Vol. 63
Latest Volume
All Volumes
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]
2006-08-26
Rigorous Full Vectorial Analysis of Electromagnetic Wave Propagation in 1D
By
Progress In Electromagnetics Research, Vol. 63, 89-105, 2006
Abstract
We propose a new approach to solve the problem of the propagation of electromagnetic waves in unidimensional media with an arbitrary variation of their dielectric permittivity. This method is deduced from the Maxwell equations with a minimum of approximations and allows a full vectorial description of both the electric and magnetic fields through the direct calculation of their Cartesian coordinates.The problem is then equivalent to the solution of a pair of uncoupled ordinary differential equations. We use a very intuitive, highly accurate, pseudospectral technique to solve these equations. This pseudospectral method is based in a combination of Fourier and polynomial expansions of the solution providing very good precision and excellent stability with a relatively low computational effort. We present a simple model of a photonic crystal as an example of application of this technique to real electromagnetic problems.
Citation
Juan-Antonio Martinez-Rojas Jesus Alpuente-Hermosilla José Piñeiro Rocio Sanchez-Montero , "Rigorous Full Vectorial Analysis of Electromagnetic Wave Propagation in 1D," Progress In Electromagnetics Research, Vol. 63, 89-105, 2006.
doi:10.2528/PIER06042501
http://www.jpier.org/PIER/pier.php?paper=06042501
References

1. Brown, G., S. and R. S. Awadallah, "A Luneburg-Kline representation for wave propagation in a continuously inhomogenous medium," IEEE Trans. Antennas Propag., Vol. 46, No. 12, 1998.
doi:10.1109/8.743839

2. Rao, B. and L. Carin, "A hybrid (Parabolic Equation)- (Gaussian Beam) Algorithm for wave propagation through large inhomogenous regions," IEEE Trans. Antennas Propag., Vol. 46, No. 5, 1998.
doi:10.1109/8.668911

3. Tsang, L., Huang, C., Chan, and C. H., "Surface electric fields and impedance matrix elements of stratified media," IEEE Trans. Antennas Propag., Vol. 48, No. 10, 2000.

4. Kim, K. and H. Lim, "Invariant imbedding equations for electromagnetic waves in stratified magnetic media: Applications to one-dimensional photonic crystals," J. Korean Phys. Soc., Vol. 39, 2001.

5. Okhmatovski, V.I.and A.C. Cangellaris, "A new technique for the derivation of closed-form electromagnetic Green's functions for unbounded planar layered media," IEEE Trans. Antennas Propag., Vol. 50, No. 7, 2002.
doi:10.1109/TAP.2002.800731

6. Wang, Y., S. K. Chaudhuri, and S. Safavi-Naeini, "An FDTD/ray-tracing analysis method for wave penetration through inhomogenous walls," IEEE Trans. Antennas Propag., Vol. 50, No. 11, 2002.

7. Einziger, P. D., L. M. Livshitz, and J. Mizrahi, "Rigorous imagederies expansions of quasi-static Green's functions for regions with planar stratification," IEEE Trans. Antennas Propag., Vol. 50, No. 12, 2002.
doi:10.1109/TAP.2002.807365

8. Bass, F. and L.Resnick, "Wave beam propagation in layered media," J. Electromagn. Waves Appl., Vol. 17, No. 3, 479-480, 2003.
doi:10.1163/156939303767868964

9. Hanson, G. W., A. I. Nosich, and E. M. Kartchevski, "Green's function expansions in dyadic root functions for shielded layered waveguides," J. Electromagn. Waves Appl., Vol. 17, No. 5, 759-761, 2003.
doi:10.1163/156939303322226455

10. Yla-Oijala, P.and M.T askinen, "Efficient formulation of closed form Green's functions for general electric and magnetic sources in multilayered media," IEEE Trans. Antennas Propag., Vol. 51, No. 8, 2003.

11. Vegni, L., A. Toscano, and F. Bilotti, "Shielding and radiation characteristics of planar layered inhomogeneous composites," IEEE Trans. Antennas Propag., Vol. 51, No. 10, 2003.
doi:10.1109/TAP.2002.802099

12. Grzegorsczyk, T. M. and J. R. Mosig, "Full-wave analysis of antennas containing horizontal and vertical metallizations embedded in planar multilayered media," IEEE Trans. Antennas Propag., Vol. 51, No. 11, 2003.

13. Hashish, E. A., "Forward and inverse scattering from an inhomogeneous dielectric slab," J. Electromagn. Waves Appl., Vol. 17, No. 5, 719-736, 2003.
doi:10.1163/156939303322226374

14. Khalaj-Amirhosseini, M., "Analysis of longitudinally inhomogeneous waveguides using Taylor's series expansion," J. Electromagn. Waves Appl., Vol. 20, No. 8, 1093-1100, 2006.
doi:10.1163/156939306776930286

15. Zhou, X., "Physical Spline Finite Element (PSFEM) solutions to one dimensional electromagnetic problems," J. Electromagn. Waves Appl., Vol. 17, No. 8, 1159-1160, 2003.
doi:10.1163/156939303322519784

16. Vrancken, M.and G.A.E.V andenbosch, "Reference forms of the complete spectral electric and magnetic Dyadic Green's Functions (DGF's) for planar stratified media," J. Electromagn. Waves Appl., Vol. 18, No. 8, 1085-1104, 2004.
doi:10.1163/1569393042955351

17. Tong, M. S., Y. Lu, Y. Chen, H.-S. Kim, T. G. Chang, K.Kagoshima, and V.Krozer, "Study of stratified dielectric slab medium structures using Pseudo-spectral Time Domain (PSTD) Algorithm," J. Electromagn. Waves Appl., Vol. 19, No. 6, 721-736, 2005.
doi:10.1163/1569393054069064

18. Tsai, W., S. Chao, and M. Wu, "Variational analysis of singlemode inhomogeneous planar optical waveguide," J. Electromagn. Waves Appl., Vol. 17, No. 8, 1225-1235, 2003.
doi:10.1163/156939303322519847

19. Brenger J.-P., "Reduction of the angular dispersion of the FDTD method in the earth-ionosphere waveguide," J. Electromagn. Waves Appl., Vol. 17, No. 8, 1225-1235, 2003.
doi:10.1163/156939303322519847

20. Saadatmandi, A., M. Razzaghi, and M. Dehghan, "Sinccollocation methods for the solution of Hallen's integral equation," J. Electromagn. Waves Appl., Vol. 19, No. 2, 245-256, 1995.
doi:10.1163/1569393054497258

21. Chew, W. C., Waves and Fields in Inhomogenous Media, IEEE Press, 1995.

22. Sakoda, K., Optical Properties of Photonic Crystals, Springer, 2001.

23. Tsang, L., J. A. Kong, and K. Ding, Scattering of Electromagnetic Waves: Theories and Applications, John Wiley & Sons, 2000.

24. Kawano, K. and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell's Equations and the Schrödinger Equation, John Wiley & Sons, 2001.

25. Zwillinger, D., Handbook of Differential Equations, 3rd edition, Academic Press, 1997.

26. Boyd, J. P., Chebyshev and Fourier Spectral Methods, 2nd edition, Dover Publishers, New York, 2001.

27. Maxima computer algebra system, version 5.9.3, http://maxima. sourceforge.net/..