This paper presents the design and analysis of guided wave notch filters using the Lagrangian formulation for metamaterials. It is shown that the application of the Lagrangian is a convenient and effective way to select an appropriate filtering structure and determine the necessary configuration for desired filter performance. A WR-187 waveguide horn antenna is investigated with notch filters composed of broadside coupled and gap coupled split ring resonators. It is shown that broadside coupling offers significant tunability in a compact size. The filter exhibits an operational bandwidth from approximately 3.9-5.7 GHz with 40-150 MHz of instantaneous bandwidth. The fabrication of the horn antenna and split ring resonators is presented along with simulated and measured data that confirms the approach.
2. Pendry, J. B., "Negative refraction makes a perfect lens," Phys. Rev. Lett., Vol. 85, 3966, 2000.
3. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of negative index of refraction," Science, Vol. 292, 77-79, 2001.
4. Ziolkowski, R. W., "Design, fabrication, and testing of double negative metamaterials," IEEE Trans. Antennas Propag., Vol. 51, No. 7, 1516-1529, 2003.
5. Solymar, L. and E. Shamonina, Waves in Metamaterials, Oxford University Press, New York, 2009.
6. Palandoken, M., Metamaterial-based Compact Filter Design, Metamaterial, X. Jiang (Ed.), InTech, 2012, DOI: 10.5772/35853.
7. Fallahzadeh, S., H. Bahrami, and M. Tayarani, "A novel dual-band bandstop waveguide filter using split ring resonators," Progress In Electromagnetics Research Letters, Vol. 12, 133-139, 2009.
8. Gangaraj, S. H. and M. Tayarani, "A novel bandstop resonator in waveguide and its application for suppressing the spurious responses with new advantages to typical resonators," PIERS Proceedings, 533-537, Suzhou, China, September 12-16, 2011.
9. Barbuto, M., F. Trotta, F. Bilotti, and A. Toscano, "Horn antennas with integrated notch filters," IEEE Trans. Antennas Propag., Vol. 63, No. 2, 781-785, 2015.
10. Barbuto, M., F. Trotta, F. Bilotti, and A. Toscano, "Varying the operation bandwidth of metamaterial-inspired filtering modules for horn antennas," Progress In Electromagnetics Research C, Vol. 58, 61-68, 2015.
11. Shehan, J. W. and R. S. Adams, "X-band horn antenna with integrated tunable notch filter," 2015 IEEE International Symposium on Antennas and Propagation (APSURSI), 2213-2214, 2015.
12. Powell, D. A., M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, "Metamaterial tuning by manipulation of near-field interactions," Phys. Rev. B, Vol. 82, 155128, 2010.
13. Powell, D. A., K. Hannam, I. V. Shadrivov, and Y. S. Kivshar, "Near-field interaction of twisted split-ring resonators," Phys. Rev. B, Vol. 83, 235420, 2011.
14. Withayachumnankul, W., C. Fumeaux, and D. Abbot, "Near-field interactions in electric inductive-capacitive resonators for metamaterials," Journal of Phys. D: Applied Phys., Vol. 45, No. 48, 485101, 2012.
15. Haus, H. A. and W. Huang, "Coupled-mode theory," Proceedings of the IEEE, Vol. 79, No. 10, 1505-1518, 1991.
16. Balanis, C. A., Antenna Theory: Analysis and Design, 3rd Ed., John Wiley & Sons, New Jersey, 2005.