Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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By Y. M. Wu and W. C. Chew

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The high frequency scattering problems of electromagnetic fields scattered from electrically large scatterers are important and challenging. On the calculation of the reflected and diffracted wave fields, the high frequency methods could be classified into the current based method and the ray based method. In this paper, first, we give a review on the progress of the modern high frequency methods for solving the electromagnetic scattering problems. Next, due to the highly oscillatory property of the high frequency electromagnetic scattered fields, we propose the numerical steepest descent path method. Finally, we comprehensively address the high frequency wave physics, including the high frequency critical point contributions, the Keller's cone, the shadow and reflection boundaries and the creeping wave fields.

Y. M. Wu and W. C. Chew, "The Modern High Frequency Methods for Solving Electromagnetic Scattering Problems (Invited Paper)," Progress In Electromagnetics Research, Vol. 156, 63-82, 2016.

1. Maxwell, J. C., "A dynamical theory of the electromagnetic field," Philosophical Transactions of the Royal Society of London, 459-512, 1865.

2. Heaviside, O., Electromagnetic Theory, Vol. 2, Cosimo, Inc., 2008.

3. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, New York, 1995.

4. Kong, J. A., Electromagnetic Wave Theory, Wiley-Interscience, New York, 1990.

5. Knott, E. F., J. F. Shaeffer, and M. T. Tuley, Radar Cross Section, Artech House, Norwood, 1993.

6. Balanis, C. A., Antenna Theory: Analysis and Design, Wiley, John Wiley-Sons, 2012.

7. Datta, S., Quantum Transport: Atom to Transistor, Cambridge University Press, 2005.

8. Cai, W., Computational Methods for Electromagnetic Phenomena: Electrostatics in Solvation, Scattering, and Electron Transport, Cambridge University Press, Cambridge, 2013.

9. Garrison, J. and R. Chiao, Quantum Optics, Oxford University Press, USA, 2014.

10. Tang, L., J. A. Kong, and B. Shin, Theory of Microwave Remote Sensing, John Wiley, New York, 1985.

11. Jin, Y. Q., Electromagnetic Scattering Modelling for Quantitative Remote Sensing, World Science Press, Singapore, 2000.

12. Harrington, R. F., Field Computation by Moment Method, Macmillan, New York, 1968.

13. Jin, J. M., The Finite Element Method in Electromagnetics, 3rd Ed., Wiley-IEEE Press, Hoboken, 2014.

14. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3rd Ed., Artech House, Boston, 2015.

15. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propag., Vol. 45, No. 10, 1488-1493, 1997.

16. Chew, W. C., J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, Boston, 2001.

17. Macdonald, H. M., "The effect produced by an obstacle on a train of electric waves," Phil. Trans. Royal Soc. London, Series A, Math. Phys. Sci., Vol. 212, 299-337, 1913.

18. Ufimtsev, P. Y., Backscatter, John Wiley and Sons, New York, 2005.

19. Ufimtsev, P. Y., Fundamentals of the Physical Theory of Diffraction, John Wiley and Sons, Inc., New York, 2007.

20. Mitzner, K. M., Incremental Length Diffraction Coefficients, Tech. Rep. No. AFAL-TR-73-296, 1974.

21. Shore, R. A. and A. D. Yaghjian, "Incremental diffraction coefficients for planar surfaces," IEEE Trans. Antennas Propag., Vol. 36, 55-70, 1988.

22. Hansen, T. B. and R. A. Shore, "Incremental length diffraction coefficients for the shadow boundary of a convex cylinder," IEEE Trans. Antennas Propag., Vol. 46, No. 10, 1458-1466, 1998.

23. Yaghjian, A. D., R. A. Shore, and M. B. Woodworth, "Shadow boundary incremental length diffraction coefficients for perfectly conducting smooth, convex surfaces," Radio Sci., Vol. 31, No. 12, 1681-1695, 1996.

24. Keller, J. B., "Geometrical theory of diffraction," J. Opt. Soc. Am., Vol. 52, No. 2, 116-130, 1962.

25. James, G. L., Geometrical Theory of Diffraction for Electromagnetic Waves, Peregrinus, Stevenage, 1980.

26. Kouyoumjian, R. G. and P. H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface," Proc. IEEE, Vol. 62, No. 11, 1448-1461, 1974.

27. Lee, S. W. and G. A. Deschamps, "A uniform asymptotic theory of electromagnetic diffraction by a curved wedge," IEEE Trans. Antennas Propag., Vol. 24, No. 1, 25-34, 1976.

28. Kouyoumjian, R. G., "Asymptotic high-frequency methods," Proc. IEEE, Vol. 53, No. 8, 864-876, 1965.

29. Pathak, P. H., "High-frequency techniques for antenna analysis," Proc. IEEE, Vol. 80, No. 1, 44-65, 1992.

30. Borovikov, V. A., Uniform Stationary Phase Method, Institution of Electrical Engineers, London, 1994.

31. Conde, O. M., J. Perez, and M. F. Catedra, "Stationary phase method application for the analysis of radiation of complex 3-D conducting structures," IEEE Trans. Antennas Propag., Vol. 49, No. 5, 724-731, 2001.

32. Carluccio, G., M. Albani, and P. H. Pathak, "Uniform asymptotic evaluation of surface integrals with polygonal integration domains in terms of UTD transition functions," IEEE Trans. Antennas Propag., Vol. 58, No. 4, 1155-1163, 2010.

