Gaussian beams techniques are high-frequency asymptotic methods that can be used to model the propagation/interaction of fields in a variety of problems. In this article, an expansion is proposed to express the scattering of magnetic/electric currents from a curved interface in terms of a new kind of elementary beams, the conformal Gaussian beams. The expansion characteristics rely on the physical properties of the configuration, which leads to represent the scattering with a small number of conformal Gaussian beams. An analytical formulation for the conformal Gaussian beams is developed, which expression is derived from an asymptotic evaluation of the radiation integrals valid at great distance from the interface. An example is presented to show that this analytical formulation is in good agreement with the reference result. Numerical tests are led on the expansion in order to show that the scattering can be represented with accuracy by adding the contribution of conformal Gaussian beams.
"Physics-Based Expansion on 3D Conformal Gaussian Beams for the Scattering from a Curved Interface," Progress In Electromagnetics Research B,
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1. Kogelnick, H. and T. Li, "Laser beams and resonators," Proceedings of the IEEE, Vol. 54, No. 10, 1312-1329, 1966. doi:10.1109/PROC.1966.5119
2. Sokoloff, J., S. Bolioli, and P. F. Combes, "Gaussian beam expansion for radiation analysis of metallic reflectors illuminated under oblique incidence ," IEEE Trans. on Mag., Vol. 38, No. 2, 697-700, 2002. doi:10.1109/20.996181
3. Chou, H. T., P. A. Pathak, and R. J. Burkholder, "Novel Gaussian beam method for the rapid analysis of large reflector antennas," IEEE Trans. on Antennas and Propag., Vol. 49, No. 6, 880-893, 2001. doi:10.1109/8.931145
4. Pascal, O., F. Lemaitre, and G. Soum, "Dielectric lens analysis using vectorial multimodal Gaussian beam expansion," Ann. Telecom., Vol. 52, No. 9-10, 519-528, 1997.
5. Chabory, A., J. Sokolo®, S. Bolioli, and P. F. Combes, "Computation of electromagnetic scattering by multilayer dielectric objects using Gaussian beam based techniques," C.R. Phys., Vol. 6, 654-662, 2005. doi:10.1016/j.crhy.2005.06.011
6. Maciel, J. J. and L. B. Felsen, "Gabor-based narrow-waisted Gaussian beam algorithm for transmission of aperture-excited 3D vector fields through arbitrarily shaped 3D dielectric layers," Radio Science, Vol. 37, No. 2, vic6.1-6.9, 2002. doi:10.1029/2001RS002556
7. Galdi, V., L. B. Felsen, and D. A. Castanon, "Quasi-ray Gaussian beam algorithm for time-harmonic two-dimensional scattering by moderately rough interfaces," IEEE Trans. on Antennas and Propag., Vol. 49, No. 9, 1305-1314, 2001. doi:10.1109/8.947022
8. Elis, K., A. Chabory, and J. Sokoloff, "3D interaction of Gaussian beams with dichroic surfaces for the modeling of quasi optical systems," International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM), 1-5, Toulouse, France, June 2012.
9. Ghannoum, I., C. Letrou, and G. Bauquet, "Frame based Gaussian beam bouncing," URSI International Symposium on Electromagnetic Theory, 68-71, 2010.
10. Bogush, A. J. and R. E. Elkins, "Gaussian field expansions for large aperture antennas," IEEE Trans. on Antennas and Propag., Vol. 34, No. 2, 228-243, 1986. doi:10.1109/TAP.1986.1143795
11. Einziger, P. D., Y. Haramaty, and L. B. Felsen, "Complex rays for radiation from discretized aperture distributions," IEEE Trans. on Antennas and Propag., Vol. 35, No. 9, 1031-1044, 1987. doi:10.1109/TAP.1987.1144219
12. Casaletti, M. and S. Maci, "Aperture beam expansion by using a spectral 2D-GPOF method," Progress In Electromagnetics Research M, Vol. 28, 245-257, 2013.
13. Imbriale, W. A. and D. J. Hoppe, "Recent trend in the analysis of quasioptical systems," Millennium Conference on Antennas and Propagation, Davos, Switzerland, 2000.
14. Chabory, A., J. Sokoloff, and S. Bolioli, "Novel Gabor-based Gaussian beam expansion for curved aperture radiation in dimension two," Progress In Electromagnetics Research, Vol. 58, 171-185, 2006. doi:10.2528/PIER05090702
15. Chabory, A., J. Sokoloff, and S. Bolioli, "Physically based expansion on conformal Gaussian beams for the radiation of curved aperture in dimension 2," IET Microw. Antennas Propag., Vol. 2, No. 2, 152-157, 2008. doi:10.1049/iet-map:20060168
16. Chabory, A., Modélisation électromagnétique des radômes par des techniques basées sur les faisceaux Gaussiens, Ph.D. Thesis, Université Paul Sabatier, Toulouse, France, 2004.
17. Hillairet, J., J. Sokoloff, and S. Bolioli, "Electromagnetic scattering of a field known on a curved interface using conformal Gaussian beams," Progress In Electromagnetics Research B, Vol. 8, 195-212, 2008. doi:10.2528/PIERB08062603
18. Felsen, L. B. and N. Marcuvitz, Radiation and Scattering of Waves, Electrical Engineering Series, Prentice Hall, Inc., 1973.
19. Chabory, A., J. Sokoloff, S. Bolioli, and K. Elis, "Application of Gaussian-beam based techniques to the quasi-optical systems of radio frequency radiometers," European Conference on Antennas and Propagation (EUCAP), 1-5, Barcelona, Spain, April 2010.