Vol. 61

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2014-09-12

Finite-Difference Frequency-Domain Algorithm for Modeling Electromagnetic Scattering from General Anisotropic Objects

By Raymond C. Rumpf, Cesar R. Garcia, Eric A. Berry, and Jay H. Barton
Progress In Electromagnetics Research B, Vol. 61, 55-67, 2014
doi:10.2528/PIERB14071606

Abstract

The finite-difference frequency-domain (FDFD) method is a very simple and powerful approach for rigorous analysis of electromagnetic structures. It may be the simplest of all methods to implement and is excellent for field visualization and for developing new ways to model devices. This paper describes a simple method for incorporating anisotropic materials with arbitrary tensors for both permittivity and permeability into the FDFD method. The algorithm is benchmarked by comparing transmission and reflection results for an anisotropic guided-mode resonant filter simulated in HFSS and FDFD. The anisotropic FDFD method is then applied to a lens and cloak designed by transformation optics.

Citation


Raymond C. Rumpf, Cesar R. Garcia, Eric A. Berry, and Jay H. Barton, "Finite-Difference Frequency-Domain Algorithm for Modeling Electromagnetic Scattering from General Anisotropic Objects," Progress In Electromagnetics Research B, Vol. 61, 55-67, 2014.
doi:10.2528/PIERB14071606
http://www.jpier.org/PIERB/pier.php?paper=14071606

References


    1. Luo, G. Q., et al., "Theory and experiment of novel frequency selective surface based on substrate integrated waveguide technology," IEEE Transactions on Antennas and Propagation, Vol. 53, 4035-4043, 2005.
    doi:10.1109/TAP.2005.860010

    2. Rumpf, R. C., "Design and optimization of nano-optical elements by coupling fabrication to optical behavior,", University of Central Florida Orlando, Florida, 2006.

    3. Sun, W., K. Liu, and C. A. Balanis, "Analysis of singly and doubly periodic absorbers by frequency-domain finite-difference method," IEEE Transactions on Antennas and Propagation, Vol. 44, 798-805, 1996.
    doi:10.1109/8.509883

    4. Wu, S.-D. and E. N. Glytsis, "Volume holographic grating couplers: Rigorous analysis by use of the finite-difference frequency-domain method," Applied Optics, Vol. 43, 1009-1023, 2004.
    doi:10.1364/AO.43.001009

    5. Shin, W. and S. Fan, "Choice of the perfectly matched layer boundary condition for frequency-domain Maxwell's equations solvers," Journal of Computational Physics, Vol. 231, 3406-3431, 2012.
    doi:10.1016/j.jcp.2012.01.013

    6. Shin, W. and S. Fan, "Accelerated solution of the frequency-domain Maxwell's equations by engineering the eigenvalue distribution of the operator," Optics Express, Vol. 21, 22578-22595, 2013.
    doi:10.1364/OE.21.022578

    7. Rumpf, R. C., "Simple implementation of arbitrarily shaped total-field/scattered-field regions in finite-difference frequency-domain," Progress In Electromagnetics Research B, Vol. 36, 221-248, 2012.
    doi:10.2528/PIERB11092006

    8. Takayama, O., L.-C. Crasovan, S. K. Johansen, D. Mihalache, D. Artigas, and L. Torner, "Dyakonov surface waves: A review," Electromagnetics, Vol. 28, 126-145, 2008.
    doi:10.1080/02726340801921403

    9. Figotin, A. and I. Vitebskiy, "Slow-wave resonance in periodic stacks of anisotropic layers," Physical Review A, Vol. 76, 053839, 2007.
    doi:10.1103/PhysRevA.76.053839

    10. Schurig, D., et al., "Metamaterial electromagnetic cloak at microwave frequencies," Science, Vol. 314, 977-980, 2006.
    doi:10.1126/science.1133628

    11. Kwon, D.-H. and D. H. Werner, "Polarization splitter and polarization rotator designs based on transformation optics," Optics Express, Vol. 16, 18731-18738, 2008.
    doi:10.1364/OE.16.018731

    12. Al-Barqawi, H., N. Dib, and M. Khodier, "A two-dimensional full-wave finite-difference frequency-domain analysis of ferrite loaded structures," International Journal of Infrared and Millimeter Waves, Vol. 29, 443-456, 2008.
    doi:10.1007/s10762-008-9349-6

    13. Loke, V. L., T. A. Nieminen, S. J. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "FDFD/T-matrix hybrid method," Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 106, 274-284, 2007.
    doi:10.1016/j.jqsrt.2007.01.040

    14. Mielewski, J., A. Cwikla, and M. Mrozowski, "Analysis of shielded anisotropic dielectric resonators using FDFD and the Arnoldi method," 12th International Conference on Microwaves and Radar MIKON'98, 335-339, 1998.
    doi:10.1109/MIKON.1998.740799

    15. Pinheiro, H. F., A. J. Giarola, and C. L. D. S. S. Sobrinho, "Dispersion characteristics of asymmetric coupled anisotropic dielectric waveguides using FDFD," International Journal of Infrared and Millimeter Waves, Vol. 16, 1965-1975, 1995.
    doi:10.1007/BF02072551

    16. Rappaport, C. M. and B. J. McCartin, "FDFD analysis of electromagnetic scattering in anisotropic media using unconstrained triangular meshes," IEEE Transactions on Antennas and Propagation, Vol. 39, 345-349, 1991.
    doi:10.1109/8.76332

    17. Rappaport, C. M. and E. Smith, "Anisotropic FDFD computed on conformal meshes," IEEE Transactions on Magnetics, Vol. 27, 3848-3851, 1991.
    doi:10.1109/20.104941

    18. Zhao, Y.-J., K.-L. Wu, and K.-K. Cheng, "A compact 2-D full-wave finite-difference frequency-domain method for general guided wave structures," IEEE Transactions on Microwave Theory and Techniques, Vol. 50, 1844-1848, 2002.
    doi:10.1109/TMTT.2002.800447

    19. Chen, M.-Y., S.-M. Hsu, and H.-C. Chang, "A finite-difference frequency-domain method for full-vectroial mode solutions of anisotropic optical waveguides with arbitrary permittivity tensor," Optics Express, Vol. 17, 5965-5979, 2009.
    doi:10.1364/OE.17.005965

    20. Lavranos, C., G. Kyriacou, and J. Sahalos, "A 2-D finite difference frequency domain (FDFD) eigenvalue method for orthogonal curvilinear coordinates," PIERS Proceedings, 397-400, PISA, Italy, Mar. 28-31, 2004.

