Vol. 154
Latest Volume
All Volumes
PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2015-12-29
Simulating Wave Phenomena in Large Graded-Pattern Arrays with Random Perturbation
By
Progress In Electromagnetics Research, Vol. 154, 127-141, 2015
Abstract
Efficient and accurate computer simulation of wave phenomena plays an important role in invention, development, cost reduction and optimization of many systems ranging from ultra-high-speed electronics to delicate nanoscale optical devices and systems. Understanding the physics of many modern technological applications such as optical nanomaterials calls for the solution of very complex computer models involving hundreds of millions to billions of unknowns. Integral equation (IE) methods are increasingly becoming the method of choice when comes to numerical modeling of wave phenomena for various reasons specifically since the introduction of FMM and MLFMA acceleration that tremendously reduce the computational costs associate with naive implementation of IE methods. In this work, a new acceleration technique specifically designed for the modeling of large, inhomogeneous, finite array problems it introduced. Specifically we use the new method for modelling and design of some metamaterial structures. At last, the presented method is used to study the some of the undesired random effects that occur in metamaterial array fabrication.
Citation
Davood Ansari Oghol Beig, Jierong Cheng, Cristian Della Giovampaola, Amirnader Askarpour, Andrea Alu, Nader Engheta, and Hossein Mosallaei, "Simulating Wave Phenomena in Large Graded-Pattern Arrays with Random Perturbation," Progress In Electromagnetics Research, Vol. 154, 127-141, 2015.
doi:10.2528/PIER15100405
References

1. Strikwerda, J., Finite Difference Schemes and Partial Differential Equations, 2nd Ed., SIAM, 2004.
doi:10.1137/1.9780898717938

2. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed., 2005.

3. Solin, P., K. Segeth, and I. Dolezel, Higher-order Finite Element Methods, Chapman & Hall/CRC Press, 2003.
doi:10.1201/9780203488041

4. Strang, G. and G. Fix, An Analysis of The Finite Element Method, Prentice Hall, 1973.

5. Rao, S. M., D. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antenna Prop., Vol. 30, No. 3, 1982.

6. Annigeri, B. S. and K. Tseng, "Boundary element methods in engineering," Proceedings of the International Symposium on Boundary Element Methods: Advances in Solid and Fluid Mechanics, 1989.

7. Lee, J., R. Lee, and A. Cangellaris, "Time-domain finite-element methods," IEEE Trans. Antenna Prop., Vol. 45, No. 3, 1997.

8. Chew, W. C., "Computational electromagnetics: The physics of smooth versus oscillatory fields," Phil. Trans. R. Soc. Lond. A, No. 12, 2004.

9. Engheta, N., W. D. Murphy, V. Rokhlin, and M. S. Vassiliou, "The fast multipole method, FMM for electromagnetic scattering problems," IEEE Trans. Antenna Prop., Vol. 40, No. 6, 1992.

10. Coifman, R., V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Ant. and Prop. Magazine, Vol. 35, 1993.

11. Rokhlin, V., "Rapid solution of integral equations of scattering theory in two dimensions," J. Computational Phys., Vol. 86, No. 2, 1990.

12. Song, J., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antenna Prop., Vol. 45, No. 10, 1997.

13. Phillips, J. R. and J. K. White, "A precorrected-FFT method for electrostatic analysis of complicated 3-D structures," IEEE Trans. Computer-Aided Design Integration Circuits Syst., Vol. 16, No. 10, 1997.
doi:10.1109/43.662670

14. Seo, S. M. and J. Lee, "A fast IE-FFT algorithm for solving PEC scattering problems," IEEE Transactions on Magnetics, Vol. 41, No. 5, 2005.

15. Barrowes, B., F. Teixeira, and J. Kong, "Fast algorithm for matrix-vector multiply of asymmetric multilevel block-toeplitz matrices," Antennas and Propagation Society International Symposium, 2001.

16. Li, M. and W. C. Chew, "Multiscale simulation of complex structures using equivalence principle algorithm with high-order field point sampling scheme," IEEE Trans. Antenna Prop., Vol. 56, No. 8, 2008.

17. Li, M. and W. C. Chew, "Wave-field interaction with complex structures using equivalence principle algorithm," IEEE Trans. Antenna Prop., Vol. 55, No. 1, 2007.

18. Burner, D., M. Junge, P. Rapp, M. Bebendorf, and L. Gau, "Comparison of the fast multipole method with hierarchical matrices for the Helmholtz-BEM," CMES, Vol. 58, No. 2, 2010.

19. Banjai, L. and W. Hackbusch, "Hierarchical matrix techniques for low and high frequency Helmholtz problems," IMA Journal of Numer. Anal., Vol. 28, No. 4, 2008.

20. Della Giovampaola, C. and N. Engheta, "Digital Metamaterials," Nat. Mater., Vol. 13, No. 12, 2014.
doi:10.1038/nmat4082

21. Johnson, P. and R. Christy, "Optical constants of the noble metals," Phys. Rev. B, Vol. 6, 1972.
doi:10.1103/PhysRevB.6.4370

22. Malitson, I. H., "Interspecimen comparison of the refractive index of fused silica," JOSA, Vol. 55, 1965.

23. Memarzadeh, B. and H. Mosallaei, "Array of planar plasmonic scatterers functioning as light concentrator," Optics Letters, Vol. 36, 2011.

24. Memarzadeh, B. and H. Mosallaei, "Multimaterial loops as the building block for a functional metasurface," J. Opt. Soc. Am. B, Vol. 30, No. 7, 2013.
doi:10.1364/JOSAB.30.001827

25. Cheng, J. and H. Mosallaie, "Optical metasurfaces for beam scanning in space," Optics Letters, Vol. 39, No. 9, 2014.
doi:10.1364/OL.39.002719

26. Monticone, F., N. Mohammadi Estakhri, and A. Alu, "Full control of nanoscale optical transmission with a composite metascreen," Physical Review Letters, Vol. 110, No. 20, 2013.
doi:10.1103/PhysRevLett.110.203903

27. Pfeiffer, C. and A. Grbic, "Cascaded metasurfaces for complete phase and polarization control," Applied Physics Letters, Vol. 102, No. 23, 2013.
doi:10.1063/1.4810873

28. Ansari-Oghol-Beig, D. and H. Mosalaei, "Array IE-FFT solver for simulation of supercells and aperiodic penetrable metamaterials," Journal of Computational and Theoretical Nanoscience, Vol. 12, No. 10, 2015.

29. Araujo, M. G., J. M. Taboada, J. Rivero, and F. Obelleiro, "Comprison of surface integral equations for left-handed materials," Progress In Electromagnetics Research, Vol. 118, 425-440, 2011.
doi:10.2528/PIER11031110