33. Sommerfeld, A., "Mathematische theorie der diffraction," Mathematische Annalen., Vol. 47, No. 319, 317-374, 1896.

34. Fock, V. A., "The distributions of currents induced by a plane wave on the surface of a conductor," J. Phys., Vol. 10, 130-136, 1946.

35. Kline, M., Mathematical Theory of Optics, Brown University Notes, Providence, RI, 1944.

36. Ling, H., R. C. Chou, and S. W. Lee, "Shooting and bouncing rays: Calculating the RCS of an arbitrarily shaped cavity," IEEE Trans. Antennas Propag., Vol. 37, No. 2, 194-205, 1989.

37. Lee, S. W. and R. Mittra, "Fourier transform of a polygonal shape function and its application in electromagnetics," IEEE Trans. Antennas Propag., Vol. 31, No. 1, 99-103, 1983.

38. Gordon, W. B., "High-frequency approximations to the physical optics scattering integral," IEEE Trans. Antennas Propag., Vol. 42, No. 3, 427-432, 1994.

39. Engquist, B., E. Fatemi, and S. Osher, "Numerical solution of the high frequency asymptotic expansion for the scalar wave equation," J. Comput. Phys., Vol. 120, No. 1, 145-155, 1995.

40. Engquist, B. and O. Runborg, "Computational high frequency wave propagation," Acta Numerica, Vol. 12, 181-266, 2003.

41. Wong, R., Asymptotic Approximations of Integrals, SIAM, New York, 2001.

42. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover, Norwood, MA, 1972.

43. Josef, S. and B. Roland, Introduction to Numerical Analysis, Springer-Verlag, New York, 1980.

44. Asheim, A. and D. Huybrechs, "Asymptotic analysis of numerical steepest descent with path approximations," Found. Comput. Math., Vol. 10, No. 6, 647-671, 2010.

45. Bondia, F. V., M. Ferrando-Bataller, and A. Valero-Nogueira, "A new fast physical optics for smooth surfaces by means of a numerical theory of diffraction," IEEE Trans. Antennas Propag., Vol. 58, No. 3, 773-789, 2010.

46. Zhang, J., B. Xu, and T. J. Cui, "An alternative treatment of saddle stationary phase points in physical optics for smooth surfaces," IEEE Trans. Antennas Propag., Vol. 62, No. 2, 986-991, 2014.

47. Wu, Y., L. J. Jiang, and W. C. Chew, "An efficient method for computing highly oscillatory physical optics integral," Progress In Electromagnetics Research, Vol. 127, 211-257, 2012.

48. Wu, Y. M., L. J. Jiang, and W. C. Chew, "An efficient method for computing highly oscillatory physical optics integral," Symp. on Antennas and Propag. (IEEE APS12), 2012.

49. Wu, Y. M., L. J. Jiang, W. E. I. Sha, and W. C. Chew, "The numerical steepest descent path method for calculating physical optics integrals on smooth conducting surfaces," IEEE Trans. Antennas Propag., Vol. 61, No. 8, 4183-4193, 2013.

50. Wu, Y. M., L. J. Jiang, and W. C. Chew, "Computing highly oscillatory physical optics integral on the polygonal domain by an efficient numerical steepest descent path method," J. Comput. Phys., Vol. 236, 408-425, 2013.

51. Wu, Y. M., L. Jiang, and W. C. Chew, "The contour deformation method for calculating the high frequency scattered fields by the Fock current on the surface of the 3-D convex cylinder," Symp. on Antennas and Propag. (IEEE APS14), 2014.

52. Wu, Y. M., L. J. Jiang, W. C. Chew, and Y. Q. Jin, "The contour deformation method for calculating the high frequency scattered field by the Fock current on the surface of the 3-D convex cylinder," IEEE Trans. Antennas Propag., Vol. 63, No. 5, 2180-2190, 2015.

53. Perrey-Debain, E., J. Trevelyan, and P. Bettess, "Wave boundary elements: A theoretical overview presenting applications in scattering of short waves," Eng. Anal. Bound. Elem., Vol. 28, 131-141, 2004.

54. Engquist, B., A. Fokas, E. Hairer, and A. Iserles, Highly Oscillatory Problems, London Mathematical Society Lecture Note Series, Cambridge University Press, 2009.

55. Chandler, S. N. and S. Langdon, Acoustic Scattering: High Frequency Boundary Element Methods and Unified Transform Methods, SIAM, New York, 2015.

56. Cheng, H., W. Y. Crutchfield, Z. Gimbutas, L. F. Greengard, J. F. Ethridge, J. Huang, V. Rokhlin, N. Yarvin, and J. Zhao, "A wideband fast multipole method for the Helmholtz equation in three dimensions," J. Comput. Phys., Vol. 216, No. 1, 300-325, 2006.

57. Bruno, O. P., Fast, High-order, High-frequency Integral Methods for Computational Acoustics and Electromagnetics, Springer, Berlin Heidelberg, 2003.

58. Umul, Y. Z., "Rigorous expressions for the equivalent edge currents," Progress In Electromagnetics Research B, Vol. 15, 77-94, 2009.

59. Michaeli, A., "Equivalent edge currents for arbitrary aspects of observation," IEEE Trans. Antennas Propag., Vol. 32, 252-258, 1984.

60. Chou, H. T., P. H. Pathak, and P. R. Rousseau, "TD-UTD solutions for the transient radiation and surface fields of pulsed antennas placed on PEC smooth convex surfaces," IEEE Trans. Antennas Propag., Vol. 59, No. 5, 1626-1637, 2011.

61. Johansen, P. M., "Time-domain version of the physical theory of diffraction," IEEE Trans. Antennas Propag., Vol. 47, 261-270, 1999.

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