volume | PIER Journals

Abstract

The problem of electromagnetic (EM) wave scattering on small particles is reduced to solving the Fredholm integral equation of the second kind. Integral representation of solution to the scattering problem leads to necessity to determine some unknown function contained in integrand of this equation. The respective linear algebraic system (LAS) for the components of this unknown vector function is derived and solved by the successive approximation method. The region of convergence of the proposed method is substantiated. The numerical results show rapid convergence of the method in the wide region of the physical and geometrical parameters of problem. Comparison of the obtained results with Mie type and asymptotic solutions demonstrates high degree of accuracy of the proposed method. The numerical results of scattering on particles of several forms and sizes are presented.

1. Andriychuk, M. I. and A. G. Ramm, "Scattering by many small particles and creating materials with a desired refraction coefficient," Intern. Journ. of Computing Science and Mathematics, Vol. 3, No. 1/2, 102-121, 2010.
doi:10.1504/IJCSM.2010.033929

2. Andriychuk, M. I., S. W. Indratno, and A. G. Ramm, "Electromagnetic wave scattering by a small impedance particle: Theory and modeling," Optics Communications, Vol. 285, 1684-1691, 2012.
doi:10.1016/j.optcom.2011.12.055

3. Attaran, A., W. B. Handler, K. Wawrzyn, R. S. Menon, and B. A. Chronik, "Reliable RF B/E-field probes for time-domain monitoring of EM exposure during medical device testing," IEEE Trans. Antennas Propagat., Vol. 65, No. 9, 4815-4823, 2017.
doi:10.1109/TAP.2017.2723085

4. Barber, P. W. and S. C. Hill, Light Scattering by Particles: Computational Methods, World Scientific, Singapure, 1990.
doi:10.1142/0784

5. Chen, Y., Y. Ge, G. B. M. Heuvelink, R. An, and Y. Chen, "Object-based superresolution land-cover mapping from remotely sensed imagery," IEEE Transactions on Geoscience and Remote Sensing, Vol. 56, No. 1, 328-340, 2018.
doi:10.1109/TGRS.2017.2747624

6. Faran, J. J., "Sound scattering by solid cylinders and spheres," J. Acoust. Soc. Amer., Vol. 23, No. 4, 405-418, July 1951.
doi:10.1121/1.1906780

7. Gensheimer, P. D., C. K. Walker, R. W. Ziolkowski, and C. D. D’Aubigny, "Full-scale three-dimensional electromagnetic simulations of a terahertz folded-waveguide traveling-wave tube using ICEPIC," IEEE Transactions on Terahertz Science and Technology, Vol. 2, No. 2, 222-230, 2012.
doi:10.1109/TTHZ.2011.2178931

8. Glisson, A. W., "Electromagnetic scattering by arbitrarily shaped surfaces with impedance boundary conditions," Radio Sci., Vol. 27, No. 6, 935-943, November 1992.
doi:10.1029/92RS01782

9. Helander, J., A. Ericsson, M. Gustafsson, T. Martin, D. Shoberg, and C. Larsson, "Compressive sensing techniques for mm-wave nondestructive testing of composite panels," IEEE Trans. Antennas Propagat., Vol. 65, No. 10, 5523-5531, 2017.
doi:10.1109/TAP.2017.2738034

10. Van De Hulst, H. G., Light Scattering by Small Particles, Dover, New York, 1981.

11. Ishimaru, A., Electromagnetic Wave Propagation, Radiation and Scattering, Englewood Cliffs, Prentice-Hall, NJ, 1991.

12. Kantorovich, L. V. and V. I. Krylov, Approximate Methods of Higher Analysis, Noordhoff, Groningen, 1958.

13. Kaye, M., P. K. Murthy, and G. A. Thiele, "An iterative method for solving scattering problems," IEEE Trans. Antennas Propagat., Vol. 33, No. 11, 1272-1279, November 1985.
doi:10.1109/TAP.1985.1143510

14. Ko, W. L. and R. Mittra, "A new approach based on a combination of integral equation and asymptotic techniques for solving electromagnetic scattering problems," IEEE Trans. Antennas Propagat., Vol. 25, No. 2, 187-1977, March 19.
doi:10.1109/TAP.1977.1141571

15. Korn, G. A. and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Company, 1968.

16. Kyurkchan, A. G. and S. A. Manenkov, "Solving the problem of electromagnetic wave diffraction at a finite plane grating with small elements," Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 180, 92-100, 2016.
doi:10.1016/j.jqsrt.2016.04.014

17. Landau, L., E. Lifschitz, and L. Pitaevsky, Electromagnetizm of Continuous Medium, Pergamon Press, Oxford, 1984.

18. Lu, K.-Y., S.-C. Tuan, H.-T. Chou, and H.-H. Chou, "Analytical analysis of electromagnetic transient scattering from perfectly conducting ellipsoidal surfaces illuminated by a plane wave," Proc. of IEEE International Symposium on Antennas and Propagation (APS-URSI), 2523-2526, 2011.

19. Mason, W. P. and R. N. Thurston, "Physical acoustics principles and methods," Academic, Vol. XV, 191-202, New York, 1981.

