OPTIMIZATION OF THE SCATTERING MATRIX OF FREQUENCY -DETUNED ADD/DROP FILTERS FOR MULTIPLEXERS BUILT ON SYSTEMS OF OPTICAL DIELECTRIC RESONATORS WITH WHISPERING GALLERY MODES
DOI:
https://doi.org/10.20535/2411-2976.22024.39-52Keywords:
scattering, dielectric resonator, scattering matrix, notch filter, laterally coupled add/drop filter, parallel-coupled add/drop filter, twisted double-channel SCISSOR, diplexerAbstract
Background. A significant increase in the speed of information transmission in fiber-optic communication networks is determined by the strict requirements imposed on the elemental base of receiving and transmitting devices. One of the important components of such devices is diplexers built on different notch and bandpass filters, which are often performed on dielectric resonators (DR) with whispering gallery mode (WGM) oscillations. Calculation and optimization of the parameters of multilink filters and diplexers built on DR is impossible without further development of the theory of their design. The development of the theory of diplexers today is often based on electrodynamic modelling, which is built on preliminary calculations of filter scattering parameters in various transmission lines with a complex topology of connections.
Objective. The aim of this study is to construct electrodynamics' models of wave scattering on complex multi-connected DR structures with degenerate types of WGM natural oscillations, which contain several frequency-detuned bandpass or notch filters located in one or several transmission lines. To solve the scattering problem, we proposed a system of equations derived from perturbation theory for Maxwell's equations [24], modified to describe the DR fields with whispering gallery oscillations in transmission lines. The construction of such solutions is complicated by the fact that each of the partial optical resonators of the filters, in the case of excitation of azimuthally inhomogeneous WGM in it, has, as a rule, two degenerate types of natural oscillations. Moreover, each such type of oscillation is characterized by different complex values of the coupling coefficients with the line, open space, and also with other resonators. The latter circumstance leads to the fact that the systems of equations for the amplitudes of natural and forced oscillations of resonators are doubled. The signs of the coefficients of mutual coupling are usually different, this leads to the fact that the behaviour of DRs in the system becomes more difficult to predict, therefore the second objective of this work is to study the patterns of the scattering characteristics of line waves on systems of frequency-detuned DRs with degenerate types of oscillations with the possibility of constructing multiplexers for modern optical communication systems.
Methods. The methods of technical electrodynamics are used for calculating and analysing scattering matrices. The end result is obtaining new analytical equations and formulas for new complex structures of coupled dielectric resonators with whispering gallery oscillations in the different transmission lines.
Results. Frequency dependences of scattering matrices on complex structures of frequency-detuned filters built on coupled optical DR with whispering gallery oscillations located in one or more transmission lines are considered. Electromagnetic models of bandstop and add/drop filters are built, consisting of various optical resonators with degenerate types of natural oscillations. General analytical expressions of vector coefficients and matrices for building systems of equations describing coupled oscillations, as well as forced oscillations of resonators in cases of their use in optical filters with serial and parallel arrangement, are given. General solutions for the scattering field on frequency-detuned resonators located in different optical transmission lines have been found. Examples of calculating frequency dependences of the scattering matrix for the most interesting structures consisting of two different frequency-detuned filters are given. The frequency scattering characteristics of several types of devices are calculated, which consist of two notch filters with different blocking bands, made on detuned DRs in one transmission line. The possibilities of the earlier proposed method are demonstrated in the example of calculating the scattering characteristics of known types of diplexers built on the basis of the use of two add/drop filters with different frequency bandwidths. The frequency dependences of the scattering matrices of the two most common types of devices, located in parallel between two or four regular transmission lines of add/drop filters with different numbers of resonators; laterally coupled add/drop filters; parallel-coupled add/drop filters; twisted double-channel side-coupled integrated space sequence of resonators (SCISSORs), were studied. New scattering models of diplexers consisting of optical resonators of different connection topologies were built: serial, parallel with the use of laterally coupled add/drop filters; parallel-coupled add/drop filters; twisted double-channel SCISSORs. The frequency dependences scattering matrix of the diplexers were also calculated. The characteristics of the designed diplexers obtained from the examined filters of different types were compared.
Conclusions. The theory of diplexer construction, which takes place on the simultaneous optimization of the scattering matrix of several filters built on complex systems of dielectric resonators with degenerate types of whispering gallery oscillations is expanded. A calculation method was developed and new analytical relations were found for the scattering matrix coefficients of optical diplexers of various types.
References
Haus H.A., Popovic M.A., Watts M.R., Manolatou C., Little B.E., Chu S.T. Optical resonators and filters. Optical Microcavities. Edited By: Kerry Vahala (California Institute of Technology, USA) Ch. 00, 2004. 516 p.
E. J. Klein, D. H. Geuzebroek, H. Kelderman, G. Sengo, N. Baker, A. Driessen. Reconfigurable Optical Add–Drop Multiplexer Using Microring Resonators // IEEE Photonics Technology Letters · December 2005. pp. 2358 – 2360.
Y. Kokubun. Vertically Coupled Microring Resonator Filter for Integrated Add/Drop Node // IEICE Trans. Electron. Vol. E88-C, No. 3. 2005. pp. 349 – 362.
