A full-wave evaluation of the electromagnetic field in conformal structures with linear loading materials is presented in this paper. The analysis is performed considering at first conformal components with conventional isotropic and homogeneous media in the generalized orthogonal curvilinear reference system. In this first case, a summary of the possible analytical solutions of the vector wave equation obtainable through various factorization techniques is given. Then, the attention is focused on conformal structures involving non-conventional media (anisotropic, chiral, bianisotropic) and in this case the field solution is demanded to a new generalization of the transmission line approach. As an aside, exploiting a contravariant field formulation, which allows writing Maxwell's equations in the generalized reference system as in the Cartesian one, a useful relationship between the local curvature of the geometry and a suitable inhomogeneity of a related planar structure is presented. Finally, some results, obtained simulating the behavior of patch radiators mounted on curved bodies through the combined application of an extended Method of Line (MoL) numerical algorithm and the theoretical approach here derived, are presented.
1. Zeng, L. R. and Y. Wang, "Accurate solutions of elliptical and cylindrical striplines and microstrip lines," IEEE Trans. Microwave Theory Tech., Vol. MTT-34, No. 2, 259-264, 1986. doi:10.1109/TMTT.1986.1133320
2. Alexoploulos, N. G. and A. Nakatani, "Cylindrical substrate microstrip line characterization," IEEE Trans. Microwave Theory Tech., Vol. MTT-35, No. 9, 843-849, 1987. doi:10.1109/TMTT.1987.1133761
3. Luk, K. M., K. F. Lee, and J. S. Dahele, "Analysis of the cylindrical-rectangular patch antenna," IEEE Trans. Antennas Propagat., Vol. AP-37, No. 2, 143-147, 1989.
4. Luk, K. M. and K. F. Lee, "Characteristics of the cylindricalcircular patch antenna," IEEE Trans. Antennas Propagat., Vol. AP-38, No. 7, 1119-1123, 1990.
5. Ke, B. and A. A. Kishk, Analysis of spherical circular microstrip antennas, IEE Proc., Vol. 138, No. 12, 542-548, 1991.
6. Descardeci, J. R. and A. J. Giarola, "Microstrip antennas on a conical surface," IEEE Trans. Antennas Propagat., Vol. AP-40, No. 4, 460-463, 1992. doi:10.1109/8.138851
7. Kempel, L. C. and J. L. Volakis, "Scattering by cavitybacked antennas on a circular cylinder," IEEE Trans. Antennas Propagat., Vol. AP-42, No. 9, 1268-1279, 1994. doi:10.1109/8.318648
8. Chen, H. M. and K. L. Wong, "Characterization of coupled cylindrical microstrip lines mounted inside a ground cylinder," Microwave Opt. Technol. Lett., Vol. 10, 330-333, 1995.
9. Kempel, L. C., J. L. Volakis, and R. J. Sliva, Radiation by cavity-backed antennas on circular cylinder, IEE Proc.-Microw. Antennas Propag., Vol. 142, No. 6, 233-239, 1995.
10. Su, H. C. and K. L. Wong, "Dispersion characteristics of cylindrical coplanar waveguides," IEEE Trans. Microwave Theory Tech., Vol. MTT-44, No. 11, 2120-2122, 1996.
11. Chi-Wei, W., L. C. Kempel, and E. J. Rothwell, "Radiation by cavity-backed antennas on an elliptic cylinder," 2001 IEEE Antennas Propagat. Inter. Symp., Vol. 1, 342-345, 2001.
12. Macon, C. A., L. C. Kempel, and S. W. Schneider, "Modeling conformal antennas on prolate spheroids using the finite elementboundary integral method," 2001 IEEE Antennas Propagat. Inter. Symp., Vol. 2, 358-361, 2001.
13. Macon, C. A., L. C. Kempel, and S. W. Schneider, "Modeling cavity-backed apertures conformal to prolate spheroids using the finite element-boundary integral technique," 2002 IEEE Antennas Propagat. Inter. Symp., Vol. 1, 550-553, 2002.
14. Wong, K. L., Design of Nonplanar Microstrip Antennas and Transmission Lines, John Wiley and Sons, Inc., 1999.
15. Varadan, V. K., V. V. Varadan, and A. Lakhtakia, "On the possibility of designing broadband anti-reflection coatings with chiral composites," J. Wave Material Interaction, Vol. 2, No. 1, 71-81, 1987.
16. Cory, H. and I. Rosenhouse, "Minimization of reflection coefficient at feed of random-covered reflector antenna by chiral device," Electron. Lett., Vol. 27, No. 25, 2345-2347, 1991.
