Scattering of Electromagnetic Waves by Loss and Gain Systems of Dielectric Resonators

Authors

  • A. A. Trubin Institute of Telecommunication Systems of National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine https://orcid.org/0000-0002-9596-195X

DOI:

https://doi.org/10.20535/RADAP.2024.97.58-66

Keywords:

scattering, dielectric resonator, scattering matrix, active dielectric, band-pass filter, band-stop filter, add-drop filter, Double-channel SCISSOR

Abstract

The problem of wave scattering on a system of coupled Dielectric Resonators (DR) made of an active or absorbing dielectric is considered. The solution of the scattering problem is decomposed over the field of natural oscillations of the DR system. The field describing the natural oscillations of the DR system is decomposed by the field of partial resonators, which are made of a dielectric with a complex permittivity. A system of equations is given, the solution of which allows to determine the frequencies and amplitudes of the natural oscillations of the system of active or absorbing resonators. In the work, a new system of linear equations for amplitudes of forced oscillations of resonators was obtained. General solutions for the scattering field on resonators located in a regular transmission line or in a break of a regular line have been found. Several examples of calculation of the frequency dependences of the scattering matrix for different bands to pand band-pass filters, consisting of coupled active or absorbing dielectric resonators are given. The possibilities of the proposed method are demonstrated on the example of optimization of scattering characteristics on band-stop and band-pass filters made of an active dielectric. It is shown that the use of resonators made of an active dielectric will make it possible to build and optimize the frequency characteristics of a new class of devices that simultaneously perform the functions of filters and amplifiers. The conditions under which it is possible to build filters with the functions of amplifiers are defined. In the future, the proposed devices may find application in optical communication systems.

References

References

Freter L., Mirmoosa M. S., Sihvola A., Simovski C. R., Tretyakov S. A. (2024). Electromagnetic effects in anti-Hermitian media with gain and loss. Physical Review Research, Vol. 6, 013070, doi:10.1103/PhysRevResearch.6.013070.

Frigenti G., Berneschi S., Farnesi D., Pelli S., Righini G. C. et al. (2023). Rare earth-doped glass whispering gallery mode micro-lasers. The European Physical Journal Plus, Vol. 138, article number 679, doi:10.1140/epjp/s13360-023-04275-9.

Su Y., Fan H., Zhang S., Cao T. (2023). Tunable parity-time symmetry vortex laser from a phase change material-based microcavity. Microsystems & Nanoengineering, Vol. 9, 142, doi:10.1038/s41378-023-00622-z.

Hlushchenko A. V., Novitsky D. V., Tuz V. R. (2022). Trapped mode excitation in all-dielectric metamaterials with loss and gain. Physical Review B, Vol. 106, 155429, pp. 155429-1–155429-9, doi:10.1103/PhysRevB.106.155429.

Hashemi A., Busch K., Ozdemir S. K., El-Ganainy R. (2022). Uniform optical gain as a non-Hermitian control knob. Physical Review Research, Vol. 4, 043169, doi:10.1103/PhysRevResearch.4.043169.

Ren J., Franke S., Hughes S. (2021). Quasinormal Modes, Local Density of States, and Classical Purcell Factors for Coupled Loss-Gain Resonators. Physical Review X, Vol. 11, 041020, doi:10.1103/PhysRevX.11.041020.

Gandhi H. K., Rocco D., Carletti L., De Angelis C. (2020). Gain-loss engineering of bound states in the continuum for enhanced nonlinear response in dielectric nanocavities. Optics Express, Vol. 28, Iss. 3, pp. 3009-3016, doi:10.1364/OE.380280.

Grant M. J., Digonnet M. J. F. (2019). Loss-Gain Coupled Ring Resonator Gyroscope. Optical, Opto-Atomic, and Entanglement-Enhanced Precision Metrology, edited by Selim M. Shahriar, Jacob Scheuer. Proc. of SPIE, Vol. 10934, id. 109340T 13 pp., doi:10.1117/12.2515657.

Phang, S., Vukovic, A., Gradoni, G., Sewell, P. D., Benson, T. M., Creagh, S. C. (2017). Theory and Numerical Modelling of Parity-Time Symmetric Structures in Photonics: Boundary Integral Equation for Coupled Microresonator Structures. In: Agrawal, A., Benson, T., De La Rue, R., Wurtz, G. (eds) Recent Trends in Computational Photonics. Springer Series in Optical Sciences, Vol 204, Springer, Cham., doi:10.1007/978-3-319-55438-9_7.

