The system of Maxwell equations with an initial condition in a vacuum is solved in a cylindrical coordinate system. It derives the cylindrical transverse electromagnetic wave mode in which the electric field and magnetic field are not in phase. Such electromagnetic wave can generate and exist in actual application, and there is no violation of the law of conservation of energy during the electromagnetic field interchanges.
2. Van Bladel, J., Electromagnetic Fields, McGraw-Hill, New York, 1964.
3. Jackson, J. D. and Classical Electrodynamics, , 3rd Ed., John Wiley and Sons, 1998.
4. Landau, L. D. and E. M. Lifshitz, The Classical Theory of Fields, Butterworth-Heinemann, 1980.
5. Tsang, T., Classical Electrodynamics, World Scientific Pub. Co. Inc., 1997.
6. Yang, R. R. G. and T. T. Y. Wong, Electromagnetic Fields and Waves, Higher Education Press, 2006.
7. Harrington, R. F., "Time-harmonic Electromagnetic Fields," McGraw-Hill, 1961.
8. Brittingham, J. N., "Focus waves modes in homogeneous Maxwell equations: Transverse electric mode," J. Appl. Phys., Vol. 54, 1179-1189, 2009.
9. Chen, R., "The optimum differential equations," Chin. J. Engin. Math., Vol. 17, 82-86, 2000.
10. Chen, R., "The uniqueness of the eigenvalue assemblage for optimum differential equations," Chin. J. Engin. Math., Vol. 20, 121-124, 2003.
11. Chen, R., "The problem of initial value for the plane transverse electromagnetic mode," Acta Phys. Sin-CH ED, Vol. 49, 2514-2518, 2000.
12. Coleman, S. and D. Grischkowsky, "A THz transverse electro-magnetic mode two-dimensional interconnect layer incorporating quasi-optics," Appl. Phys. Lett., Vol. 83, 3656-3658, 2003.
13. Chu, C. and T. Ohkawa, "Transverse electromagnetic waves," Phys. Rev. Lett., Vol. 48, 837-838, 1982.
14. Davis, L. W. and G. Patsakos, "TM and TE electromagnetic beams in free space," Opt. Lett., Vol. 6, 22-23, 1981.
15. Chew, , W. C. and W. C. Weedon, "A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates," Micro. Opt. Tech. Lett., Vol. 7, 599-604, 1994.
16. Elliott, R. S., Electromagnetics --- History, Theory, and Applications, IEEE Press, New York, 1993.
17. Karlsson, A. and G. Kristensson, "Constitutive relations, dissipation, and reciprocity for the Maxwell equations in the time domain," Journal of Electromagnetic Waves and Applications, Vol. 6, No. 1-6, 537-551, 1992.
18. Ruan, Z., M. Yan, C. W. Neff, and M. Qiu, "Ideal cylindrical cloak: Perfect but sensitive to tiny perturbations," Phys. Rev. Lett., Vol. 99, 113903, 2007.
19. Isic, G., R. Gajic, B. Novakovic, Z. Popovic, K. Hingerl, and , "Radiation and scattering from imperfect cylindrical electromagnetic cloaks," Opt. Express, Vol. 16, 1413-1422, 2008.
20. Naqvi, A., S. Ahmed, and Q. A. Naqvi, "Perfect electromagnetic conductor and fractional dual interface placed in a chiral nihility medium," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 14-15, 1991-1999, 2010.
21. Chen, H.-Y., L.-J. Deng, and P.-H. Zhou, "Suppression of surface wave from finite conducting surfaces with impedance loading at margins," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 14-15, 1977-1989, 2010.
22. Pinel, N., J. Saillard, and C. Bourlier, "Extension of the roughness criterion of a one-step surface to a one-step layer," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 8-9, 1195-1205, 2010.