volume | PIER Journals

Abstract

To solve radiation problems in time domain directly the modal representation of transient electromagnetic fields is considered. Using evolutionary approach the initial nonstationary three-dimensional electrodynamic problem is transformed into the problem for one-dimensional evolutionary equations by the construction of the modal basis for electromagnetic fields with arbitrary time dependence in spherical coordinate system. Elimination of the radial components of electrical and magnetic field from Maxwell equation system permits to form the four-dimensional differential operators. It is proved that the operators are self- adjoint ones. The eigen-functions of the operators form the basis. The completeness of the basis is proved by means of Weyl Theorem about orthogonal detachments of Hilbert space. The expansion coefficients of arbitrary electromagnetic field are found from the set of evolutionary equations. The transient electromagnetic field can be found directly without Fourier transform application by means of one-dimensional FDTD method for the medium with dependence on longitudinal coordinate and time or using Laplace transform and wave splitting for the case of homogeneous stationary medium. The above mentioned methods are compared with the three-dimensional FDTD method for the case of the problem of small loop excitation by transient current.

1. Taflove, A. and S. C. Hagness, Computational Electromagnetics: The Finite-difference Time-domain Method, 2nd Ed., Artech House, Boston, London, Norwood, MA, USA, 2000.

2. Sirenko, Y. K., S. Strom, and N. P. Yashina, Modeling and Analysis of Transient Processes in Open Resonant Structures, New Methods and Techniques, Springer, New York, 2007.

3. Shreim, A. M. and M. F. Hadi, "Integral PML absorbing boundary conditions for the high-order M24 FDTD algorithm," Progress In Electromagnetics Research, Vol. 76, 141-152, 2007.
doi:10.2528/PIER07070303 Google Scholar

4. Zheng, K., W. Y. Tam, D. B. Ge, and J. D. Xu, "Unaxial PML absorbing boundary condition for truncating the boundary of DNG metamaterials," Progress In Electromagnetics Research Letters, Vol. 8, 125-134, 2009.
doi:10.2528/PIERL09030901 Google Scholar

5. Liang, F. and G. Wang, "Fourth-order locally one-dimensional FDTD method," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 14-15, 2035-2043, 2008.
doi:10.1163/156939308787538017 Google Scholar

6. LaComb, J. A., "Spoke top antenna for transient radiation," Progress In Electromagnetics Research Letters, Vol. 11, 1-9, 2009.
doi:10.2528/PIERL09080602 Google Scholar

7. Tretyakov, O. A., "Modal basis method," Radiotekhika i electronika, Vol. 31, No. 6, 1071-1082, 1986 (in Russian). Google Scholar

8. Tretyakov, O. A. and F. Erden, "Temporal cavity oscillations caused by a wide-band waveform," Progress In Electromagnetics Research B, Vol. 6, 183-204, 2008.
doi:10.2528/PIERB08031222 Google Scholar

9. Antyufeyeva, M. S., A. Y. Butrym, and O. A. Tretyakov, "Transient electromagnetic fields in a cavity with dispersive double negative medium," Progress In Electromagnetics Research M, Vol. 8, 51-65, 2009.
doi:10.2528/PIERM09062307 Google Scholar

10. Antyufeyeva, M. S. and O. A. Tretyakov, "Electromagnetic fields in a cavity filled with some nonstationary medium," Progress In Electromagnetics Research B, Vol. 19, 177-203, 2010.
doi:10.2528/PIERB09112402 Google Scholar

11. Tretyakov, O. A., "Evolutionary waveguide equations," Radiotekhika i electronika, Vol. 34, No. 5, 917-926, 1989 (in Russian). Google Scholar

12. Tretyakov, O. A., "Essentials of nonstationary and nonlinear electromagnetic field theory," Analytical and Numerical Methods in Electromagnetic Wave Theory, M. Hashimoto, M. Idemen, and O. A. Tretyakov (eds.), Vol. 572, Science House Co., Ltd, Tokyo, 1993. Google Scholar

13. Weyl, H., "The method of orthogonal projection in potential theory ," Duke Math. J., Vol. 7, 411-444, 1940.
doi:10.1215/S0012-7094-40-00725-6 Google Scholar

14. Velychko, L. G. and Y. K. Sirenko, "Controlled changes in spectra of open quasi-optical resonators," Progress In Electromagnetics Research B, Vol. 16, 85-105, 2009.
doi:10.2528/PIERB09060202 Google Scholar

15. Motavali, H. and A. Rostami, "Exactly modal analysis of inhomogeneous slab waveguide using Nikiforov-Uvarov method," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 5-6, 681-692, 2008.
doi:10.1163/156939308784159507 Google Scholar

