An analytical approach for calculation of the dyadic Green's functions inside the rectangular cavity over a broad range of frequency is presented. Both vector potential and electric field dyadic Green's functions are considered. The method is based on the extraction of the Green's function at an imaginary wave number from itself to obtain a rapidly convergent eigenfunction expansion of the dyadic Green's function. The extracted term encompasses the singularity of the Green's function and are computed using spatial expansions. Results are illustrated for rectangular cavity up to 5 wavelengths in size with thousand of cavity modes obtained by the 6th order convergent expansion. It is shown that for an accurate and broadband simulation, the proposed method is many times faster than the Ewald method.
1. Tai, C.-T., "Dyadic Green functions in electromagnetic theory," Institute of Electrical & Electronics Engineers, IEEE, 1994.
2. Collin, R. E., Field Theory of Guided Waves, McGraw-Hill, New York, 1960.
3. Felsen, L. B. and N. Marcuvitz, Radiation and Scattering of Waves, Vol. 31, John Wiley & Sons, 1994. doi:10.1109/9780470546307
4. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, 1995.
5. Marliani, F. and A. Ciccolella, "Computationally efficient expressions of the dyadic Green's function for rectangular enclosures," Progress In Electromagnetics Research, Vol. 31, 195-223, 2001. doi:10.2528/PIER00062901
6. Park, M.-J. and S. Nam, "Rapid summation of the Green's function for the rectangular waveguide," IEEE Transactions on Microwave Theory and Techniques, Vol. 46, No. 12, 2164-2166, 1998. doi:10.1109/22.739301
7. Araneo, R. and G. Lovat, "An efficient mom formulation for the evaluation of the shielding effectiveness of rectangular enclosures with thin and thick apertures," IEEE Transactions on Electromagnetic Compatibility, Vol. 50, No. 2, 294-304, 2008. doi:10.1109/TEMC.2008.919031
8. Hill, D. A., Electromagnetic Fields in Cavities: Deterministic and Statistical Theories, Vol. 35, John Wiley & Sons, 2009. doi:10.1002/9780470495056
9. Soler, F. J. P., F. D. Q. Pereira, D. Ca nete Rebenaque, Alejandro Alvarez Melcon, and Juan R Mosig, "A novel efficient technique for the calculation of the Green's functions in rectangular waveguides based on accelerated series decomposition," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 10, 3260-3270, 2008. doi:10.1109/TAP.2008.929438
10. Park, M.-J., "Accelerated summation of the Green's function for the rectangular cavity," IEEE Microwave and Wireless Components Letters, Vol. 19, No. 5, 260-262, 2009. doi:10.1109/LMWC.2009.2017579
11. Gruber, M. E. and T. F. Eibert, "A hybrid ewald-spectral cavity Green's function boundary element method with spectral domain acceleration for modeling of over-moded cavities," IEEE Transactions on Antennas and Propagation, Vol. 63, No. 6, 2627-2635, 2015. doi:10.1109/TAP.2015.2418783
12. Campione, S. and F. Capolino, "Ewald method for 3D periodic dyadic Green's functions and complex modes in composite materials made of spherical particles under the dual dipole approximation," Radio Science, Vol. 47, No. 6, 1-11, 2012. doi:10.1029/2012RS005031
13. Borji, A. and S. Safavi-Naeini, "Rapid calculation of the Green's function in a rectangular enclosure with application to conductor loaded cavity resonators," IEEE Transactions on Microwave Theory and Techniques, Vol. 52, No. 7, 1724-1731, 2004. doi:10.1109/TMTT.2004.830488
14. Tsang, L. and S. Huang, "Broadband Green's function with low wavenumber extraction for arbitrary shaped waveguide and applications to modeling of vias in finite power/ground plane," Progress In Electromagnetics Research, Vol. 152, 105-125, 2015. doi:10.2528/PIER15072605
15. Tan, S. and L. Tsang, "Green's functions, including scatterers, for photonic crystals and metamaterials," JOSA B, Vol. 34, No. 7, 1450-1458, 2017. doi:10.1364/JOSAB.34.001450
16. Tan, S. and L. Tsang, "Scattering of waves by a half-space of periodic scatterers using broadband Green's function," Optics Letters, Vol. 42, No. 22, 4667-4670, 2017. doi:10.1364/OL.42.004667
17. Tan, S. and L. Tsang, "Efficient broadband evaluations of lattice Green's functions via imaginary wavenumber components extractions," Progress In Electromagnetics Research, Vol. 164, 63-74, 2019.
18. Tsang, L. and S. Tan, "Calculations of band diagrams and low frequency dispersion relations of 2D periodic dielectric scatterers using broadband Green’s function with low wavenumber extraction (BBG)," Optics Express, Vol. 24, No. 2, 945-965, 2016. doi:10.1364/OE.24.000945
19. Huang, S. and L. Tsang, "Fast electromagnetic analysis of emissions from printed circuit board using broadband Green's function method," IEEE Transactions on Electromagnetic Compatibility, Vol. 58, No. 5, 1642-1652, 2016. doi:10.1109/TEMC.2016.2565584
20. Arcioni, P., M. Bozzi, M. Bressan, G. Conciauro, and L. Perregrini, "The BI-RME method: An historical overview," 2014 International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applicatio, 1-4, IEEE, 2014.
21. Bozzi, M., L. Perregrini, and K. Wu, "Modeling of conductor, dielectric, and radiation losses in substrate integrated waveguide by the boundary integral-resonant mode expansion method," IEEE Transactions on Microwave Theory and Techniques, Vol. 56, No. 12, 3153-3161, 2008. doi:10.1109/TMTT.2008.2007140
22. Guglielmi, M., R. Sorrentino, and G. Conciauro, Advanced Modal Analysis: CAD Techniques for Waveguide Components and Filter, John Wiley & Sons, Inc., 1999.
23. Tsang, L., K.-H. Ding, T.-H. Liao, and S. Huang, "Modeling of scattering in arbitrary-shape waveguide using broadband Green's function with higher order low wavenumber extractions," IEEE Transactions on Electromagnetic Compatibility, Vol. 60, No. 1, 16-25, 2017. doi:10.1109/TEMC.2017.2727958
24. Chew, W. C., "Some observations on the spatial and eigenfunction representations of dyadic Green's functions (electromagnetic theory)," IEEE Transactions on Antennas and Propagation, Vol. 37, No. 10, 1322-1327, 1989. doi:10.1109/8.43544
25. Wang, J., "A unified and consistent view on the singularities of the electric dyadic Green's function in the source region," IEEE Transactions on Antennas and Propagation, Vol. 30, No. 3, 463-468, 1982. doi:10.1109/TAP.1982.1142802
26. Yaghjian, A. D., "Electric dyadic Green's functions in the source region," Proceedings of the IEEE, Vol. 68, No. 2, 248-263, 1980. doi:10.1109/PROC.1980.11620
27. Johnson, W. A., A. Q. Howard, and D. G. Dudley, "On the irrotational component of the electric Green's dyadic," Radio Science, Vol. 14, No. 6, 961-967, 1979. doi:10.1029/RS014i006p00961
28. Rahmat-Samii, Y., "On the question of computation of the dyadic Green's function at the source region in waveguides and cavities (short papers)," IEEE Transactions on Microwave Theory and Techniques, Vol. 23, No. 9, 762-765, 1975. doi:10.1109/TMTT.1975.1128671