A Novel System of Two Coupled Equations for the Longitudinal Components of the Electromagnetic Field in a Waveguide
In this paper, a novel wave equation for electromagnetic
waves in a medium having anisotropic permittivity has been derived
with the help of Maxwell-s curl equations. The x and y components
of the Maxwell-s equations are written with the permittivity () being
a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey,
Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z
components of the Maxwell-s curl are then used to arrive to the
generalized Helmholtz equations for Ez and Hz.
[1] C. A. Valagiannopoulos,On measuring the permittivity tensor of an
anisotropic material from the transmission coefficients, Progress In Electromagnetics
Research B, Vol. 9, 105116, 2008.
[2] Wang,M.Y., J.Xu, J.Wu, B.Wei, H.L. Li, T.Xu, and D.B. Ge,FDTD
study on wave propagation in layered structures with biaxial anisotropic
metamaterials, Progress In Electromagnetics Research, PIER 81, 253-
265, 2008.
[3] Liu, S.-H., C.-H. Liang, W. Ding, L. Chen, and W.-T. Pan, Electromagnetic
wave propagation through a slab waveguide , Progress In
Electromagnetics Research M,PIER 76, 467-475, 2007.
[4] Ding, W., L. Chen, and C.-H. Liang, Characteristics of electromagnetic
wave propagation in biaxial anisotropic lefthanded materials , Progress
In Electromagnetics Research, PIER 70, 3752, 2007.
[5] Gong, Z. and G. Q. Zhu, FDTD analysis of an anisotropically coated
missile, Progress In Electromagnetics Research, PIER 64, 6980, 2006.
[6] Kristensson, G., S. Poulsen, and S. Rikte, Propagators and scattering
of electromagnetic waves in planar bianisotropic slabs An application
to frequency selective structures, Progress In Electromagnetics Research,
PIER 48, 125, 2004.
[7] Bass, F. and L. Resnick, The electromagnetic-wave propagation through
a stratified inhomogeneous anisotropic medium,Progress In Electromagnetics
Research, PIER 48, 6783, 2004.
[8] A. Wexler, Computation of electromagnetic fields, IEEE Trans. Microwave
Theory Tech., vol. MTT-17, pp. 416-439, Aug. 1969.
[9] D. M. Pozar, Microwave Engineering, Reading, MA:Addison Wesley,
2004.
[10] C. A. Balanis, Advanced Engineering Electromagnetics, New
York:Wiley, 2005.
[11] N. N. Rao, Elements of Engineering Electromagnetics, 3rd ed. New
Jersey: Prentice Hall, 2002, p. 328.
[12] W. H. Hayt, Engineering Electromagnerics, New York: McGraw- Hill,
2005, pp. 121, 184-192.
[13] C. R. Paul and S. A. Nasar, Analysis of bi-anisotropic Pbg structure
using plane wave expansion method, Progress In Electromagnetics Research,
PIER 42, 233246, 2003.
[14] Zheng, L. G. and W. X. Zhang, Higher-order numerical methods for
transient wave equations, Springer, New York, 2002.
[15] K. S. Yee, Numerical solution of initial boundary value problems
involving Maxwell-s equations isotropic media, IEEE Trans. Antennas
Propagation, Vol.14, no.5, pp.302-307, May 1966.
[16] Zhang, M., L. W. Li, T. S. Yeo, and M. S. Leong, Scattering by a
gyrotropic bianisotropic cylinder of arbitrary cross section: An analysis
using generalized multipole technique, Progress In Electromagnetics
Research, PIER 40, 315333, 2003.
[17] Wei, B. and D. B. Ge, Scattering by a two-dimensional cavity filled with
anisotropic medium, Waves in Random Media, Vol. 13, No. 4, 223240,
2003.
[18] Chen, H. T., G. Q. Zhu, and S. Y. He, Using genetic algorithm to reduce
the radar cross section of three-dimensional anisotropic impedance
object, Progress In Electromagnetics Research B, Vol. 9, 231248, 2008.
[19] Yang, L. L., D. B. Ge, and B. Wei, An equivalent anisotropic coating
technique based on dyadic surface impedance boundary condition,
Chinese Journal of Electronics, Vol. 14, No. 4, 712716, 2005.
[20] Huang, P. K. and H. C. Yin, Equivalent currents on an anisotropic
material backed by a metal surface and their relation, Journal of Systems
Engineering and Electronics, Vol. 11, No. 4, 110, 2000.