Feng L., El-Ganainy R., Ge Li. (2017). Non-Hermitian photonics based on parity–time symmetry. Nature Photonics, Vol. 11, pp. 752–762, doi:10.1038/s41566-017-0031-1.

Gao Z., Fryslie S. T. M., Thompson B. J., Carney P. S., Choquette K. D. (2017). Parity-time symmetry in coherently coupled vertical cavity laser arrays. Optica, Vol. 4, No. 3, pp. 323–329. doi:10.1364/OPTICA.4.000323.

Wang H., Liu S., Chen L., Shen D., Wu X. (2016). Dual-wavelength single-frequency laser emission in asymmetric coupled microdisks. Scientific Reports, Vol. 6, 38053, doi:10.1038/srep38053.

Giden I. H., Dadashi Kh., Botey M., Herrero R., Staliunas K., Kurt H. (2015). Nonreciprocal Light Transmission in Gain-Loss Modulated Micro Ring Resonators. 2015 17th International Conference on Transparent Optical Networks (ICTON), DOI: 10.1109/ICTON.2015.7193652.

Phang S., Vukovic A., Creagh S. C., Benson T. M., Sewell P. D., Gradoni G. (2015). Parity-time symmetric coupled microresonators with a dispersive gain/loss. Optics Express, Vol. 23, Iss. 9, pp. 11493-11507, doi:10.48550/arXiv.1501.07455.

Peng Bo, Özdemir S. K., Lei F., Monifi F., Gianfreda M. et al. (2014). Parity–time-symmetric whispering-gallery Microcavities. Nature Physics, Vol. 10, pp. 394-398, doi:10.1038/nphys2927.

Mescia L., Bia P., De Sario M., Di Tommaso A., Prudenzano F. (2012). Design of mid-infrared amplifiers based on fiber taper coupling to erbium-doped microspherical resonator. Optics Express, Vol. 20, Iss. 7, pp. 7616-7629, doi.org/10.1364/OE.20.007616.

Kulishov M., Kress B. (2012). Free space diffraction on active gratings with balanced phase and gain/loss modulations. Optics Express, Vol. 20, Iss. 28, pp. 29319–29328, doi:10.1364/OE.20.029319.

Rüter C. E., Makris K. G., El-Ganainy R., Christodoulides D. N., Segev M., Kip D. (2010). Observation of parity–time symmetry in optics. Nature Physics, Vol. 6, pp. 192–195, doi:10.1038/nphys1515.

Armellini C., Biljanovic P., Berneschi S., Bhaktha S.N.B., Boulard B. et al. (2008). Optical properties and fabrication of glass-based erbium activated micro-nano photonic structures. Conference: Proceedings of MIPRO, pp. 21–26.

Kulishov M., Laniel J. M., Bélanger N., Plant D. V. (2005). Trapping light in a ring resonator using a grating-assisted coupler with asymmetric transmission. Optics Express, Vol. 13, Iss. 9, pp. 3567-3578, doi:10.1364/OPEX.13.003567.

Hoffmann K., Sokol V., Škvor Z. (2001). Arbitrary Q-factor Dielectric Resonator. Radioengineering, Vol. 10, Iss. 4, pp. 21–23.

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

Trubin A. A. (1996). Scattering of electromagnetic waves on a system of coupling high-Q dielectric resonators. MMET'96. VIth International Conference on Mathematical Methods in Electromagnetic Theory. Proceedings, pp. 350–353, DOI: 10.1109/MMET.1996.565731.

Trubin A. (2016). Lattices of Dielectric Resonators. Part of the book series: Springer Series in Advanced Microelectronics. Springer International Publishing, Vol. 53, 171 p., doi:10.1007/978-3-319-25148-6.

Downloads

Published

2024-09-30

How to Cite

Trubin, A. A. (2024) “Scattering of Electromagnetic Waves by Loss and Gain Systems of Dielectric Resonators”, Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia, (97), pp. 58-66. doi: 10.20535/RADAP.2024.97.58-66.

Issue

Section

Functional Electronics. Micro- and Nanoelectronic Technology