volume | PIER Journals

Abstract

In this paper, we develop numerical methods for using vector spherical and spheroidal waves in the hybrid method to calculate the multiple scattering of objects of complex shapes, based on the rigorous solutions of Maxwell equations in the form of Foldy-Lax multiple scattering equations (FL). The steps in the hybrid method are: (1) calculating the T-matrix of each single object using vector spherical/spheroidal waves and (2) vector spherical/spheroidal waves addition theorem. We utilize the commercial software HFSS to calculate the scattered fields of a complex object on the circumscribing sphere or spheroid for multiple incidences and polarizations. The T-matrix of spherical waves or spheroidal waves are then obtained from these scattered fields. To perform wave transformations (i.e. addition theorem) for vector spherical/spheroidal waves, we develop robust numerical methods. Numerical results are illustrated for T-matrices and numerical vector addition theorems.

1. Tsang, L., J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing, Wiley, 1985.

2. Chandrasekhar, S., "Radiative Transfer," Courier Corporation, 2013. Google Scholar

3. Ishimaru, A., Electromagnetic Wave Propagation, Radiation, and Scattering: From Fundamentals to Applications, John Wiley and Sons, 2017.
doi:10.1002/9781119079699

4. Mishchenko, M. I., L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering, Cambridge University Press, 2006.

5. Ulaby, F. T., K. Sarabandi, K. Y. Mcdonald, M. Whitt, and M. C. Dobson, "Michigan microwave canopy scattering model," InternationalJournal ofRemote Sensing, Vol. 11, No. 7, 1223-1253, 1990. Google Scholar

6. Liao, T. H., S. B. Kim, S. Tan, L. Tsang, C. Su, and T. J. Jackson, "Multiple scattering effects with cyclical correction in active remote sensing of vegetated surface using vector radiative transfer theory," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 9, No. 4, 1414-1429, 2016.
doi:10.1109/JSTARS.2015.2505638 Google Scholar

7. Lang, R. H. and J. S. Sighu, "Electromagnetic backscattering from a layer of vegetation: A discrete approach," IEEE Transactions on Geoscience and Remote Sensing, Vol. 1, No. 1, 62-71, 1983.
doi:10.1109/TGRS.1983.350531 Google Scholar

8. Chauhan, N. S., R. H. Lang, and K. J. Ranson, "Radar modeling of a boreal forest," IEEE Transactions on Geoscience and Remote Sensing, Vol. 29, No. 4, 627-638, 1991.
doi:10.1109/36.135825 Google Scholar

9. Kim, S. B., J. J. Van Zyl, et al. "Surface soil moisture retrieval using the L-band synthetic aperture radar onboard the soil moisture active-passive satellite and evaluation at core validation sites," IEEE Transactions on Geoscience and Remote Sensing, Vol. 55, No. 4, 1897-1914, 2017.
doi:10.1109/TGRS.2016.2631126 Google Scholar

10. Huang, H., T.-H. Liao, L. Tsang, E. G. Njoku, A. Colliander, T. J. Jackson, M. S. Burgin, and S. Yueh, "Modelling and validation of combined active and passive microwave remote sensing of agricultural vegetation at L-band," Progress In Electromagnetics Research B, Vol. 78, 94-124, 2017. Google Scholar

11. Frisch, U., Wave Propagation in Random Media, Institue d’Astrophysique Centre National de la Recherche, Paris, Academic Press Inc., 1968.

12. Tsang, L. and J. A. Kong, Scattering of Electromagnetic Waves: Advanced Topics, John Wiley and Sons, 2004.

13. Tsang, L. and A. Ishimaru, "Theory of backscattering enhancement of random discrete isotropic scatterers based on the summation of all ladder and cyclical terms," JOSA A, Vol. 2, No. 8, 1331-1338, 1985.
doi:10.1364/JOSAA.2.001331 Google Scholar

14. Tsang, L., J. A. Kong, and C. O. Ao, "Scattering of Electromagnetic Waves: Numerical Simulations," John Wiley and Sons, 2004. Google Scholar

15. Tsang, L., C. E. Mandt, and K. H. Ding, "Monte Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres based on solution of Maxwell's equations," Optics Letters, Vol. 17, 314-316, 1992.
doi:10.1364/OL.17.000314 Google Scholar

16. Xu, X., D. Liang, et al. "Active remote sensing of snow using NMM3D/DMRT and comparison with CLPX II airborne data," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 3, 689-697, 2010.
doi:10.1109/JSTARS.2010.2053919 Google Scholar

17. Tsang, L., H. Chen, C. C. Huang, and V. Jandhyala, "Modeling of multiple scattering among vias in planar waveguides using Foldy-Lax equations," Microwave and Optical Technology Letters, Vol. 31, 201-208, 2001.
doi:10.1002/mop.1398 Google Scholar

18. Huang, H., L. Tsang, E. G. Njoku, A. Colliander, T.-H. Liao, and K. H. Ding, "Propagation and scattering by a layer of randomly distributed dielectric cylinders using Monte Carlo simulations of 3D Maxwell equations with applications in microwave interactions with vegetation," IEEE Access, Vol. 5, 11985-12003, 2017.
doi:10.1109/ACCESS.2017.2714620 Google Scholar

19. Huang, H., L. Tsang, A. Colliander, and S. Yueh, "Propagation of waves in randomly distributed cylinders using three-dimensional vector cylindrical wave expansions in Foldy-Lax equations," IEEE Journal on Multiscale and Multiphysics Computational Techniques, Vol. 4, 214-226, 2019.
doi:10.1109/JMMCT.2019.2948022 Google Scholar