[21] Yin, H. C., Z. M. Chao, and Y. P. Xu, A new free-space method
for measurement of electromagnetic parameters of biaxial materials at
microwave frequencies, Microwave and Optical Technology Letters, Vol.
46, No. 1, 7278, Jul. 5, 2005.
[22] Valagiannopoulos, C. A., On measuring the permittivity tensor of
an anisotropic material from the transmission coefficients, Progress In
Electromagnetics Research B, Vol. 9, 105116, 2008.
[23] Chen, X., T. M. Grzegorczyk, and J. A. Kong, Optimization approach to
the retrieval of the constitutive parameters of slab of general bianisotropic
medium, Progress In Electromagnetics Research, PIER 60, 118, 2006.
[24] Fedorov, F. I., G. N. Borzdov, and L. M. Barkovskii, Operator for
the indices of refraction of plane waves in dispersive anisotropic media,
Journal of Applied Spectroscopy, Vol. 43, No. 4, 1176 1182, 1985.
[25] Borzdov, G. N., An intrinsic tensor technique in Minkowski space with
applications to boundary value problems, J. Math. Phys., Vol. 34, No. 7,
31623196, 1993.
[26] Lijun Zhang and Shanjia Xu, Edge-element analysis of anisotropic
waveguides with full permittivity and permeability matrices, International
Journal of Infrared and Millimeter Waves , vol. 16, no.8 1995, Springer,
New York.
[27] G. N. Borzdov, L. M. Barkovskii and F. I. Fedorov, Generalized
dielectric permittivity tensor Translated from Zhurnal Prikladnoi Spektroskopii,
Generalized dielectric permittivity tensor Vol. 43, No. 3, pp.
488495, September, 1985.
[28] M. Ohtaka, Analysis of the guided modes in the anisotropic dielectric
rectangular waveguides, Trans. Inst. Electron. Commun. Eng. Japan, vol.
364-C, pp. 674-681, Oct. 1981.
[29] Y. Xu and R.G. Bosisio, An efficient method for study of general bianisotropic
waveguides, IEEE Trans. Microwave Th. Tech., vol. 43, pp.
873-879, Apr. 1995.
[30] H.Y. Yang and P.L.E. Uslenghi, Planar bianisotropic waveguides, Radio
Sci., vol. 28, pp. 919-927, Sept.-Oct. 1993.
[31] J.L. Tsalamengas, Interaction of electromagnetic waves with general
bianisotropic slabs, IEEE Trans. Microwave Theory Tech., vol. 40, pp.
1870-1878, Oct. 1992.
[32] Haruhito Noro and Tsuneyoshi Nakayama, A New Approach to Scalar
and Semivector Mode Analysis of Optical Waveguides, J. Lightwave
Technol., Vol.14, No.6, pp.1546-1556, June 1996.
[33] C. Angulo Barrios, V. R. Almedia, R. Panepucci, and M. Lipson,
Electrooptic Modulation of Silicon-on- Insulator Submicrometer-Size
Waveguide Devices, J. Lightwave Technol., Vol.21, No.10, pp.2332-2339
Oct.2003.
[34] Harish Parthasarathy, Advanced Engineering Physics, First Edition , Ane
books, India, 2006.
[35] M. Ohtaka, Analysis of the guided modes in the anisotropic dielectric
rectangular waveguides, Trans. Inst. Electron. Comrnun. Eng. Japan, vol.
364-C, pp. 674-681, Oct. 1981.
[36] Haruhito Noro and Tsuneyoshi Nakayama, A New Approach to Scalar
and Semivector Mode Analysis of Optical Waveguides, J. Lightwave
Technol., Vol.14, No.6, pp.1546-1556, June 1996.
[37] C. Angulo Barrios, V. R. Almedia, R. Panepucci, and M. Lipson,
Electrooptic Modulation of Silicon-on- Insulator Submicrometer-Size
Waveguide Devices, J. Lightwave Technol., Vol.21, No.10, pp.2332-2339
Oct.2003.
[38] R. C. Alferness, Waveguide electrooptic modulators, IEEE Trans.
Microwave Theory Tech., vol. MTT-30, pp. 1121-1137, Aug. 1982.
[39] Erwin Keryszig, Advanced Engineering Mathematics, 8th Ed. New
York: Wiley, 2005.
[1] C. A. Valagiannopoulos,On measuring the permittivity tensor of an
anisotropic material from the transmission coefficients, Progress In Electromagnetics
Research B, Vol. 9, 105116, 2008.
