(r, r)(ρˆ×H)+(ρˆ×E)G(r, r)+(ρˆ·E)G(r, r)]ds,
G(R)=1+jkR4πRexp(-jkR)
G(R)=G(ϕ)=12πk=-+Gk exp[-jk(ϕ-ϕ)],
G(R)=G(ϕ)=12πk=-+Gk exp[-jk(ϕ-ϕ)],
Gk=-ππG(ϕ)cos kϕdϕ,
Gk=-ππG(ϕ)cos kϕdϕ.
Etρscat(r)=-St[jωμ0Gρˆ·(zˆ×H)+(zˆ×E)(ρˆ·G)+(zˆ·E)(ρˆ·G)]ds=i=1I0 max-1k=0ρ cos kϕ[jωμ0(Hρ,kigsk+Hϕ,kigck)+(z-z)(Eρ,kihck-Eϕ,kihsk)-Ez,ki(ρhck-ρh0k)],
Etϕscat(r)=-St[jωμ0Gϕˆ·(zˆ×H)+(zˆ×E)(ϕˆ·G)+(zˆ·E)(ϕˆ·G)]ds=i=1I0 max-1k=0ρ sin kϕ[jωμ0(Hρ,kigck+Hϕ,kigsk)+(z-z)(Eρ,kihsk-Eϕ,kihck)-Ez,kiρhsk],
Etzscat(r)=St[jωμ0Gzˆ·(zˆ×H)+(zˆ×E)(zˆ·G)+(zˆ·E)(zˆ·G)]ds=-i=1I0 max-1k=0ρ cos kϕ{-[ρEρ,ki+(z-z)Ez,ki]h0k+ρ(Eρ,kihck-Eϕ,kihsk)},
gc,khc,k=Δldl-ππ cos ϕ cos kϕG(ϕ)G(ϕ)dϕ,
gs,khs,k=Δldl-ππ sin ϕ sin kϕG(ϕ)G(ϕ)dϕ,
g0,kh0,k=Δldl-ππ cos kϕG(ϕ)G(ϕ)dϕ,

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