    21. Pereda, J. A., A. Vegas, and A. Prieto, "An improved compact 2D full-wave FDFD method for general guided wave structures," Microwave and Optical Technology Letters, Vol. 38, 331-335, 2003.
    doi:10.1002/mop.11052

    22. Zainud-Deen, S. H., A. Z. Botros, and M. S. Ibrahim, "Scattering from bodies coated with metamaterial using FDFD method," Progress In Electromagnetics Research B, Vol. 2, 279-290, 2008.
    doi:10.2528/PIERB07112803

    23. Taflove, A. and S. C. Hagness, Computational Electrodynamics, Vol. 160, Artech House Boston, 2000.

    24. Umashankar, K. and A. Taflove, "A novel method to analyze electromagnetic scattering of complex objects," IEEE Transactions on Electromagnetic Compatibility, 397-405, 1982.
    doi:10.1109/TEMC.1982.304054

    25. Berenger, J.-P., "A perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics, Vol. 114, 185-200, 1994.
    doi:10.1006/jcph.1994.1159

    26. Margengo, E., C. M. Rappaport, and E. L. Miller, "Optimum PML ABC conductivity profile in FDFD," IEEE Transactions on Magnetics, Vol. 35, 1506-1509, 1999.
    doi:10.1109/20.767253

    27. Sacks, Z. S., D. M. Kingsland, R. Lee, and J.-F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Transactions on Antennas and Propagation, Vol. 43, 1460-1463, 1995.
    doi:10.1109/8.477075

    28. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations," IEEE Transactions on Antennas and Propagation, Vol. 14, 302-307, 1966.
    doi:10.1109/TAP.1966.1138693

    29. Jordán, K., Calculus of Finite Differences, American Mathematical Soc., 1965.

    30. Rumpf, R. C., C. R. Garcia, H. H. Tsang, J. E. Padilla, and M. D. Irwin, "Electromagnetic isolation of a microstrip by embedding in a spatially variant anisotropic metamaterial," Progress In Electromagnetics Research, Vol. 142, 243-260, 2013.
    doi:10.2528/PIER13070308

    31. Horn, A., "Doubly stochastic matrices and the diagonal of a rotation matrix," Amer. J. Math, Vol. 76, 620-630, 1954.
    doi:10.2307/2372705

    32. Magnusson, R. and S. Wang, "New principle for optical filters," Applied Physics Letters, Vol. 61, 1022-1024, 1992.
    doi:10.1063/1.107703

    33. Barton, J. H., R. C. Rumpf, R. W. Smith, C. L. Kozikowski, and P. A. Zellner, "All-dielectric frequency selective surfaces with few number of periods," Progress In Electromagnetics Research B, Vol. 41, 269-283, 2012.
    doi:10.2528/PIERB12042404

    34. Boonruang, S., A. Greenwell, and M. Moharam, "Multiline two-dimensional guided-mode resonant filters," Applied Optics, Vol. 45, 5740-5747, 2006.
    doi:10.1364/AO.45.005740

    35. Pung, A. J., S. R. Carl, I. R. Srimathi, and E. G. Johnson, "Method of fabrication for encapsulated polarizing resonant gratings," IEEE Photonics Technology Letters, Vol. 25, 1432-1434, 2013.
    doi:10.1109/LPT.2013.2266575

    36. Tibuleac, S. and R. Magnusson, "Re°ection and transmission guided-mode resonance filters," JOSA A, Vol. 14, 1617-1626, 1997.
    doi:10.1364/JOSAA.14.001617

    37. Garcia, C. R., J. Correa, D. Espalin, J. H. Barton, R. C. Rumpf, R. Wicker, and V. Gonzalez, "3D printing of anisotropic metamaterials," Progress In Electromagnetics Research Letters, Vol. 34, 75-82, 2012.
    doi:10.2528/PIERL12070311

    38. Leonhardt, U., "Optical conformal mapping," Science, Vol. 312, 1777-1780, 2006.
    doi:10.1126/science.1126493

    39. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, 1780-1782, 2006.
    doi:10.1126/science.1125907

    40. Ward, A. and J. Pendry, "Refraction and geometry in Maxwell's equations," Journal of Modern Optics, Vol. 43, 773-793, 1996.
    doi:10.1080/09500349608232782

    41. Landau, L. D. and E. M. Lifshits, The Classical Theory of Fields, Vol. 2, Butterworth-Heinemann, 1975.

    42. Post, E. J., Formal Structure of Electromagnetics: General Covariance and Electromagnetics, Courier Dover Publications, 1997.

    43. Kwon, D.-H. and D. H. Werner, "Transformation optical designs for wave collimators, flat lenses and right-angle bends ," New Journal of Physics, Vol. 10, 115023, 2008.
    doi:10.1088/1367-2630/10/11/115023

    44. Cai, W., U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nature Photonics, Vol. 1, 224-227, 2007.
    doi:10.1038/nphoton.2007.28