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2009-10-05
Electromagnetic Source Transformations and Scalarization in Stratified Gyrotropic Media
By
Progress In Electromagnetics Research B, Vol. 18, 165-183, 2009
Abstract
It is known that with restrictions on the type of the constitutive equations, Maxwell's equations in non-uniform media can sometimes be reduced to two 2nd order differential equations for 2 scalar quantities only. These results have previously been obtained in two quite different ways, either by a "scalarization of the sources", where the relevant scalar quantities are essentially vector potential components, and the derivation was limited to isotropic media, or alternatively by using the "scalar Hertz potentials", and this method has been applied to more general media. In this paper it is shown that both methods are equivalent for gyrotropic media. We show that the scalarization can be obtained by a combination of transformations between electric and magnetic sources and gauge transformations. It is shown that the method based on the vector potential, which previously used a non-traditional definition of the vector potentials, can also be obtained using the traditional definition provided a proper gauge condition is applied and this method is then extended from isotropic to gyrotropic media. It is shown that the 2 basic scalar Hertz potentials occurring in the second method are invariant under the source scalarization transformations of the first method and therefore are the natural potentials for obtaining scalarization. Finally it is shown that both methods are also equivalent with a much older third method based on Hertz vectors.
Citation
Patrick De Visschere, "Electromagnetic Source Transformations and Scalarization in Stratified Gyrotropic Media," Progress In Electromagnetics Research B, Vol. 18, 165-183, 2009.
doi:10.2528/PIERB09070904
References

1. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, 3 Ed., Princeton University Press, 2008.

2. Monk, P., Finite Element Methods for Maxwell's Equations , Numerical Mathematics and Scientific Computation, Oxford University Press, 2003.

3. Olyslager, F. and I. Lindell, "Field decomposition and factorization the Helmholtz determinant operator for bianisotropic media," IEEE Transactions on Antennas and Propagation, Vol. 49, No. 4, 660-665, Apr. 2001.
doi:10.1109/8.923328

4. Nisbet, A., "Hertzian electromagnetic potentials and associated gauge transformations," Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934--1990), Vol. 231, No. 1185, 250-263, Aug. 1955.
doi:10.1098/rspa.1955.0170

5. Nisbet, A., "Electromagnetic potentials in a heterogeneous non-conducting medium," Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934--1990), Vol. 240, No. 1222, 375-381, Jun. 1957.
doi:10.1098/rspa.1957.0092

6. Mohsen, A., "Electromagnetic field representation in inhomogeneous anisotropic media," Applied Physics A: Materials Science & Processing, Vol. 2, No. 3, 123-128, Sep. 1973.

7. Mohsen, A., "Electromagnetic-field representation in source region," Applied Physics, Vol. 10, No. 1, 53-55, Jan. 1976.
doi:10.1007/BF00929528

8. Przeźiecki, S. and R. A. Hurd, "A note on scalar Hertz potentials for gyrotropic media," Applied Physics, Vol. 20, No. 4, 313-317, Dec. 1979.
doi:10.1007/BF00895002

9. Weiglhofer, W. S. and W. Papousek, "Scalar Hertz potentials for anisotropic media," Aeu-Arch Elektron. Ub, Vol. 39, No. 6, 343-346, Jan. 1985.

10. Weiglhofer, W. and S. Hansen, "Faraday chiral media revisited. I. Fields and sources," IEEE Transactions on Antennas and Propagation, Vol. 47, No. 5, 807-814, May 1999.
doi:10.1109/8.774134

11. Weiglhofer, W. S., "Scalar Hertz potentials for nonhomogeneous uniaxial dielectric-magnetic mediums," Int. J. Appl. Electrom., Vol. 11, No. 3, 131-140, Jan. 2000.

12. Georgieva, N. and W. S. Weiglhofer, "Electromagnetic vector potentials and the scalarization of sources in a nonhomogeneous medium," Physical Review E, Vol. 66, No. 4, Oct. 8, 2002.

13. Weiglhofer, W. S. and N. Georgieva, "Vector potentials and scalarization for nonhomogeneous isotropic mediums," Electromagnetics, Vol. 23, No. 5, 387-398, Jul. 2003.
doi:10.1080/02726340390202550

14. Jackson, J. D., "From Lorenz to Coulomb and other explicit gauge transformations," Am. J. Phys., Vol. 70, No. 9, 917-928, 2002.
doi:10.1119/1.1491265

15. Jackson, J. D., Classical Electrodynamics, 3 Ed., 280-282, John Wiley & Sons, 1999.

16. Sein, J. J., "Solutions to time-harmonic Maxwell equations with a hertz vector," Am. J. Phys., Vol. 57, No. 9, 834-839, Jan. 1989.
doi:10.1119/1.15905

17. Berreman, D. W., "Optics in stratified and anisotropic media --- 4×4 matrix formulation," J. Opt. Soc. Am., Vol. 62, No. 4, 502-510, Jan. 1972.
doi:10.1364/JOSA.62.000502