Methods of Analysis and Synthesis of Switching Circuits of Photonic Switches Using the Example of Spanke Architecture

The development of high-speed rail requires introduction of new telecommunications technology implemented in an integrated digital technological communication system (IDTC). Features of building such systems comprise provision of switching optical data channels using photonic switches (PS). Switching processes in PS occur at the photon (optical) level. A feature of construction of PS is the use of multi-tier topologies, performed using binary switches (BSs). BS is the simplest switching element with the number of input/output ports equal to one or two. The concepts for constructing PS are based on the technology of the well-known switching circuits using BS whose architecture and topology are assigned the names of their creators (Benes, Spanke, Spanke–Benes architecture, Clos network, etc. With an increase in PS capacity, its structure becomes more complicated: the number of links in the switching circuit, the total number of BSs, the length of switching routes, and the redundancy factor increase. In addition, it becomes necessary to calculate the probabilities of the occurrence of internal blocking in switching circuits, speed of switching optical signals, the value of attenuation of the optical signal in PS circuit, etc. The objective of the study was to develop methods of analysis and synthesis of switching circuits of photonic switches using the example of a circuit of Spanke architecture of a given capacity with calculation of the probabilities of occurrence of internal blocking. The authors used general scientific and engineering methods of mathematical modelling, probability and queuing theory and an example of an algorithm for analysing the structures of Spanke topology with capacities from 4×4 to 128×128. Their topological and probabilistic characteristics (the number of links in the switching circuit, the total number of BS, the length of the switching routes, the probability of occurrence of internal blocking in PS circuits) have been determined. The results of calsulations are presented in the form of tables. The developed methods of analysis and synthesis can be used in the study of similar switching circuits built using BS.

1. Agrawal, G. P. Nonlinear Fiber Optics. 3rd ed. Eds.: Kelley, P. L., Kaminow, I. P., Agrawal, G. P. Boston, Academic Press, 2000, 468 p. [Electronic resource]: http://read.pudn.com/downloads143/ebook/620953/Nonlinear_Fiber_Optics_3E.pdf. Last accessed 09.01.2021. DOI: 10.1007/3-540-46629-0_9.

2. Liu, Ai-qun; Zhang, Xuming; Lu, Cheng; Wang, F.; Liu, Zishun. Optical and mechanical models for a variable optical attenuator using a micromirror drawbridge. Journal of Micromechanics and Microengineering, 2003, Vol. 13 (3), pp. 400–411. [Electronic resource]: https://www.researchgate.net/publication/228697763_Optical_and_mechanical_models_for_a_variable_optical_attenuator_using_a_micromirror_drawbridge. Last accessed 09.01.2021.

3. Säckinger, E. Broadband Circuits for Optical Fiber Communication. John Wiley & Sons, Inc., Hoboken, New Jersey, 2005, 453 p. [Electronic resource]: https://b-ok.global/book/490967/864d86. Last accessed 09.01.2021.

4. Grade, J. D., Jerman, H., Kenny, T. W. Design of Large Deflection Electrostatic Actuators. Journal of Microelectromechanical Systems, 2003, Vol. 12, Iss. 3, pp. 335–343. DOI: 10.1109/JMEMS.2003.811750.

5. Bryzek, J., Abbott, E., Flannery, A., Cagle, D., Maitan, J. Control Issues for MEMS. 42nd IEEE International Conference on Decision and Control (IEEE Cat. No. 03CH37475), Maui, Hawaii, Dec 2003. DOI: 10.1109/CDC.2003.1273090.

6. Hiroyuki, Fujita; Hiroshi, Toshiyoshi. Electrostatic Micro Torsion Mirrors for an Optical Switch Matrix. Journal of Microelectromechanical Systems, 1996, Vol. 5, Iss. 4, pp. 231–237. [Electronic resource]: https://www.researchgate.net/profile/Hiroyuki_Fujita/publication/3329122_Electrostatic_micro_torsion_mirrors_for_an_optical_switch_matrix/links/0deec52b39513cd648000000/Electrostatic-micro-torsion-mirrors-for-an-optical-switchmatrix.pdf. Last accessed 09.01.2021.

