volume | PIER Journals

2008-04-09

Scattering Properties of the Strip with Fractional Boundary Conditions and Comparison with the Impedance Strip

Maxim Ivakhnychenko,

Dr. Maxim Ivakhnychenko

IRE NAS of Ukraine

Ukraine

Homepage

Eldar Veliev,

Dr. Eldar Veliev

Institute of Radiophysics and Electronics

National Academy of Sciences

Ukraine

Homepage

Turab Ahmedov

Dr. Turab Ahmedov

Institute of Mathematics NAS of Azerbaijan

Baku

Homepage

Progress In Electromagnetics Research C, Vol. 2, 189-205, 2008

doi:10.2528/PIERC08031502

Abstract

In this paper two-dimensional problem of plane-wave diffraction by a "fractional strip" is studied. "Fractional strip" is introduced as a strip with fractional boundary conditions (FBC) involving fractional derivatives of the field components. FBC describe intermediate boundary between perfect electric conductor (PEC) and perfect magnetic conductor (PMC). It is shown that "fractional strip" has scattering properties similar to the well-known impedance strip. For one important case of fractional order equal to 0.5 the solution of the wave diffraction problem by a "fractional strip" can be found analytically. Detailed comparison analysis of the physical characteristics of the scattered fields for both fractional and impedance strips is presented. The relation between the fractional order and the value of impedance is derived. It is shown that in a wide range of input parameters the physical characteristics of the "fractional strip" are similar to the strip with pure imaginary impedance.

Citation

Copy Export

Maxim Ivakhnychenko, Eldar Veliev, and Turab Ahmedov, "Scattering Properties of the Strip with Fractional Boundary Conditions and Comparison with the Impedance Strip," Progress In Electromagnetics Research C, Vol. 2, 189-205, 2008.
doi:10.2528/PIERC08031502

References

1. Veliev, E., M. V. Ivakhnychenko, and T. M. Ahmedov, "Fractional boundary conditions in plane waves diffraction on a strip," Progress In Electromagnetics Research, Vol. 79, 443-462, 2008.
doi:10.2528/PIER07102406

2. Samko, S. G., A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach Science Publishers, Langhorne, PA, 1993.

3. Senior, T. B. and J. L. Volakis, Approximate Boundary Conditions in Electromagnetics, The institution of Electrical Engineers, London, United Kingdom, 1995.

4. Engheta, N., "Use of fractional integration to propose some 'Fractional' solutions for the scalar Helmholtz equation," Progress In Electromagnetics Research, (Monograph Series), Vol. 12, 107-132, 1996.

5. Veliev, E. and N. Engheta, "Generalization of Green's Theorem with Fractional Differintegration," 2003 IEEE AP-S International Symposium & USNC/URSI National Radio Science Meeting, 2003.

6. Veliev, E. and T. M. Ahmedov, "Fractional solution of Helmholtz equation — A new presentation," Reports of NAS of Azerbaijan, No. 4, 20-27, 2005.

7. Honl, H., A. W. Maue, and K. Westpfahl, Theorie der Beugung, Springer-Verlag, 1961.

8. Balanis, C. A., Advanced Engineering Electromagnetic, 1989.

9. Ikiz, T., S. Koshikawa, K. Kobayashi, E. I. Veliev, and A. H. Serbest, "Solution of the plane wave diffraction problem by an impedance strip using a numerical-analytical method: E-polarized case," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 3, 315-340, 2001.
doi:10.1163/156939301X00481

10. Colton, D. L. and R. Kress, Integral Equation Methods in Scattering Theory, 1983.

11. Veliev, E. and V. P. Shestopalov, "A general method of solving dual integral equations," Sov. Physics Dokl., Vol. 33, No. 6, 411-413, 1988.

12. Veliev, E. and V. V. Veremey, "Numerical-analytical approach for the solution to the wave scattering by polygonal cylinders and flat strip structures," Analytical and Numerical Methods in Electromagnetic Wave Theory, M. Hashimoto, M. Idemen, and O. A. Tretyakov (eds.), Chap. 10, Science House, Tokyo, 1993.

13. Engheta, N., "Fractionalization methods and their applications to radiation and scattering problems," Proceedings of MMET*00, Vol. 1, 34-40, Kharkiv, Ukraine, 2000.

14. Veliev, E., M. V. Ivakhnychenko, and T. M. Ahmedov, "Fractional operators approach in electromagnetic wave reflection problems," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1787-1802, 2007.