Scattering of Electromagnetic Waves by Frequency-Detuned Systems of Dielectric Resonators




scattering, detuned dielectric resonator, scattering matrix, bandpass filter, bandstop filter, elliptical filter, demultiplexer


The general problem of scattering on a system of frequency-detuned coupled Dielectric Resonators (DRs) located in one or several transmission lines is considered. The field describing the natural oscillations of the system of detuned DRs is decomposed over the field of partial resonators. A system of equations is derived, the solution of which allows one to determine the frequencies and amplitudes of the system’s natural oscillations. It is shown that the resulting system of equations, by means of algebraic transformations, can be reduced to the problem of determining the eigenfunctions and eigenvalues of a finite-dimensional operator, determined through the elements of the coupling operator of frequency-detuned DRs. The limitations of the proposed calculation method are noted. The solution to the scattering problem is expanded in terms of the natural oscillation field of the system of detuned DRs. A system of linear equations for the amplitudes of forced oscillations is obtained. It is shown that in the particular case of identical resonator frequencies, the found system exactly coincides with the equations obtained previously for various types of DR. General solutions are found for the scattered field on frequency-detuned resonators located in different transmission lines. Several examples are given of calculating the frequency dependences of the scattering matrix for the most interesting structures consisting of coupled dielectric resonators detuned in natural oscillation frequencies. The frequency characteristics of the scattering of two bandstop filters with different stop bands, made on detuned DRs in the same transmission line, are calculated. The frequency dependences of the scattering matrix on two bandpass filters located parallel between regular lines are calculated. The scattering characteristics of bandpass filters of complex designs containing various DRs are calculated: a bandpass filter built on a system of coupled DRs in a transmission line break and several DRs in a regular line, as well as an elliptical bandpass filter. The capabilities of the proposed method are demonstrated by the example of optimizing the scattering characteristics of a demultiplexer built on the basis of two bandpass filters with different passband frequencies. The proposed method also makes it possible to calculate the scattering characteristics of bandpass and bandstop filters with several operating frequency bands used in modern communication systems.



Kajfez D., Guillon P. (1986). Dielectric Resonators. Artech House, 201 p.

Dielectric Resonators. (1989). Edited by M.E. Ilchenko. M.: Radio and communication, 327 p.

Luk K. M., Leung K. W. (2002). Dielectric Resonator Antennas. Research studies press ltd. Baldock, Hertfordshire, England, 388 p.

Petosa A. (2007). Dielectric Resonator Antenna Handbook. Artech House, 308 p.

Haus H. A., Popovic M. A., Watts M. R. and Manolatou C., Little B. E., Chu S. T. (2004). Optical resonators and filters. Optical Microcavities. Edited By: Kerry Vahala (California Institute of Technology, USA) Ch. 00, 516 p.

Rabus D. G. (2007). Integrated Ring Resonators: : The Compendium. Springer, 254 p.

Heebner J., Grover R., Ibrahim T. (2008). Optical Microresonators: Theory, Fabrication, and Applications. Springer, 263 p.

Hong J.-C., Lancaster M. J. (2001). Microstrip Filters for RF/Microwave Applications. John Wiley & Sons, Inc., 471 p.

Saha N., Brunetti G., di Toma A., Armenise M. N., Ciminelli C. (2024). Silicon Photonic Filters: A Pathway from Basics to Applications. Adv. Photonics Res., 44 p., doi:10.1002/adpr.202300343.

Robins L., Bartlett C., Arsanjani A., Teschl R., Bosch W., Hoft M. (2023). A 3-D-Printed Dielectric Resonators for Triple-Mode Applications. Microwave and Wireless Technology Letters, Vol. 33, Iss. 11, pp. 1517-1520. DOI: 10.1109/LMWT.2023.3311812.

Lee C., Jeon S., Kim S. J., Kim S. J. (2023). Near-flat top bandpass filter based on non-local resonance in a dielectric metasurface. Optics Express, Vol. 31, No. 3, pp. 4920–4931. doi:10.1364/OE.480757.

Wu X., Cao Y., Yuan B., Qi Y., Wang G. (2023). Bandpass Filters Using Single and Cascaded Novel Triple-mode Ceramic Monoblocks. IEEE Trans. on Components Packaging and Manufacturing Technology, Vol. 13, Iss. 7, pp. 1–13. DOI: 10.1109/TCPMT.2023.3296108.

Qin W., Liu J., Zhang H.-L., Yang W.-W., Chen J.-X. (2022). Bandpass Filter and Diplexer Based on Dual-Mode Dielectric Filled Waveguide Resonators. IEEE Access, Vol. 10, pp. 29333–29340. DOI: 10.1109/ACCESS.2022.3158984.

Rong C., Xu Y., Zhang Y. (2022). Dielectric-Loaded Miniaturized Cavity Bandpass Filter with Improved Power Capacity. Electronics, Vol. 11, Iss. 9, 1441; doi:10.3390/electronics11091441.

Wldaa A., Hoft M. (2022). Miniaturized Dual-Band Dual-Mode TM-Mode Dielectric Filter in Planar Configuration. IEEE Jornal of Microwaves, Vol. 2, No. 2, pp. 326–336. DOI: 10.1109/JMW.2022.3145906.

