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.
Davood Ansari Oghol Beig,
Cristian Della Giovampaola,
"Simulating Wave Phenomena in Large Graded-Pattern Arrays with Random Perturbation," Progress In Electromagnetics Research,
Vol. 154, 127-141, 2015. doi:10.2528/PIER15100405
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
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