16. Butrym, A. Y. and B. A. Kochetov, "Time domain mode basis method for a waveguide with transverse inhomogeneous multi-connected cross-section. 1. The general theory of method," Radio Physics and Radio Astronomy, Vol. 14, No. 2, 162-173, 2009 (in Russian). Google Scholar

17. Tretyakov, O. A. and A. N. Dumin, "Radiation of transient electromagnetic fields from plane radiator," Electromagnetic Waves & Electron. Systems, Vol. 3, No. 1, 12-22, 1998 (in Russian). Google Scholar

18. Dumin, A. N., "Radiation of transient localized waves from an open-ended coaxial waveguide with infinite flange," Telecommunications and Radio Engineering, Vol. 53, No. 6, 30-34, 1999. Google Scholar

19. Dumin, A. N., A. Y. Butrym, O. A. Tretyakov, V. A. Katrich, and O. A. Dumina, "Transient electromagnetic fields in unbounded space with inhomogeneous medium," Proceedings of the 2nd International Workshop on Ultrawideband and Ultrashort Impulse Signals (UWBUSIS'04), 104-106, Sevastopol, Ukraine, 2004.

20. Butrym, A. Y. and B. A. Kochetov, "Mode expansion in time domain for conical lines with angular medium inhomogeneity," Progress In Electromagnetics Research B, Vol. 19, 151-176, 2010.
doi:10.2528/PIERB09102606 Google Scholar

21. Butrym, A. Yu., B. A. Kochetov, and M. N. Legenkiy, "Numerical analysis of simply TEM conical-like antennas using mode matching in time domain ," Proceedings of the 3rd European Conference on Antennas and Propagation (EuCAP 2009), 3471-3475, Berlin, Germany, 2009.

22. Zhou, S.-G., J. Ma, J.-Y. Deng, and Q.-Z. Liu, "A low-profile and broadband conical antenna," Progress In Electromagnetics Research Letters, Vol. 7, 97-103, 2009.
doi:10.2528/PIERL09021602 Google Scholar

23. Ghosh, D., T. K. Sarkar, and E. L. Mokole, "Design of a wide-angle biconical antenna for wideband communications," Progress In Electromagnetics Research B, Vol. 16, 229-245, 2009.
doi:10.2528/PIERB09061508 Google Scholar

24. Shlivinski, A. and E. Heyman, "Time-domain near-field analysis of short-pulse antennas --- Part I: Spherical wave (multipole) expansion ," IEEE Trans. Antennas and Propagation, Vol. 47, No. 2, 271-279, 1999.
doi:10.1109/8.761066 Google Scholar

25. Tretyakov, O., A. Dumin, O. Dumina, and V. Katrich, "Modal basis method in radiation problems," Proc. Int. Conf. on Math. Methods in Electromagnetic Theory (MMET-2004), 312-314, Dnepropetrovsk, Ukraine, 2004.

26. Dumin, O. M., O. O. Dumina, and V. O. Katrich, "Propagation of spherical transient electromagnetic wave through radially inhomogeneous medium," Proc. Int. Conf. on Ultrawideband and Ultrashort Impulse Signals (UWBUSIS-2006), 276-278, Sevastopol, Ukraine, 2006.

27. Dumin, O., O. Dumina, and V. Katrich, "Evolution of transient electromagnetic fields in spherical coordinate system," Proc. XI-th Int. Conf. on Math. Methods in Electromagnetic Theory (MMET-2006), 363-365, Kharkiv, Ukraine, 2006.

28. Dumin, O. M., O. O. Dumina, and V. O. Katrich, "Comparative analysis of the analytical and numerical solutions of transient wave propagation problem ," Proc. XI-th Int. Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic wave Theory (DIPED-06) , 43-46, Tbilisi, Georgia, 2006.

29. Butrym, A. Y. and B. A. Kochetov, "Mode basis method for spherical TEM-transmission lines and antennas," Proc. Int. Conf. on Antenna Theory and Techniques (ICATT-2007), 243-245, Sevastopol, Ukraine, 2007.

30. Kamke, E., "Handbook of Ordinary Di®erential Equations," Nauka, Moscow, 1965 (in Russian). Google Scholar

31. Zheng, Y., B. A. Kochetov, and A. Y. Butrym, "Finite difference scheme in time domain and analytical solution for Klein-Gordon Equation," Bulletin of Karazin Kharkiv National University, No. 712, ''Radiophysics and electronics", No. 10, 91-94, 2006 (in Russian). Google Scholar

32. Sorour, T. E. and A. B. El-Rouby, "An isotropic algorithm for solving Maxwell's Equations in 2D," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 5-6, 829-838, 2008.
doi:10.1163/156939308784159615 Google Scholar

Dr. Oleksandr M. Dumin

Dr. O. O. Dumina

Dr. Victor A. Katrich