7. Kurzweg, T. P., Morris III, A. S. Macro-Modeling of Systems Including Free-Space Optical MEMS. 2000 International Conference on Modeling and Simulation of Microsystems – MSM 2000, Tech. Proc. San Diego, California, USA, March 27–29, pp. 146–149. [Electronic resource]: https://www.researchgate.net/publication/2635436_Macro-Modeling_of_Systems_Including_Free-Space_Optical_MEMS. Last accessed 09.01.2021.

8. Agrawal, G. Nonlinear Fibre Optics. [Russian ed., trans. from English]. Moscow, Mir publ., 1996, 323 p. [Electronic resource]: https://www.studmed.ru/agraval-gpnelineynaya-volokonnaya-optika_56ae28bf45d.html. Last accessed 09.01.2021.

9. Ubaydullaev, R. R. Fiber-optic networks [Volokonnoopticheskie seti]. Moscow, Eco-Trends publ., 2001, 267 p. [Electronic resource]: https://docplayer.ru/26025483-R-rubaydullaev-volokonno-opticheskie-seti.html. Last accessed 09.01.2021.

10. Fokin, V. G. Coherent optical networks: Study guide [Kogerentnie opticheskie seti: Ucheb. posobie]. Siberian State University of Telecommunications and Informatics; Department of multichannel telecommunications and optical systems. Novosibirsk, 2015, 372 p. [Electronic resource]: https://docplayer.ru/61495673-Kogerentnye-opticheskie-seti.html. Last accessed 09.01.2021.

11. Dmitriev, S. A., Slepov, N. N. Fiber-optic technology: current state and prospects [Volokonno-opticheskaya tekhnika: sovremennoe sostoyanie i perspektivy]. 2nd ed. Moscow, LLC Fiber-optic technology, 2005, 576 p. [Electronic resource]: https://www.studmed.ru/dmitriev-s-aslepov-n-n-volokonno-opticheskaya-tehnika-sovremennoesostoyanie-i-perspektivy_c0ecd82d2ee.html. Last accessed 09.01.2021.

12. Sklyarov, O. K. Fiber-optic networks and communication systems: Study guide [Volokonnoopticheskie seti i sistemy svyazi: Uchebnoe posobie]. 2nd ed., ster. St. Petersburg, Publishing house «Lan», 2010, 272 p. [Electronic resource]: https://www.studmed.ru/sklyarov-ok-volokonno-opticheskie-seti-i-sistemy-svyaziuchebnoe-posobie_45ecba93b72.html. Last accessed 09.01.2021.

13. Rudenko, D. V. Structural constraints of optical multiplexer. World of Transport and Transportation, 2012, Vol.10, Iss. 4, pp. 125–129. [Electronic resource]: https://mirtr.elpub.ru/jour/article/view/714/1063. Last accessed 09.01.2021.

14. Barabanova, E. A. Optical two-stage switching system for processing substantial amounts of data [Opticheskaya dvukhkaskadnaya kommutatsionnaya sistema dlya obrabotki bolshikh ob’emov dannykh]. Scientific Bulletin of NSTU, 2018, Iss. 1 (70), pp. 7–18. DOI: 10.17212/1814-1196-2018-1-7-18.

15. Listvin, A. V., Listvin, V. N. Reflectometry of optical fibers [Refleksometriya opticheskikh volokon]. Moscow, LESARart publ., 2005, 208 p. [Electronic resource]: https://www.studmed.ru/listvin-av-listvin-vn-reflektometriyaopticheskih-volokon_505adaab51a.html. Last accessed 09.01.2021.

16. Zhou, Ting; Jia, Hao. Method to optimize optical switch topology for photonic network-on-chip. Optics Communications, 2018, Vol. 413, pp. 230–235. DOI: 10.1016/j.optcom.2017.12.062.