Vol. 36
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]
0000-00-00
Validation and Numerical Convergence of the Hankel-Bessel and Mathieu Rigorous Coupled Wave Analysis Algorithms for Radially and Azimuthally --- Inhomogeneous, Elliptical, Cylindrical Systems
By
, Vol. 36, 153-177, 2002
Abstract
A Rigorous Coupled Wave Analysis (RCWA) algorithm for electromagnetic (EM) scattering from radially and azimuthally inhomogeneous material elliptical systems based on State Variable (SV) techniques and based on circular-cylindrical Hankel-Bessel expansion modes is developed for the first time. The algorithm in conjunction with the elliptical system RCWA algorithm [1], which was based on SV techniques and Mathieu expansion modes, is used to validate and study numerical convergence of both elliptical RCWA algorithms. The formulation of the SV, Hankel-Bessel elliptical algorithm is presented. Two numerical elliptical examples are studied in detail by both algorithms, a homogeneous one which consists of three different uniform materials located in three elliptical regions and an inhomogeneous one which consists of an azimuthal, dielectric, step profile which is located between two uniform material elliptical regions. In this paper EM field scattering from a step profile which possessed a much larger dielectric step profile difference than was studied in [1] is presented. Validation and numerical convergence data of the Hankel-Bessel and the Mathieu [1] RCWA algorithm is presented for the first time, both in plot figures and in tables, when different numbers of expansion modes were used, when different number of layers were used, and when different numbers of SV harmonics were used. Validation of the RCWA algorithms was further carried out for the homogeneous case, by using Mathieu expansion modes in all regions and was carried out by using Hankel-Bessel expansion modes and Mathieu expansion modes in different regions. Validation of the Hankel-Bessel and Mathieu [1] RCWA algorithms was observed to a high degree of accuracy. It was found for the numerical example tested, that the number of modes used in the RCWA algorithms needed to exceed a critical minimum value in order to obtain meaningful, accurate results, and after this critical number of modes was exceeded, that convergence occurred rapidly as the number of modes increased. It was also found that as the number of layers used in the algorithm increased that the numerical accuracy of the RCWA solution slowly increased.
Citation
John Jarem, "Validation and Numerical Convergence of the Hankel-Bessel and Mathieu Rigorous Coupled Wave Analysis Algorithms for Radially and Azimuthally --- Inhomogeneous, Elliptical, Cylindrical Systems," , Vol. 36, 153-177, 2002.
doi:10.2528/PIER02012503
References

1. Jarem, J. M., "Rigorous coupled wave analysis of radially and azimuthally-inhomogeneous, elliptical, cylindrical systems," Progress In Electromagnetics Research, Vol. 34, 89-115, 2001.
doi:10.2528/PIER01032302

2. Moharam, M. G. and T. K. Gaylord, "Rigorous coupled-wave analysis of planar grating diffraction," J. Opt. Soc. Amer., Vol. 71, 811-818, 1981.
doi:10.1364/JOSA.71.000811

3. Moharam, M. G. and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Amer., Vol. 72, 1385-1392, 1982.
doi:10.1364/JOSA.72.001385

4. Jarem, J. M., "Rigorous coupled wave theory solution of phi-periodic circular cylindrical dielectric systems," Journal of Electromagnetic Waves and Applications, Vol. 11, 197-213, 1997.
doi:10.1163/156939397X00161

5. Jarem, J. M., "Rigorous coupled wave theory of anisotropic, azimuthally-inhomogeneous, cylindrical systems," Progress in Electromagnetics Research, Vol. 19, Chap. 4, 109–127, 1998.

6. Jarem, J. M. and P. P. Banerjee, "Bioelectromagnetics: A rigorous coupled wave analysis of cylindrical biological tissue," Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, (METMBS’00), F. Valafar (Ed.), 467–472, Vol. II, Las Vegas, Nev., June 26–29, 2000.

7. Jarem, J. M., "Rigorous coupled-wave-theory analysis of dipole scattering from a three-dimensional, inhomogeneous, spherical dielectric and permeable system," IEEE Microwave Theory and Techniques, Vol. 45, No. 8, 1193-1203, Aug. 1997.
doi:10.1109/22.618407

8. Jarem, J. M. and P. P. Banerjee, "Computational Methods for Electromagnetic and Optical Systems," Marcel Dekker, Inc., 2000.

9. Bowman, J. J., T. B. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes, Chap. 3, “The Elliptic Cylinder”, 129–180, Hemisphere Publishing Corp., New York, N.Y., revised printing, 1987.

10. Sebak, A. R., "Scattering from dielectric-coated impedance elliptic cylinder," IEEE Transactions on Antennas and Propagation, Vol. 48, No. 10, 1574-1580, Oct. 2000.
doi:10.1109/8.899674

11. Abramowitz, M. and I. Stegum, Handbook of Mathematical Functions, Chap. 20, “Mathieu Functions”, Dover publications, New York, N.Y., 1972.

12. Zhang, S. and J. Jin, "FORTRAN routines for computation of special functions,", Programs: “MTU12,MTU0,FCOEF,CVF,CVA2” at Web Site http://iris-lee3.ece.uiuc.edu/˜jjin/routines/routines.html, Mar. 8,01. (Programs associated with the book Computation of Special Functions, John Wiley and Sons. Inc.).