Y. Goebuchi, T. Kato, Y. Kokubun. Fast and Stable Wavelength-Selective Switch Using Double-Series Coupled Dielectric Microring Resonator // IEEE Photonics Technology Letters, Vol. 18, No. 3, February 1, 2006. pp. 538 – 540.
O. Schwelb. Phase-matched lossy microring resonator add/drop multiplexers // Proc. of SPIE. Vol. 6343. 2006. pp. 1 – 10.
O. Schwelb. Microring Resonator Based Photonic Circuits: Analysis and Design // 2007 8th International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Services. IEEE. Nis, Serbia and Montenegro 2007. pp. 1 – 9.
D.G. Rabus. Integrated Ring Resonators / Springer-Verlag Berlin Heidelberg 2007. 254 p.
J. Heebner, R. Grover, T. Ibrahim. Optical Microresonators Theory, Fabrication, and Applications / Springer-Verlag. 2008. 263 p.
A. W. Poon, F. Xu, X. Luo. Cascaded active silicon microresonator array cross-connect circuits for WDM networks-on-chip // Silicon Photonics III Conference, Photonics West San Jose, CA, USA, 2008, pp. 1 – 10.
A. Kaz´mierczak, W. Bogaerts, E. Drouard, F. Dortu, P. Rojo-Romeo, F. Gaffiot, D. Van Thourhout, D. Giannone. Highly Integrated Optical 4 4 Crossbar in Silicon-on-Insulator Technology // Journal of Lightwave Technology, Vol. 27, No. 16, August 15, 2009. pp. 3317 – 3323.
R. Zhang, R. R. Mansour, Dual-Band Dielectric-Resonator Filters // IEEE Trans. on MTT, Vol. 57, No. 7, 2009, pp. 1760 – 1766.
Photonic Microresonator Research and Applications / I. Chremmos, O. Schwelb, N. Uzunoglu – Editors. Springer. 2010, 517 p.
V. Prajzler, E. Strilek, J. Špirkova, V. Jerabek, Design of the novel wavelength triplexer using multiple polymer microring resonators // Radioengineering, April 2012. Vol. 21, No. 1, pp. 258 – 363.
Z. Fang, C. Z. Zhao. Recent Progress in Silicon Photonics: A Review // International Scholarly Research Network. ISRN Optics. Vol. 2012, Article ID 428690, 27 p.
S. Awasthi, A. Biswas, M. J. Akhtar. Dual-Band Dielectric Resonator Bandstop Filters // Wiley Periodicals, Inc. International Journal of RF and Microwave Computer-Aided Engineering · October 2014. pp.282 – 288.
D. Dai, J. E. Bowers. Silicon-based on-chip multiplexing technologies and devices for Peta-bit optical interconnects (Review article) // De Gruyter. Nanophotonics 2014; No. 3(4-5), pp. 283–311.
L. Zhu, R. R. Mansour, M. Yu. Compact Waveguide Dual-Band Filters and Diplexers // IEEE Trans. on MTT, Vol. 65, No. 5, may 2017. pp. 1525 – 1533.
A.B. Matsko. Practical Applications of Microresonators in Optics and Photonics / eBook - Optical Science and Engineering. CRC Press, 3 Is. 2018. - 586 p.
Z. Yao , K. Wu, B. X. Tan, J. Wang, Y. Li , Y. Zhang, A. W. Poon. Integrated Silicon Photonic Microresonators: Emerging Technologies // IEEE Jornal of selected topics in Quantum Electronics, Vol. 24, No. 6, 2018. pp. 1 – 25.
M. Liu, Z. Xiang, P. Ren, T. Xu. Quad-mode dual-band bandpass filter based on a stub-loaded circular resonator // EURASIP Journal on Wireless Communications and Networking. Springer Open (2019) 2019:48, 6 p.
W. Qin, J. Liu, H.-L. Zhang, W.-W. Yang, J.-X. Chen. Bandpass Filter and Diplexer Based on Dual-Mode Dielectric Filled Waveguide Resonators // IEEE Access. V. 10, 2022. pp. 29333 – 29340.
A. Wldaa, M. Hoft. Miniaturized Dual-Band Dual-Mode TM-Mode // Dielectric Filter in Planar Configuration // IEEE Jornal of Microwaves. Vol. 2, No. 2, April 2022. pp. 326 – 336.
N. Saha, G. Brunetti, A. di Toma, M. N. Armenise, C. Ciminelli. Silicon Photonic Filters: A Pathway from Basics to Applications // Review. Adv. Photonics Res. 2024, 2300343. pp. 1 – 44.
A.A. Trubin. Electrodynamic modeling of Add-drop filters on optical microresonators // Information and Telecommunication Sciences, V.1, N1, 2019, pp. 30 - 36.
A.A. Trubin. Modeling triplexers for optical communication systems // Modern Challenges in Telecommunications. 16 Int. Scientific Conference. 2022, pp. 63-65.
A.A. Trubin. On one possibility of constructing band-pass filters based on optical microresonators with whispering gallery oscillations // Modern Challenges in Telecommunications. 17 Int. Scientific Conference. 2023, pp. 152-154.
A.A. Trubin. Scattering of electromagnetic waves by frequency-detuned systems of dielectric resonators // Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia. 2024. Iss.96. pp. 5 – 13.