[2] Wang,M.Y., J.Xu, J.Wu, B.Wei, H.L. Li, T.Xu, and D.B. Ge,FDTD
study on wave propagation in layered structures with biaxial anisotropic
metamaterials, Progress In Electromagnetics Research, PIER 81, 253-
265, 2008.
[3] Liu, S.-H., C.-H. Liang, W. Ding, L. Chen, and W.-T. Pan, Electromagnetic
wave propagation through a slab waveguide , Progress In
Electromagnetics Research M,PIER 76, 467-475, 2007.
[4] Ding, W., L. Chen, and C.-H. Liang, Characteristics of electromagnetic
wave propagation in biaxial anisotropic lefthanded materials , Progress
In Electromagnetics Research, PIER 70, 3752, 2007.
[5] Gong, Z. and G. Q. Zhu, FDTD analysis of an anisotropically coated
missile, Progress In Electromagnetics Research, PIER 64, 6980, 2006.
[6] Kristensson, G., S. Poulsen, and S. Rikte, Propagators and scattering
of electromagnetic waves in planar bianisotropic slabs An application
to frequency selective structures, Progress In Electromagnetics Research,
PIER 48, 125, 2004.
[7] Bass, F. and L. Resnick, The electromagnetic-wave propagation through
a stratified inhomogeneous anisotropic medium,Progress In Electromagnetics
Research, PIER 48, 6783, 2004.
[8] A. Wexler, Computation of electromagnetic fields, IEEE Trans. Microwave
Theory Tech., vol. MTT-17, pp. 416-439, Aug. 1969.
[9] D. M. Pozar, Microwave Engineering, Reading, MA:Addison Wesley,
2004.
[10] C. A. Balanis, Advanced Engineering Electromagnetics, New
York:Wiley, 2005.
[11] N. N. Rao, Elements of Engineering Electromagnetics, 3rd ed. New
Jersey: Prentice Hall, 2002, p. 328.
[12] W. H. Hayt, Engineering Electromagnerics, New York: McGraw- Hill,
2005, pp. 121, 184-192.
[13] C. R. Paul and S. A. Nasar, Analysis of bi-anisotropic Pbg structure
using plane wave expansion method, Progress In Electromagnetics Research,
PIER 42, 233246, 2003.
[14] Zheng, L. G. and W. X. Zhang, Higher-order numerical methods for
transient wave equations, Springer, New York, 2002.
[15] K. S. Yee, Numerical solution of initial boundary value problems
involving Maxwell-s equations isotropic media, IEEE Trans. Antennas
Propagation, Vol.14, no.5, pp.302-307, May 1966.
[16] Zhang, M., L. W. Li, T. S. Yeo, and M. S. Leong, Scattering by a
gyrotropic bianisotropic cylinder of arbitrary cross section: An analysis
using generalized multipole technique, Progress In Electromagnetics
Research, PIER 40, 315333, 2003.
[17] Wei, B. and D. B. Ge, Scattering by a two-dimensional cavity filled with
anisotropic medium, Waves in Random Media, Vol. 13, No. 4, 223240,
2003.
[18] Chen, H. T., G. Q. Zhu, and S. Y. He, Using genetic algorithm to reduce
the radar cross section of three-dimensional anisotropic impedance
object, Progress In Electromagnetics Research B, Vol. 9, 231248, 2008.
[19] Yang, L. L., D. B. Ge, and B. Wei, An equivalent anisotropic coating
technique based on dyadic surface impedance boundary condition,
Chinese Journal of Electronics, Vol. 14, No. 4, 712716, 2005.
[20] Huang, P. K. and H. C. Yin, Equivalent currents on an anisotropic
material backed by a metal surface and their relation, Journal of Systems
Engineering and Electronics, Vol. 11, No. 4, 110, 2000.
[21] Yin, H. C., Z. M. Chao, and Y. P. Xu, A new free-space method
for measurement of electromagnetic parameters of biaxial materials at
microwave frequencies, Microwave and Optical Technology Letters, Vol.
46, No. 1, 7278, Jul. 5, 2005.
[22] Valagiannopoulos, C. A., On measuring the permittivity tensor of
an anisotropic material from the transmission coefficients, Progress In
Electromagnetics Research B, Vol. 9, 105116, 2008.