20. Ulaby, F. T., D. G. Long, et al. Microwave Radar and Radiometric Remote Sensing, The University of Michigan, 2014.

21. Gu, W. and L. Tsang, "Vegetation effects for remote sensing of soil moisture using NMM3D full-wave simulation," IEEE Antennas and Propagation Sympsium, Montreal, 2020. Google Scholar

22. Waterman, P. C. and R. Truell, "Multiple scattering of waves," Journal of Mathematical Physics, Vol. 2, 512-537, 1961.
doi:10.1063/1.1703737 Google Scholar

23. Peterson, B. and S. Strom, "T-matrix for electromagnetic scattering from an arbitrary number of scatterers and representations of E(3)," Physical Review D, Vol. 8, 3661, 1973.
doi:10.1103/PhysRevD.8.3661 Google Scholar

24. Tse, K. K., L. Tsang, C. H. Chan, K. H. Ding, and K. W. Leung, "Multiple scattering of waves by dense random distributions of sticky particles for applications in microwave scattering by terrestrial snow," Radio Science, Vol. 42, 1-14, 2007. Google Scholar

25. Tsang, L., K. H. Ding, G. Zhang, C. C. Hsu, and J. A. Kong, "Backscattering enhancement and clustering effects of randomly distributed dielectric cylinders overlying a dielectric half space based on Monte-Carlo simulations," IEEE Transactions on Antennas and Propagation, Vol. 43, No. 5, 488-499, 1995.
doi:10.1109/8.384193 Google Scholar

26. Valagiannopoulos, C. A. and N. L. Tsitsas, "Linearization of the T-matrix solution for quasihomogeneous scatterers," JOSA A, Vol. 26, No. 4, 870-881, 2009.
doi:10.1364/JOSAA.26.000870 Google Scholar

27. Maystre, D., "Electromagnetic scattering by a set of objects: An integral method based on scattering operator," Progress In Electromagnetics Research, Vol. 57, 55-84, 2006.
doi:10.2528/PIER05040901 Google Scholar

28. Valagiannopoulos, C. A., "A novel methodology for estimating the permittivity of a specimen rod at low radio frequencies," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 5–6, 631-640, 2010.
doi:10.1163/156939310791036331 Google Scholar

29. Hajihashemi, M. R. and M. El-Shenawee, "Inverse scattering of three-dimensional PEC objects using the level-set method," Progress In Electromagnetics Research, Vol. 116, 23-47, 2011.
doi:10.2528/PIER11012304 Google Scholar

30. Wei, Z. and X. Chen, "Physics-inspired convolutional neural network for solving full-wave inverse scattering problems," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 9, 6138-6148, 2019.
doi:10.1109/TAP.2019.2922779 Google Scholar

31. Tsang, L., J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications, John Wiley and Sons, 2004.

32. Flammer, C., Spheroidal Wave Functions, Courier Corporation, 2014.

33. Huang, H., Vegetation/forest effects in microwave remote sensing of soil moisture, Ph.D. Thesis, 2019.

34. Sinha, B. P. and R. H. MacPhie, "Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization and angle of incidence," Radio Science, Vol. 12, No. 2, 171-184, 1977.
doi:10.1029/RS012i002p00171 Google Scholar

35. Cooray, M. F. R. and I. R. Ciric, "Scattering by systems of spheroids in arbitrary configurations," Computer Physics Communications, Vol. 68, No. 1–3, 279-305, 1991.
doi:10.1016/0010-4655(91)90204-X Google Scholar

36. Nag, S. and B. P. Sinha, "Electromagnetic plane wave scattering by a system of two uniformly lossy dielectric prolate spheroids in arbitrary orientation," IEEE Transactions on Antennas and Propagation, Vol. 43, No. 3, 322-327, 1995.
doi:10.1109/8.372005 Google Scholar

37. Huang, H., L. Tsang, A. Colliander, R. Shah, X. Xu, E. G. Njoku, and S. Yueh, "Numerical 3D solutions of Maxwell equations based on hybrid method combining generalized T-matrix and Foldy-Lax multiple scattering theory for vegetation/trees scattering," 2018 IEEE International Conference on Computational Electromagnetics (ICCEM), 2018. Google Scholar

38. Visser, T. D., D. G. Fischer, and E. Wolf, "Scattering of light from quasi-homogeneous sources by quasi-homogeneous media," JOSA A, Vol. 23, No. 7, 1631-1638, 2006.
doi:10.1364/JOSAA.23.001631 Google Scholar

39. Valagiannopoulos, C. A., "Closed-form solution to the scattering of a skew strip field by metallic PIN in a slab," Progress In Electromagnetics Research, Vol. 79, 1-21, 2008.
doi:10.2528/PIER07092206 Google Scholar

40. Asano, S. and G. Yamamoto, "Light scattering by a spheroidal particle," Applied Optics, Vol. 14, No. 1, 29-49, 1976.
doi:10.1364/AO.14.000029 Google Scholar

41. Zhang, S. and J. M. Jin, Computation of Special Functions, Wiley, 1996.

42. Li, L. W., X. K. Kang, and M. S. Leong, Spheroidal Wave Functions in Electromagnetic Theory, Wiley, 2002.

Dr. Huanting Huang

Professor Leung Tsang

Dr. Andreas Colliander

Dr. Rashmi Shah

Dr. Xiaolan Xu

Dr. Simon Yueh