A well known property of large circular closed-loop arrays is that when the dimensions and the distance of the cylindrical dipoles are properly chosen, the arrays possess very narrow resonances. As far as single isolated loop arrays are concerned, the phenomenon has been predicted and analyzed in the past in the framework of ``two-term" theory. In the present paper the same methodology is, for the first time, applied to investigate the system of two coupled identical circular arrays. It is found that the spectral profile of this new array is characterized by the coupling-induced splitting of the resonances of the single loop array into symmetric and antisymmetric supermodes, in direct analogy with other types of coupled electromagnetic cavities. Due to the circular symmetry of the individual arrays, the phenomenon is strongly correlated to the optical counterpart of two coupled traveling-wave optical resonators, such as whispering gallery or microring resonators. By borrowing the resonance splitting model from optical resonators, this analogy connection is investigated and interesting conclusions are reached.
1. Fikioris, G., R. W. P. King, and T. T. Wu, "The resonant circular array of electrically short elements," J. Appl. Phys., Vol. 68, No. 4, 431-439, 1990. doi:10.1063/1.346839
2. Fikioris, G., R. W. P. King, and T. T. Wu, "A novel resonant circular array: Improved analysis," Progress In Electromagnetics Research, Vol. 8, 1-30, 1994.
3. Fikioris, G., "Experimental study of novel resonant circular arrays," IEE Proc. Microw. Antennas Propagat., Vol. 145, No. 5, 92-98, 1998. doi:10.1049/ip-map:19981553
4. King, R. W. P., G. Fikioris, and R. B. Mack, Cylindrical Antennas and Arrays, Cambridge University Press, Cambridge, 2002.
5. Fikioris, G., "Resonan t arrays of cylindrical dipoles: Theory and experiment," Ph.D. Thesis, 1993.
6. Fikioris, G., R. W. P. King, and T. T. Wu, "Novel surface-wave antenna," IEE Proc. Microw. Antennas Propagt., Vol. 143, No. 1, 1-6, 1996. doi:10.1049/ip-map:19960160
7. Freeman, D. K. and T. T. Wu, "Variational-principle formulation of the two-term theory for arrays of cylindrical dipoles," IEEE Trans. Antennas Propagat., Vol. 43, No. 4, 340-349, 1995. doi:10.1109/8.376030
8. King, R. W. P., "A microwave beacon and guiding signals for airports and their approaches," IEEE Trans. Antennas Propagat., Vol. 51, No. 1, 110-114, 2003. doi:10.1109/TAP.2003.809049
9. Fikioris, G., "Field patterns of resonant noncircular closed-loop arrays," Journal of Electromagnetic Waves and Applications, Vol. 10, No. 3, 307-327, 1996. doi:10.1163/156939396X00432
10. Fikioris, G., S. D. Zaharopoulos, and P. D. Apostolidis, "Field patterns of resonant noncircular closed-loop arrays: Further analysis," IEEE Trans. Antennas Propagat., Vol. 53, No. 12, 3906-3914, 2005. doi:10.1109/TAP.2005.859760
11. Fikioris, G., P. J. Papakanellos, J. D. Koundouros, and A. K. Patsiotis, "Difficulties in MoM analyses of resonant circular arrays of cylindrical dipoles," Electronics Letters, Vol. 41, No. 2, 54-55, 2005. doi:10.1049/el:20056848
12. Fikioris, G. and K. Matos, "Near fields of resonant circular arrays of cylindrical dipoles," Antennas and Propagation Magazine, IEEE, Vol. 50, No. 1, 97-107, 2008. doi:10.1109/MAP.2008.4494508
13. Rayleigh, L., "The problem of whispering gallery," Philos. Mag., Vol. 20, 1001-1004, 1910.
14. Vedrenne, C. and J. Arnaud, "Whisp ering-gallery modes of dielectric resonators," Proc. Inst. Elect. Eng., Vol. 129, No. 4, 183-187, 1982.
15. Matsko, A. B. and V. S. Ilchenko, "Optical resonators with whispering-gallery modes — Part I: Basics," IEEE J. Select. Topics Quantum Electron., Vol. 12, No. 1, 3-14, 2006. doi:10.1109/JSTQE.2005.862952
16. Ilchenko, V. S. and A. B. Matsko, "Optical resonators with whispering-gallery modes — Part II: Applications," IEEE J. Select. Topics Quantum Electron., Vol. 12, No. 1, 15-32, 2006. doi:10.1109/JSTQE.2005.862943
17. Little, B. E., S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, "Microring resonator channel dropping filters," IEEE J. Lightwave Technol., Vol. 15, No. 6, 998-1005, 1997. doi:10.1109/50.588673
18. Smotrova, E. I., A. I. Nosich, T. M. Benson, and P. Sewell, "Optical coupling of whispering-gallery modes of two identical microdisks and its effect on photonic molecule lasing," IEEE J. Select. Topics Quantum Electron., Vol. 12, No. 1, 78-85, 2006. doi:10.1109/JSTQE.2005.862940
19. Boriskina, S., "Spectrally engineered photonic molecules as optical sensors with enhanced sensitivity: A proposal and numerical analysis," J. Opt. Soc. Am. B, Vol. 23, No. 8, 1565-1573, 2006. doi:10.1364/JOSAB.23.001565
20. Chung, Y., D.-G. Kim, and N. Dagli, "Reflection properties of coupled-ring reflectors," IEEE J. Lightwave Technol., Vol. 24, No. 4, 1865-1874, 2006. doi:10.1109/JLT.2006.871021
21. Chremmos, I. D. and N. K. Uzunoglu, "Reflectiv e properties of double-ring resonator system coupled to a waveguide," IEEE Photon. Technol. Lett., Vol. 17, No. 10, 2110-2112, 2005. doi:10.1109/LPT.2005.854346
22. Boriskina, S. V., "Coupling of whispering-gallery modes in size-mismatched microdisk photonic molecules," Opt. Lett., Vol. 32, No. 11, 1557-1559, 2007. doi:10.1364/OL.32.001557
23. Liu, G. J., B. M. Liang, G. L. Jin, and Q. Li, "Switching characteristics of variable coupling coefficient nonlinear directional coupler," IEEE J. Lightwave Technol., Vol. 22, No. 6, 1591-1597, 2004. doi:10.1109/JLT.2004.829228