17. Engheta, N. and P. Pelet, "Reduction of surface waves in chirostrip antennas," Electron. Lett., Vol. 27, No. 1, 5-7, 1991.
18. Pozar, D. M., "Microstrip antennas and arrays on chiral substrates," IEEE Trans. Antennas Propagat., Vol. AP-40, 1260-1263, 1992. doi:10.1109/8.182462
19. Scamarcio, G., F. Bilotti, A. Toscano, and L. Vegni, "Broad band U-slot patch antenna loaded by chiral material," J. Electromag. Waves Applicat., Vol. 15, No. 10, 1303-1317, 2001.
20. Verma, A. K., "Input impedance of rectangular microstrip patch antenna with iso/anisotropic substrate-superstrate," IEEE Microwave Wireless Compon. Lett., Vol. MWCL-11, 456-458, 2001. doi:10.1109/7260.966040
21. Bilotti, F., A. Toscano, and L. Vegni, "FEM-BEM formulation for the analysis of cavity backed patch antennas on chiral substrates," IEEE Trans. Antennas Propagat., Vol. AP-51, No. 2, 306-311, 2003. doi:10.1109/TAP.2003.809076
22. Bilotti, F., L. Vegni, and A. Toscano, "Radiation and scattering features of patch antennas with bianisotropic substrates," IEEE Trans. Antennas Propagat., Vol. AP-51, No. 3, 449-456, 2003. doi:10.1109/TAP.2003.809837
23. Bilotti, F. and L. Vegni, "Chiral cover effects on microstrip antennas," IEEE Trans. Antennas Propagat., Vol. AP-51, No. 10, 2891-2898, 2003. doi:10.1109/TAP.2003.816317
24. AlÂ´u, F. Bilotti, and L. Vegni, "Method of lines numerical analysis of conformal antennas," IEEE Trans. Antennas Propagat., Vol. AP-52, No. 6, 2004.
25. Byerly, W. E., "Orthogonal curvilinear coordinates," An Elementary Treatise on Fourier's Series, 238-239, 1959.
26. Moon, P. and D. E. Spencer, Field Theory Handbook, Springer- Verlag Editions, Berlin, 1963.
27. Zhang, K. and D. Li, Electromagnetic Theory for Microwave and Optical Devices, Springler-Verlag, Berlin Heidelberg, 1998.
28. Ishimaru, A., Electromagnetic Wave Propagation Radiation and Scattering, Prentice Hall, Englewood Cliffs, New Jersey, 1991.
29. Collin, R. E., Filed Theory of Guided Waves, Wiley-IEEE Press, New York, 1990.
30. Schelkunoff, S. A., "Generalised telegraphist's equation for waveguide," Bell Syst. Tech. J., No. 7, 784-801, 1952.
31. Pregla, R. and W. Pascher, "The method of lines," Numerical Techniques for Microwave and Millimeter Wave Passive Structures, 381-346, 1989.
32. Pregla, R., New concepts in the method of lines, Proc. of PIERS 2000, Vol. '' Proc. of S 2000, No. 7, 2000.
33. Pregla, R., Efficient analysis of conformal antennas with anisotropic material, Proc. of AP2000, No. 4, 2000.
34. Kremer, D. and R. Pregla, "The method of lines for the hybrid analysis of multilayered cylindrical resonator structures," IEEE Trans. Microwave Theory Tech., Vol. MTT-45, No. 12, 2152-2155, 1997. doi:10.1109/22.643756
35. Yang, W. D. and R. Pregla, "The method of lines for the analysis of integrated optical waveguide structures with arbitrary curved interfaces," J. Lightwave Tech., Vol. 14, No. 5, 879-884, 1996. doi:10.1109/50.495171
36. Pregla, R., "General formulas for the method of lines in cylindrical coordinates," IEEE Trans. Microwave Theory Tech., Vol. MTT-43, No. 7, 1617-1620, 1995. doi:10.1109/22.392926
37. Chen, H. T., H. D. Chen, and K. L. Wong, "Analysis of sphericalcircular microstrip antennas on a uniaxial substrate," 1994 IEEE Antennas Propagat. Inter. Symp., Vol. 1, 186-189, 1994.
38. Dreher, A. and R. Pregla, "Analysis of planar waveguides with the method of lines and absorbing boundary conditions," IEEE Microw. Guided Wave Lett., No. 6, 138-140, 1991. doi:10.1109/75.91091