20. Medgyesi-Mitschang, L. N. and J. M. Putman, "Integral equation formulations for imperfectly conducting scatterers," IEEE Trans. Antennas Propagat., Vol. 33, No. 2, 206-214, February 1985.
doi:10.1109/TAP.1985.1143560

21. Mie, G., "Beitrage zur Optik tr¨uber Medien, speciell kolloidaler Metallosungen," Annalen der Physik, Vol. 330, No. 3, 377-445, 1908.
doi:10.1002/andp.19083300302

22. Mishchenko, M. I., L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles, Cambridge University Press, 2002.

23. Muller, C., Foundations of the Mathematical Theory of Electromagnetic Waves, Springer-Verlag, Berlin, 1969.
doi:10.1007/978-3-662-11773-6

24. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, 1st Ed., Wiley IEEE Press, 1977.

25. Poggio, A. J. and E. K. Miller, "Integral equation solutions of three dimensional scattering problems," Computer Techniques for Electrornagnetics, R. Mittra, ed., Chap. 4, Pergamon, Oxford, 1973.

26. Rao, S., "Innovative antenna front ends from L-band to Ka-band," IEEE Antennas & Propagation Magazine, Vol. 59, No. 5, 116-129, October 2017.

27. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. 30, No. 3, 409-418, May 1982.
doi:10.1109/TAP.1982.1142818

28. Ramm, A. G., Wave Scattering by Small Bodies of Arbitrary Shapes, World Scientific, Singapure, 2005.
doi:10.1142/5765

29. Ramm, A. G., "Many-body wave scattering by small bodies and applications," J. Math. Phys., Vol. 48, No. 10, 103511, 2007.
doi:10.1063/1.2799258

30. Ramm, A. G., "Wave scattering by many small particles embedded in a medium," Phys. Lett. A, Vol. 372/17, 3064-3070, 2008.
doi:10.1016/j.physleta.2008.01.006

31. Ramm, A. G., "Electromagnetic wave scattering by many small bodies and creating materials with a desired refraction coefficient," Progress In Electromagnetics Research M, Vol. 13, 203-215, 2010.
doi:10.2528/PIERM10072307

32. Ramm, A. G., "Scattering by many small inhomogeneities and applications,", Topics in Chaotic Systems, Selected Papers from Chaos 2010 International Conference, C. Skiadas, I. Dimotikalis, C. Skiadas, ed., 41-52, World Sci. Publishing, 2011.

33. Ramm, A. G. and M. I. Andriychuk, "Application of the asymptotic solution to EM field scattering problem for creation of media with prescribed permeability," J. Appl. Math. Comput., Vol. 45, No. 1, 461-85, 2014.
doi:10.1007/s12190-013-0732-7

34. Ramm, A. G. and M. I. Andriychuk, "Calculation of electromagnetic wave scattering by a small impedance particle of an arbitrary shape," Mathematical Modeling of Natural Phenomena, Vol. 9, No. 5, 254-269, 2014.
doi:10.1051/mmnp/20149517

35. Rylander, T., A. Bondeson, and P. Ingelstrom, Computational Electromagnetics, 2nd Ed., Springer, 2012.

36. Sheng, X.-Q., J.-M. Jin, J. Song, C.-C. Lu, and W. C. Chew, "On the formulation of hybrid finite-element and boundary-integral methods for 3D scattering," IEEE Trans. Antennas Propagat., Vol. 46, No. 3, 303-311, March 1998.
doi:10.1109/8.662648

37. Soudais, P., "Computation of the electromagnetic scattering from complex 3D objects by a hybrid FEM/BEM method," Journal of Electromagnetic Waves and Applications, Vol. 9, No. 7, 871-886, July 1995.

38. Ufimtsev, P. Y., Axially Symmetric Scattering of Acoustic Waves at Bodies of Revolution (Fundamentals of the Physical Theory of Diffraction), Wiley-IEEE Press, 2014.

39. Vesnik, M. V., "Analytical solution for electromagnetic diffraction on 2-D perfectly conducting scatterers of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. 49, No. 12, 1638-1644, December 2001.
doi:10.1109/8.982441

40. Wilton, D. R., "Review of current status and trends in the use of integral equations in computational electromagnetics," Electromagnetics, Vol. 12, 287-341, 1992.
doi:10.1080/02726349208908318

41. Yang, C. X. and M. S. Tong, "Time-domain analysis of transient electromagnetic scattering from dielectric objects based on electric field integral equations," IEEE Trans. Antennas Propagat., Vol. 65, No. 2, 966-971, 2017.
doi:10.1109/TAP.2016.2632699

42. Yla-Oijala, P., S. P. Kiminki, H. Walln, and A. Sihvola, "Uniform surface integral equation formulation for mixed impedance boundary conditions," IEEE Trans. Antennas Propagat., Vol. 63, No. 12, 5718-5726, 2015.
doi:10.1109/TAP.2015.2496100

43. Yuan, X. C., "Three-dimensional electromagnetic scattering from inhomogeneous objects by the hybrid moment and finite element method," IEEE Trans. Microwave Theory Tech., Vol. 38, No. 8, 1053-1058, August 1990.
doi:10.1109/22.57330

44. Zhong, Y., M. Lambert, D. Lesselier, and X. Chen, "A new integral equation method to solve highly nonlinear inverse scattering problems," IEEE Trans. Antennas Propagat., Vol. 64, No. 5, 1788-1799, 2016.
doi:10.1109/TAP.2016.2535492

Dr. Mykhaylo I. Andriychuk