[23] Chen, X., T. M. Grzegorczyk, and J. A. Kong, Optimization approach to
the retrieval of the constitutive parameters of slab of general bianisotropic
medium, Progress In Electromagnetics Research, PIER 60, 118, 2006.
[24] Fedorov, F. I., G. N. Borzdov, and L. M. Barkovskii, Operator for
the indices of refraction of plane waves in dispersive anisotropic media,
Journal of Applied Spectroscopy, Vol. 43, No. 4, 1176 1182, 1985.
[25] Borzdov, G. N., An intrinsic tensor technique in Minkowski space with
applications to boundary value problems, J. Math. Phys., Vol. 34, No. 7,
31623196, 1993.
[26] Lijun Zhang and Shanjia Xu, Edge-element analysis of anisotropic
waveguides with full permittivity and permeability matrices, International
Journal of Infrared and Millimeter Waves , vol. 16, no.8 1995, Springer,
New York.
[27] G. N. Borzdov, L. M. Barkovskii and F. I. Fedorov, Generalized
dielectric permittivity tensor Translated from Zhurnal Prikladnoi Spektroskopii,
Generalized dielectric permittivity tensor Vol. 43, No. 3, pp.
488495, September, 1985.
[28] M. Ohtaka, Analysis of the guided modes in the anisotropic dielectric
rectangular waveguides, Trans. Inst. Electron. Commun. Eng. Japan, vol.
364-C, pp. 674-681, Oct. 1981.
[29] Y. Xu and R.G. Bosisio, An efficient method for study of general bianisotropic
waveguides, IEEE Trans. Microwave Th. Tech., vol. 43, pp.
873-879, Apr. 1995.
[30] H.Y. Yang and P.L.E. Uslenghi, Planar bianisotropic waveguides, Radio
Sci., vol. 28, pp. 919-927, Sept.-Oct. 1993.
[31] J.L. Tsalamengas, Interaction of electromagnetic waves with general
bianisotropic slabs, IEEE Trans. Microwave Theory Tech., vol. 40, pp.
1870-1878, Oct. 1992.
[32] Haruhito Noro and Tsuneyoshi Nakayama, A New Approach to Scalar
and Semivector Mode Analysis of Optical Waveguides, J. Lightwave
Technol., Vol.14, No.6, pp.1546-1556, June 1996.
[33] C. Angulo Barrios, V. R. Almedia, R. Panepucci, and M. Lipson,
Electrooptic Modulation of Silicon-on- Insulator Submicrometer-Size
Waveguide Devices, J. Lightwave Technol., Vol.21, No.10, pp.2332-2339
Oct.2003.
[34] Harish Parthasarathy, Advanced Engineering Physics, First Edition , Ane
books, India, 2006.
[35] M. Ohtaka, Analysis of the guided modes in the anisotropic dielectric
rectangular waveguides, Trans. Inst. Electron. Comrnun. Eng. Japan, vol.
364-C, pp. 674-681, Oct. 1981.
[36] Haruhito Noro and Tsuneyoshi Nakayama, A New Approach to Scalar
and Semivector Mode Analysis of Optical Waveguides, J. Lightwave
Technol., Vol.14, No.6, pp.1546-1556, June 1996.
[37] C. Angulo Barrios, V. R. Almedia, R. Panepucci, and M. Lipson,
Electrooptic Modulation of Silicon-on- Insulator Submicrometer-Size
Waveguide Devices, J. Lightwave Technol., Vol.21, No.10, pp.2332-2339
Oct.2003.
[38] R. C. Alferness, Waveguide electrooptic modulators, IEEE Trans.
Microwave Theory Tech., vol. MTT-30, pp. 1121-1137, Aug. 1982.
[39] Erwin Keryszig, Advanced Engineering Mathematics, 8th Ed. New
York: Wiley, 2005.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:53201", author = "Arti Vaish and Harish Parthasarathy", title = "A Novel System of Two Coupled Equations for the Longitudinal Components of the Electromagnetic Field in a Waveguide", abstract = "In this paper, a novel wave equation for electromagnetic
waves in a medium having anisotropic permittivity has been derived
with the help of Maxwell-s curl equations. The x and y components
of the Maxwell-s equations are written with the permittivity () being
a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey,
Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z
components of the Maxwell-s curl are then used to arrive to the
generalized Helmholtz equations for Ez and Hz.", keywords = "Electromagnetism, Maxwell's Equations, Anisotropic permittivity, Wave equation, Matrix Equation, Permittivity tensor.", volume = "5", number = "3", pages = "306-4", }
