Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 16, Issue 5, 1999, Pages 1131-1142

  Prather, Dennis W ^a   Shi, Shouyuan ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; ELECTROMAGNETIC FIELDS; FINITE DIFFERENCE METHOD; OPTICAL DEVICES; TIME DOMAIN ANALYSIS;

DIFFRACTIVE OPTICAL ELEMENTS (DOE); FINITE-DIFFERENCE TIME-DOMAIN (FDTD) METHOD;

DIFFRACTIVE OPTICS;

EID: 0032621437     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.16.001131     Document Type: Article

References (50)

1. T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894-937 (1985).
2. G. Granet and 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).
3. P. Lalanne and G. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779-784 (1996).
4. P. Lalanne, “Improved formulation of the coupled-wave method for two-dimensional gratings,” J. Opt. Soc. Am. A 14, 1592-1598 (1997).
5. B. Lichtenberg and N. C. Gallagher, “Numerical modeling of diffractive devices using the finite element method,” Opt. Eng. 33, 3518-3526 (1994).
6. D. W. Prather, M. S. Mirotznik, and J. N. Mait, “Boundary element method for vector modeling diffractive optical elements,” in Diffractive and Holographic Optics Technology II, I. Cindrich and S. H. Lee, eds., Proc. SPIE 2404, 28-39 (1995).
7. M. S. Mirotznik, D. W. Prather, and J. N. Mait, “A hybrid finite-boundary element method for the analysis of diffractive elements,” J. Mod. Opt. 43, 1309-1322 (1996).
8. 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).
9. 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).
10. P. D. Maker, D. W. Wilson, and 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 and P. S. Guilfoyle, eds., Proc. SPIE CR 62, 415-430 (1996).
11. A. Wang and A. Prata, “Lenslet analysis by rigorous vector diffraction theory,” J. Opt. Soc. Am. A 12, 1161-1169 (1995).
12. D. W. Prather, S. Shi, M. S. Mirotznik, and 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 and 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).
14. M. Andreasen, “Scattering from bodies of revolution,” IEEE Trans. Antennas Propag. AP-13, 303-310 (1965).
15. J. Mautz and R. Harrington, “Radiation and scattering from bodies of revolution,” Appl. Sci. Res. 20, 405-435 (1969).
16. T. Wu and L. Tsai, “Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,” Radio Sci. 12, 709-718 (1977).
17. J. Mautz and R. Harrington, “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag. 33, 71 -80 (1979).
18. M. Morgan and K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-27, 202-214 (1979).
19. A. Kishk and 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).
20. L. Medgyesi-Mitschang and J. Putnam, “Electromagnetic scattering from axially inhomogeneous bodies of revolution,” IEEE Trans. Antennas Propag. AP-32, 797-806 (1984).
21. A. Kishk and 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).
22. S. Gedney and 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).
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).
25. A. Taflove, Computational Electromagnetics: The Finite-Difference Time Domain Method (Artech House, Boston, Mass., 1995).
26. Y. Chen, R. Mittra, and 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).
27. D. Ge, S. Shi, and Z. Zhu, “A new FDTD scheme for introducing incident fields,” Microwave J. 11, 187-190 (1995).
28. F. Teixeira and W. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett. 7, 371-373 (1997).
29. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1994).
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).
32. K. Umashankar and A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. EMC-24, 397-405 (1982).
33. A. Taflove and K. R. Umashankar, “The finite-difference time-domain (FD-TD) method for numerical modeling of electromagnetic scattering,” IEEE Trans. Magn. 25, 3086-3091 (1989).
34. D. S. Katz, E. T. Thiele, and 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).
35. W. C. Chew and 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).
36. E. A. Navarro, C. Wu, P. Y. Chung, and J. Litva, “Application of PML superabsorbing boundary condition to nonorthogonal FDTD method,” Electron. Lett. 30, 1654-1656 (1994).
37. Z. S. Sacks, D. M. Kingsland, R. Lee, and J. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
38. W. V. Andrew, C. A. Balanis, and 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).
39. B. Stupfel and R. Mittra, “A theoretical study of numerical absorbing boundary conditions,” IEEE Trans. Antennas Propag. 43, 478-486 (1995).
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).
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).
42. J. A. Roden and 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).
43. F. L. Teixeira and W. C. Chew, “PML-FDTD in cylindrical and spherical grids,” IEEE Microwave Guided Wave Lett. 7, 285-287 (1997).
44. A. Taflove and 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).
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).
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 multilevel diffractive optical elements,” Tech. Rep. 914 (MIT, Cambridge, Mass., 1991).
49. D. W. Prather, J. N. Mait, M. S. Mirotznik, and J. P. Collins, “Vector-based synthesis of finite aperiodic subwave-length diffractive optical elements,” J. Opt. Soc. Am. A 15, 1599-1607 (1998).
50. J. N. Mait, D. W. Prather, and M. S. Mirotznik, “Binary subwavelength diffractive-lens design,” Opt. Lett. 23, 1343-1345 (1998).