Liu M., Xiang Z., Ren P., Xu T. (2019). Quad-mode dual-band bandpass filter based on a stub-loaded circular resonator. EURASIP Journal on Wireless Communications and Networking, 2019:48, 6 p. doi:10.1186/s13638-019-1362-z.

Bakr M. S., Hunter I. C., Bosch W. (2018). Miniature Triple-Mode Dielectric Resonator Filters. IEEE/MTT-S International Microwave Symposium, pp. 1249–1252,

Yao Z., Wu K., Tan B. X. et al. (2018). Integrated Silicon Photonic Microresonators: Emerging Technologies. IEEE Jornal of Selected Topics in Quantum Electronics, Vol. 24, No. 6, pp. 1–25. DOI: 10.1109/JSTQE.2018.2846047.

Nocella V., Pelliccia L., Tomassoni C., Sorrentino R. (2016). Miniaturized Dual-Band Waveguide Filter Using TM Dielectric-Loaded Dual-Mode Cavities. IEEE Microwave and Wireless Component Letters, Vol. 26, No. 5, pp. 310–312. DOI: 10.1109/LMWC.2016.2549181.

Awasthi S., Biswas A., Akhtar M. J. (2014). Dual-Band Dielectric Resonator Bandstop Filters. International Journal of RF and Microwave Computer-Aided Engineering, pp. 282–288, doi:10.1002/mmce.20860.

Pidgurska T. V., Trubin A. A. (2014). Novel dual-band rectangular dielectric resonator filter. X International Symposium on Telecommunications – BIHTEL, pp. 27-29. DOI: 10.1109/BIHTEL.2014.6987634.

Zhang R., Mansour R. R. (2009). Dual-Band Dielectric-Resonator Filters. IEEE Trans. on MTT, Vol. 57, No. 7, pp. 1760–1766. DOI: 10.1109/TMTT.2009.2022876.

Dai D., Bowers J. E. (2014). Silicon-based on-chip multiplexing technologies and devices for Peta-bit optical interconnects (Review article). Nanophotonics, No. 3, Iss. 4-5, pp. 283–311, doi:10.1515/nanoph-2013-0021.

Prajzler V., Strilek E., Špirkova J., Jerabek V. (2012). Design of the Novel Wavelength Triplexer Using Multiple Polymer Microring Resonators. Radioengineering, Vol. 21, No. 1, pp. 258–363.

Bizan M. S., Naseri H., Pourmohammadi P., Melouki N., Iqbal A., Denidni T. A. (2023). Dual-Band Dielectric Resonator Antenna with Filtering Features for Microwave and Mm-Wave Applications. Micromachines, 14(6), 1236; doi:10.3390/mi14061236.

Patel U., Upadhyaya T. (2022). Four-Port Dual-Band Multiple-Input Multiple-Output Dielectric Resonator Antenna for Sub-6 GHz 5G Communication Applications. Micromachines, Vol. 13(11), doi:10.3390/mi13112022.

Altaf A., Seo M. (2018). Triple-Band Dual-Sense Circularly Polarized Hybrid Dielectric Resonator Antenna. Sensors, Vol. 18(11), 3899; doi:10.3390/s18113899.

Chang T.-H., Kiang J.-F. (2007). Dualband Split Dielectric Resonator Antenna. IEEE Trans. on Antennas and Propagation, Vol. 55, No. 11, pp. 3155–3162. DOI: 10.1109/TAP.2007.908830.

Gangwar K., Sharma A., Das G., Gangwar R. K. (2019). Investigation on novel wideband fractal antenna design based on cylindrical shape dielectric resonator. Int J RF Microw Comput Aided Eng., 10 p., doi:10.1002/mmce.21943.

Lin J.-H., Shen W.-H., Shi Z.-D., Zhong S.-S. (2017). Circularly Polarized Dielectric Resonator Antenna Arrays with Fractal Cross-Slot-Coupled DRA Elements. Hindawi International Journal of Antennas and Propagation, Vol. 2017, Article ID 8160768, doi:10.1155/2017/8160768.

Kumari R., Behera S. K. (2014). Investigation on Log-Periodic Dielectric Resonator Antenna Array for Ku-Band Applications. Electromagnetics, Vol. 34, Iss. 1, pp.19–33, doi:10.1080/02726343.2014.846175.

Trubin A. A. (1997). Scattering of electromagnetic waves on the Systems of Coupling Dielectric Resonators. Radio electronics, No. 2, pp. 35-42.

Trubin A. A. (2017). Modeling of the Optical Filters on Different WGM Disk Microresonators. Information and Telecommunication Sciences, Vol. 8, Iss. 1, pp. 26-30.




How to Cite

Trubin, O. O. (2024) “Scattering of Electromagnetic Waves by Frequency-Detuned Systems of Dielectric Resonators”, Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia, (96), pp. 5-13. doi: 10.20535/RADAP.2024.96.5-13.



Electrodynamics. Microwave devices. Antennas